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Math Help - help with a parts integration

  1. #1
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    help with a parts integration

    I need help with the following indefinite integral: int (x+2)/sqrt(4-x^2).

    I have tried parts several times and have come up empty. Thanks!
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  2. #2
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    Hello, bmnorvil!

    \int \frac{x+2}{\sqrt{4-x^2}}\,dx
    Make two integrals . . .

    \int\left[\frac{x}{\sqrt{4-x^2}} + \frac{2}{\sqrt{4-x^2}}\right]\,dx


    . . =\;\underbrace{\int x(4-x^2)^{-\frac{1}{2}}\,dx}_{u \:=\: 4-x^2}    \;+ \;2\underbrace{\int\frac{dx}{\sqrt{4-x^2}}}_{\text{arcsine}}

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  3. #3
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    Thanks Soroban!
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