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人気のある微分積分 >

integral of sin^3(x)e^{cos(x)}

解

\int sin^{3} (x) e^{c o s (x)} d x

解

- (2 (- e^{c o s (x)} + e^{c o s (x)} cos (x)) + e^{c o s (x)} sin^{2} (x)) + C

解答ステップ

\int sin^{3} (x) e^{c o s (x)} d x

三角関数による置換を適用する

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

定数を除く:

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

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

部分積分を適用する

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

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

= - (e^{u} (- u^{2} + 1) - (- 2 (e^{u} u - e^{u})))

代用を戻す

u = cos (x)

= - (e^{c o s (x)} (- cos^{2} (x) + 1) - (- 2 (e^{c o s (x)} cos (x) - e^{c o s (x)})))

簡素化

- (e^{c o s (x)} (- cos^{2} (x) + 1) - (- 2 (e^{c o s (x)} cos (x) - e^{c o s (x)}))) : - (2 (- e^{c o s (x)} + e^{c o s (x)} cos (x)) + e^{c o s (x)} sin^{2} (x))

= - (2 (- e^{c o s (x)} + e^{c o s (x)} cos (x)) + e^{c o s (x)} sin^{2} (x))

定数を解答に追加する

= - (2 (- e^{c o s (x)} + e^{c o s (x)} cos (x)) + e^{c o s (x)} sin^{2} (x)) + C

グラフ

人気の例

integral of 15(2x+4)^4

\int 15 (2 x + 4)^{4} d x

integral of (sqrt(1+x^8))/x

\int \frac{1 + x ^{8}}{x} d x

integral of sin(18x)cos(11x)

\int sin (18 x) cos (11 x) d x

integral of 1/((81x^2+4)^2)

\int \frac{1}{( 81 x ^{2} + 4 ) ^{2}} d x

integral of sqrt((4-x)/(2+x))

\int \frac{4 - x}{2 + x} d x