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受欢迎的微积分 >

integral of sec^3(8x)tan(8x)

解答

\int sec^{3} (8 x) tan (8 x) d x

解答

\frac{1}{24} sec^{3} (8 x) + C

求解步骤

\int sec^{3} (8 x) tan (8 x) d x

使用换元积分法

= \int sec^{3} (u) tan (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 sec^{3} (u) tan (u) d u

使用换元积分法

= \frac{1}{8} \cdot \int \frac{1}{3} d v

常数积分:

\int a d x = a x

= \frac{1}{8} \cdot \frac{1}{3} v

代回

= \frac{1}{8} \cdot \frac{1}{3} sec^{3} (8 x)

化简

\frac{1}{8} \cdot \frac{1}{3} sec^{3} (8 x) : \frac{1}{24} sec^{3} (8 x)

= \frac{1}{24} sec^{3} (8 x)

解答补常数

= \frac{1}{24} sec^{3} (8 x) + C

作图

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