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## Homework Statement

I need to evaluate this particular integral and I'm confused on what method to use. I'm currently learning integration calculus and I tried doing some introduction on electromagnetic field. Quite unexpectedly the integral turned to be heavy.

[tex]\int_{-a}^a \frac{1}{\left(x^2+y^2\right)^{3/2}} \, dy[/tex]

## The Attempt at a Solution

I have tried on using integration by substitution. I came up with this indefinite integral which is not correct according to the solution:

Let u = [tex]\left(x^2+y^2\right)[/tex]

du = [tex]2y\text{dy}[/tex]

Hence:

[tex]\int \frac{1}{\left(x^2+y^2\right)^{3/2}} \, dy

\int \frac{u^{-3/2}}{2} \, du

\frac{1}{2} \int u^{-3/2} \, du

\frac{\frac{1}{\sqrt{u}}}{\frac{2 (-1)}{2}}-\frac{1}{\sqrt{u}}-\frac{1}{\sqrt{x^2+y^2}}-\frac{1}{\sqrt{x^2+y^2}}[/tex]

[tex]-\frac{1}{\sqrt{x^2+y^2}}[/tex]

If it is possible I also would like to know what type of integral is this because I'm afraid I've not reached the level for this type of problem. I'm sorry if my formatting is bad, this is my first time using LaTex.

Thank You

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