What substitution could I use to integrate

a/(a^2 + x^2)^3/2 dx

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  1. Let u = x/(x^2 + a^2)^1/2

    and you will find that

    (1/a^2)* du
    = integral of dx/(x^2+a^2)^3/2
    which is the integral you want.
    Therefore u/a^2
    = (x/a^2)/(x^2 + a^2)^1/2
    is the answer.

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  2. Computer program says the answer is

    x/(a*(a^2 + x^2)^(1/2))

    which is slightly different from your answer. Thanks so much for the help on this one. I was really stuck.

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  3. I did x = a tan u
    dx = a (sec u)^2 du

    int of a/(a^2 + x^2)^3/2 dx
    = int of (a sec u)^2/(a^2 + (a tan u)^2)^3/2 du
    = int of (a sec u)^2/(a sec u)^3 du
    = int of (cos u)/a du
    = (sin u)/a + K
    since u = atan (x/a)
    = x/(a*(a^2 + x^2)^(1/2)) + K

    Thanks again...

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