Question

\( -\int \sin x \times \log (\cos x) d x \)

Answer 1

\(-\int\)sin x log (cos x) dx

let cos x = t 

⇒ - sin x dx = dt

∴ \(-\int\)sin x log (cos x) dx = \(\int\) log t  dt

= t log t - t + c

= cos x log (cos x) - cos x + c

⇒ \(-\int\)sin x log(cos x) dx = cos x (log(cos x) - 1) + c