Spaces:
Sleeping
Sleeping
| # A collection of failing integrals from the issues. | |
| from sympy.core.numbers import (I, Rational, oo, pi) | |
| from sympy.core.singleton import S | |
| from sympy.core.symbol import symbols | |
| from sympy.functions.elementary.complexes import sign | |
| from sympy.functions.elementary.exponential import (exp, log) | |
| from sympy.functions.elementary.hyperbolic import (sech, sinh) | |
| from sympy.functions.elementary.miscellaneous import sqrt | |
| from sympy.functions.elementary.piecewise import Piecewise | |
| from sympy.functions.elementary.trigonometric import (acos, atan, cos, sin, tan) | |
| from sympy.functions.special.delta_functions import DiracDelta | |
| from sympy.functions.special.gamma_functions import gamma | |
| from sympy.integrals.integrals import (Integral, integrate) | |
| from sympy.simplify.fu import fu | |
| from sympy.testing.pytest import XFAIL, slow, tooslow | |
| from sympy.abc import x, k, c, y, b, h, a, m, z, n, t | |
| def test_issue_3880(): | |
| # integrate_hyperexponential(Poly(t*2*(1 - t0**2)*t0*(x**3 + x**2), t), Poly((1 + t0**2)**2*2*(x**2 + x + 1), t), [Poly(1, x), Poly(1 + t0**2, t0), Poly(t, t)], [x, t0, t], [exp, tan]) | |
| assert not integrate(exp(x)*cos(2*x)*sin(2*x) * (x**3 + x**2)/(2*(x**2 + x + 1)), x).has(Integral) | |
| def test_issue_4212_real(): | |
| xr = symbols('xr', real=True) | |
| negabsx = Piecewise((-xr, xr < 0), (xr, True)) | |
| assert integrate(sign(xr), xr) == negabsx | |
| def test_issue_4212(): | |
| # XXX: Maybe this should be expected to fail without real assumptions on x. | |
| # As a complex function sign(x) is not analytic and so there is no complex | |
| # function whose complex derivative is sign(x). With real assumptions this | |
| # works (see test_issue_4212_real above). | |
| assert not integrate(sign(x), x).has(Integral) | |
| def test_issue_4511(): | |
| # This works, but gives a slightly over-complicated answer. | |
| f = integrate(cos(x)**2 / (1 - sin(x)), x) | |
| assert fu(f) == x - cos(x) - 1 | |
| assert f == ((x*tan(x/2)**2 + x - 2)/(tan(x/2)**2 + 1)).expand() | |
| def test_integrate_DiracDelta_no_meijerg(): | |
| assert integrate(integrate(integrate( | |
| DiracDelta(x - y - z), (z, 0, oo)), (y, 0, 1), meijerg=False), (x, 0, 1)) == S.Half | |
| def test_integrate_DiracDelta_fails(): | |
| # issue 6427 | |
| # works without meijerg. See test_integrate_DiracDelta_no_meijerg above. | |
| assert integrate(integrate(integrate( | |
| DiracDelta(x - y - z), (z, 0, oo)), (y, 0, 1)), (x, 0, 1)) == S.Half | |
| def test_issue_4525(): | |
| # Warning: takes a long time | |
| assert not integrate((x**m * (1 - x)**n * (a + b*x + c*x**2))/(1 + x**2), (x, 0, 1)).has(Integral) | |
| def test_issue_4540(): | |
| # Note, this integral is probably nonelementary | |
| assert not integrate( | |
| (sin(1/x) - x*exp(x)) / | |
| ((-sin(1/x) + x*exp(x))*x + x*sin(1/x)), x).has(Integral) | |
| def test_issue_4891(): | |
| # Requires the hypergeometric function. | |
| assert not integrate(cos(x)**y, x).has(Integral) | |
| def test_issue_1796a(): | |
| assert not integrate(exp(2*b*x)*exp(-a*x**2), x).has(Integral) | |
| def test_issue_4895b(): | |
| assert not integrate(exp(2*b*x)*exp(-a*x**2), (x, -oo, 0)).has(Integral) | |
| def test_issue_4895c(): | |
| assert not integrate(exp(2*b*x)*exp(-a*x**2), (x, -oo, oo)).has(Integral) | |
| def test_issue_4895d(): | |
| assert not integrate(exp(2*b*x)*exp(-a*x**2), (x, 0, oo)).has(Integral) | |
| def test_issue_4941(): | |
| assert not integrate(sqrt(1 + sinh(x/20)**2), (x, -25, 25)).has(Integral) | |
| def test_issue_4992(): | |
| # Nonelementary integral. Requires hypergeometric/Meijer-G handling. | |
| assert not integrate(log(x) * x**(k - 1) * exp(-x) / gamma(k), (x, 0, oo)).has(Integral) | |
| def test_issue_16396a(): | |
| i = integrate(1/(1+sqrt(tan(x))), (x, pi/3, pi/6)) | |
| assert not i.has(Integral) | |
| def test_issue_16396b(): | |
| i = integrate(x*sin(x)/(1+cos(x)**2), (x, 0, pi)) | |
| assert not i.has(Integral) | |
| def test_issue_16046(): | |
| assert integrate(exp(exp(I*x)), [x, 0, 2*pi]) == 2*pi | |
| def test_issue_15925a(): | |
| assert not integrate(sqrt((1+sin(x))**2+(cos(x))**2), (x, -pi/2, pi/2)).has(Integral) | |
| def test_issue_15925b(): | |
| f = sqrt((-12*cos(x)**2*sin(x))**2+(12*cos(x)*sin(x)**2)**2) | |
| assert integrate(f, (x, 0, pi/6)) == Rational(3, 2) | |
| def test_issue_15925b_manual(): | |
| assert not integrate(sqrt((-12*cos(x)**2*sin(x))**2+(12*cos(x)*sin(x)**2)**2), | |
| (x, 0, pi/6), manual=True).has(Integral) | |
| def test_issue_15227(): | |
| i = integrate(log(1-x)*log((1+x)**2)/x, (x, 0, 1)) | |
| assert not i.has(Integral) | |
| # assert i == -5*zeta(3)/4 | |
| def test_issue_14716(): | |
| i = integrate(log(x + 5)*cos(pi*x),(x, S.Half, 1)) | |
| assert not i.has(Integral) | |
| # Mathematica can not solve it either, but | |
| # integrate(log(x + 5)*cos(pi*x),(x, S.Half, 1)).transform(x, y - 5).doit() | |
| # works | |
| # assert i == -log(Rational(11, 2))/pi - Si(pi*Rational(11, 2))/pi + Si(6*pi)/pi | |
| def test_issue_14709a(): | |
| i = integrate(x*acos(1 - 2*x/h), (x, 0, h)) | |
| assert not i.has(Integral) | |
| # assert i == 5*h**2*pi/16 | |
| def test_issue_14398(): | |
| assert not integrate(exp(x**2)*cos(x), x).has(Integral) | |
| def test_issue_14074(): | |
| i = integrate(log(sin(x)), (x, 0, pi/2)) | |
| assert not i.has(Integral) | |
| # assert i == -pi*log(2)/2 | |
| def test_issue_14078b(): | |
| i = integrate((atan(4*x)-atan(2*x))/x, (x, 0, oo)) | |
| assert not i.has(Integral) | |
| # assert i == pi*log(2)/2 | |
| def test_issue_13792(): | |
| i = integrate(log(1/x) / (1 - x), (x, 0, 1)) | |
| assert not i.has(Integral) | |
| # assert i in [polylog(2, -exp_polar(I*pi)), pi**2/6] | |
| def test_issue_11845a(): | |
| assert not integrate(exp(y - x**3), (x, 0, 1)).has(Integral) | |
| def test_issue_11845b(): | |
| assert not integrate(exp(-y - x**3), (x, 0, 1)).has(Integral) | |
| def test_issue_11813(): | |
| assert not integrate((a - x)**Rational(-1, 2)*x, (x, 0, a)).has(Integral) | |
| def test_issue_11254c(): | |
| assert not integrate(sech(x)**2, (x, 0, 1)).has(Integral) | |
| def test_issue_10584(): | |
| assert not integrate(sqrt(x**2 + 1/x**2), x).has(Integral) | |
| def test_issue_9101(): | |
| assert not integrate(log(x + sqrt(x**2 + y**2 + z**2)), z).has(Integral) | |
| def test_issue_7147(): | |
| assert not integrate(x/sqrt(a*x**2 + b*x + c)**3, x).has(Integral) | |
| def test_issue_7109(): | |
| assert not integrate(sqrt(a**2/(a**2 - x**2)), x).has(Integral) | |
| def test_integrate_Piecewise_rational_over_reals(): | |
| f = Piecewise( | |
| (0, t - 478.515625*pi < 0), | |
| (13.2075145209219*pi/(0.000871222*t + 0.995)**2, t - 478.515625*pi >= 0)) | |
| assert abs((integrate(f, (t, 0, oo)) - 15235.9375*pi).evalf()) <= 1e-7 | |
| def test_issue_4311_slow(): | |
| # Not slow when bypassing heurish | |
| assert not integrate(x*abs(9-x**2), x).has(Integral) | |
| def test_issue_20370(): | |
| a = symbols('a', positive=True) | |
| assert integrate((1 + a * cos(x))**-1, (x, 0, 2 * pi)) == (2 * pi / sqrt(1 - a**2)) | |
| def test_polylog(): | |
| # log(1/x)*log(x+1)-polylog(2, -x) | |
| assert not integrate(log(1/x)/(x + 1), x).has(Integral) | |
| def test_polylog_manual(): | |
| # Make sure _parts_rule does not go into an infinite loop here | |
| assert not integrate(log(1/x)/(x + 1), x, manual=True).has(Integral) | |