Question

integrate 2+sin(2*sqrt(x)) dx

Answer 1

\[\int\limits \left(2+\sin \left(2 \sqrt{x}\right)\right) \, dx\]
Let u=\(\sqrt{x}\)
\[du=\frac{1}{2\sqrt{x}}dx\]
\[2\sqrt{x}du=dx\]
\[\int\limits 2+\sin(2u)[2\sqrt{x}du] \\ \\ \int\limits 2+2usin(2u)du \\ \\ 2 \int\limits 1du+2 \int\limits usin(2u)du\]
Then integration by parts for the right integral

Answer 2

thanks SAM alot :)