Please help me integrate this!!!?

Question

Please help me integrate: cos x^1/2 dx

Answer 1

If you put sqrtx=z 1/2sqrtx dx =dz and dx = 2z dz

So we have the Integral 2 Int zcos z dz.
By parts = 2 [ z sinz -Int sinz dz] =2 (z sin z +cos z)

= 2[(sqrt(x)*sin(sqrt x) +cos(sqrt x)]