Integration

I'd start off by writing the second bracket as:
$\displaystyle 1-\frac{X_{j+1}-X}{h_j}=\frac{h_j}{h_j}-\frac{h_j+X_j-X}{h_j}=\frac{X-X_j}{h_j}$

Hi, just wondering what integration technique you would use to integrate this to keep it simple, avoiding expanding the brackets. This is because it should cancel down to something simple and it gets incredibly messy once brackets are expanded.

I think it should cancel to h_ j / 6 but i can't seem to get it:

I've just had a look but can't get it myself either as once you sub in hj = whatever it was, you get into a mess which I can't get myself out of!
I have a gut feeling that integration by partial fractions may come into it, but then again I might be wrong!

We are integrating wrt x, and I think the $h_j$ and $X_{j+1}$ are constants that don't depend on x. So I don't think it's anything more complicated than integrating something like ax and $(x-a)^2$.

Okay, thank you for the help.

I give up on this, at least the OP's got it

Incase you were interested:



Thanks for the help