integral of (ln(x))/(x^{20)}

解

\int \frac{ln ( x )}{x ^{20}} d x

- \frac{ln ( x )}{19 x ^{19}} - \frac{1}{361 x ^{19}} + C

解答ステップ

\int \frac{ln ( x )}{x ^{20}} d x

部分積分を適用する

= - \frac{ln ( x )}{19 x ^{19}} - \int - \frac{1}{19 x ^{20}} d x

\int - \frac{1}{19 x ^{20}} d x = \frac{1}{361 x ^{19}}

= - \frac{ln ( x )}{19 x ^{19}} - \frac{1}{361 x ^{19}}

定数を解答に追加する

= - \frac{ln ( x )}{19 x ^{19}} - \frac{1}{361 x ^{19}} + C