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

[astenroo]

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).

Homework Equations

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.

 

[rock.freak667]

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]

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

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

 

[astenroo]

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!