Question

integrate sinx/sqrt(1+cosx) dx

Answer 1

Use the substitution
\[u=1+\cos x\]
Then
\[du = -\sin x\, dx\]
and so the integral becomes
\[-\int\limits_{}^{} u^{-1/2} du\]
which can be solved easilty to give
\[-2u^{1/2} + c\]
and so the original integral is
\[-2\sqrt{1+\cos x} + c\]