MATLAB int function problem while evaluating a symbolic definite integral

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this is my code
syms x y z b
assume(b, 'positive')
h(x,y,z) = z /(x^2 + y^2 + z^2)^(3/2) ;
int(h, x , [0 b])
i want to get the result of this integral wich is:
(2 b z)/((y^2 + z^2) Sqrt[b^2 + y^2 + z^2])
but instead i get :
ans(y, z) =
piecewise(y^2 + z^2 == 1 & ((z^2)^(1/2) == z | z + (z^2)^(1/2) == 0), (b*z)/(b^2 + 1)^(1/2), y^2 + z^2 ~= 1 | (z^2)^(1/2) ~= z & z + (z^2)^(1/2) ~= 0, int(z/(x^2 + y^2 + z^2)^(3/2), x, 0, b))
what can i do to get the first answer ? is there something wrong in my code ?
  1 Comment
Walter Roberson
Walter Roberson on 10 Sep 2020
Your proposed answer is not correct when there are certain relationships between the complex values x, y, z .
You have the assumption that b > 0, which implies that b is real, but the calculation needs to take into account that x, y, z are complex.

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Accepted Answer

Walter Roberson
Walter Roberson on 10 Sep 2020
simplify(ans, 'steps', 100)

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