How do you integrate int cosxsqrtsinxcosxsinx using substitution?

1 Answer
Dec 18, 2016

Let u = sinxu=sinx. Then du = cosxdxdu=cosxdx and dx = (du)/cosxdx=ducosx.

=int(cosxsqrt(u))/cosx du=cosxucosxdu

=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=23sin3x+C

=2/3sinxsqrt(sinx) + C=23sinxsinx+C

Hopefully this helps!