What is the integral of (ln(1+x))/(sqrt(1+x)) ?

The integral of (ln(1+x))/(sqrt(1+x)) is 2ln(1+x)sqrt(1+x)-4sqrt(1+x)+C

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{2}{1 + x} d x = 4 1 + x

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

Add a constant to the solution

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

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What is the integral of (ln(1+x))/(sqrt(1+x)) ?
The integral of (ln(1+x))/(sqrt(1+x)) is 2ln(1+x)sqrt(1+x)-4sqrt(1+x)+C