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) 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 (\frac{2}{x} + \frac{4}{x ^{3}}) d x

\int \frac{1}{( a + x )} d x

\int + 0.0025 x - 0.075 d x

\int \frac{x ^{3} - 4 x - 1}{x ^{2}} d x

\int - x^{2} + 2 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