Here's the question you clicked on:
Albertoimus
Evaluate the following indefinite integrals.
^ oh yeah u substitution :D
@Albertoimus Do you get it? I know it looks a little messy but if you want I can rewrite so you can see it better.
\[\int\limits_{}^{}\frac{\cos \sqrt{x}}{\sqrt{x}}dx\] where we say that \[u=\sqrt{x}\]and if we square both sides that means that \[x=u^2\]and if we take the derivative of that we get \[dx=2u\]
The next step is a matter of replacing things
woops the last part should be \[dx=2udu\]
\[\int\limits_{}^{}\frac{cosu}{u}*2udu\] we cancel the u on the top with the u on the bottom. Also since 2 is a constant we take it outside the integral \[2\int\limits_{}^{}cosu*du\] the integral of cos u du is simply sin u \[2* \sin u\] And now we want it to convert it back into x instead of u and we know already that \[u=\sqrt{x}\] So it comes out as \[2*\sin \sqrt{x}\]