integral of x17^x

解答

\int x 1 7^{x} d x

\frac{1 7 ^{x} x}{ln ( 17 )} - \frac{1 7 ^{x}}{ln ^{2} ( 17 )} + C

求解步骤

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

使用分布积分法

= \frac{1 7 ^{x} x}{ln ( 17 )} - \int \frac{1 7 ^{x}}{ln ( 17 )} d x

\int \frac{1 7 ^{x}}{ln ( 17 )} d x = \frac{1 7 ^{x}}{ln ^{2} ( 17 )}

= \frac{1 7 ^{x} x}{ln ( 17 )} - \frac{1 7 ^{x}}{ln ^{2} ( 17 )}

解答补常数

= \frac{1 7 ^{x} x}{ln ( 17 )} - \frac{1 7 ^{x}}{ln ^{2} ( 17 )} + C

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