integral of (ln(x))/(x^{16)}

解

\int \frac{ln ( x )}{x ^{16}} d x

- \frac{ln ( x )}{15 x ^{15}} - \frac{1}{225 x ^{15}} + C

解答ステップ

\int \frac{ln ( x )}{x ^{16}} d x

部分積分を適用する

= - \frac{ln ( x )}{15 x ^{15}} - \int - \frac{1}{15 x ^{16}} d x

\int - \frac{1}{15 x ^{16}} d x = \frac{1}{225 x ^{15}}

= - \frac{ln ( x )}{15 x ^{15}} - \frac{1}{225 x ^{15}}

定数を解答に追加する

= - \frac{ln ( x )}{15 x ^{15}} - \frac{1}{225 x ^{15}} + C