integral of (ln(3x))/(x^3)

解

\int \frac{ln ( 3 x )}{x ^{3}} d x

- \frac{ln ( 3 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}} + C

解答ステップ

\int \frac{ln ( 3 x )}{x ^{3}} d x

部分積分を適用する

= - \frac{ln ( 3 x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x

\int - \frac{1}{2 x ^{3}} d x = \frac{1}{4 x ^{2}}

= - \frac{ln ( 3 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}}

定数を解答に追加する

= - \frac{ln ( 3 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}} + C