# Maths integration problem

#### webpower

Joined Jul 13, 2012
16
Hi this is a maths question its related to finding a charge distribution along a line.

But it boils down to solving an integral.

Now I have the solution from the text book but I can not figure out how they solved it. Can anyone on here do this integration. as follows

integral x/(x^2+y^2)^(3/2) dy = y/(x sqrt(x^2+y^2))+constant

How was that worked out? Really would appreciate any ones help on this.
It looks really simple but I have tried substitution and looked up all the ordinary qouted lists of integrals but I can't do it.

#### wayneh

Joined Sep 9, 2010
17,189
That's a tough one. The integral tables show something pretty close.

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#### shteii01

Joined Feb 19, 2010
4,644
That's a tough one. The integral tables show something pretty close.

Is a variable or is it a constant?

The OP equation has a x and a y. The integral is taken with respect to y so y is variable. What is x? Is it also variable or is it constant?

#### wayneh

Joined Sep 9, 2010
17,189
It's odd form but the OP's x has to be constant when you'er integrating over dy, just as "a" is constant when integrating over dx in (41). In other words, the OP's "Y" is "x" in the integral table. His "x" is "a", any constant.

#### MrAl

Joined Jun 17, 2014
9,633
Hello,

Because the solution is already given we know that x can be treated as a constant.

We should be able to use trigonometric substitution using the substitution:
y=x*tan(A)
where A is the angle.

Try that and see if you can solve it. You might have to look up some trigonometric identities, but once done it should simplify to a very simple ratio involving one trig factor which can then be easily integrated.

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