integral of (ln(x+1))/((x+1)^3)

解

\int \frac{ln ( x + 1 )}{( x + 1 ) ^{3}} d x

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

解答ステップ

\int \frac{ln ( x + 1 )}{( x + 1 ) ^{3}} d x

部分積分を適用する

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

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

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

定数を解答に追加する

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