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Math Help - Simple indefinate integral

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    Simple indefinate integral

    calc test soon, drawing a lot of blanks pon the subject. I have to find the integral(5x/sqrt(9-4x^2)). I came up with an answer, but i'm pretty sure i used some steps that you shouldnt ever use in math....so im stuck. Any help? Thanks....
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    \int \frac{5x}{\sqrt{9-4x^2}} \ dx

    Do a u-sub: u = 9 -4x^2 \ \Rightarrow \ du = -8x \ dx \iff x dx = -\frac{du}{8}

    Making the subs:
    = \int \frac{5 \ \frac{du}{8}}{\sqrt{u}} = \frac{5}{8} \int \frac{1}{u^{\frac{1}{2}}} \ du
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    Quote Originally Posted by 92stealth View Post
    calc test soon, drawing a lot of blanks pon the subject. I have to find the integral(5x/sqrt(9-4x^2)). I came up with an answer, but i'm pretty sure i used some steps that you shouldnt ever use in math....so im stuck. Any help? Thanks....
    integration by substitution.

    let u = 9 - 4x^2

    or even better (if you can handle it), let u^2 = 9 - 4x^2
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    got it, thank you
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