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

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

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integral of sin(t)ln(cos(t))

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

cos (t) - cos (t) ln (cos (t)) + C

Solution steps

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

Apply Integration By Parts

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

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

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

= - (- cos (t)) - cos (t) ln (cos (t))

Simplify

= cos (t) - cos (t) ln (cos (t))

Add a constant to the solution

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

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