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

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

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

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

arcsin (ln (x)) + C

Solution steps

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

\frac{d}{d θ} (- 3 sin (θ))

\int 5 sin (x) cos (x) d x

\int (- 3 x + 2 x) d x

\int_{2}^{5} (2 - x) (x - 5) d x

\frac{\partial}{\partial x} (1 - \frac{5}{y} + x)

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