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: Trig Sub Integration

  1. Mar 20, 2016 #1
    1. The problem is as follows: ∫(√1+x^2)dx/(x)

    2. Using trig sub --> x = atanΘ with a = √1 = 1. So x = tanΘ and dx = sec^2ΘdΘ.

    3. Picture included of attempted solution. I tried u substitution with both u = secΘ and u=tanΘ but didn't have the right du. I then tried breaking the sec^3Θ/tanΘ (second to last step shown in work) into sines and cosines but, once again, no luck. Any help would be greatly appreciated.

    Note: I hope the format of my question is adequate this time. Sorry for the last post.

    Attached Files:

  2. jcsd
  3. Mar 20, 2016 #2

    Charles Link

    User Avatar
    Homework Helper
    Gold Member

    As I previously suggested, try multiplying numerator and denominator by ## \sin(\theta) ## and letting ## u=\cos(\theta) ## after a little algebra. (e.g. ## \sin^2(\theta)=1-\cos^2(\theta)) ## Then try using partial fractions to get the integral expression involving "u" in workable form.
  4. Mar 20, 2016 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You could also try a hyperbolic trig substititution: ##x = \sinh u##.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted