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受欢迎的微积分 >

integral of (x^5)/((x^6+1)^2)

解答

\int \frac{x ^{5}}{( x ^{6} + 1 ) ^{2}} d x

解答

- \frac{1}{6 ( x ^{6} + 1 )} + C

求解步骤

\int \frac{x ^{5}}{( x ^{6} + 1 ) ^{2}} d x

使用换元积分法

= \int \frac{1}{6 u ^{2}} d u

提出常数:

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

= \frac{1}{6} \cdot \int \frac{1}{u ^{2}} d u

使用幂法则

= \frac{1}{6} (- \frac{1}{u})

u = x^{6} + 1

代回

= \frac{1}{6} (- \frac{1}{x ^{6} + 1})

化简

\frac{1}{6} (- \frac{1}{x ^{6} + 1}) : - \frac{1}{6 ( x ^{6} + 1 )}

= - \frac{1}{6 ( x ^{6} + 1 )}

解答补常数

= - \frac{1}{6 ( x ^{6} + 1 )} + C

作图

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