Look at this calculation.
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
Look at this calculation.
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?:
= =
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
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.
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
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