<s>[INST] Kindly provide the stepwise solution for this integral. $$\int_{-b}^b\int_{-a}^a\frac{1}{(x^2+y^2+h^2)^{3/2}}dxdy$$
First I put x=$\sqrt{y^2+h^2}tan\theta$ and arrive at: 
$$\int_{-b}^b\frac{2a}{(y^2+h^2)(y^2+h^2+a^2)^{1/2}}dy$$
Can you please tell me what to do after this?
 [/INST] If we substitute
$$y=\sqrt{a^2+h^2}\tan u$$
$$dy=\sqrt{a^2+h^2}\sec^2u \text{ }du$$
We get the integral
$$\int \frac{2a(\sqrt{a^2+h^2}\sec^2u)}{((a^2+h^2)\tan^2u+h^2)((a^2+h^2)\tan^2u+a^2+h^2)^{1/2}}du$$
Remembering that $\tan^2x+1=\sec^2x$, we get
$$\int \frac{2a\sqrt{a^2+h^2}\sec^2u}{((a^2+h^2)\sec^2u -h^2)((a^2+h^2)\sec^2u)^{1/2}}du$$ 
Now you can simplify quite a bit.
Hope this helps!
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