Integral Trigonometri – Fungsi Beserta Contoh Soal dan Jawaban

Umumnya, jika fungsi $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a990a5545cac26c1c6821dca95d898bc80fe3a8" alt="{\displaystyle \sin(x)}" width="2581" height="1223.9">$ adalah suatu fungsi trigonometri, dan $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb9af7ed6f44822021b74bb82b431022c7fd66b3" alt="{\displaystyle \cos(x)}" width="2691" height="1223.9">$ adalah turunannya,

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/154b38df0c0fa60ddc26626e87de3a009d0c89a6" alt="{\displaystyle \int a\cos nx\;\mathrm {d} x={\frac {a}{n}}\sin nx+C}" width="12907.1" height="2443.8">

Dalam semua rumus, konstanta a diasumsikan bukan nol, dan C melambangkan konstanta integrasi.

Integral trigonometri – Integrand melibatkan hanya sinus

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4485ed89b0b82dd17f28ca1369cc8dabc1cb9d1" alt="{\displaystyle \int [fusion_builder_container hundred_percent=" width="12943.1" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c8e17b2f73633c06ae22b11dc458b9c6dcb0355" alt="{\displaystyle \int \sin ^{2}{ax}\;\mathrm {d} x={\frac {x}{2}}-{\frac {1}{4a}}\sin 2ax+C={\frac {x}{2}}-{\frac {1}{2a}}\sin ax\cos ax+C\!}" width="27800.9" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3acfffa52d730b2b3b978e4fdbb4cabfcb5e7e97" alt="{\displaystyle \int \sin ^{3}{ax}\;\mathrm {d} x={\frac {\cos 3ax}{12a}}-{\frac {3\cos ax}{4a}}+C\!}" width="17114.5" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf1f04085c8e96c7ba2d5fcee830965c7de4f52c" alt="{\displaystyle \int x\sin ^{2}{ax}\;\mathrm {d} x={\frac {x^{2}}{4}}-{\frac {x}{4a}}\sin 2ax-{\frac {1}{8a^{2}}}\cos 2ax+C\!}" width="23033.6" height="2659.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92a6151657077977dc3d1bbd3d4285bc8a6492ea" alt="{\displaystyle \int x^{2}\sin ^{2}{ax}\;\mathrm {d} x={\frac {x^{3}}{6}}-\left({\frac {x^{2}}{4a}}-{\frac {1}{8a^{3}}}\right)\sin 2ax-{\frac {x}{4a^{2}}}\cos 2ax+C\!}" width="28027.3" height="2730.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f1aab13ba7db6c2cbcfe3ac8fd54002f556679c" alt="{\displaystyle \int \sin [fusion_builder_container hundred_percent=" width="34958.8" height="2802.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e311b4da92157a16a7fd96befdc8312b25916091" alt="{\displaystyle \int \sin ^{n}{ax}\;\mathrm {d} x=-{\frac {\sin ^{n-1}ax\cos ax}{na}}+{\frac {n-1}{n}}\int \sin ^{n-2}ax\;\mathrm {d} x\qquad {\mbox{(for }}n&gt;0{\mbox{)}}\,\!}" width="32064.2" height="2659.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dfc668c3e5bdfae0c1596a1d1eee4ea882e1c83" alt="{\displaystyle \int {\frac {\mathrm {d} x}{\sin ax}}={\frac {1}{a}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="12810.2" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a16c66c90d9b70ea5c25f63165a60b135a1d9c8" alt="{\displaystyle \int {\frac {\mathrm {d} x}{\sin ^{n}ax}}={\frac {\cos ax}{a(1-n)\sin ^{n-1}ax}}+{\frac {n-2}{n-1}}\int {\frac {\mathrm {d} x}{\sin ^{n-2}ax}}\qquad {\mbox{(for }}n&gt;1{\mbox{)}}\,\!}" width="30216.4" height="2730.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd5c9057354cb15bd57a832addb2fb976342b371" alt="{\displaystyle \int x\sin ax\;\mathrm {d} x={\frac {\sin ax}{a^{2}}}-{\frac {x\cos ax}{a}}+C\,\!}" width="17027.9" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/feda236e5d012d5fcf5fe48f675a2b692123be42" alt="{\displaystyle \int x^{n}\sin ax\;\mathrm {d} x=-{\frac {x^{n}}{a}}\cos ax+{\frac {n}{a}}\int x^{n-1}\cos ax\;\mathrm {d} x=\sum _{k=0}^{2k\leq n}(-1)^{k+1}{\frac {x^{n-2k}}{a^{1+2k}}}{\frac {n!}{(n-2k)!}}\cos ax+\sum _{k=0}^{2k+1\leq n}(-1)^{k}{\frac {x^{n-1-2k}}{a^{2+2k}}}{\frac {n!}{(n-2k-1)!}}\sin ax\qquad {\mbox{(for }}n&gt;0{\mbox{)}}\,\!}" width="63967.8" height="3233.2">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/078855946f28ae28958ebc1d73382f97b2f82fc8" alt="{\displaystyle \int {\frac {\sin ax}{x}}\mathrm {d} x=\sum _{n=0}^{\infty }(-1)^{n}{\frac {(ax)^{2n+1}}{(2n+1)\cdot (2n+1)!}}+C\,\!}" width="21178" height="3017.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8aff54d4b55d5dfad44f8ddfd261cc88cec0b3ef" alt="{\displaystyle \int {\frac {\sin ax}{x^{n}}}\mathrm {d} x=-{\frac {\sin ax}{(n-1)x^{n-1}}}+{\frac {a}{n-1}}\int {\frac {\cos ax}{x^{n-1}}}\mathrm {d} x\,\!}" width="22123.9" height="2587.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7876a5e8bc9a7a2e1f9ef307e754c8c495a555be" alt="{\displaystyle \int {\frac {\mathrm {d} x}{1\pm \sin ax}}={\frac {1}{a}}\tan \left({\frac {ax}{2}}\mp {\frac {\pi }{4}}\right)+C}" width="16326.4" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d0b0e7a53bd662f298d1a41107a9fd20980e1e4" alt="{\displaystyle \int {\frac {x\;\mathrm {d} x}{1+\sin ax}}={\frac {x}{a}}\tan \left({\frac {ax}{2}}-{\frac {\pi }{4}}\right)+{\frac {2}{a^{2}}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="26647.4" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f8c4fce7c63c093a6181ffd15ac9925de7cb2ee" alt="{\displaystyle \int {\frac {x\;\mathrm {d} x}{1-\sin ax}}={\frac {x}{a}}\cot \left({\frac {\pi }{4}}-{\frac {ax}{2}}\right)+{\frac {2}{a^{2}}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="26425.4" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/980ed886db7e23a0befad5c81965c38cb0135ca4" alt="{\displaystyle \int {\frac {\sin ax\;\mathrm {d} x}{1\pm \sin ax}}=\pm x+{\frac {1}{a}}\tan \left({\frac {\pi }{4}}\mp {\frac {ax}{2}}\right)+C}" width="18900.3" height="2515.6">

