integral of (ln(x))/(x^7)

解

\int \frac{ln ( x )}{x ^{7}} d x

- \frac{ln ( x )}{6 x ^{6}} - \frac{1}{36 x ^{6}} + C

解答ステップ

\int \frac{ln ( x )}{x ^{7}} d x

部分積分を適用する

= - \frac{ln ( x )}{6 x ^{6}} - \int - \frac{1}{6 x ^{7}} d x

\int - \frac{1}{6 x ^{7}} d x = \frac{1}{36 x ^{6}}

= - \frac{ln ( x )}{6 x ^{6}} - \frac{1}{36 x ^{6}}

定数を解答に追加する

= - \frac{ln ( x )}{6 x ^{6}} - \frac{1}{36 x ^{6}} + C