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

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

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

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

- ln (sin (x)) cot (x) - x - cot (x) + C

Solution steps

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

Apply Integration By Parts

= - ln (sin (x)) cot (x) - \int - cot^{2} (x) d x

\int - cot^{2} (x) d x = x + cot (x)

= - ln (sin (x)) cot (x) - (x + cot (x))

Simplify

= - ln (sin (x)) cot (x) - x - cot (x)

Add a constant to the solution

= - ln (sin (x)) cot (x) - x - cot (x) + C

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