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Math Help - Evaluate

  1. #1
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    Evaluate

    \int\frac{dx}{\sqrt{5-16x^2}}
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  2. #2
    Senior Member
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    Quote Originally Posted by cazimi View Post
    \int\frac{dx}{\sqrt{5-16x^2}}
    \int \frac{dx}{\sqrt{5-16x^2}}

    \int \frac{dx}{\sqrt{(\sqrt{5})^2-(4x)^2}}
    let u = 4x
    du = 4dx

    \int \frac{du}{\sqrt{(\sqrt{5})^2-(u)^2}}\frac{du}{4}

    from the rule:
    \int \frac{du}{\sqrt{a^2 - u^2}} = sin^{-1}(\frac{u}{a})

    thus
    \frac{1}{4}\sin^{-1}{(\frac{u}{\sqrt{5}})} + C

    \frac{1}{4}\sin^{-1}{(\frac{4x}{\sqrt{5}})} + C

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