Use integration by parts to solve. Simplify final answer and write in factored form. integral cos(x) log(sin(x)) dx

Answer 1

∫cosxlog(sinx)dx u = log(sinx) v = sinx

du = cosx / ln10sinxdx dv = cosxdx

= sinxlog(sinx) - 1/ln10 ∫cosxdx

= sinxlog(sinx) - 1/ln10 sinx + C

= sinx(log(sinx) - 1/ln10) + C