help with a parts integration

**bmnorvil** · October 3rd 2008, 08:00 AM

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!

**Soroban** · October 3rd 2008, 08:09 AM

Hello, bmnorvil!

$\int \frac{x+2}{\sqrt{4-x^2}}\,dx$

Make two integrals . . .

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

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

**bmnorvil** · October 3rd 2008, 08:24 AM

Thanks Soroban!

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