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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

= 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

\int 5 - (x - 1)^{2} d x

\int (x + 1)^{2} (1 - \frac{1}{x}) d x

\int (\frac{y ^{3} - 1}{y})^{2} d y

\int 5 x sin (3 x) d x

\int \frac{cos ( x )}{1 - ( cos ( x ) ) ^{2}} d x

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