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Math Help - [SOLVED] Help with trigonometric substitution

  1. #1
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    [SOLVED] Help with trigonometric substitution

    \int\ (dx/4+x^{2})^{2}
    dont know how to do this problem without the square root
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  2. #2
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    Quote Originally Posted by vinson24 View Post
    \int\ (dx/4+x^{2})^{2}
    dont know how to do this problem without the square root
    Are you sure it's not

    \int{\frac{dx}{(4 + x^2)^2}}?
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    Yes that's how you write it sorry
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    \int{\frac{dx}{(4 + x^2)^2}}

    x = 2\tan{t}

    dx = 2\sec^2{t} \, dt

    \int \frac{2\sec^2{t}}{(4 + 4\tan^2{t})^2} \, dt

    \frac{1}{8} \int \frac{\sec^2{t}}{(1 + \tan^2{t})^2} \, dt

    \frac{1}{8} \int \frac{\sec^2{t}}{(\sec^2{t})^2} \, dt

    \frac{1}{8} \int \frac{1}{\sec^2{t})} \, dt

    \frac{1}{8} \int \cos^2{t} \, dt

    take it from here?
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