Integral trigonometri – Integrand melibatkan hanya kosinus

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf48148c2f2551f320d14b44087faade82eff3b8" alt="{\displaystyle \int \cos ax\;\mathrm {d} x={\frac {1}{a}}\sin ax+C\,\!}" width="12164.6" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22f3a549538075b161710d3de8ed8530a53e31d7" alt="{\displaystyle \int \cos ^{2}{ax}\;\mathrm {d} x={\frac {x}{2}}+{\frac {1}{4a}}\sin 2ax+C={\frac {x}{2}}+{\frac {1}{2a}}\sin ax\cos ax+C\!}" width="27910.9" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ed015aabd8d89a8728a771e9fa19df9b4e941b0" alt="{\displaystyle \int \cos ^{n}ax\;\mathrm {d} x={\frac {\cos ^{n-1}ax\sin ax}{na}}+{\frac {n-1}{n}}\int \cos ^{n-2}ax\;\mathrm {d} x\qquad {\mbox{(for }}n&gt;0{\mbox{)}}\,\!}" width="31505.7" height="2659.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de4f46e55c023e737c26af3d41639140d31f585f" alt="{\displaystyle \int x\cos ax\;\mathrm {d} x={\frac {\cos ax}{a^{2}}}+{\frac {x\sin ax}{a}}+C\,\!}" width="17137.9" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77e9a51f8c9a107ed7d2c954db63e8c8102a8dea" alt="{\displaystyle \int x^{2}\cos ^{2}{ax}\;\mathrm {d} x={\frac {x^{3}}{6}}+\left({\frac {x^{2}}{4a}}-{\frac {1}{8a^{3}}}\right)\sin 2ax+{\frac {x}{4a^{2}}}\cos 2ax+C\!}" width="28137.3" height="2730.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f83f28bfabedbfc669233383f1cdf5348c759fbb" alt="{\displaystyle \int x^{n}\cos ax\;\mathrm {d} x={\frac {x^{n}\sin ax}{a}}-{\frac {n}{a}}\int x^{n-1}\sin ax\;\mathrm {d} x\,=\sum _{k=0}^{2k+1\leq n}(-1)^{k}{\frac {x^{n-2k-1}}{a^{2+2k}}}{\frac {n!}{(n-2k-1)!}}\cos ax+\sum _{k=0}^{2k\leq n}(-1)^{k}{\frac {x^{n-2k}}{a^{1+2k}}}{\frac {n!}{(n-2k)!}}\sin ax\!}" width="55461.3" height="3233.2">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef9927ebeaec09fab122d7891bafa8ef9aaff66f" alt="{\displaystyle \int {\frac {\cos ax}{x}}\mathrm {d} x=\ln[/fusion_text][/fusion_builder_column] [/fusion_builder_row][/fusion_builder_container]|ax|[fusion_builder_container hundred_percent=" width="20731.8" height="3017.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a84c4e0dcb38f68d37353a30c20da666dbb795bf" alt="{\displaystyle \int {\frac {\cos ax}{x^{n}}}\mathrm {d} x=-{\frac {\cos ax}{(n-1)x^{n-1}}}-{\frac {a}{n-1}}\int {\frac {\sin ax}{x^{n-1}}}\mathrm {d} x\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\,\!}" width="28787.5" height="2587.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103d2bcc98cdf888bd853f8f794b825c0c6b3ee5" alt="{\displaystyle \int {\frac {\mathrm {d} x}{\cos ax}}={\frac {1}{a}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="16104.9" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3691fdd78f99348b2dad004ff75b489eefeaeb3" alt="{\displaystyle \int {\frac {\mathrm {d} x}{\cos ^{n}ax}}={\frac {\sin ax}{a(n-1)\cos ^{n-1}ax}}+{\frac {n-2}{n-1}}\int {\frac {\mathrm {d} x}{\cos ^{n-2}ax}}\qquad {\mbox{(for }}n&gt;1{\mbox{)}}\,\!}" width="30546.4" height="2659.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2db02bf89ec890b6e841f68304d7e28a3edde51f" alt="{\displaystyle \int {\frac {\mathrm {d} x}{1+\cos ax}}={\frac {1}{a}}\tan {\frac {ax}{2}}+C\,\!}" width="13418.3" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25c98b3e02e04094379615e1533038142f86e1f4" alt="{\displaystyle \int {\frac {\mathrm {d} x}{1-\cos ax}}=-{\frac {1}{a}}\cot {\frac {ax}{2}}+C}" width="13918.1" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/affe021010cfe4ed02f1b174837899768ac93cca" alt="{\displaystyle \int {\frac {x\;\mathrm {d} x}{1+\cos ax}}={\frac {x}{a}}\tan {\frac {ax}{2}}+{\frac {2}{a^{2}}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="20387.8" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a20539258a72e739c7c6b7233c123087064cc610" alt="{\displaystyle \int {\frac {x\;\mathrm {d} x}{1-\cos ax}}=-{\frac {x}{a}}\cot {\frac {ax}{2}}+{\frac {2}{a^{2}}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="20944.3" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aeba7fad7f702e58fd2b72d5a0a8f71e2dd62c86" alt="{\displaystyle \int {\frac {\cos ax\;\mathrm {d} x}{1+\cos ax}}=x-{\frac {1}{a}}\tan {\frac {ax}{2}}+C\,\!}" width="15213.7" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edfa05cb70dff2af793d724e554871a862f28b89" alt="{\displaystyle \int {\frac {\cos ax\;\mathrm {d} x}{1-\cos ax}}=-x-{\frac {1}{a}}\cot {\frac {ax}{2}}+C\,\!}" width="15880.2" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e16f64b59fabd69040d3106eb7c090d0c5656c5c" alt="{\displaystyle \int \cos [/fusion_text][fusion_builder_container hundred_percent=" width="34420.8" height="2802.6">

