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Math Help - Antidifferentiation

  1. #1
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    Antidifferentiation

    I was working on some new homework and I'm having a hard time antidifferentiating problems like these:

    \int_2^5 (3-(6/x))^2dx

    For this one, I tried multiplying it out and got

    {\int _2^5 (9-36/x+36/x^2)}dx
    and tried to use that to find the integral, but I ran into the problem of having to differentiate 36/x^2

    Another problem that I can't do is
    x={\int_0^y\sqrt{9t^2+6t}dt} for when y is greater than or equal to 1 and less than or equal to 5.
    On this problem, I have to find the length of the curve. I know the process, but I can't do it if I can't antidifferentiate that equation.
    Last edited by linlinrocks; May 8th 2009 at 07:42 PM. Reason: error message
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  2. #2
    Senior Member Pinkk's Avatar
    Joined
    Mar 2009
    From
    Uptown Manhattan, NY, USA
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    Do you mean you were having a problem finding the antiderivative of \frac{36}{x^{2}}?

    \int 36x^{-2}\,\,dx= \frac{36x^{-2+1}}{-1} = -\frac{36}{x}.

    With your second problem, complete the square and use trig substitution.
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