integral of sin^2(x)os(x)

解答

\int sin^{2} (x) d cos (x) d x

\frac{d}{3} sin^{3} (x) + C

求解步骤

\int sin^{2} (x) d cos (x) d x

提出常数:

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

= d \cdot \int sin^{2} (x) cos (x) d x

使用换元积分法

= d \cdot \int u^{2} d u

使用幂法则

= d \frac{u ^{3}}{3}

u = sin (x)

代回

= d \frac{sin ^{3} ( x )}{3}

化简

d \frac{sin ^{3} ( x )}{3} : \frac{d}{3} sin^{3} (x)

= \frac{d}{3} sin^{3} (x)

解答补常数

= \frac{d}{3} sin^{3} (x) + C

\int sin (4 y) d y

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