## Albertoimus 2 years ago Evaluate the following indefinite integrals.

1. Albertoimus

2. amoodarya

3. RyanL.

^ oh yeah u substitution :D

4. RyanL.

@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.

5. Albertoimus

by all means.

6. RyanL.

$\int\limits_{}^{}\frac{\cos \sqrt{x}}{\sqrt{x}}dx$ 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 $dx=2u$

7. RyanL.

The next step is a matter of replacing things

8. RyanL.

woops the last part should be $dx=2udu$

9. RyanL.

$\int\limits_{}^{}\frac{cosu}{u}*2udu$ 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 $2*\sin \sqrt{x}$

10. RyanL.

Done!

11. Albertoimus

thanks