Thread: Integration by Substitution question?

Can you please show me the steps to integrate:

∫(x/2-x) dx ?? i let u = (2-x) and then??

Help is very appreciated! thanks!!

Originally Posted by Yehia

Can you please show me the steps to integrate:

∫(x/2-x) dx ?? i let u = (2-x) and then??

Then differentiate to get besides Can you take it?

Originally Posted by Krizalid

Then differentiate to get besides Can you take it?

I do do that! to get: ∫ (u-2)/u du

and that simplifies to : ∫ 1 - 2u^-1 du

still stumped though :S

Well done, you almost got it. (Oh, the numerador is actually )

Next step is to note that and

Originally Posted by Krizalid

Well done, you almost got it. (Oh, the numerador is actually )

Next step is to note that and

But the numerator is MINUS x isnt it? and if x = 2 - u, then -x = u - 2 ? if im not wrong?

And i dont understand your second bit (which is right btw, according to the book) can you explain?

thanks a lot

Ah yes, you're right, I forgot the minus sign when differentiating.

The latter are basic formulae which you should know, I can't help you any further about that, so check your notes.