Integral trigonometri – Integrand melibatkan hanya tangen

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f219a2fbeefe1b98c9ef74e5797f1f245282cc3f" alt="{\displaystyle \int \tan ax\;\mathrm {d} x=-{\frac {1}{a}}\ln[/fusion_text][/fusion_builder_column] [/fusion_builder_row][/fusion_builder_container]|\cos ax|[fusion_builder_container hundred_percent=" width="23536.6" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52db4697835a8a3d0f348e8bd9b1b0f79fe7a11b" alt="{\displaystyle \int \tan ^{2}{x}\,\mathrm {d} x=\tan {x}-x+C}" width="12345" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a2d7138cec9b413b0e1fe6b7aa28f609b464e45" alt="{\displaystyle \int \tan ^{n}ax\;\mathrm {d} x={\frac {1}{a(n-1)}}\tan ^{n-1}ax-\int \tan ^{n-2}ax\;\mathrm {d} x\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\,\!}" width="30110.4" height="2587.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d249d3153e49e8c9a0504c17856170c856e37544" alt="{\displaystyle \int {\frac {\mathrm {d} x}{q\tan ax+p}}={\frac {1}{p^{2}+q^{2}}}(px+{\frac {q}{a}}\ln[/fusion_text][/fusion_builder_column] [/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="35964.6" height="2587.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/834122594f50a913368a245de0b32c3b817a5b70" alt="{\displaystyle \int {\frac {\mathrm {d} x}{\tan ax+1}}={\frac {x}{2}}+{\frac {1}{2a}}\ln[/fusion_text][/fusion_builder_column] [/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="21160.7" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d30f450ce88c198f15660689748585ad51dd6f5b" alt="{\displaystyle \int {\frac {\mathrm {d} x}{\tan ax-1}}=-{\frac {x}{2}}+{\frac {1}{2a}}\ln[/fusion_text][/fusion_builder_column] [/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="21939.2" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/687fc88c5eb1a3635735d6996b9ec534051311d9" alt="{\displaystyle \int {\frac {\tan ax\;\mathrm {d} x}{\tan ax+1}}={\frac {x}{2}}-{\frac {1}{2a}}\ln[/fusion_text][/fusion_builder_column] [/fusion_builder_row][/fusion_builder_container]|\sin ax+\cos ax|[fusion_builder_container hundred_percent=" width="21160.7" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99fdf0e90369e96e5f7af0f71a0828aacef03c61" alt="{\displaystyle \int {\frac {\tan ax\;\mathrm {d} x}{\tan ax-1}}={\frac {x}{2}}+{\frac {1}{2a}}\ln[/fusion_text][/fusion_builder_column] [/fusion_builder_row][/fusion_builder_container]|\sin ax-\cos ax|[fusion_builder_container hundred_percent=" width="21160.7" height="2515.6">

Integral trigonometri – Integrand melibatkan hanya sekan

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec334e9560b0664b9c86445ef967255f6104c398" alt="{\displaystyle \int \sec {ax}\,\mathrm {d} x={\frac {1}{a}}\ln {\left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="17381.6" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca63419cb8d63f84553f904b221eecbca813037f" alt="{\displaystyle \int \sec ^{2}{x}\,\mathrm {d} x=\tan {x}+C}" width="10386.6" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c93596f1fc36e72157fb7ba557148a5be5b26a65" alt="{\displaystyle \int \sec ^{3}x\,dx={\frac {1}{2}}\sec x\tan x+{\frac {1}{2}}\ln[/fusion_text][/fusion_builder_column] [/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="23255.3" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62dc65596e4c2444f35c6ef2932e1914bfced296" alt="{\displaystyle \int \sec ^{n}{ax}\,\mathrm {d} x={\frac {\sec ^{n-2}{ax}\tan {ax}}{a(n-1)}}\,+\,{\frac {n-2}{n-1}}\int \sec ^{n-2}{ax}\,\mathrm {d} x\qquad {\mbox{ (for }}n\neq 1{\mbox{)}}\,\!}" width="31915.8" height="2802.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7bf13c8fd9c6fe5b56e33503d3c1aaeac4f3040" alt="{\displaystyle \int {\frac {\mathrm {d} x}{\sec {x}+1}}=x-\tan {\frac {x}{2}}+C}" width="12875.9" height="2515.6">

