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人気のある微分積分 >

integral of csc^4(3x-1)

解

\int csc^{4} (3 x - 1) d x

解

\frac{1}{3} (- \frac{1}{3} csc^{3} (3 x - 1) cos (3 x - 1) - \frac{2}{3} cot (3 x - 1)) + C

解答ステップ

\int csc^{4} (3 x - 1) d x

u置換積分法を適用する

= \int csc^{4} (u) \frac{1}{3} d u

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int csc^{4} (u) d u

積分換算を適用する

= \frac{1}{3} (- \frac{cos ( u ) csc ^{3} ( u )}{3} + \frac{2}{3} \cdot \int csc^{2} (u) d u)

\int csc^{2} (u) d u = - cot (u)

= \frac{1}{3} (- \frac{cos ( u ) csc ^{3} ( u )}{3} + \frac{2}{3} (- cot (u)))

代用を戻す

u = 3 x - 1

= \frac{1}{3} (- \frac{cos ( 3 x - 1 ) csc ^{3} ( 3 x - 1 )}{3} + \frac{2}{3} (- cot (3 x - 1)))

簡素化

\frac{1}{3} (- \frac{cos ( 3 x - 1 ) csc ^{3} ( 3 x - 1 )}{3} + \frac{2}{3} (- cot (3 x - 1))) : \frac{1}{3} (- \frac{1}{3} csc^{3} (3 x - 1) cos (3 x - 1) - \frac{2}{3} cot (3 x - 1))

= \frac{1}{3} (- \frac{1}{3} csc^{3} (3 x - 1) cos (3 x - 1) - \frac{2}{3} cot (3 x - 1))

定数を解答に追加する

= \frac{1}{3} (- \frac{1}{3} csc^{3} (3 x - 1) cos (3 x - 1) - \frac{2}{3} cot (3 x - 1)) + C

グラフ

人気の例

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