1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integral of rational function

  1. Oct 5, 2014 #1
    • moved from technical forums
    Im trying to find the integral of ( sec(t)^2 ) / ( (tan(t)^3) + (tan(t)^2) ). I've managed to get the
    integral into the form

    1 / (u^3 + u^2) where u = tan(t), however Im having difficulty proceeeding from there.

    Could someone take a look at the working out I have attached and let me know what Im not doing right? (the correct answer is written in red pen on 2nd page)

    Attached Files:

  2. jcsd
  3. Oct 5, 2014 #2
    In order to evaluate ##\int\frac{1}{u^2(u+1)}\ du##, you want to use partial fraction decomposition, and that alone. You do not need to do any integration by parts. You have a correct general form $$\frac{1}{u^2(u+1)}=\frac{A}{u^2}+\frac{B}{u+1}+\frac{C}{u}$$ for the PFD, but then it looks like it all goes south after that, and you just gave up on that idea. Stick with that Idea.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted