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

The integral of (ln(x))/(xsqrt(1-ln(x))) is -2ln(x)sqrt(1-ln(x))-4/3 (1-ln(x))^{3/2}+C

Popular >

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

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

- 2 ln (x) 1 - ln (x) - \frac{4}{3} (1 - ln (x))^{\frac{3}{2}} + C

Solution steps

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

Apply Integration By Parts

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

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

\int - \frac{2 1 - ln ( x )}{x} d x = \frac{4}{3} (1 - ln (x))^{\frac{3}{2}}

= - 2 ln (x) 1 - ln (x) - \frac{4}{3} (1 - ln (x))^{\frac{3}{2}}

Add a constant to the solution

= - 2 ln (x) 1 - ln (x) - \frac{4}{3} (1 - ln (x))^{\frac{3}{2}} + C

\frac{d}{d x} (15 + x^{2})

\int 17 arctan (x) d x

\frac{d}{d x} \frac{8}{( 9 x ^{2} - 7 ) ^{5}}

\int \frac{5}{2 + x ^{2}} d x

(x^{2} + 1) \frac{d y}{d x} + 3 x y = 6 x

What is the integral of (ln(x))/(xsqrt(1-ln(x))) ?
The integral of (ln(x))/(xsqrt(1-ln(x))) is -2ln(x)sqrt(1-ln(x))-4/3 (1-ln(x))^{3/2}+C