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Math Help - Intergration help

  1. #1
    Super Member 11rdc11's Avatar
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    Intergration help

    I'm having problems with these 2 integrals and any help would be great.

    \int\frac{dx}{\sqrt{x^2-9}}

    here is my work

    x = 3\sec{\theta}

    dx = 3\tan{\theta}\sec{\theta}

    plugging that in

    \int \frac{3\tan{\theta}\sec{\theta}d\theta}{3\tan{\the  ta}}

    \int \sec{\theta}d\theta

    \ln{|\sec{\theta}+\tan{\theta}|}

    \ln|\frac{x}{3} + \frac{\sqrt{x^2-9}}{3}| + C

    but the book has

    \ln|x+ \sqrt{x^2-9}| + C

    where did I go wrong?


    The other problem is

    \int \frac{dx}{(4x^2-9)^3}

    I know I have to divide

    4x^2-9

    by 4 to get

    x^2 - \frac{9}{4}

    but what do I divide the numerator by then, 64?

    Thanks in advance
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  2. #2
    Junior Member Evales's Avatar
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    Re: integration help

    Hi,
    I can't figure out what is going on with the first integral. I plugged it into Wolfram Alpha which gives an alternative answer which is quite confusing.

    However with your second one yes, simply divide the numerator/ whole integral by 64.
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  3. #3
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    I solved the first problem and got the same answer you did. I used Wolfram Mathematica to confirm it, and your answer is correct. I guess the book answer is wrong.

    Patrick
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  4. #4
    Super Member 11rdc11's Avatar
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    ok thanks but I'm still having problems on the last problem

    \int \frac{dx}{(4x^2-9)^3}

    \int \frac{\frac{dx}{64}}{(x^2-\frac{9}{4})^3}

    x = \frac{2}{3}\sec{\theta}

    dx = \frac{2}{3}\sec{\theta}\tan{\theta}

    plugging all that in I get

    \frac{2}{2187} \int \frac{\sec{\theta}\tan{\theta}d\theta}{\tan^6{\the  ta}}

    and this is where I get stuck. Could someone check my work and show me how to solve it? Thanks in advance.
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  5. #5
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by PatrickFoster View Post
    I solved the first problem and got the same answer you did. I used Wolfram Mathematica to confirm it, and your answer is correct. I guess the book answer is wrong.

    Patrick
    I figured out what the book did.

    \ln|\frac{x+\sqrt{x^2-9}}{3}|+ C

    \ln{|x+\sqrt{x^2-9}|}-\ln{3}+C

    they just combine the constant of ln3 with the constant.
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