Question-48703

Question Number 48703 by cesar.marval.larez@gmail.com last updated on 27/Nov/18

Answered by tanmay.chaudhury50@gmail.com last updated on 27/Nov/18

3) \int {s i n}^{3} (2 x) c o s (2 x) d x

t = s i n 2 x d t = 2 c o s 2 x d x

= \frac{1}{2} \int t^{3} d t

= \frac{1}{2} \times \frac{t^{4}}{4} + c

= \frac{{(s i n 2 x)}^{4}}{8} + c

4) \int {c o s}^{5} (2 x) {s i n}^{3} (2 x) d x

t = c o s 2 x d t = - 2 s i n 2 x d x

\int t^{5} \times (1 - t^{2}) \times \frac{d t}{- 2}

= \frac{- 1}{2} \int t^{5} - t^{7} d t

= \frac{- 1}{2} [\frac{t^{6}}{6} - \frac{t^{8}}{8}] + c

= \frac{- 1}{2} [\frac{{(c o s 2 x)}^{6}}{6} - \frac{{(c o s 2 x)}^{8}}{8}] + c