I'm trying to use Maple to do something like this integral:
$\displaystyle\int \frac{a\mu-b}{||a\mu-b||^3} \mathrm{d}\mu$
Where $a, b$ are vectors and $\mu$ is a scalar I'm integrating by. But I can't figure out to tell Maple to treat them like vectors, and specifically have it figure out how to distribute the dot products in the denominator (calculate the squared length of a vector by dotting it with itself).
Right now I'm solving this specific integral like this:
int((a*u-b)/sqrt(C*u^2-2*u*D+E)^3, u)
I've basically been multiplying out the denominator in to dot products, and treating the dot products as separate variables (eg: $a \cdot a = C, a \cdot b = D, b \cdot b = E$). But this adds a lot of bookkeeping and I'm tired of doing it like this. The equations I'm trying to integrate are becoming increasingly complex and I'd like the computer to handle more of the work.
What's the proper way to solve this integral in Maple?
Alternatively, is there a way to get Mathematica to do this integration?