Integrating with Law of Cos

  • Thread starter cbirk
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Main Question or Discussion Point

I hope I am posting this in the correct area. This is not specificly a homework question, but something that keeps stumping me on numerous Electrostatic problems.

When attempting to Intigrate for finding the electric field or potential, I frequently end up with an integral over the form ∫∫∫ [itex]r^{2}[/itex] / ( [itex]r^{2}[/itex] + [itex]b^{2}[/itex] - 2rb cosθ) dr sinθ dθ dΦ

I was wondering if there is some sort of method the integrate this that I seem to be missing. A basic U sub doesn't work, and I can't get Integration by parts to do anything but make it worse. I have never been very good at remembering the trig tricks to integration so I was really hoping someone could help me out here. I am lost, and this is costing me lots of points on homeworks and tests.

Thanks in advance.
 
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Also after being stumped for days, I am pretty sure that the way the law of cosines is layed out... that cosθ is equivelent to Adjasent / Hyp = b/r which would simplify the entire denominator to a simple [itex]r^{2}[/itex] - [itex]b^{2}[/itex]

This look at all correct? I have added a picture so you can see the layout

stuff.jpg
 

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