Updates:
Status: Fixed
Comment #9 on issue 1690 by [email protected]:
integrate(A*x**2*exp(-B*x**2), (x, 0, oo)) gives wrong solution
http://code.google.com/p/sympy/issues/detail?id=1690
And this now gives
pprint(_)
⎧ ___
⎪ ╲╱ π ⋅z π
⎪ ─────── for │periodic_argument(y, ∞)│ < ─
⎪ 3/2 2
⎪ 4⋅y
⎪
⎨∞
⎪⌠
⎪⎮ 2
⎪⎮ 2 -x ⋅y
⎪⎮ x ⋅z⋅ℯ dx otherwise
⎪⌡
⎩0
also
integrate(z*x**2*exp(-y*x**2), (x, 0, oo))
Piecewise((sqrt(pi)*z/(4*y**(3/2)), Abs(periodic_argument(y, oo)) < pi/2),
(Integral(x**2*z*exp(-x**2*y), (x, 0, oo)), True))
pprint(_)
⎧ ___
⎪ ╲╱ π ⋅z π
⎪ ─────── for │periodic_argument(y, ∞)│ < ─
⎪ 3/2 2
⎪ 4⋅y
⎪
⎨∞
⎪⌠
⎪⎮ 2
⎪⎮ 2 -x ⋅y
⎪⎮ x ⋅z⋅ℯ dx otherwise
⎪⌡
⎩0
integrate(z*x**2*exp(-y*x**2), (x, 0, oo)).subs(z,A).subs(y,B) ==
integrate(A*x**2*exp(-B*x**2), (x, 0, oo))
True
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