Incorrect result for divergent integral

[ppurka]

From google spreadsheet which no one reads X-(

sage: integrate(x^2/exp(-1/(x^2+1))/(x^2+1),(x,-infinity,infinity)).n()
-3.3357920860949157

Wolfram alpha ​gives the correct answer.

The problem comes from here:

sage: D=1.00000000000000*x^2*e^(1/(x^2 + 1.00000000000000))/(x^2 + 1.00000000000
....: 000)
sage: numerical_integral(D,-oo,+oo)
(-3.3357920860949157, 4.262178610048295e-09)

and in one specific algorithm

sage: numerical_integral(D,-oo,+oo, algorithm="qag")
(-3.3357920860949157, 4.262178610048295e-09)
sage: numerical_integral(D,-oo,+oo, algorithm="qng")
(nan, nan)
sage: numerical_integral(D,-oo,+oo, algorithm="qags")
(nan, nan)

and this case is handled by gsl_integration_qagi

And the problem can be cut into two parts:

sage: numerical_integral(D,0,+oo)
(-1.6678960430474579, 2.1310893050241475e-09)
sage: numerical_integral(D,-oo,0)
(-1.6678960430474579, 2.1310893050241475e-09)

[kcrisman]

This is not a symbolic Maxima problem, as the integral is just returned, so it's something about how we evaluate n on these unevaluated integrals.

[chapoton]

here is a proposal : check that the limit is zero before doing the numerical integral

---

New commits:

​0661926

add some safety check for numerical integrals up to infinity

[chapoton]

green bot, please review

[tscrim]

LGTM.

[mkoeppe]

These have been merged into 9.2.beta4