# Integrate: sin square root x

Solution:

$\\ \\ I=\int \sin \sqrt{x}\hspace{0.1cm}dx\hspace{0.5cm} Let \hspace{0.5cm}\sqrt{x}=t \\ \\ \frac{1}{2\sqrt{x}}dx=dt\Rightarrow dx=2\sqrt{x}dt=2tdt\\ \\ I=\int 2t \sin t dt=2[t(-\cos t)+\sin t]+c\\ \\ I=2[-\sqrt{x}\cos \sqrt{x}+\sin \sqrt{x}]+c$

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