Status: Accepted
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Labels: Type-Defect Priority-Medium Integration
New issue 2810 by [email protected]: Cannot do integrate(cos(k*x)/(x**2 +
a**2)/(x**2 + b**2), (x, -oo, oo))
http://code.google.com/p/sympy/issues/detail?id=2810
This is in Tom's gsoc-3 branch. Heurisch of course doesn't stand a chance
with this since the integral is non-elementary.
In [20]: integrate(cos(k*x)/(x**2 + a**2)/(x**2 + b**2), (x, -oo, oo),
meijerg=True)
Out[20]:
∞
⌠
⎮ cos(k⋅x)
⎮ ─────────────────── dx
⎮ ⎛ 2 2⎞ ⎛ 2 2⎞
⎮ ⎝a + x ⎠⋅⎝b + x ⎠
⌡
-∞
a, b, and k are real.
The answer can easily be computed using residue calculations. I think it's
given as
2*pi*I*(exp(-k*abs(a))/(2*abs(a)*I*(b**2 - a**2)) +
exp(-k*abs(b))/(2*abs(b)*I*(a**2 - b**2)))
Note that it would be awesome if we could do this, since it appears that
WolframAlpha cannot, though it can if you give it a specific k.
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