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) \cdot 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

f (x) = \frac{2 x}{( x ^{3} - 8 ) ^{2}}

cos (x^{4})

(- sin (3 x) \cdot 3)^{^{'}}

x \to \infty lim (\frac{( e ^{2 x} )}{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