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

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

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

\int \frac{1}{x 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

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

in v erse l a pl a ce \frac{s}{( s + 4 ) ^{2}}

a re a y = x, y = 0, y = x - 2

x \to 3 + lim (\frac{2}{x - 3})

y^{^{'}} = y - 4 y^{2}

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

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