integral of 16csch^2(x)coth(x)

解答

\int 16 csch^{2} (x) coth (x) d x

- 8 csch^{2} (x) + C

求解步骤

\int 16 csch^{2} (x) coth (x) d x

提出常数:

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

= 16 \cdot \int csch^{2} (x) coth (x) d x

使用换元积分法

= 16 \cdot \int - \frac{1}{2} d u

常数积分:

\int a d x = a x

= 16 (- \frac{1}{2}) u

u = csch^{2} (x)

代回

= 16 (- \frac{1}{2}) csch^{2} (x)

化简

16 (- \frac{1}{2}) csch^{2} (x) : - 8 csch^{2} (x)

= - 8 csch^{2} (x)

解答补常数

= - 8 csch^{2} (x) + C

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