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Homework Help: Integral (4/(x^2+4))2

  1. Feb 28, 2010 #1
    find the integral:

    integral (4/(x^2+4))2

    Ill use S for my integral
    So what i did so far is move the 4^2 out of the integral and get this:

    16 S 1/(x^2+4)^2

    I tried using partial fractions but got nothing. im not sure what to do. So far all I have learned was U sub, integral by parts, partial fractions, and trig substitution.

    Would trig substitution work?
    if i make x=2tan (theta)

    or is there another method i haven't seen yet.
  2. jcsd
  3. Feb 28, 2010 #2


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    Homework Helper

    Re: Integral

    Yes that substitution will work well. Try it and remember your trig identities.
  4. Feb 28, 2010 #3
    Re: Integral

    the answer i got when i did it was:

    .5archtan(x/2) +x(x^2+4) + C

    is that what you guys got?
    i made x=2tan (theta)
    dx= 2sec^2(theta)
  5. Feb 28, 2010 #4


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    Re: Integral

    Your first term is correct, where did you get the x(x2+4) term from?
  6. Feb 28, 2010 #5
    Re: Integral

    that came from the 2nd half of the equation
    i had the integral:
    S cos^2 theta
    used the power reducing formulas
    S (1+cos2 theta)/2
    and took derivative (just talking about
    = .5 d(theta) + S .5 cos2theta
    took derivative and used the double angle formula for the cos 2 theta (its would be .5 sin 2 theta when derivative taken)

    and answer came out to be:
    .5 arctan (x/2) + .25* 2 sin (theta) cos (theta)

    sin theta= x... oh wait i did x*sqr x^2 + 4... not divided
    im going to redue my work and show my final answer.
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