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

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

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

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

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

Solution steps

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

Apply Integration By Parts

= ln (sin (x)) tan (x) - \int 1 d x

\int 1 d x = x

= ln (sin (x)) tan (x) - x

Add a constant to the solution

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

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