Question

integrate the function cosx/√(1 + sinx).dx

Answer 1

this is answer ................

Answer 2

$\bf{I=\int{\frac{cosx}{\sqrt{1+sinx}}}\,dx}$
Let (1 + sinx ) = t
differentiate both sides,
cosx.dx = dt , put it in I.

I = $\bf{\int{ \frac{cosx.dx}{\sqrt{1+sinx}}}}$

= $\bf{\int{\frac{dt}{\sqrt{t}}}}\\\\=\bf{\int{t^{-1/2}}\,dt}\\\\=\bf{\frac{t^{-1/2+1}}{-1/2+1}+C}\\\\=\bf{2\sqrt{t}+C}\\\text{put,t=(1+sinx)}\\=\bf{2\sqrt{1+sinx}+C}$

hence, I = 2√(1 + sinx) + C