Tough integration problem

1. Apr 4, 2004

mathrocks

Does anyone know how to integrate cos(sqrt x) ?? I know the answer, i need to know the steps to do it?

Thanks

2. Apr 4, 2004

HallsofIvy

Let $u= \sqrt{x}= x^{\frac{1}{2}}$. Then $du= \frac{1}{2}x^{-\frac{1}{2}}dx$ so that $dx= 2x^{\frac{1}{2}}du= 2udu$.

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

Now use integration by parts.

Last edited by a moderator: Apr 4, 2004
3. Apr 4, 2004

Dr Transport

let $$\sqrt{x} = y$$ be the variable substution and integrate by parts.

4. Apr 4, 2004

Dr Transport

as I was typing, HallsofIvy gopt it down first.....