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

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

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

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

cos (x) - cos (x) ln (cos (x)) + C

Solution steps

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

Apply Integration By Parts

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

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

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

= - (- cos (x)) - cos (x) ln (cos (x))

Simplify

= cos (x) - cos (x) ln (cos (x))

Add a constant to the solution

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

x \to 2 lim (\frac{4 - x ^{2}}{x - 2})

e^{- 2 u + v^{2}} ((1 + u) d u + 2 uv d v) = 0

5 cos (x - \frac{16}{25})

\int x^{3} cos (\frac{x}{2}) d x

- 9 x^{2} y + y^{^{'}} = 9 x^{2}

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