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人気のある微分積分 >

integral of sin^3(x)cos(cos(x))

解

\int sin^{3} (x) cos (cos (x)) d x

解

- (2 (sin (cos (x)) - cos (cos (x)) cos (x)) + sin^{2} (x) sin (cos (x))) + C

解答ステップ

\int sin^{3} (x) cos (cos (x)) d x

u置換積分法を適用する

= \int - cos (u) (1 - u^{2}) d u

定数を除く:

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

= - \int cos (u) (1 - u^{2}) d u

部分積分を適用する

= - (sin (u) (1 - u^{2}) - \int - 2 u sin (u) d u)

\int - 2 u sin (u) d u = - 2 (- u cos (u) + sin (u))

= - (sin (u) (1 - u^{2}) - (- 2 (- u cos (u) + sin (u))))

代用を戻す

u = cos (x)

= - (sin (cos (x)) (1 - cos^{2} (x)) - (- 2 (- cos (x) cos (cos (x)) + sin (cos (x)))))

簡素化

- (sin (cos (x)) (1 - cos^{2} (x)) - (- 2 (- cos (x) cos (cos (x)) + sin (cos (x))))) : - (2 (sin (cos (x)) - cos (cos (x)) cos (x)) + sin^{2} (x) sin (cos (x)))

= - (2 (sin (cos (x)) - cos (cos (x)) cos (x)) + sin^{2} (x) sin (cos (x)))

定数を解答に追加する

= - (2 (sin (cos (x)) - cos (cos (x)) cos (x)) + sin^{2} (x) sin (cos (x))) + C

グラフ

人気の例

integral of 3sin^5(x)cos^4(x)

\int 3 sin^{5} (x) cos^{4} (x) d x

integral of cos(1/5)x

\int cos (\frac{1}{5}) x d x

integral of 1/((x^2+1)*(x^2+4))

\int \frac{1}{( x ^{2} + 1 ) \cdot ( x ^{2} + 4 )} d x

integral of 34d

\int 3 d^{4} ddd

integral of 7e^t-e^3

\int 7 e^{t} - e^{3} d t