What is the integral of cos(2x)ln(tan(x)) ?

The integral of cos(2x)ln(tan(x)) is -x+1/2 ln(tan(x))sin(2x)+C

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integral of cos(2x)ln(tan(x))

\int cos (2 x) ln (tan (x)) d x

- x + \frac{1}{2} ln (tan (x)) sin (2 x) + C

Solution steps

\int cos (2 x) ln (tan (x)) d x

Apply Integration By Parts

: - \int 1 d x + \frac{1}{2} ln (tan (x)) sin (2 x)

= - \int 1 d x + \frac{1}{2} ln (tan (x)) sin (2 x)

\int 1 d x = x

= - x + \frac{1}{2} ln (tan (x)) sin (2 x)

Add a constant to the solution

= - x + \frac{1}{2} ln (tan (x)) sin (2 x) + C

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What is the integral of cos(2x)ln(tan(x)) ?
The integral of cos(2x)ln(tan(x)) is -x+1/2 ln(tan(x))sin(2x)+C