What is the integral of 1/(xsqrt(1-(ln(x^2)))) ?

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

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integral of 1/(xsqrt(1-(ln(x^2))))

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

- 1 - 2 ln (x) + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{2 u} d u

= \int - \frac{1}{2 u} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

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

Substitute back

u = 1 - ln (x^{2})

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

Simplify

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

= - 1 - 2 ln (x)

Add a constant to the solution

= - 1 - 2 ln (x) + C

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