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

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

to this

[tex]\pi[/tex]k[tex]\sigma[/tex]y[tex]\frac{-2}{(x^{2} + y ^{2})^{1/2}}[/tex] (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 [tex](x^2+y^2)'=2x[/tex]. So just substitute [tex]z=x^2+y^2[/tex] and u ll have [tex]dz=2xdx[/tex] and the integral becomes

[tex]\int z^{-3/2} dz[/tex]

 

[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!