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

The integral of ln(sin(x))cos(x) is ln(sin(x))sin(x)-sin(x)+C

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integral of ln(sin(x))cos(x)

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

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

Solution steps

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

Apply Integration By Parts

= ln (sin (x)) sin (x) - \int cos (x) d x

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

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

Add a constant to the solution

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

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