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受欢迎的微积分 >

integral of cos^{12}(7t)sin(7t)

解答

\int cos^{12} (7 t) sin (7 t) d t

解答

- \frac{1}{91} cos^{13} (7 t) + C

求解步骤

\int cos^{12} (7 t) sin (7 t) d t

使用换元积分法

= \int cos^{12} (u) sin (u) \frac{1}{7} d u

提出常数:

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

= \frac{1}{7} \cdot \int cos^{12} (u) sin (u) d u

使用换元积分法

= \frac{1}{7} \cdot \int - v^{12} d v

提出常数:

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

= \frac{1}{7} (- \int v^{12} d v)

使用幂法则

= \frac{1}{7} (- \frac{v ^{13}}{13})

代回

= \frac{1}{7} (- \frac{cos ^{13} ( 7 t )}{13})

化简

\frac{1}{7} (- \frac{cos ^{13} ( 7 t )}{13}) : - \frac{1}{91} cos^{13} (7 t)

= - \frac{1}{91} cos^{13} (7 t)

解答补常数

= - \frac{1}{91} cos^{13} (7 t) + C

作图

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