(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi all, as part of an electrodynamics-problem, I encountered:

[itex]\int {\frac{x}{{{{({x^2} + 1)}^3}}} \cdot dx} [/itex]

I know how to get the answer with my computer, but I wanted to know how to do it by hand. It’s getting to the point here in physics-grad-school that I need to know how to do this stuff “off the cuff”, so to speak.

2. Relevant equations

3. The attempt at a solution

Well....this is part of a solution of a bigger problem. I know there's some sort of trig substitution or trig identity. It happens that x = r/d, where "r" is an in-plane polar distance (x^2 + y^2), and "d" is distance above the plane, and I rearranged the integral I got into getting the dimensionless length scale x = r/d ... and by the above geometry, if you consider theta to be the angle between "r" and "d", then r/d = tan(theta). But:

dx = d(r/d) = d(tan(theta)) = (1 + tan(theta)^2)*d(theta)

That's just a mess.

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# Homework Help: Integration Tricks

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