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

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

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integral of 1/(x*sqrt(1-(ln(x))^2))

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

arcsin (ln (x)) + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{1 - u ^{2}} d u = arcsin (u)

= arcsin (u)

Substitute back

u = ln (x)

= arcsin (ln (x))

Add a constant to the solution

= arcsin (ln (x)) + C

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