積分記号 (ln(1+x^2))/(x^2)

解

積分記号

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

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

解答ステップ

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

部分積分を適用する

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

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

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

簡素化

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

定数を解答に追加する

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