symbolic integration with undefined variable

i created the following script code

syms r,x,r,z; a=int((r^2*x*z)/(r^2+z^2)^(3/2),0,2*pi) b=int(a, r, 0, r)

because i can't do definite integrals of multidimensional problems. But the answer for b is not making sense to me as i keep getting this piecewise answer that does not make sense. It appears that its trying to evaluate the value of z over which answer is valid. how can i force it to know that z is always a positive value > 0 so i can avoid this?

here is what i get out, note a is correct, but b is confused.

a = (2*pi^2*r^2*z)/(r^2 + z^2)^(3/2)

b = piecewise([z in {-1, 1}, (2*pi^2*r^3*z*hypergeom([3/2, 3/2], [5/2], -r^2))/3], [not z in {-1, 1}, int((2*pi^2*r^2*z)/(r^2 + z^2)^(3/2), r, 0, r)])

Answer 1

[David Sanchez]

Point out that z>0 like this:

>> assume(z>0);
>> b=int(a, r, 0, r)

b =

-2*pi^2*z*(log(z) - log(r + (r^2 + z^2)^(1/2)) + r/(r^2 + z^2)^(1/2))

[james hopper]

Thanks. That's just what I needed!