integral of x17^x

解

\int x 1 7^{x} d x

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

解答ステップ

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

部分積分を適用する

= \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 )}

定数を解答に追加する

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