Question

Find ∫(cos√x) dx=?

Answer 1

$I=\int cos\,x\,dx$
Put
$\sqrt{x}=t$ so that
$\frac{1}{2\sqrt{x}}dx=dt$
∴$I=f(cos\,t)2tdt = 2\int tcos\,t\,dt$
Integrating by parts, we get
$I=2[tsin\,t-\int 1.sint\,dt]$
=$2[tsint+cost]$
=$2[x\,sin\,x+cos\,x]$.