I'm working through Griffith's Electrodynamics book during the winter break, and I'm having trouble on evaluating this integral from problem 2.7 of Introduction to Electrodynamics 4th edition. I have my electric field right? $$ \frac<4\pi\epsilon_> \sigma R^ 2\pi \int_^ <\pi>\frac<(R^2+z^2 -2Rz\cos\theta)^<3/2>> \sin\theta \ d\theta $$ The integral i want to evaluate is (obviously) $$ \int_^ <\pi>\frac<(R^2+z^2 -2Rz\cos\theta)^<3/2>> \sin\theta \ d\theta $$ The solution manual says to use partial fractions, but I feel like that would take quite a bit of working out to do. I want to avoid using a lot of algebra as possible (to reduce possible hiccups). Also, looking around, a lot solution of the internet just go the route of plugging it in mathematica or maple. I'm trying to avoid using those tools. Is there an integral table that that has something of this form or is there a much clever way of evaluating this? Thank you. Edit: If it helps, this is the integral evaluated from $0$ to $\pi$ (based off of the solution manual). $$ \frac<4\pi\epsilon_> \frac <\sigma R^2\pi> \Bigg\< \frac <|z-R|>- \frac <|z+R|>\Bigg\> $$ Their will conditions of course, such as, when $z>R$ and $z
$\begingroup$ @vnd sorry, it was 1 in the morning when i typed this. I missed a trig function inside of this. I've fixed it. $\endgroup$
Commented Dec 23, 2015 at 15:43$\begingroup$ @GaussTheBauss Yes. They represent real numbers. $z$ is the distance of the point charge from the center of the sphere and $R$ is the radius of the sphere. Nice username by the way. $\endgroup$
Commented Dec 23, 2015 at 15:45$\begingroup$ @DarthLazar Well, I'm not sure if this will help, but I couldn't help but notice that the denominator is exactly $| R e^ - z |^3$. So you couldd possibly use complex analysis for this. And thanks haha. $\endgroup$