sin-2x-cos-xd-x-

Question Number 53051 by Abror last updated on 16/Jan/19

\int \sin (2 x) \cos x d (x) =

Answered by tanmay.chaudhury50@gmail.com last updated on 16/Jan/19

\frac{1}{2} \int 2 s i n 2 x c o s x d x

= \frac{1}{2} \int (s i n 3 x + s i n x) d x

= \frac{1}{2} [\frac{- c o s 3 x}{3} + \frac{- c o s x}{}] + c

Answered by kaivan.ahmadi last updated on 16/Jan/19

\int 2 sinxcosx . cosxdx = 2 \int sinx . \cos^{2} xdx

u = cosx \Rightarrow du = - sinxdx \Rightarrow

- 2 \int u^{2} du = - 2 \frac{u^{3}}{3} + C = - \frac{2}{3} \cos^{3} x + C