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  1. #1
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    antiderrivative of...

    Im having trouble finding the antiderrivative of r/[sqrt(4+r^2)]


    the answer is [sqrt(4+r^2)]...but how can that be?
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  2. #2
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    Quote Originally Posted by johntuan View Post
    Im having trouble finding the antiderrivative of r/[sqrt(4+r^2)]


    the answer is [sqrt(4+r^2)]...but how can that be?

    \int \frac{r}{\sqrt{4+r^2}}dr

    let u=4+r^2 \implies du=2rdr \iff \frac{du}{2}=rdr

    \int \frac{r}{\sqrt{4+r^2}}dr=\frac{1}{2}\int \frac{1}{u^{1/2}}du=...
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  3. #3
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    but then wouldnt the answer be over 2?

    u^(1/2)/2

    but the answer doesnt have a denominator:s
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    Behold, the power of SARDINES!
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    Not quite

    \frac{1}{2}\int \frac{1}{u^{1/2}}du=\frac{1}{2}\int u^{-1/2}du=\frac{\frac{1}{2}}{\frac{1}{2}}u^{1/2}=\sqrt{u}=\sqrt{4+r^2}
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