Integration - U substitution

Question

I am given the following indefinite integral:

$\int x\sqrt{1+2x}~dx$ using the substitution $u=\sqrt{1+2x}$

I am not sure where to begin, I know that $du=\dfrac{1}{\sqrt{1+2x}}$

But how can I get this integral in terms of $u$ when there is a $x$ in front?

Any help would be appreciated.

Thanks.

Answer 1

Hint : Use $x=\frac{u^2-1}{2}$ to get dx = u du

Answer 2

Try $u = 1 + 2x$, so $x = (u - 1)/2$. This will make the integral easy.