simplify integrate

asked 2013-10-08 05:52:51 -0500

Kamel gravatar image

updated 2015-01-14 06:56:54 -0500

FrédéricC gravatar image

Hi,

I would like to calculate this double integral with Sage

var('x y') ; var('a b')
f(x, y) = 1/(x^2 + y^2 + 1)^(3/2)
assume(b > 0) ; assume(a > 0)
val(a, b) = integrate(integrate(f(x,y),y,0,b), x, 0, a) ; val(a, b)

I think the result is atan(a*b/sqrt(a^2+b^2+1)) but instead Sage says b*integrate(sqrt(b^2 + x^2 + 1)/(x^4 + (b^2 + 2)*x^2 + b^2 + 1), x, 0, a)

How could I simplify it ?

Thanks.

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