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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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