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受欢迎的微积分 >

integral of-15cos^2(5x)sin(5x)

解答

\int - 15 cos^{2} (5 x) sin (5 x) d x

解答

cos^{3} (5 x) + C

求解步骤

\int - 15 cos^{2} (5 x) sin (5 x) d x

提出常数:

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

= - 15 \cdot \int cos^{2} (5 x) sin (5 x) d x

使用换元积分法

= - 15 \cdot \int cos^{2} (u) sin (u) \frac{1}{5} d u

提出常数:

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

= - 15 \cdot \frac{1}{5} \cdot \int cos^{2} (u) sin (u) d u

使用换元积分法

= - 15 \cdot \frac{1}{5} \cdot \int - v^{2} d v

提出常数:

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

= - 15 \cdot \frac{1}{5} (- \int v^{2} d v)

使用幂法则

= - 15 \cdot \frac{1}{5} (- \frac{v ^{3}}{3})

代回

= - 15 \cdot \frac{1}{5} (- \frac{cos ^{3} ( 5 x )}{3})

化简

- 15 \cdot \frac{1}{5} (- \frac{cos ^{3} ( 5 x )}{3}) : cos^{3} (5 x)

= cos^{3} (5 x)

解答补常数

= cos^{3} (5 x) + C

作图

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