# Integration problem

Integral of cos√x

We are supposed to use substitution and integration by parts but I really don't know where to even start.

No matter what I substitute for U I will be left without a du.

gabbagabbahey
Homework Helper
Gold Member
what are your limits of integration?...what does your integral become when you use the substitution u=sqrt(x)? What is du?

There are no limits it is indefinite. If you let U= √x then du= 1/2√x and that is my problem because I am left with with integral of cos(u) and no du.

gabbagabbahey
Homework Helper
Gold Member
doesn't $du=\frac{1}{2\sqrt{x}}dx$ and doesn't that mean that $dx=2 \sqrt{x} du= 2udu$?

Yes it does. So does that mean when I integrate I get u^2 sinu and from there I just need to back substitute?

gabbagabbahey
Homework Helper
Gold Member
Well, that means that

$\int cos(\sqrt{x})dx= \int 2ucos(u)du$

now you'll need to integrate by-parts....try using f(u)=2u and g'(u)=cos(u)du

oh ok. Thank you for the help.