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

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

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integral of 1/(x*sin^2(ln(x)))

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

- cot (ln (x)) + C

Solution steps

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

Apply u-substitution

: \int csc^{2} (u) d u

= \int csc^{2} (u) d u

Use the common integral:

\int csc^{2} (u) d u = - cot (u)

= - cot (u)

Substitute back

u = ln (x)

= - cot (ln (x))

Add a constant to the solution

= - cot (ln (x)) + C

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