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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

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    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

    vela

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    You could also try a hyperbolic trig substititution: ##x = \sinh u##.
     
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