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

解答

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

2 x ln (x + 1) - 4 (- arctan (x) + x) + C

求解步骤

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

使用分布积分法

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

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

= 2 x ln (x + 1) - 4 (- arctan (x) + x)

解答补常数

= 2 x ln (x + 1) - 4 (- arctan (x) + x) + C

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