integral of sqrt(2/(x+1))

解

\int \frac{2}{x + 1} d x

\frac{2}{x + 1} x + \frac{2 ( x + 2 )}{x + 1} + C

解答ステップ

\int \frac{2}{x + 1} d x

部分積分を適用する

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

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

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

簡素化

= \frac{2}{x + 1} x + \frac{2 ( x + 2 )}{x + 1}

定数を解答に追加する

= \frac{2}{x + 1} x + \frac{2 ( x + 2 )}{x + 1} + C