Integral trigonometri – Integrands melibatkan hanya kosekan

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07d958ca9498f8077e3b94856a4b701fa8f7605a" alt="{\displaystyle \int csc(ax)\mathrm {d} x=-{\frac {1}{a}}\ln {\left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="18546.8" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0217a0f47b8759f528ec432cb0876db88f34ad5" alt="{\displaystyle \int \csc ^{2}{x}\,\mathrm {d} x=-\cot {x}+C}" width="11219.7" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0d3ed83f51f62a5ddd8193721a1ad795f9ef0ae" alt="{\displaystyle \int \csc ^{n}{ax}\,\mathrm {d} x=-{\frac {\csc ^{n-1}\left(ax\right)\cos \left(ax\right)}{a(n-1)}}\,+\,{\frac {n-2}{n-1}}\int \csc ^{n-2}{ax}\,\mathrm {d} x\qquad {\mbox{ (for }}n\neq 1{\mbox{)}}\,\!}" width="33812" height="2874.4">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4326e336ac8980749a9fd280fcfa17b7930d251d" alt="{\displaystyle \int {\frac {\mathrm {d} x}{\csc {x}+1}}=x-{\frac {2\sin {\frac {x}{2}}}{\cos {\frac {x}{2}}+\sin {\frac {x}{2}}}}+C}" width="16345.1" height="3089.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03c24b35ac9127c6344e76833e4c913e388c0b5e" alt="{\displaystyle \int {\frac {\mathrm {d} x}{\csc {x}-1}}={\frac {2\sin {\frac {x}{2}}}{\cos {\frac {x}{2}}-\sin {\frac {x}{2}}}}-x+C}" width="16345.1" height="3089.6">

Integral trigonometri – Integrand melibatkan hanya kotangen

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54449d79cb807b69a1d7e1dc0692fb2aea914199" alt="{\displaystyle \int \cot ax\;\mathrm {d} x={\frac {1}{a}}\ln[/fusion_text][/fusion_builder_column] [/fusion_builder_row][/fusion_builder_container]|\sin ax|[fusion_builder_container hundred_percent=" width="13884.9" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b44972559d7106e2a84220c61cdb9d5bc1f1207b" alt="{\displaystyle \int \cot ^{n}ax\;\mathrm {d} x=-{\frac {1}{a(n-1)}}\cot ^{n-1}ax-\int \cot ^{n-2}ax\;\mathrm {d} x\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\,\!}" width="30552.9" height="2587.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f2b19a3daee6179aaa42651542fae13c161555c" alt="{\displaystyle \int {\frac {\mathrm {d} x}{1+\cot ax}}=\int {\frac {\tan ax\;\mathrm {d} x}{\tan ax+1}}\,\!}" width="13208.3" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/948489d6f3978ce2b0bb416f93716260f64a04ee" alt="{\displaystyle \int {\frac {\mathrm {d} x}{1-\cot ax}}=\int {\frac {\tan ax\;\mathrm {d} x}{\tan ax-1}}\,\!}" width="13208.3" height="2515.6">

