Question

how do you integrate:
∫ x/(x^2+y^2+z^2)^3/2 dx

with respect to x

Answer 1

\[1/2\int\limits_{?}^{?}d(x^2+y^2+z^2)/(x^2+y^2+z^2)\]
1/2ln(x^2+y^2+z^2)+C

Answer 2

u substitution.
u=x^2+y^2+z^2
du= 2x+2y+2z dx
1/2 du=x+y+z

1/2 ∫1/u^3/2 du = 1/2(-2/sqrt(u))
-1/sqrt(u)

Substitute U back in and you have your answer

Answer 3

that one makes sense. thank you!

Answer 4

ugh, i sort of messed up on the du. du=2xdx, so 1/2 du= x dx.