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integral of cos^6(8x)sin(8x)

解答

\int cos^{6} (8 x) sin (8 x) d x

解答

- \frac{1}{56} cos^{7} (8 x) + C

求解步骤

\int cos^{6} (8 x) sin (8 x) d x

使用换元积分法

: \int cos^{6} (u) sin (u) \frac{1}{8} d u

= \int cos^{6} (u) sin (u) \frac{1}{8} d u

提出常数:

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

= \frac{1}{8} \cdot \int cos^{6} (u) sin (u) d u

使用换元积分法

: \int - v^{6} d v

= \frac{1}{8} \cdot \int - v^{6} d v

提出常数:

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

= \frac{1}{8} (- \int v^{6} d v)

使用幂法则

: \frac{v ^{7}}{7}

= \frac{1}{8} (- \frac{v ^{7}}{7})

代回

= \frac{1}{8} (- \frac{cos ^{7} ( 8 x )}{7})

化简

\frac{1}{8} (- \frac{cos ^{7} ( 8 x )}{7}) : - \frac{1}{56} cos^{7} (8 x)

= - \frac{1}{56} cos^{7} (8 x)

解答补常数

= - \frac{1}{56} cos^{7} (8 x) + C

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