Full question:

Evaluate the following integral(s) (I'm posting the first one):

I have no idea how to do it.. I tried using partial fractions and got something horrible like

ln[(x+1)^{-0.5} (x-1)^{1.5}] + lnk

- Oct 21st 2013, 07:06 AMMukilabIntegrate a fraction with x function on top and polynomial on bottom
Full question:

Evaluate the following integral(s) (I'm posting the first one):

I have no idea how to do it.. I tried using partial fractions and got something horrible like

ln[(x+1)^{-0.5} (x-1)^{1.5}] + lnk - Oct 21st 2013, 08:01 AMPlatoRe: Integrate a fraction with x function on top and polynomial on bottom
Look at this calculation.

- Oct 21st 2013, 09:17 AMMukilabRe: Integrate a fraction with x function on top and polynomial on bottom
Ok so that's partial fractions but I wouldn't know where to go from there.

How do I integrate the (x+1)^-1 or (x-1)^-1? - Oct 21st 2013, 10:25 AMtopsquarkRe: Integrate a fraction with x function on top and polynomial on bottom
- Oct 21st 2013, 11:14 AMMukilabRe: Integrate a fraction with x function on top and polynomial on bottom
Thanks for your help topsquark.

Is the dx you are using what is usually at the end of an integration (you are integrating with respect to d) or is it just a constant? If it is the former, I had no idea you're allowed to put it into the equation that you are integrating.

Assuming it is just a constant, your du/u would give you d. Integrating this would give you x.

Therefore for my integral above, would this be correct?:

= = - Oct 21st 2013, 11:29 AMtopsquarkRe: Integrate a fraction with x function on top and polynomial on bottom
The "dx" gets moved around sometimes. You typically see it in one of three places:

It all means the same thing.

The partial fraction decomposition is good, but the RHS is not correct. The fractions don't add up to 1 in general. The idea is to break the denominator into linear factors (if possible) then integrating them to get a ln function.

-Dan - Oct 22nd 2013, 06:04 AMMukilabRe: Integrate a fraction with x function on top and polynomial on bottom
Thank you, sorry that was a bit silly of me.

From = =

The answer would be

Is that correct?

It can be simplified into

I still don't see how you would use the u=x+1 substitution though. You would have to integrate a constant d.... with respect to...? Assuming with respect to x you would integrate it as x. Giving the answer to be 3/2(x) - 1/2(x) + c which isn't the same as the ln one.

Please could you explain the process for substituting u in and then solving it? I've never seen it done before nor have I done it myself. I've*just*learned about integrating to get ln a few days ago in class. - Oct 22nd 2013, 06:54 AMHallsofIvyRe: Integrate a fraction with x function on top and polynomial on bottom
There is NO "constant d! That was what topsquark told you and you said you understood.

. Whoever gave you this problem clearly expects you to know that. - Oct 22nd 2013, 12:01 PMMukilabRe: Integrate a fraction with x function on top and polynomial on bottom
At no point did topsquark say d is not a constant :(

Thanks for the formula, I had no idea about it. The question is from the physics aptitude test for oxford university which can feature stuff that can at times be far beyond my syllabus or not taught in schools such as lunar phases... or the above (although I'm guessing it will be taught at some stage in my education).

Thanks again :) - Oct 22nd 2013, 03:23 PMtopsquarkRe: Integrate a fraction with x function on top and polynomial on bottom
- Oct 22nd 2013, 11:30 PMMukilabRe: Integrate a fraction with x function on top and polynomial on bottom
- Oct 23rd 2013, 04:03 AMProve ItRe: Integrate a fraction with x function on top and polynomial on bottom
- Oct 23rd 2013, 08:36 AMtopsquarkRe: Integrate a fraction with x function on top and polynomial on bottom
I think Mukilab was trying to say that (s)he isn't in a college Calculus class and the Forum doesn't allow for integral questions in the Pre-Calculus forum.

Still, if it's an integration problem, it's Calculus and you posted in the correct forum. My point still stands...If you are this far along and having that basic a problem you need to consult with your instructor.

-Dan - Oct 23rd 2013, 12:14 PMMukilabRe: Integrate a fraction with x function on top and polynomial on bottom
Thanks guys, is there any different between putting ln(k) or C for the constant?

- Oct 23rd 2013, 01:36 PMtopsquarkRe: Integrate a fraction with x function on top and polynomial on bottom