Vector and Tensor Calculus

Consider a sphere S of radius R with its center at the origin. Let x be a point on the surface. **Using vector/tensor suffix notation**, Evaluate

$\displaystyle \int\int_{S}$ $\displaystyle \frac{dA}{r}$ ; $\displaystyle r= \mid x-P \mid$

over the surface of the sphere, where P is a fixed point and integration is withr espect to x. COnsider separately the cases in which P lies inside or outside the sphere.

Hint: for P outside the sphere, expand 1/r in a taylor series expansion about $\displaystyle \mid x \mid $ and evaluate each term. For P inside the sphere, expand 1/r about $\displaystyle \mid P \mid$= 0.

you're supposed to use the 3 variable form of the taylor expansion.