Integral trigonometri – Integrand melibatkan sinus dan kosinus

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/113beceea048ad32eb073ec40a49b01088b277c3" alt="{\displaystyle \int {\frac {\mathrm {d} x}{\cos ax\pm \sin ax}}={\frac {1}{a{\sqrt {2}}}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="21160.1" height="2730.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d94b786c5a6b4af095c8072838869d61f196c53" alt="{\displaystyle \int {\frac {\mathrm {d} x}{(\cos ax\pm \sin ax)^{2}}}={\frac {1}{2a}}\tan \left(ax\mp {\frac {\pi }{4}}\right)+C}" width="19807.5" height="2659.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33f94702aa187930334c44bf5f828804e17bbf17" alt="{\displaystyle \int {\frac {\mathrm {d} x}{(\cos x+\sin x)^{n}}}={\frac {1}{n-1}}\left({\frac {\sin x-\cos x}{(\cos x+\sin x)^{n-1}}}-2(n-2)\int {\frac {\mathrm {d} x}{(\cos x+\sin x)^{n-2}}}\right)}" width="35483.5" height="2730.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ba779445bf35ae788e1bc3a75524a7402c45054" alt="{\displaystyle \int {\frac {\cos ax\;\mathrm {d} x}{\cos ax+\sin ax}}={\frac {x}{2}}+{\frac {1}{2a}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="22551.3" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae173fa53f8e6e5bd063f39ce1a1b4693b065ce4" alt="{\displaystyle \int {\frac {\cos ax\;\mathrm {d} x}{\cos ax-\sin ax}}={\frac {x}{2}}-{\frac {1}{2a}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="22551.3" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1c0aef659b13d42ce7748f9d53e8f2b8af1a2b0" alt="{\displaystyle \int {\frac {\sin ax\;\mathrm {d} x}{\cos ax+\sin ax}}={\frac {x}{2}}-{\frac {1}{2a}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|\sin ax+\cos ax\right|[fusion_builder_container hundred_percent=" width="22551.3" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/896cb840f9947218e2ed07a7f4c49433b53d2d2e" alt="{\displaystyle \int {\frac {\sin ax\;\mathrm {d} x}{\cos ax-\sin ax}}=-{\frac {x}{2}}-{\frac {1}{2a}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|\sin ax-\cos ax\right|[fusion_builder_container hundred_percent=" width="23329.8" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5a372fd412bebe59f7a308148c14235e0771ad5" alt="{\displaystyle \int {\frac {\cos ax\;\mathrm {d} x}{\sin ax(1+\cos ax)}}=-{\frac {1}{4a}}\tan ^{2}{\frac {ax}{2}}+{\frac {1}{2a}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|\tan {\frac {ax}{2}}\right|[fusion_builder_container hundred_percent=" width="25508.5" height="2659.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca0efe29351ecc571402fa61f7ce3247adb43a1b" alt="{\displaystyle \int {\frac {\cos ax\;\mathrm {d} x}{\sin ax(1-\cos ax)}}=-{\frac {1}{4a}}\cot ^{2}{\frac {ax}{2}}-{\frac {1}{2a}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|\tan {\frac {ax}{2}}\right|[fusion_builder_container hundred_percent=" width="25396.5" height="2659.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39972034bd7df5d4da8216c59dec6990ee43bdfd" alt="{\displaystyle \int {\frac {\sin ax\;\mathrm {d} x}{\cos ax(1+\sin ax)}}={\frac {1}{4a}}\cot ^{2}\left({\frac {ax}{2}}+{\frac {\pi }{4}}\right)+{\frac {1}{2a}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|\tan \left({\frac {ax}{2}}+{\frac {\pi }{4}}\right)\right|[fusion_builder_container hundred_percent=" width="30987.5" height="2659.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67d77825e42eaf3f8c1d51418f9b0b8f10205024" alt="{\displaystyle \int {\frac {\sin ax\;\mathrm {d} x}{\cos ax(1-\sin ax)}}={\frac {1}{4a}}\tan ^{2}\left({\frac {ax}{2}}+{\frac {\pi }{4}}\right)-{\frac {1}{2a}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|\tan \left({\frac {ax}{2}}+{\frac {\pi }{4}}\right)\right|[fusion_builder_container hundred_percent=" width="31099.5" height="2659.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2642e16a0d3978d32b4b1fbbd7d7a9f098b7a5e" alt="{\displaystyle \int \sin ax\cos ax\;\mathrm {d} x=-{\frac {1}{2a}}\cos ^{2}ax+C\,\!}" width="16672.4" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7ac0500e6421696f90e19ce8f60253613f1df75" alt="{\displaystyle \int \sin a_{1}x\cos a_{2}x\;\mathrm {d} x=-{\frac {\cos((a_{1}-a_{2})x)}{2(a_{1}-a_{2})}}-{\frac {\cos((a_{1}+a_{2})x)}{2(a_{1}+a_{2})}}+C\qquad {\mbox{(for }}[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|a_{1}|\neq |a_{2}|[fusion_builder_container hundred_percent=" width="36867.3" height="2802.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48d533e0047c71b04eeab16688c6cb596ffbbd5a" alt="{\displaystyle \int \sin ^{n}ax\cos ax\;\mathrm {d} x={\frac {1}{a(n+1)}}\sin ^{n+1}ax+C\qquad {\mbox{(for }}n\neq -1{\mbox{)}}\,\!}" width="27328.1" height="2587.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f737a060765cd789897333578ee006f002f98c5" alt="{\displaystyle \int \sin ax\cos ^{n}ax\;\mathrm {d} x=-{\frac {1}{a(n+1)}}\cos ^{n+1}ax+C\qquad {\mbox{(for }}n\neq -1{\mbox{)}}\,\!}" width="28216.6" height="2587.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d2d0a0e9aee77581451d9b2fb5d83e70b2146e5" alt="{\displaystyle \int \sin ^{n}ax\cos ^{m}ax\;\mathrm {d} x=-{\frac {\sin ^{n-1}ax\cos ^{m+1}ax}{a(n+m)}}+{\frac {n-1}{n+m}}\int \sin ^{n-2}ax\cos ^{m}ax\;\mathrm {d} x\qquad {\mbox{(for }}m,n&gt;0{\mbox{)}}\,\!}" width="42383.5" height="2802.6">

juga:

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/696fa0a1e13ab5ee5746cc132b0cc7425ef18fe5" alt="{\displaystyle \int \sin ^{n}ax\cos ^{m}ax\;\mathrm {d} x={\frac {\sin ^{n+1}ax\cos ^{m-1}ax}{a(n+m)}}+{\frac {m-1}{n+m}}\int \sin ^{n}ax\cos ^{m-2}ax\;\mathrm {d} x\qquad {\mbox{(for }}m,n&gt;0{\mbox{)}}\,\!}" width="41605" height="2802.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d851b3f674c81d37c02b96b1cb02c3e679feab3" alt="{\displaystyle \int {\frac {\mathrm {d} x}{\sin ax\cos ax}}={\frac {1}{a}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="15225" height="2515.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b40652cb8b84da7cb1d1666b3b62a9545b1bc0fe" alt="{\displaystyle \int {\frac {\mathrm {d} x}{\sin ax\cos ^{n}ax}}={\frac {1}{a(n-1)\cos ^{n-1}ax}}+\int {\frac {\mathrm {d} x}{\sin ax\cos ^{n-2}ax}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\,\!}" width="33025.5" height="2659.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed932bffc5175dd9e9b84177848b89dc90f2fff2" alt="{\displaystyle \int {\frac {\mathrm {d} x}{\sin ^{n}ax\cos ax}}=-{\frac {1}{a(n-1)\sin ^{n-1}ax}}+\int {\frac {\mathrm {d} x}{\sin ^{n-2}ax\cos ax}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\,\!}" width="33694" height="2730.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27e7c293b491ab9f27c2dd7e5fc7e5b4b48dce87" alt="{\displaystyle \int {\frac {\sin ax\;\mathrm {d} x}{\cos ^{n}ax}}={\frac {1}{a(n-1)\cos ^{n-1}ax}}+C\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\,\!}" width="23720.1" height="2659.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8d6cf7a626245e5b525924441bc9bc095309a37" alt="{\displaystyle \int {\frac {\sin ^{2}ax\;\mathrm {d} x}{\cos ax}}=-{\frac {1}{a}}\sin ax+{\frac {1}{a}}\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="23411.4" height="2659.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac70a5dd1703d07d1d0b7de956efa8a3fe654178" alt="{\displaystyle \int {\frac {\sin ^{2}ax\;\mathrm {d} x}{\cos ^{n}ax}}={\frac {\sin ax}{a(n-1)\cos ^{n-1}ax}}-{\frac {1}{n-1}}\int {\frac {\mathrm {d} x}{\cos ^{n-2}ax}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\,\!}" width="31772.5" height="2802.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2776622a8bff5aefed3bbc405e15420e0493ceb" alt="{\displaystyle \int {\frac {\sin ^{n}ax\;\mathrm {d} x}{\cos ax}}=-{\frac {\sin ^{n-1}ax}{a(n-1)}}+\int {\frac {\sin ^{n-2}ax\;\mathrm {d} x}{\cos ax}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\,\!}" width="27158.7" height="2802.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f263d5917e6307246bcb46a6ca11e48041a37893" alt="{\displaystyle \int {\frac {\sin ^{n}ax\;\mathrm {d} x}{\cos ^{m}ax}}={\frac {\sin ^{n+1}ax}{a(m-1)\cos ^{m-1}ax}}-{\frac {n-m+2}{m-1}}\int {\frac {\sin ^{n}ax\;\mathrm {d} x}{\cos ^{m-2}ax}}\qquad {\mbox{(for }}m\neq 1{\mbox{)}}\,\!}" width="35089.6" height="2802.6">

