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Math Help - Integration question

  1. #1
    Senior Member
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    Integration question

    I'm stuck integrating this:

    \displaystyle\int\frac{1}{(x^2+3)^{\frac{3}{2}}} \ dx

    I really just need a hint on how to start this question.

    EDIT: I think I worked out how to do it

    Let x=\sqrt{3}\tan\theta \Rightarrow dx=\sqrt{3}\sec^2\theta \ d\theta

    =\displaystyle\int\frac{\sqrt{3}\sec^2\theta}{(3\t  an^2\theta+3)^{\frac{3}{2}}} \ d\theta

    =\displaystyle\int\frac{\sqrt{3}\sec^2\theta}{3^{\  frac{3}{2}}\sec^3\theta} \ d\theta

    =\displaystyle\int\frac{1}{3\sec\theta} \ d\theta

    =\displaystyle\frac{1}{3}\int\cos\theta \ d\theta

    =\displaystyle\frac{1}{3}\sin\theta+C

    \dfrac{x}{\sqrt{3}}=\tan\theta \Rightarrow \sin\theta=\dfrac{x}{\sqrt{x^2+3}}

    =\dfrac{x}{3\sqrt{x^2+3}}+C
    Last edited by acevipa; September 6th 2010 at 01:50 AM.
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  2. #2
    Super Member
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    Your answer is correct.
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