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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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