integral of 1/(7x^7)

解答

\int \frac{1}{7 x ^{7}} d x

- \frac{1}{42 x ^{6}} + C

求解步骤

\int \frac{1}{7 x ^{7}} d x

提出常数:

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

= \frac{1}{7} \cdot \int \frac{1}{x ^{7}} d x

使用幂法则

= \frac{1}{7} (- \frac{1}{6 x ^{6}})

化简

\frac{1}{7} (- \frac{1}{6 x ^{6}}) : - \frac{1}{42 x ^{6}}

= - \frac{1}{42 x ^{6}}

解答补常数

= - \frac{1}{42 x ^{6}} + C

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