# I need help with an integral 2x dx /(x^2+y^2)^3/2

## Homework Statement

I need help with an integral, since my calculus skills aren't the greatest. I need help with getting from this

$$\pi$$k$$\sigma$$y$$\int$$ $$\frac{2x dx}{(x^{2} + y ^{2})^{3/2}}$$ (i)

to this

$$\pi$$k$$\sigma$$y$$\frac{-2}{(x^{2} + y ^{2})^{1/2}}$$ (ii)

I integrate from 0 to a (didn't know how to get the limits into TeX in (i) and the gargantuan brackets going on either side in (ii).

## The Attempt at a Solution

Am I supposed to do a substitution here or? In my physics textbook I saw the numerator of (i) written as d(x^2) and the denumerator unchanged as the following step. Now, I believe I have two functions here that i need to integrate 2x and 1/(x^2+y^2)^3/2.

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rock.freak667
Homework Helper
From the looks of it, I think they have y2 as constant. So all you need to do is make a substitution like u=x2+y2.

Delta2
Homework Helper
Gold Member
This is straightforward when u notice that $$(x^2+y^2)'=2x$$. So just substitute $$z=x^2+y^2$$ and u ll have $$dz=2xdx$$ and the integral becomes

$$\int z^{-3/2} dz$$

Thank you for your replies. I actually managed to solve the integral, but haven't been able to log on to the forum earlier. I did the u substitution and it worked fine fine. Thank you all again for your help!