juga:

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b347956bcf9af09029e7a5bf3a5223b97216a8ef" alt="{\displaystyle \int {\frac {\sin ^{n}ax\;\mathrm {d} x}{\cos ^{m}ax}}=-{\frac {\sin ^{n-1}ax}{a(n-m)\cos ^{m-1}ax}}+{\frac {n-1}{n-m}}\int {\frac {\sin ^{n-2}ax\;\mathrm {d} x}{\cos ^{m}ax}}\qquad {\mbox{(for }}m\neq n{\mbox{)}}\,\!}" width="35249" height="2802.6">

juga:

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/223ee05bc798b7cd8150e1fbec738dc8218b2c06" alt="{\displaystyle \int {\frac {\sin ^{n}ax\;\mathrm {d} x}{\cos ^{m}ax}}={\frac {\sin ^{n-1}ax}{a(m-1)\cos ^{m-1}ax}}-{\frac {n-1}{m-1}}\int {\frac {\sin ^{n-2}ax\;\mathrm {d} x}{\cos ^{m-2}ax}}\qquad {\mbox{(for }}m\neq 1{\mbox{)}}\,\!}" width="34170.5" height="2802.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e41c74e0a7379bcdabeb3408aacfc41251b744d" alt="{\displaystyle \int {\frac {\cos ax\;\mathrm {d} x}{\sin ^{n}ax}}=-{\frac {1}{a(n-1)\sin ^{n-1}ax}}+C\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\,\!}" width="24498.6" height="2730.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ec01cb9859e14793e0ff78b9c215826d8255d5e" alt="{\displaystyle \int {\frac {\cos ^{2}ax\;\mathrm {d} x}{\sin ax}}={\frac {1}{a}}\left(\cos ax+\ln \left[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]|\tan {\frac {ax}{2}}\right|[fusion_builder_container hundred_percent=" width="19807" height="2659.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60b78d915cc06401720e1d9b59e4247449b67b63" alt="{\displaystyle \int {\frac {\cos ^{2}ax\;\mathrm {d} x}{\sin ^{n}ax}}=-{\frac {1}{n-1}}\left({\frac {\cos ax}{a\sin ^{n-1}ax)}}+\int {\frac {\mathrm {d} x}{\sin ^{n-2}ax}}\right)\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}" width="31312.5" height="3233.2">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8fab9a7c69246623d87885c9464347e9eaf3ac26" alt="{\displaystyle \int {\frac {\cos ^{n}ax\;\mathrm {d} x}{\sin ^{m}ax}}=-{\frac {\cos ^{n+1}ax}{a(m-1)\sin ^{m-1}ax}}-{\frac {n-m+2}{m-1}}\int {\frac {\cos ^{n}ax\;\mathrm {d} x}{\sin ^{m-2}ax}}\qquad {\mbox{(for }}m\neq 1{\mbox{)}}\,\!}" width="35978.1" height="2874.4">

juga:

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dca6cf047c64a430ac87b18c840b6685df1c393a" alt="{\displaystyle \int {\frac {\cos ^{n}ax\;\mathrm {d} x}{\sin ^{m}ax}}={\frac {\cos ^{n-1}ax}{a(n-m)\sin ^{m-1}ax}}+{\frac {n-1}{n-m}}\int {\frac {\cos ^{n-2}ax\;\mathrm {d} x}{\sin ^{m}ax}}\qquad {\mbox{(for }}m\neq n{\mbox{)}}\,\!}" width="34580.5" height="2874.4">

juga:

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bddedd61a0605e3db7e2abc89183963c7814705" alt="{\displaystyle \int {\frac {\cos ^{n}ax\;\mathrm {d} x}{\sin ^{m}ax}}=-{\frac {\cos ^{n-1}ax}{a(m-1)\sin ^{m-1}ax}}-{\frac {n-1}{m-1}}\int {\frac {\cos ^{n-2}ax\;\mathrm {d} x}{\sin ^{m-2}ax}}\qquad {\mbox{(for }}m\neq 1{\mbox{)}}\,\!}" width="35059" height="2874.4">

Integral trigonometri – Integrand melibatkan baik sinus dan tangen

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc722392a76d9c89bad4f9862e8eeea2872a2c4a" alt="{\displaystyle \int \sin ax\tan ax\;\mathrm {d} x={\frac {1}{a}}(\ln[/fusion_text][/fusion_builder_column] [/fusion_builder_row][/fusion_builder_container]|[fusion_builder_container hundred_percent=" width="24987.3" height="2443.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af2399ad5df5c1a98ab8e956715fdee0d7674b05" alt="{\displaystyle \int {\frac {\tan ^{n}ax\;\mathrm {d} x}{\sin ^{2}ax}}={\frac {1}{a(n-1)}}\tan ^{n-1}(ax)+C\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\,\!}" width="25181.1" height="2659.1">

