# Integrate ## \int \frac{zdz \cdot \hat z}{(\sqrt{p^2 + z¸^2)^3}}##

happyparticle
Homework Statement:
integration
Relevant Equations:
F = GMm/r^2
Hi,

I'm trying to integrate ## \int \frac{zdz \cdot \hat z}{(\sqrt{p^2 + z¸^2)^3}}## and ## \int \frac{pdz \cdot \hat p}{(\sqrt{p^2 + z¸^2)^3}}##

I get ## \frac{\hat z}{(\sqrt{p^2 + z¸^2)}}## and ## \frac{2z \cdot \hat p}{(\sqrt{p^2 + z¸^2)}}##

But the correct answer should be ## \frac{z \hat z}{(\sqrt{p^2 + z¸^2)}}## and ## \frac{2z \cdot \hat p}{(p\sqrt{p^2 + z¸^2)}}##

I'm not sure how to deal with ##\hat z## and ##\hat p##

Homework Helper
Gold Member
2022 Award
Apart from the unit vectors, your integrals do not seem to have any vector terms. That would make the unit vectors constants which can be moved outside the integral.
It would also mean the two official answers you quote only differ by a constant factor, but the given integrals do not fit that.
Should some of the occurrences of z and p be vectors?

happyparticle
Sorry, yes z and p are vectors using cylindrical coordinates.

Homework Helper
Gold Member
2022 Award
Sorry, yes z and p are vectors using cylindrical coordinates.
But changing all z, p, dz to vectors doesn’t work either.
Is it that ##dz\hat z## is the same as ##\vec{dz}##?
If not, please post a version which clarifies it.

happyparticle
Sorry, I'm not sure to understand. dz is for the derivative of z.