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)

Simplify

= - 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