\(\int \sin \sqrt{x}dx\)

\(2(\sin\sqrt{x}-\sqrt{x}\cos\sqrt{x})+c\) \(2(\sin\sqrt{x}+\sqrt{x}\cos\sqrt{x})+c\) \(2(\sin\sqrt{x}-\cos\sqrt{x})+c\) \(2(\sin\sqrt{x}+\cos\sqrt{x})+c\)

\(2(\sin\sqrt{x}-\sqrt{x}\cos\sqrt{x})+c\)

$\int \sin \sqrt{x}dx$ let $x=t^2$ so $dx=2t\,dt$ $⇒I=2\int t\sin tdt=2(-t\cos t+\int\cos t dt)$ $=2(\sin t-t\cos t)+C$ $=2(\sin\sqrt{x}-\sqrt{x}\cos\sqrt{x})+C$