How Do You Integrate cos(sqrt x)?

[mathrocks]

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

Thanks

 

[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.

 

[Dr Transport]

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

 

[Dr Transport]

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