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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

= 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)

Add a constant to the solution

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

\int \frac{3 x}{( 1 + 9 x ^{2} ) ^{4}} d x

sin^{2} (t)

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