integral of x/((5x+2)^3)

解答

\int \frac{x}{( 5 x + 2 ) ^{3}} d x

- \frac{x}{10 ( 5 x + 2 ) ^{2}} - \frac{1}{50 ( 5 x + 2 )} + C

求解步骤

\int \frac{x}{( 5 x + 2 ) ^{3}} d x

使用分布积分法

= - \frac{x}{10 ( 5 x + 2 ) ^{2}} - \int - \frac{1}{10 ( 5 x + 2 ) ^{2}} d x

\int - \frac{1}{10 ( 5 x + 2 ) ^{2}} d x = \frac{1}{50 ( 5 x + 2 )}

= - \frac{x}{10 ( 5 x + 2 ) ^{2}} - \frac{1}{50 ( 5 x + 2 )}

解答补常数

= - \frac{x}{10 ( 5 x + 2 ) ^{2}} - \frac{1}{50 ( 5 x + 2 )} + C

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