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Math Help - Evaluate the indefinite integral

  1. #1
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    Evaluate the indefinite integral

    I need to evaluate this integral

    dt/(t^2-1)^2


    I originally tried trig sub, by setting t=secx, but I only got so far as secx/(tanx)^3.
    Any help would be greatly appreciated.

    Thanks,
    Mike
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  2. #2
    Senior Member Educated's Avatar
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    \displaystyle \int \dfrac{dt}{(t^2 - 1)^2} = \int \dfrac{dt}{(1-t^2)^2} =

    Substitute in t^2 = \sin^2(x) and use the pythagorean identity.

    EDIT: Actually, Nevermind.
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  3. #3
    MHF Contributor harish21's Avatar
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    Use partial fractions first and then integrate:

     \displaystyle{\frac{1}{(t^{2}-1)^2} = \frac{1}{4(t+1)}- \frac{1}{4(t-1)}+ \frac{1}{4(t+1)^2}+ \frac{1}{4(t-1)^2}}
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