integral of (10)/(x^9)

解答

\int \frac{10}{x ^{9}} d x

- \frac{5}{4 x ^{8}} + C

求解步骤

\int \frac{10}{x ^{9}} d x

提出常数:

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

= 10 \cdot \int \frac{1}{x ^{9}} d x

使用幂法则

= 10 (- \frac{1}{8 x ^{8}})

化简

10 (- \frac{1}{8 x ^{8}}) : - \frac{5}{4 x ^{8}}

= - \frac{5}{4 x ^{8}}

解答补常数

= - \frac{5}{4 x ^{8}} + C

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