How to integrate sin sqrt(x)





\[∫sin√x dx\]

By Substitution \begin{aligned} \text { suppose } \Rightarrow z=\sqrt{x} \\ z^{2}=x \\ 2 z d z=d x \end{aligned} By Parts \begin{array}{lc} \text { Let } \Rightarrow u=2 z & d v=\sin z \\ d u=2 & v=-\cos z \\ -2 z \cos z+4 \int \cos z \mathrm{~d} z \\ -2 z \cos z+4 \sin z+C \\ -2 \sqrt{x} \cos \sqrt{x}+4 \sin \sqrt{x}+C \end{array}

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