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

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

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

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

- 2 1 - ln (x) + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{u} d u

= \int - \frac{1}{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= - 2 u^{\frac{1}{2}}

Substitute back

u = 1 - ln (x)

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

Apply radical rule:

= - 2 1 - ln (x)

Add a constant to the solution

= - 2 1 - ln (x) + C

\int x e^{\frac{2 x}{3}} d x

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

\int \frac{1}{x ^{8} ( 1 - x ^{2} )} d x

\int \frac{3}{4 x ^{2}} d x

\int \frac{3 x + 6}{( x - 1 ) ^{2} ( x ^{2} + x + 1 )} d x

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