Originally Posted by

**rebghb** Hi!

I remember at school there used to be this formula that we blindly used as a tool whenever something like this popped up, then we learnt that it's in fact a form substitution method:

$\displaystyle \int u'(x) . u^n (x) dx = \int u^n du $.

⌠

⌡ u'(x) . u^n(x) dx =

⌠

⌡ u^n du

Can you know why? Just remeber that $\displaystyle u' = \frac{du}{dx}$ u' = du/dx.

And remeber, by this so called *change of variable method* we're now integrating w.r.t. $\displaystyle u$ and not $\displaystyle x$. So if $\displaystyle u = 2x+1$ and the limits are$\displaystyle x=0, 1$ x = 0, 1, the limits of $\displaystyle u$ are $\displaystyle 1, 3$ 1, 3.

That plus TKHunny's hint, can you complete this?

Editing Note: Sorry, there's a problem with the LaTeX compiler