How do you integrate int cosxsqrtsinx∫cosx√sinx using substitution?
1 Answer
Dec 18, 2016
Let
=int(cosxsqrt(u))/cosx du=∫cosx√ucosxdu
=sqrt(u) du=√udu
= u^(1/2) du=u12du
=2/3u^(3/2) + C=23u32+C
=2/3(sinx)^(3/2) + C=23(sinx)32+C
=2/3sqrt(sin^3x) + C=23√sin3x+C
=2/3sinxsqrt(sinx) + C=23sinx√sinx+C
Hopefully this helps!