Integral trigonometri – Integrand melibatkan baik kosinus dan tangen

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e71f890eaeba1f080c4038cd49e2d2298fe83cae" alt="{\displaystyle \int {\frac {\tan ^{n}ax\;\mathrm {d} x}{\cos ^{2}ax}}={\frac {1}{a(n+1)}}\tan ^{n+1}ax+C\qquad {\mbox{(for }}n\neq -1{\mbox{)}}\,\!}" width="25347.2" height="2659.1">

Integral trigonometri – Integrand melibatkan baik sinus dan kotangen

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c744b979124cd1b60b8fd4e558b0df34be620ed6" alt="{\displaystyle \int {\frac {\cot ^{n}ax\;\mathrm {d} x}{\sin ^{2}ax}}=-{\frac {1}{a(n+1)}}\cot ^{n+1}ax+C\qquad {\mbox{(for }}n\neq -1{\mbox{)}}\,\!}" width="25901.7" height="2659.1">

Integral trigonometri – Integrand melibatkan baik kosinus dan kotangen

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ea6b7204180e592aad1f681341e93d3c84be2a5" alt="{\displaystyle \int {\frac {\cot ^{n}ax\;\mathrm {d} x}{\cos ^{2}ax}}={\frac {1}{a(1-n)}}\tan ^{1-n}ax+C\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\,\!}" width="24456.7" height="2659.1">

Integral trigonometri – Integrand melibatkan baik sekan dan tangen

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/833796429fe5f1749a93b86fbe8cae0a7cbd06cb" alt="{\displaystyle \int \sec x\tan x\;\mathrm {d} x=\sec x+C}" width="12233.1" height="2443.8">

Integral dengan limit simetris

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15eb77904de9735a630976e29fe6df1e42775b48" alt="{\displaystyle \int _{-c}^{c}\sin {x}\;\mathrm {d} x=0\!}" width="6850.2" height="2587.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b47bb5a2390b43983fdf6f1a76400a45f1ac713c" alt="{\displaystyle \int _{-c}^{c}\cos {x}\;\mathrm {d} x=2\int _{0}^{c}\cos {x}\;\mathrm {d} x=2\int _{-c}^{0}\cos {x}\;\mathrm {d} x=2\sin {c}\!}" width="23282.5" height="2730.8">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5926e6c1b89f86e39548221b89fad9e565f094b3" alt="{\displaystyle \int _{-c}^{c}\tan {x}\;\mathrm {d} x=0\!}" width="7067.2" height="2587.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32dfede31ebd403068303a2b68554ffe356928a5" alt="{\displaystyle \int _{-{\frac {a}{2}}}^{\frac {a}{2}}x^{2}\cos ^{2}{\frac {n\pi x}{a}}\;\mathrm {d} x={\frac {a^{3}(n^{2}\pi ^{2}-6)}{24n^{2}\pi ^{2}}}\qquad {\mbox{(for }}n=1,3,5...{\mbox{)}}\,\!}" width="25523.8" height="3233.2">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca60cc9bb140488cd69085c14cc9794a84712289" alt="{\displaystyle \int _{\frac {-a}{2}}^{\frac {a}{2}}x^{2}\sin ^{2}{\frac {n\pi x}{a}}\;\mathrm {d} x={\frac {a^{3}(n^{2}\pi ^{2}-6(-1)^{n})}{24n^{2}\pi ^{2}}}={\frac {a^{3}}{24}}(1-6{\frac {(-1)^{n}}{n^{2}\pi ^{2}}})\qquad {\mbox{(for }}n=1,2,3,...{\mbox{)}}\,\!}" width="37536.1" height="3233.2">

Integral satu lingkaran penuh

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f223363eb61110230efb46c2ea2304da39899a3e" alt="{\displaystyle \int _{0}^{2\pi }\sin ^{2m+1}{x}\cos ^{2n+1}{x}\;\mathrm {d} x=0\!\qquad \{n,m\}\in \mathbb {Z} }" width="19953.8" height="2659.1">

Fungsi	Singkatan	Deskripsi	Identitas (memggunakan radian)
Sinus	sin	$<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cb996c2707412027b9255dbd26f00033ebfb773" alt="{\displaystyle {\frac {\textrm {a}}{\textrm {c}}}}" aria-hidden="true" width="860.5" height="2013.3">$	$<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/428c399c3bb96883b7e57751b23642c23f5feac5" alt="{\displaystyle \sin \theta \equiv \cos \left({\frac {\pi }{2}}-\theta \right)\equiv {\frac {1}{\csc \theta }}\,}" aria-hidden="true" width="12140.6" height="2300.3">$
Kosinus	cos	$<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a1450c1bba336efacd11aecf07b113016b5f14e" alt="{\displaystyle {\frac {\textrm {b}}{\textrm {c}}}}" aria-hidden="true" width="916.5" height="2300.3">$	$<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96f9cdacd80cd0e05e2a1ea80d0626351013a345" alt="{\displaystyle \cos \theta \equiv \sin \left({\frac {\pi }{2}}-\theta \right)\equiv {\frac {1}{\sec \theta }}\,}" aria-hidden="true" width="12140.6" height="2300.3">$
Tangen	tan (atau tg)	$<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/270b60dc1d46e0cd611285a608d8fa726b6a4434" alt="{\displaystyle {\frac {\textrm {a}}{\textrm {b}}}}" aria-hidden="true" width="916.5" height="2085">$	$<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8f7a451850784dc137a90b7ef581737f627cd25" alt="{\displaystyle \tan \theta \equiv {\frac {\sin \theta }{\cos \theta }}\equiv \cot \left({\frac {\pi }{2}}-\theta \right)\equiv {\frac {1}{\cot \theta }}\,}" aria-hidden="true" width="16073.3" height="2372">$
Kotangen	cot (atau ctg atau ctn)	$<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ec8e5984eb20427ba6882c760eec20ba4735090" alt="{\displaystyle {\frac {\textrm {b}}{\textrm {a}}}}" aria-hidden="true" width="916.5" height="2300.3">$	$<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c87ee9af5d763a410e6e3a7e8f7e41faf392ba3a" alt="{\displaystyle \cot \theta \equiv {\frac {\cos \theta }{\sin \theta }}\equiv \tan \left({\frac {\pi }{2}}-\theta \right)\equiv {\frac {1}{\tan \theta }}\,}" aria-hidden="true" width="16185.3" height="2372">$
Sekan	sec	$<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25f3b90f3f8ab2c46876c15182d6b41453b0b952" alt="{\displaystyle {\frac {\textrm {c}}{\textrm {b}}}}" aria-hidden="true" width="916.5" height="2085">$	$<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32ced6dcfe37f646b2e16bce1604b57a07aff9a6" alt="{\displaystyle \sec \theta \equiv \csc \left({\frac {\pi }{2}}-\theta \right)\equiv {\frac {1}{\cos \theta }}\,}" aria-hidden="true" width="12194.6" height="2300.3">$
Kosekan	csc (atau cosec)	$<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e673c1211c68eceb285ca168ae7afeab10f3c3b" alt="{\displaystyle {\frac {\textrm {c}}{\textrm {a}}}}" aria-hidden="true" width="860.5" height="2013.3">$	$<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2cff093f97f437c7e6a5e266e680fb95566c6bc" alt="{\displaystyle \csc \theta \equiv \sec \left({\frac {\pi }{2}}-\theta \right)\equiv {\frac {1}{\sin \theta }}\,}" aria-hidden="true" width="12084.6" height="2300.3">$

Integral Trigonometri – Fungsi Beserta Contoh Soal dan Jawaban

Daftar integral dari fungsi trigonometri

Integral trigonometri – Integrand melibatkan hanya sinus

Integral trigonometri – Integrand melibatkan hanya kosinus

Integral trigonometri – Integrand melibatkan hanya tangen

Integral trigonometri – Integrand melibatkan hanya sekan

Integral trigonometri – Integrands melibatkan hanya kosekan

Integral trigonometri – Integrand melibatkan hanya kotangen

Integral trigonometri – Integrand melibatkan sinus dan kosinus

Integral trigonometri – Integrand melibatkan baik sinus dan tangen

Integral trigonometri – Integrand melibatkan baik kosinus dan tangen

Integral trigonometri – Integrand melibatkan baik sinus dan kotangen

Integral trigonometri – Integrand melibatkan baik kosinus dan kotangen

Integral trigonometri – Integrand melibatkan baik sekan dan tangen

Integral dengan limit simetris

Integral satu lingkaran penuh

Fungsi trigonometrik

Contoh Soal dan Jawaban Integral trigonometri

1. Soal: Tentukan hasil dari ∫sin⁴ x dx =…

3. Soal: = …..

4. Soal: ∫ cos⁴ x dx

5. Soal: ∫ (tan 2x − sec 2x)² dx =…

6. Soal: ∫ (tan²4x + 3) dx =…

7. Soal:

8. Soal:

9. Soal:

10. Soal:

∫ (x + 3) cos (2x − π)dx =…..
|| |______|
u dv

11. Soal:

Bacaan Lainnya Yang Dapat Membuat Anda lebih Pintar

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Daftar integral dari fungsi trigonometri

Integral trigonometri – Integrand melibatkan hanya sinus

Integral trigonometri – Integrand melibatkan hanya kosinus

Integral trigonometri – Integrand melibatkan hanya tangen

Integral trigonometri – Integrand melibatkan hanya sekan

Integral trigonometri – Integrands melibatkan hanya kosekan

Integral trigonometri – Integrand melibatkan hanya kotangen

Integral trigonometri – Integrand melibatkan sinus dan kosinus

Integral trigonometri – Integrand melibatkan baik sinus dan tangen

Integral trigonometri – Integrand melibatkan baik kosinus dan tangen

Integral trigonometri – Integrand melibatkan baik sinus dan kotangen

Integral trigonometri – Integrand melibatkan baik kosinus dan kotangen

Integral trigonometri – Integrand melibatkan baik sekan dan tangen

Integral dengan limit simetris

Integral satu lingkaran penuh

Fungsi trigonometrik

Contoh Soal dan Jawaban Integral trigonometri

1. Soal: Tentukan hasil dari ∫sin4 x dx =…

3. Soal: <img decoding="async" src="http://latex.codecogs.com/gif.latex?%5Cint&amp;space;sin%5E2%5C;3x%5C;&amp;space;dx" alt="\int sin^2\;3x\; dx" width="101" height="41"> = …..

4. Soal: ∫ cos4 x dx

5. Soal: ∫ (tan 2x − sec 2x)2 dx =…

6. Soal: ∫ (tan24x + 3) dx =…

10. Soal:

∫ (x + 3) cos (2x − π)dx =….. |____| |__________| u dv

11. Soal: <img decoding="async" title="Rendered by QuickLaTeX.com" src="https://idschool.net/wp-content/ql-cache/quicklatex.com-a74547252e6b49e73506586ebcdb55cc_l3.png" alt="\[ \int cos \left( 2x + 5 \right) \; dx = ...\]" width="144" height="33">

Bacaan Lainnya Yang Dapat Membuat Anda lebih Pintar

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1. Soal: Tentukan hasil dari ∫sin⁴ x dx =…

3. Soal: = …..

4. Soal: ∫ cos⁴ x dx

5. Soal: ∫ (tan 2x − sec 2x)² dx =…

6. Soal: ∫ (tan²4x + 3) dx =…

∫ (x + 3) cos (2x − π)dx =…..
|| |______|
u dv

11. Soal: