2.4.7 Integrals 601 to 700

2.4.7.1 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{a+i b \arcsin \left (1-i d x^2\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(I+d*x**2)),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(318\)

2.4.7.2 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a+i b \arcsin \left (1-i d x^2\right )\right )^2} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(I+d*x**2))**2,x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(319\)

2.4.7.3 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a+i b \arcsin \left (1-i d x^2\right )\right )^3} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(I+d*x**2))**3,x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(320\)

2.4.7.4 Sympy [F(-2)]

Exception generated. \[ \int \left (a-i b \arcsin \left (1+i d x^2\right )\right )^4 \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((a+b*asinh(-I+d*x**2))**4,x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(321\)

2.4.7.5 Sympy [F(-2)]

Exception generated. \[ \int \left (a-i b \arcsin \left (1+i d x^2\right )\right )^3 \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((a+b*asinh(-I+d*x**2))**3,x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(322\)

2.4.7.6 Sympy [F(-2)]

Exception generated. \[ \int \left (a-i b \arcsin \left (1+i d x^2\right )\right )^2 \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((a+b*asinh(-I+d*x**2))**2,x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(323\)

2.4.7.7 Sympy [F(-2)]

Exception generated. \[ \int \left (a-i b \arcsin \left (1+i d x^2\right )\right ) \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(a+b*asinh(-I+d*x**2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(324\)

2.4.7.8 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{a-i b \arcsin \left (1+i d x^2\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(-I+d*x**2)),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(325\)

2.4.7.9 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a-i b \arcsin \left (1+i d x^2\right )\right )^2} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(-I+d*x**2))**2,x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(326\)

2.4.7.10 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a-i b \arcsin \left (1+i d x^2\right )\right )^3} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(-I+d*x**2))**3,x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(327\)

2.4.7.11 Sympy [F(-2)]

Exception generated. \[ \int \left (a+i b \arcsin \left (1-i d x^2\right )\right )^{5/2} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((a+b*asinh(I+d*x**2))**(5/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(328\)

2.4.7.12 Sympy [F(-2)]

Exception generated. \[ \int \left (a+i b \arcsin \left (1-i d x^2\right )\right )^{3/2} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((a+b*asinh(I+d*x**2))**(3/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(329\)

2.4.7.13 Sympy [F(-2)]

Exception generated. \[ \int \sqrt {a+i b \arcsin \left (1-i d x^2\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((a+b*asinh(I+d*x**2))**(1/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(330\)

2.4.7.14 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\sqrt {a+i b \arcsin \left (1-i d x^2\right )}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(I+d*x**2))**(1/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(331\)

2.4.7.15 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a+i b \arcsin \left (1-i d x^2\right )\right )^{3/2}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(I+d*x**2))**(3/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(332\)

2.4.7.16 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a+i b \arcsin \left (1-i d x^2\right )\right )^{5/2}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(I+d*x**2))**(5/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(333\)

2.4.7.17 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a+i b \arcsin \left (1-i d x^2\right )\right )^{7/2}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(I+d*x**2))**(7/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(334\)

2.4.7.18 Sympy [F(-2)]

Exception generated. \[ \int \left (a-i b \arcsin \left (1+i d x^2\right )\right )^{5/2} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((a+b*asinh(-I+d*x**2))**(5/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(335\)

2.4.7.19 Sympy [F(-2)]

Exception generated. \[ \int \left (a-i b \arcsin \left (1+i d x^2\right )\right )^{3/2} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((a+b*asinh(-I+d*x**2))**(3/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(336\)

2.4.7.20 Sympy [F(-2)]

Exception generated. \[ \int \sqrt {a-i b \arcsin \left (1+i d x^2\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((a+b*asinh(-I+d*x**2))**(1/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(337\)

2.4.7.21 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\sqrt {a-i b \arcsin \left (1+i d x^2\right )}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(-I+d*x**2))**(1/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(338\)

2.4.7.22 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a-i b \arcsin \left (1+i d x^2\right )\right )^{3/2}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(-I+d*x**2))**(3/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(339\)

2.4.7.23 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a-i b \arcsin \left (1+i d x^2\right )\right )^{5/2}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(-I+d*x**2))**(5/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(340\)

2.4.7.24 Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a-i b \arcsin \left (1+i d x^2\right )\right )^{7/2}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a+b*asinh(-I+d*x**2))**(7/2),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real -I

input file name 7_Inverse_hyperbolic_functions/7.1_Inverse_hyperbolic_sine/7.1.5_Inverse_hyperbolic_sine_functions.txt

Test file number \(188\)

Integral number in file \(341\)

2.4.7.25 Sympy [F(-2)]

Exception generated. \[ \int e^{n \text {arctanh}(a x)} (c-a c x)^{5/2} \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate(exp(n*atanh(a*x))*(-a*c*x+c)**(5/2),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input file name 7_Inverse_hyperbolic_functions/7.3_Inverse_hyperbolic_tangent/7.3.6_Exponentials_of_inverse_hyperbolic_tangent_functions.txt

Test file number \(196\)

Integral number in file \(279\)

2.4.7.26 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{n \text {arctanh}(a x)}}{(c-a c x)^{7/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate(exp(n*atanh(a*x))/(-a*c*x+c)**(7/2),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input file name 7_Inverse_hyperbolic_functions/7.3_Inverse_hyperbolic_tangent/7.3.6_Exponentials_of_inverse_hyperbolic_tangent_functions.txt

Test file number \(196\)

Integral number in file \(285\)

2.4.7.27 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{-\text {arctanh}(a x)}}{c-\frac {c}{a x}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/(a*x+1)*(-a**2*x**2+1)**(1/2)/(c-c/a/x),x)

[Out]

Exception raised: TypeError >> Invalid comparison of non-real zoo

input file name 7_Inverse_hyperbolic_functions/7.3_Inverse_hyperbolic_tangent/7.3.6_Exponentials_of_inverse_hyperbolic_tangent_functions.txt

Test file number \(196\)

Integral number in file \(489\)

2.4.7.28 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{n \text {arctanh}(a x)}}{\left (c-\frac {c}{a^2 x^2}\right )^{5/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate(exp(n*atanh(a*x))/(c-c/a**2/x**2)**(5/2),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input file name 7_Inverse_hyperbolic_functions/7.3_Inverse_hyperbolic_tangent/7.3.6_Exponentials_of_inverse_hyperbolic_tangent_functions.txt

Test file number \(196\)

Integral number in file \(799\)

2.4.7.29 Sympy [F(-2)]

Exception generated. \[ \int x^{-1+n} \text {arctanh}\left (a+b x^n\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate(x**(-1+n)*atanh(a+b*x**n),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input file name 7_Inverse_hyperbolic_functions/7.3_Inverse_hyperbolic_tangent/7.3.7_Inverse_hyperbolic_tangent_functions.txt

Test file number \(197\)

Integral number in file \(29\)

2.4.7.30 Sympy [F(-2)]

Exception generated. \[ \int x^{-1+n} \coth ^{-1}\left (a+b x^n\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate(x**(-1+n)*acoth(a+b*x**n),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input file name 7_Inverse_hyperbolic_functions/7.4_Inverse_hyperbolic_cotangent/7.4.1_Inverse_hyperbolic_cotangent_functions.txt

Test file number \(198\)

Integral number in file \(294\)

2.4.7.31 Sympy [F(-2)]

Exception generated. \[ \int e^{n \coth ^{-1}(a x)} (c-a c x)^{5/2} \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate(exp(n*acoth(a*x))*(-a*c*x+c)**(5/2),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input file name 7_Inverse_hyperbolic_functions/7.4_Inverse_hyperbolic_cotangent/7.4.2_Exponentials_of_inverse_hyperbolic_cotangent_functions.txt

Test file number \(199\)

Integral number in file \(372\)

2.4.7.32 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{n \coth ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate(exp(n*acoth(a*x))/(-a*c*x+c)**(7/2),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input file name 7_Inverse_hyperbolic_functions/7.4_Inverse_hyperbolic_cotangent/7.4.2_Exponentials_of_inverse_hyperbolic_cotangent_functions.txt

Test file number \(199\)

Integral number in file \(378\)

2.4.7.33 Sympy [F(-2)]

Exception generated. \[ \int \frac {(-8-3 x) \log ^2(x)+(-4-x) \log ^2(x) \log \left (4 x^2+x^3\right )+\left (-8-2 x+(-8-2 x) \log (x)+\left (20 x^2+5 x^3\right ) \log ^2(x)\right ) \log ^2\left (4 x^2+x^3\right )}{\left (4 x+x^2\right ) \log ^2(x) \log \left (4 x^2+x^3\right )+\left (\left (8 x+2 x^2\right ) \log (x)+\left (8 x^2+22 x^3+5 x^4\right ) \log ^2(x)\right ) \log ^2\left (4 x^2+x^3\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((5*x**3+20*x**2)*ln(x)**2+(-2*x-8)*ln(x)-2*x-8)*ln(x**3+4*x**2)**2+(-4-x)*ln(x)**2*ln(x**3+4*x**2)
+(-3*x-8)*ln(x)**2)/(((5*x**4+22*x**3+8*x**2)*ln(x)**2+(2*x**2+8*x)*ln(x))*ln(x**3+4*x**2)**2+(x**2+4*x)*ln(x)
**2*ln(x**3+4*x**2)),x)

[Out]

Exception raised: PolynomialError >> 1/(25*_t0**2*x**6 + 120*_t0**2*x**5 + 84*_t0**2*x**4 + 16*_t0**2*x**3 + 2
0*_t0*x**4 + 88*_t0*x**3 + 32*_t0*x**2 + 4*x**2 + 16*x) contains an element of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(8\)

2.4.7.34 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^2 \left (100+40 x+4 x^2\right )+e^2 \left (100+40 x+4 x^2\right ) \log (x)+\left (20 x^3-4 e^5 x^3\right ) \log ^3(x)}{e^2 \left (-25 x-10 x^2-x^3\right ) \log (x)+\left (10 x^4+2 x^5+e^5 \left (10 x^3+2 x^4\right )\right ) \log ^3(x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((-4*x**3*exp(5)+20*x**3)*ln(x)**3+(4*x**2+40*x+100)*exp(2)*ln(x)+(4*x**2+40*x+100)*exp(2))/(((2*x**
4+10*x**3)*exp(5)+2*x**5+10*x**4)*ln(x)**3+(-x**3-10*x**2-25*x)*exp(2)*ln(x)),x)

[Out]

Exception raised: PolynomialError >> 1/(4*x**10 + 16*x**9*exp(5) + 24*x**8*exp(10) + 16*x**7*exp(15) + 4*x**6*
exp(20)) contains an element of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(21\)

2.4.7.35 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {18}{2 x^2+x^2 \log (x)}} \left (-90+4 x^2+\left (-36+4 x^2\right ) \log (x)+x^2 \log ^2(x)\right )}{4 x^2+4 x^2 \log (x)+x^2 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((x**2*ln(x)**2+(4*x**2-36)*ln(x)+4*x**2-90)*exp(18/(x**2*ln(x)+2*x**2))/(x**2*ln(x)**2+4*x**2*ln(x)+
4*x**2),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(86\)

2.4.7.36 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{14 x/5} \left (-360-165 x-15 x^2\right )+\left (45 x+15 x^2+e^{14 x/5} \left (888 x+447 x^2+42 x^3\right )\right ) \log (x)+\left (-360-165 x-15 x^2+\left (-120 x-15 x^2\right ) \log (x)\right ) \log (8+x)}{\left (360 x+285 x^2+70 x^3+5 x^4\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-15*x**2-120*x)*ln(x)-15*x**2-165*x-360)*ln(x+8)+((42*x**3+447*x**2+888*x)*exp(2/5*x)**2*exp(x)**
2+15*x**2+45*x)*ln(x)+(-15*x**2-165*x-360)*exp(2/5*x)**2*exp(x)**2)/(5*x**4+70*x**3+285*x**2+360*x)/ln(x)**2,x
)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(89\)

2.4.7.37 Sympy [F(-2)]

Exception generated. \[ \int \frac {100-105 x+31 x^2+3 e^{2 x} x^2+e^x \left (-30 x+24 x^2-x^3\right )+\left (30 x-19 x^2-6 e^x x^2\right ) \log (x)+3 x^2 \log ^2(x)}{75+10 x-83 x^2+30 x^3+e^{2 x} \left (3 x^2+3 x^3\right )+e^x \left (-30 x-17 x^2+19 x^3\right )+\left (30 x+17 x^2-19 x^3+e^x \left (-6 x^2-6 x^3\right )\right ) \log (x)+\left (3 x^2+3 x^3\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((3*x**2*ln(x)**2+(-6*exp(x)*x**2-19*x**2+30*x)*ln(x)+3*exp(x)**2*x**2+(-x**3+24*x**2-30*x)*exp(x)+31
*x**2-105*x+100)/((3*x**3+3*x**2)*ln(x)**2+((-6*x**3-6*x**2)*exp(x)-19*x**3+17*x**2+30*x)*ln(x)+(3*x**3+3*x**2
)*exp(x)**2+(19*x**3-17*x**2-30*x)*exp(x)+30*x**3-83*x**2+10*x+75),x)

[Out]

Exception raised: PolynomialError >> 1/(3*x**4 + 6*x**3 + 3*x**2) contains an element of the set of generators
.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(99\)

2.4.7.38 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {4 x^3}{11 x-2 e^2 x-2 x^2+2 \log (x)}} \left (-8 x^2+88 x^3-16 e^2 x^3-8 x^4+24 x^2 \log (x)\right )}{121 x^2+4 e^4 x^2-44 x^3+4 x^4+e^2 \left (-44 x^2+8 x^3\right )+\left (44 x-8 e^2 x-8 x^2\right ) \log (x)+4 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((24*x**2*ln(x)-16*x**3*exp(2)-8*x**4+88*x**3-8*x**2)*exp(2*x**3/(2*ln(x)-2*exp(2)*x-2*x**2+11*x))**2
/(4*ln(x)**2+(-8*exp(2)*x-8*x**2+44*x)*ln(x)+4*x**2*exp(2)**2+(8*x**3-44*x**2)*exp(2)+4*x**4-44*x**3+121*x**2)
,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(152\)

2.4.7.39 Sympy [F(-2)]

Exception generated. \[ \int \frac {3-3 x+(-12+3 x-3 \log (x)) \log (4-x+\log (x))+\left (64+e^2 (32-8 x)+e^4 (4-x)-16 x+\left (16+8 e^2+e^4\right ) \log (x)\right ) \log ^2(4-x+\log (x))}{\left (-12 x+3 x^2-3 x \log (x)\right ) \log (4-x+\log (x))+\left (64 x-16 x^2+e^2 \left (32 x-8 x^2\right )+e^4 \left (4 x-x^2\right )+\left (16 x+8 e^2 x+e^4 x\right ) \log (x)\right ) \log ^2(4-x+\log (x))} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((exp(2)**2+8*exp(2)+16)*ln(x)+(-x+4)*exp(2)**2+(-8*x+32)*exp(2)-16*x+64)*ln(ln(x)-x+4)**2+(-3*ln(x
)+3*x-12)*ln(ln(x)-x+4)-3*x+3)/(((x*exp(2)**2+8*exp(2)*x+16*x)*ln(x)+(-x**2+4*x)*exp(2)**2+(-8*x**2+32*x)*exp(
2)-16*x**2+64*x)*ln(ln(x)-x+4)**2+(-3*x*ln(x)+3*x**2-12*x)*ln(ln(x)-x+4)),x)

[Out]

Exception raised: PolynomialError >> 1/(-_t0*x + x**2 - 4*x) contains an element of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(211\)

2.4.7.40 Sympy [F(-2)]

Exception generated. \[ \int \frac {-2 x+2 \log (x)+(x-\log (x)) \log \left (2 x^2\right )+(1-x) \log \left (2 x^2\right ) \log \left (\frac {x}{\log \left (2 x^2\right )}\right )}{\left (x^3-2 x^2 \log (x)+x \log ^2(x)\right ) \log \left (2 x^2\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((1-x)*ln(2*x**2)*ln(x/ln(2*x**2))+(x-ln(x))*ln(2*x**2)+2*ln(x)-2*x)/(x*ln(x)**2-2*x**2*ln(x)+x**3)/
ln(2*x**2),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(222\)

2.4.7.41 Sympy [F(-2)]

Exception generated. \[ \int \frac {3750 x+300 x^2+6 x^3+\left (4000 x^2+300 x^3+6 x^4\right ) \log (x)+\left (\left (4000 x^2+310 x^3+6 x^4\right ) \log (x)+\left (3750 x+300 x^2+6 x^3\right ) \log (x) \log (\log (x))\right ) \log \left (\frac {6400 x^2+480 x^3+9 x^4+\left (12000 x+930 x^2+18 x^3\right ) \log (\log (x))+\left (5625+450 x+9 x^2\right ) \log ^2(\log (x))}{5625+450 x+9 x^2}\right )}{\left (2000 x+155 x^2+3 x^3\right ) \log (x)+\left (1875+150 x+3 x^2\right ) \log (x) \log (\log (x))} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((6*x**3+300*x**2+3750*x)*ln(x)*ln(ln(x))+(6*x**4+310*x**3+4000*x**2)*ln(x))*ln(((9*x**2+450*x+5625
)*ln(ln(x))**2+(18*x**3+930*x**2+12000*x)*ln(ln(x))+9*x**4+480*x**3+6400*x**2)/(9*x**2+450*x+5625))+(6*x**4+30
0*x**3+4000*x**2)*ln(x)+6*x**3+300*x**2+3750*x)/((3*x**2+150*x+1875)*ln(x)*ln(ln(x))+(3*x**3+155*x**2+2000*x)*
ln(x)),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(255\)

2.4.7.42 Sympy [F(-2)]

Exception generated. \[ \int \frac {x^3 \log (2)+\left (18 x^2-3 x^3\right ) \log (2) \log (6-x)+\left (12 x-2 x^2+(-12+2 x) \log (2)\right ) \log ^2(6-x)}{\left (6 x^3-x^4\right ) \log (2) \log (6-x)+\left (6 x^2-x^3+\left (6-13 x+2 x^2\right ) \log (2)\right ) \log ^2(6-x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((2*x-12)*ln(2)-2*x**2+12*x)*ln(-x+6)**2+(-3*x**3+18*x**2)*ln(2)*ln(-x+6)+x**3*ln(2))/(((2*x**2-13*
x+6)*ln(2)-x**3+6*x**2)*ln(-x+6)**2+(-x**4+6*x**3)*ln(2)*ln(-x+6)),x)

[Out]

Exception raised: PolynomialError >> 1/(x**5 - 6*x**4 - 4*x**4*log(2) + 4*x**3*log(2)**2 + 26*x**3*log(2) - 28
*x**2*log(2)**2 - 12*x**2*log(2) + 25*x*log(2)**2 - 6*log(2)**2) contains an element of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(256\)

2.4.7.43 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^x \left (e^{1+\frac {1}{4} (-2+x)} \left (36-27 x+3 x^2\right )+e \left (144-144 x+16 x^2\right )\right )}{192 x^2+96 e^{\frac {1}{4} (-2+x)} x^2+12 e^{\frac {1}{2} (-2+x)} x^2} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((3*x**2-27*x+36)*exp(1)*exp(1/4*x-1/2)+(16*x**2-144*x+144)*exp(1))*exp(x)/(12*x**2*exp(1/4*x-1/2)**
2+96*x**2*exp(1/4*x-1/2)+192*x**2),x)

[Out]

Exception raised: PolynomialError >> (3*_t0**5*x**2*exp(6) - 27*_t0**5*x*exp(6) + 36*_t0**5*exp(6) + 16*_t0**4
*x**2*exp(13/2) - 144*_t0**4*x*exp(13/2) + 144*_t0**4*exp(13/2))/(12*_t0**2*x**2*exp(9/2) + 96*_t0*x**2*exp(5)
+ 192*x**2*exp(1

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(275\)

2.4.7.44 Sympy [F(-2)]

Exception generated. \[ \int \frac {4 x+\left (-4 x+x^3\right ) \log (x)+\left (-4 x+3 x^2\right ) \log (x) \log \left (\frac {\log (x)}{x}\right )+3 x \log (x) \log ^2\left (\frac {\log (x)}{x}\right )+\log (x) \log ^3\left (\frac {\log (x)}{x}\right )}{\left (-7 x^3+x^4\right ) \log (x)+\left (-17 x^2+3 x^3\right ) \log (x) \log \left (\frac {\log (x)}{x}\right )+\left (-15 x+3 x^2\right ) \log (x) \log ^2\left (\frac {\log (x)}{x}\right )+(-5+x) \log (x) \log ^3\left (\frac {\log (x)}{x}\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((ln(x)*ln(ln(x)/x)**3+3*x*ln(x)*ln(ln(x)/x)**2+(3*x**2-4*x)*ln(x)*ln(ln(x)/x)+(x**3-4*x)*ln(x)+4*x)/
((-5+x)*ln(x)*ln(ln(x)/x)**3+(3*x**2-15*x)*ln(x)*ln(ln(x)/x)**2+(3*x**3-17*x**2)*ln(x)*ln(ln(x)/x)+(x**4-7*x**
3)*ln(x)),x)

[Out]

Exception raised: PolynomialError >> 1/(_t0**2*x**4 - 20*_t0**2*x**3 + 150*_t0**2*x**2 - 500*_t0**2*x + 625*_t
0**2) contains an element of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(280\)

2.4.7.45 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {x}{4+2 x+2 \log \left (x^2\right )}} \left (-16+8 x+20 x^2+6 x^3+\left (-16+17 x+11 x^2\right ) \log \left (x^2\right )+(-4+6 x) \log ^2\left (x^2\right )\right )}{8 x^3-8 x^4-6 x^5+4 x^6+2 x^7+\left (8 x^3-12 x^4+4 x^6\right ) \log \left (x^2\right )+\left (2 x^3-4 x^4+2 x^5\right ) \log ^2\left (x^2\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((6*x-4)*ln(x**2)**2+(11*x**2+17*x-16)*ln(x**2)+6*x**3+20*x**2+8*x-16)*exp(x/(2*ln(x**2)+2*x+4))/((2
*x**5-4*x**4+2*x**3)*ln(x**2)**2+(4*x**6-12*x**4+8*x**3)*ln(x**2)+2*x**7+4*x**6-6*x**5-8*x**4+8*x**3),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(284\)

2.4.7.46 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^3 \left (-3+5 x-x^2\right )+e^6 \left (-12+20 x-4 x^2\right ) \log (x)+\left (e^6 \left (-12 x+4 x^2\right )+e^6 (12-4 x) \log \left (3 x-x^2\right )\right ) \log \left (-x+\log \left (3 x-x^2\right )\right )}{30 x^2-10 x^3+\left (-30 x+10 x^2\right ) \log \left (3 x-x^2\right )+\log (x) \left (e^3 \left (240 x^2-80 x^3\right )+e^3 \left (-240 x+80 x^2\right ) \log \left (3 x-x^2\right )\right )+\log ^2(x) \left (e^6 \left (480 x^2-160 x^3\right )+e^6 \left (-480 x+160 x^2\right ) \log \left (3 x-x^2\right )\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-4*x+12)*exp(3)**2*ln(-x**2+3*x)+(4*x**2-12*x)*exp(3)**2)*ln(ln(-x**2+3*x)-x)+(-4*x**2+20*x-12)*e
xp(3)**2*ln(x)+(-x**2+5*x-3)*exp(3))/(((160*x**2-480*x)*exp(3)**2*ln(-x**2+3*x)+(-160*x**3+480*x**2)*exp(3)**2
)*ln(x)**2+((80*x**2-240*x)*exp(3)*ln(-x**2+3*x)+(-80*x**3+240*x**2)*exp(3))*ln(x)+(10*x**2-30*x)*ln(-x**2+3*x
)-10*x**3+30*x**2),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(307\)

2.4.7.47 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {5}{-4 x^2+x^2 \log (\log (x))}} (-5+40 \log (x)-10 \log (x) \log (\log (x)))}{16 x^3 \log (x)-8 x^3 \log (x) \log (\log (x))+x^3 \log (x) \log ^2(\log (x))} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((-10*ln(x)*ln(ln(x))+40*ln(x)-5)*exp(5/(x**2*ln(ln(x))-4*x**2))/(x**3*ln(x)*ln(ln(x))**2-8*x**3*ln(x
)*ln(ln(x))+16*x**3*ln(x)),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(330\)

2.4.7.48 Sympy [F(-2)]

Exception generated. \[ \int \frac {4 x^3 \log (x) \log ^2(\log (x))+e^{\frac {-8 x-5 e^3 x+x^2-10 \log (\log (x))}{\log (\log (x))}} \left (8+5 e^3-x+\left (-8-5 e^3+2 x\right ) \log (x) \log (\log (x))\right )+e^{\frac {-8 x-5 e^3 x+x^2-10 \log (\log (x))}{2 \log (\log (x))}} \left (8 x^2+5 e^3 x^2-x^3+\left (-8 x^2-5 e^3 x^2+2 x^3\right ) \log (x) \log (\log (x))+4 x \log (x) \log ^2(\log (x))\right )}{\log (x) \log ^2(\log (x))} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-5*exp(3)+2*x-8)*ln(x)*ln(ln(x))+5*exp(3)+8-x)*exp(1/2*(-10*ln(ln(x))-5*x*exp(3)+x**2-8*x)/ln(ln(
x)))**2+(4*x*ln(x)*ln(ln(x))**2+(-5*x**2*exp(3)+2*x**3-8*x**2)*ln(x)*ln(ln(x))+5*x**2*exp(3)-x**3+8*x**2)*exp(
1/2*(-10*ln(ln(x))-5*x*exp(3)+x**2-8*x)/ln(ln(x)))+4*x**3*ln(x)*ln(ln(x))**2)/ln(x)/ln(ln(x))**2,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(473\)

2.4.7.49 Sympy [F(-2)]

Exception generated. \[ \int \frac {(12+6 x) \log ^2\left (\frac {x}{2+x}\right )+e^{\frac {5 x}{\log \left (\frac {x}{2+x}\right )}} \left (-20+(20+10 x) \log \left (\frac {x}{2+x}\right )\right )}{(2+x) \log ^2\left (\frac {x}{2+x}\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((10*x+20)*ln(x/(2+x))-20)*exp(5*x/ln(x/(2+x)))+(6*x+12)*ln(x/(2+x))**2)/(2+x)/ln(x/(2+x))**2,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(598\)

2.4.7.50 Sympy [F(-2)]

Exception generated. \[ \int \frac {1-11 x+4 x^2+(-8-8 x) \log (2+2 x)+(-20-20 x) \log ^2(2+2 x)}{-15-4 x+9 x^2-2 x^3+\left (-60-28 x+28 x^2-4 x^3\right ) \log (2+2 x)+\left (-60-40 x+20 x^2\right ) \log ^2(2+2 x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((-20*x-20)*ln(2+2*x)**2+(-8*x-8)*ln(2+2*x)+4*x**2-11*x+1)/((20*x**2-40*x-60)*ln(2+2*x)**2+(-4*x**3+
28*x**2-28*x-60)*ln(2+2*x)-2*x**3+9*x**2-4*x-15),x)

[Out]

Exception raised: PolynomialError >> 1/(5*x + 5) contains an element of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(618\)

2.4.7.51 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (4-4 x^2\right ) \log (5)+\left (-1+x^2\right ) \log ^2(5) \log (-1+x)+\left (\left (-4+4 x^2+e^7 \left (-4-4 x+8 x^2\right )\right ) \log (5)+e^7 \left (-x-x^2\right ) \log ^2(5)+\left (1-x^2+e^7 \left (1+x-2 x^2\right )\right ) \log ^2(5) \log (-1+x)\right ) \log (x)+\left (\left (-4-4 x+8 x^2\right ) \log (5)+\left (-x-x^2\right ) \log ^2(5)+\left (1+x-2 x^2\right ) \log ^2(5) \log (-1+x)\right ) \log (x) \log \left (\frac {\log (x)}{x}\right )}{\left (-16 x^2-16 x^3+16 x^4+16 x^5+\left (8 x^2+8 x^3-8 x^4-8 x^5\right ) \log (5) \log (-1+x)+\left (-x^2-x^3+x^4+x^5\right ) \log ^2(5) \log ^2(-1+x)\right ) \log (x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-2*x**2+x+1)*ln(5)**2*ln(-1+x)+(-x**2-x)*ln(5)**2+(8*x**2-4*x-4)*ln(5))*ln(x)*ln(ln(x)/x)+(((-2*x
**2+x+1)*exp(7)-x**2+1)*ln(5)**2*ln(-1+x)+(-x**2-x)*exp(7)*ln(5)**2+((8*x**2-4*x-4)*exp(7)+4*x**2-4)*ln(5))*ln
(x)+(x**2-1)*ln(5)**2*ln(-1+x)+(-4*x**2+4)*ln(5))/((x**5+x**4-x**3-x**2)*ln(5)**2*ln(-1+x)**2+(-8*x**5-8*x**4+
8*x**3+8*x**2)*ln(5)*ln(-1+x)+16*x**5+16*x**4-16*x**3-16*x**2)/ln(x),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(675\)

2.4.7.52 Sympy [F(-2)]

Exception generated. \[ \int \frac {8+(80-20 x) \log \left (\frac {324}{16-8 x+x^2}\right )+\left (-4+21 x-5 x^2\right ) \log ^2\left (\frac {324}{16-8 x+x^2}\right )}{(-80+20 x) \log \left (\frac {324}{16-8 x+x^2}\right )+\left (-20 x+5 x^2\right ) \log ^2\left (\frac {324}{16-8 x+x^2}\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((-5*x**2+21*x-4)*ln(324/(x**2-8*x+16))**2+(-20*x+80)*ln(324/(x**2-8*x+16))+8)/((5*x**2-20*x)*ln(324
/(x**2-8*x+16))**2+(20*x-80)*ln(324/(x**2-8*x+16))),x)

[Out]

Exception raised: PolynomialError >> 1/(5*x**3 - 20*x**2) contains an element of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(694\)

2.4.7.53 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-8 x^2+2 x^3-2 x^4\right ) \log (5) \log \left (\frac {1}{4} \left (-4 x+x^2-x^3\right )\right )+\left (16-8 x+12 x^2+\left (-4 x^2+2 x^3-3 x^4\right ) \log (5)\right ) \log \left (-4+x^2 \log (5)\right )+\left (8 x^2-2 x^3+2 x^4\right ) \log (5) \log \left (\frac {1}{4} \left (-4 x+x^2-x^3\right )\right ) \log \left (\log \left (\frac {1}{4} \left (-4 x+x^2-x^3\right )\right )\right )}{\left (-16 x+4 x^2-4 x^3+\left (4 x^3-x^4+x^5\right ) \log (5)\right ) \log \left (\frac {1}{4} \left (-4 x+x^2-x^3\right )\right ) \log ^2\left (-4+x^2 \log (5)\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((2*x**4-2*x**3+8*x**2)*ln(5)*ln(-1/4*x**3+1/4*x**2-x)*ln(ln(-1/4*x**3+1/4*x**2-x))+((-3*x**4+2*x**3
-4*x**2)*ln(5)+12*x**2-8*x+16)*ln(x**2*ln(5)-4)+(-2*x**4+2*x**3-8*x**2)*ln(5)*ln(-1/4*x**3+1/4*x**2-x))/((x**5
-x**4+4*x**3)*ln(5)-4*x**3+4*x**2-16*x)/ln(-1/4*x**3+1/4*x**2-x)/ln(x**2*ln(5)-4)**2,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(700\)

2.4.7.54 Sympy [F(-2)]

Exception generated. \[ \int \frac {3+x^2+e^4 x^2+\left (2 x+2 e^4 x\right ) \log (3)+\left (1+e^4\right ) \log ^2(3)+e^{2 x} \left (x^4+e^4 x^4\right ) \log ^2(3)+e^x \left (3 x^2+3 x^3+\left (-2 x^3-2 e^4 x^3\right ) \log (3)+\left (-2 x^2-2 e^4 x^2\right ) \log ^2(3)\right )}{-3 x-x^2+x^3+e^4 x^3+\left (-3-2 x+2 x^2+2 e^4 x^2\right ) \log (3)+\left (-1+x+e^4 x\right ) \log ^2(3)+e^x \left (3 x^3+\left (6 x^2+2 x^3-2 x^4-2 e^4 x^4\right ) \log (3)+\left (2 x^2-2 x^3-2 e^4 x^3\right ) \log ^2(3)\right )+e^{2 x} \left (-3 x^4 \log (3)+\left (-x^4+x^5+e^4 x^5\right ) \log ^2(3)\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((x**4*exp(4)+x**4)*ln(3)**2*exp(x)**2+((-2*x**2*exp(4)-2*x**2)*ln(3)**2+(-2*x**3*exp(4)-2*x**3)*ln(
3)+3*x**3+3*x**2)*exp(x)+(exp(4)+1)*ln(3)**2+(2*x*exp(4)+2*x)*ln(3)+x**2*exp(4)+x**2+3)/(((x**5*exp(4)+x**5-x*
*4)*ln(3)**2-3*x**4*ln(3))*exp(x)**2+((-2*x**3*exp(4)-2*x**3+2*x**2)*ln(3)**2+(-2*x**4*exp(4)-2*x**4+2*x**3+6*
x**2)*ln(3)+3*x**3)*exp(x)+(x*exp(4)+x-1)*ln(3)**2+(2*x**2*exp(4)+2*x**2-2*x-3)*ln(3)+x**3*exp(4)+x**3-x**2-3*
x),x)

[Out]

Exception raised: PolynomialError >> 1/(x**5*log(3)**3 + 2*x**5*exp(4)*log(3)**3 + x**5*exp(8)*log(3)**3 - 6*x
**4*exp(4)*log(3)**2 - 2*x**4*exp(4)*log(3)**3 - 6*x**4*log(3)**2 - 2*x**4*log(3)**3 + x**3*log(3)**3 + 6*x**3
*log(3)**2 + 9*x*

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(702\)

2.4.7.55 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{-\frac {x}{\log (2 x)}} \left (e^{-4+x} x^2-e^{-4+x} x^2 \log (2 x)+e^{-4+x} \left (2 x+x^2\right ) \log ^2(2 x)\right )}{\log ^2(2 x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((x**2+2*x)*exp(x-4)*ln(2*x)**2-x**2*exp(x-4)*ln(2*x)+x**2*exp(x-4))/ln(2*x)**2/exp(x/ln(2*x)),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(743\)

2.4.7.56 Sympy [F(-2)]

Exception generated. \[ \int \frac {-10+4 x+\left (-2+2 x-x^2\right ) \log (x)+(2-x) \log \left (-\frac {x}{-2+x}\right )}{-2 x+x^2+\left (-4 x+2 x^2\right ) \log (x)+\left (-2 x+x^2\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-x**2+2*x-2)*ln(x)+(2-x)*ln(-x/(-2+x))+4*x-10)/((x**2-2*x)*ln(x)**2+(2*x**2-4*x)*ln(x)+x**2-2*x),x
)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(778\)

2.4.7.57 Sympy [F(-2)]

Exception generated. \[ \int \frac {4^{\frac {-16-8 x-x^2}{-2-2 x+2 \log \left (\log \left (x^2\right )\right )}} \left (\left (32+48 x+18 x^2+2 x^3\right ) \log (4)+\left (2+8 x+10 x^2+4 x^3+\left (-8 x-6 x^2+3 x^3+x^4\right ) \log (4)\right ) \log \left (x^2\right )+\left (-4-12 x-8 x^2+\left (-8 x-10 x^2-2 x^3\right ) \log (4)\right ) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+(2+4 x) \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )\right )}{\left (2+4 x+2 x^2\right ) \log \left (x^2\right )+(-4-4 x) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+2 \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((4*x+2)*ln(x**2)*ln(ln(x**2))**2+(2*(-2*x**3-10*x**2-8*x)*ln(2)-8*x**2-12*x-4)*ln(x**2)*ln(ln(x**2)
)+(2*(x**4+3*x**3-6*x**2-8*x)*ln(2)+4*x**3+10*x**2+8*x+2)*ln(x**2)+2*(2*x**3+18*x**2+48*x+32)*ln(2))*exp(2*(-x
**2-8*x-16)*ln(2)/(2*ln(ln(x**2))-2*x-2))/(2*ln(x**2)*ln(ln(x**2))**2+(-4-4*x)*ln(x**2)*ln(ln(x**2))+(2*x**2+4
*x+2)*ln(x**2)),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(835\)

2.4.7.58 Sympy [F(-2)]

Exception generated. \[ \int \frac {-8-2 x+\left (7+9 x-15 x^2-2 x^3\right ) \log (x)+\left (-x-2 x^2\right ) \log ^2(x)+(1+2 x) \log (x) \log (\log (x))}{\left (64 x+32 x^2+4 x^3\right ) \log (x)+\left (16 x+4 x^2\right ) \log ^2(x)+x \log ^3(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((1+2*x)*ln(x)*ln(ln(x))+(-2*x**2-x)*ln(x)**2+(-2*x**3-15*x**2+9*x+7)*ln(x)-2*x-8)/(x*ln(x)**3+(4*x*
*2+16*x)*ln(x)**2+(4*x**3+32*x**2+64*x)*ln(x)),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(917\)

2.4.7.59 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^4 \left (-1+17 x-4 x^2-12 x^3+3 x^4\right )+e^4 \left (4 x-3 x^3\right ) \log (x)+\left (e^4 \left (20-5 x-12 x^2+3 x^3\right )+e^4 \left (5-3 x^2\right ) \log (x)\right ) \log (-4+x-\log (x))+\left (e^4 \left (-4 x+x^2\right )-e^4 x \log (x)+\left (e^4 (-4+x)-e^4 \log (x)\right ) \log (-4+x-\log (x))\right ) \log (x+\log (-4+x-\log (x)))}{4 x-x^2+x \log (x)+(4-x+\log (x)) \log (-4+x-\log (x))} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-exp(4)*ln(x)+(x-4)*exp(4))*ln(-ln(x)+x-4)-x*exp(4)*ln(x)+(x**2-4*x)*exp(4))*ln(ln(-ln(x)+x-4)+x)
+((-3*x**2+5)*exp(4)*ln(x)+(3*x**3-12*x**2-5*x+20)*exp(4))*ln(-ln(x)+x-4)+(-3*x**3+4*x)*exp(4)*ln(x)+(3*x**4-1
2*x**3-4*x**2+17*x-1)*exp(4))/((ln(x)-x+4)*ln(-ln(x)+x-4)+x*ln(x)-x**2+4*x),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1003\)

2.4.7.60 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (\frac {x+4 \log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )}{\log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )}\right )^{\frac {1}{\log \left (x^2\right )}} \left (-x \log \left (x^2\right )+\left (-x+x^2\right ) \log \left (x^2\right ) \log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )+\left (\left (2 x-2 x^2\right ) \log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )+(8-8 x) \log ^2\left (\frac {(-4+4 x) \log (4)}{5 x}\right )\right ) \log \left (\frac {x+4 \log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )}{\log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )}\right )\right )}{\left (-x^2+x^3\right ) \log ^2\left (x^2\right ) \log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )+\left (-4 x+4 x^2\right ) \log ^2\left (x^2\right ) \log ^2\left (\frac {(-4+4 x) \log (4)}{5 x}\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-8*x+8)*ln(2/5*(-4+4*x)*ln(2)/x)**2+(-2*x**2+2*x)*ln(2/5*(-4+4*x)*ln(2)/x))*ln((4*ln(2/5*(-4+4*x)
*ln(2)/x)+x)/ln(2/5*(-4+4*x)*ln(2)/x))+(x**2-x)*ln(x**2)*ln(2/5*(-4+4*x)*ln(2)/x)-x*ln(x**2))*exp(ln((4*ln(2/5
*(-4+4*x)*ln(2)/x)+x)/ln(2/5*(-4+4*x)*ln(2)/x))/ln(x**2))/((4*x**2-4*x)*ln(x**2)**2*ln(2/5*(-4+4*x)*ln(2)/x)**
2+(x**3-x**2)*ln(x**2)**2*ln(2/5*(-4+4*x)*ln(2)/x)),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1049\)

2.4.7.61 Sympy [F(-2)]

Exception generated. \[ \int \frac {4+4 \log \left (\frac {5 \log (3)}{e^2 x}\right )+(-4-8 x) \log ^2\left (\frac {5 \log (3)}{e^2 x}\right )+\left (-2-2 \log \left (\frac {5 \log (3)}{e^2 x}\right )+(2+4 x) \log ^2\left (\frac {5 \log (3)}{e^2 x}\right )\right ) \log \left (\frac {x+\left (-x-x^2\right ) \log \left (\frac {5 \log (3)}{e^2 x}\right )}{\log \left (\frac {5 \log (3)}{e^2 x}\right )}\right )}{-x \log \left (\frac {5 \log (3)}{e^2 x}\right )+\left (x+x^2\right ) \log ^2\left (\frac {5 \log (3)}{e^2 x}\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((4*x+2)*ln(5*ln(3)/exp(2)/x)**2-2*ln(5*ln(3)/exp(2)/x)-2)*ln(((-x**2-x)*ln(5*ln(3)/exp(2)/x)+x)/ln
(5*ln(3)/exp(2)/x))+(-8*x-4)*ln(5*ln(3)/exp(2)/x)**2+4*ln(5*ln(3)/exp(2)/x)+4)/((x**2+x)*ln(5*ln(3)/exp(2)/x)*
*2-x*ln(5*ln(3)/exp(2)/x)),x)

[Out]

Exception raised: PolynomialError >> 1/(x**3 + 2*x**2 + x) contains an element of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1116\)

2.4.7.62 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{-\frac {x}{\log \left (\frac {48 x}{4+3 x}\right )}} \left (1036+(-1036-777 x) \log \left (\frac {48 x}{4+3 x}\right )\right )}{(4+3 x) \log ^2\left (\frac {48 x}{4+3 x}\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-777*x-1036)*ln(48*x/(4+3*x))+1036)/(4+3*x)/ln(48*x/(4+3*x))**2/exp(x/ln(48*x/(4+3*x))),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1259\)

2.4.7.63 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {3-x+3 \log \left (\frac {-20-5 x-2 x^2}{6 x}\right )}{\log \left (\frac {-20-5 x-2 x^2}{6 x}\right )}} \left (60-20 x-6 x^2+2 x^3+\left (-20 x-5 x^2-2 x^3\right ) \log \left (\frac {-20-5 x-2 x^2}{6 x}\right )\right )}{\left (20 x+5 x^2+2 x^3\right ) \log ^2\left (\frac {-20-5 x-2 x^2}{6 x}\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-2*x**3-5*x**2-20*x)*ln(1/6*(-2*x**2-5*x-20)/x)+2*x**3-6*x**2-20*x+60)*exp((3*ln(1/6*(-2*x**2-5*x-
20)/x)+3-x)/ln(1/6*(-2*x**2-5*x-20)/x))/(2*x**3+5*x**2+20*x)/ln(1/6*(-2*x**2-5*x-20)/x)**2,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1276\)

2.4.7.64 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{2+2 x} (36-9 x)+4 x-x^2+e^{1+x} \left (8 x-6 x^2+x^3\right )+\left (-8 x+2 x^2+e^{1+x} (-72+18 x)\right ) \log (x)+(36-9 x) \log ^2(x)+\left (e^{2+2 x} (-48-9 x)-e^{1+x} x^2+\left (x^2+e^{1+x} (96+18 x)\right ) \log (x)+(-48-9 x) \log ^2(x)\right ) \log \left (\frac {x^2+e^{1+x} (48+9 x)+(-48-9 x) \log (x)}{-12 e^{1+x}+12 \log (x)}\right )}{e^{1+x} x^2+e^{2+2 x} (48+9 x)+\left (e^{1+x} (-96-18 x)-x^2\right ) \log (x)+(48+9 x) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((-9*x-48)*ln(x)**2+((18*x+96)*exp(1+x)+x**2)*ln(x)+(-9*x-48)*exp(1+x)**2-x**2*exp(1+x))*ln(((-9*x-
48)*ln(x)+(9*x+48)*exp(1+x)+x**2)/(12*ln(x)-12*exp(1+x)))+(-9*x+36)*ln(x)**2+((18*x-72)*exp(1+x)+2*x**2-8*x)*l
n(x)+(-9*x+36)*exp(1+x)**2+(x**3-6*x**2+8*x)*exp(1+x)-x**2+4*x)/((9*x+48)*ln(x)**2+((-18*x-96)*exp(1+x)-x**2)*
ln(x)+(9*x+48)*exp(1+x)**2+x**2*exp(1+x)),x)

[Out]

Exception raised: PolynomialError >> 1/(27*x**3 + 288*x**2 + 768*x) contains an element of the set of generato
rs.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1296\)

2.4.7.65 Sympy [F(-2)]

Exception generated. \[ \int \frac {100+40 x+4 x^2+\left (-50-40 x-6 x^2\right ) \log (x)+\left (10 x+2 x^2\right ) \log ^2(x)-4 x \log ^3(x)+(-4+2 x) \log ^4(x)+2 \log ^5(x)+\left ((-100-20 x) \log (x)-20 \log ^3(x)\right ) \log (-2+\log (x))+\left (-200-40 x+(100+40 x) \log (x)-10 x \log ^2(x)\right ) \log ^2(-2+\log (x))+100 \log (x) \log ^3(-2+\log (x))+(100-50 \log (x)) \log ^4(-2+\log (x))}{-2 x \log ^3(x)+x \log ^4(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-50*ln(x)+100)*ln(ln(x)-2)**4+100*ln(x)*ln(ln(x)-2)**3+(-10*x*ln(x)**2+(40*x+100)*ln(x)-40*x-200)*
ln(ln(x)-2)**2+(-20*ln(x)**3+(-20*x-100)*ln(x))*ln(ln(x)-2)+2*ln(x)**5+(2*x-4)*ln(x)**4-4*x*ln(x)**3+(2*x**2+1
0*x)*ln(x)**2+(-6*x**2-40*x-50)*ln(x)+4*x**2+40*x+100)/(x*ln(x)**4-2*x*ln(x)**3),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1331\)

2.4.7.66 Sympy [F(-2)]

Exception generated. \[ \int \frac {(64-16 x) \log (x)+\left (-64 x+16 x^2\right ) \log (x) \log (2 x)+(64-16 x+(64-48 x) \log (x)) \log (2 x) \log \left (\frac {e^x}{\log (2 x)}\right )}{\left (-64 x^2+48 x^3-12 x^4+x^5\right ) \log ^2(x) \log (2 x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-48*x+64)*ln(x)-16*x+64)*ln(2*x)*ln(exp(x)/ln(2*x))+(16*x**2-64*x)*ln(x)*ln(2*x)+(-16*x+64)*ln(x)
)/(x**5-12*x**4+48*x**3-64*x**2)/ln(x)**2/ln(2*x),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1387\)

2.4.7.67 Sympy [F(-2)]

Exception generated. \[ \int \frac {-240 x-48 x^2+\left (240 x+48 x^2\right ) \log (x)+\left (\left (240 x+96 x^2\right ) \log (x)+(45+18 x) \log ^2(x)\right ) \log \left (\frac {16 x+3 \log (x)}{\log (x)}\right ) \log \left (2 \log \left (\frac {16 x+3 \log (x)}{\log (x)}\right )\right )}{\left (16 x \log (x)+3 \log ^2(x)\right ) \log \left (\frac {16 x+3 \log (x)}{\log (x)}\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((18*x+45)*ln(x)**2+(96*x**2+240*x)*ln(x))*ln((3*ln(x)+16*x)/ln(x))*ln(2*ln((3*ln(x)+16*x)/ln(x)))+
(48*x**2+240*x)*ln(x)-48*x**2-240*x)/(3*ln(x)**2+16*x*ln(x))/ln((3*ln(x)+16*x)/ln(x)),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1455\)

2.4.7.68 Sympy [F(-2)]

Exception generated. \[ \int \frac {-45+39 x-56 x^2+40 x^3-11 x^4+x^5+\left (-45+30 x-170 x^2+119 x^3-58 x^4+13 x^5-x^6\right ) \log (x)+\left (9 x^2-6 x^3+13 x^4-11 x^5-x^6-4 x^7-5 x^8+x^9\right ) \log ^2(x)}{\left (45 x-39 x^2+56 x^3-40 x^4+11 x^5-x^6\right ) \log (x)+\left (9 x^3-6 x^4+19 x^5-12 x^6+11 x^7-6 x^8+x^9\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((x**9-5*x**8-4*x**7-x**6-11*x**5+13*x**4-6*x**3+9*x**2)*ln(x)**2+(-x**6+13*x**5-58*x**4+119*x**3-17
0*x**2+30*x-45)*ln(x)+x**5-11*x**4+40*x**3-56*x**2+39*x-45)/((x**9-6*x**8+11*x**7-12*x**6+19*x**5-6*x**4+9*x**
3)*ln(x)**2+(-x**6+11*x**5-40*x**4+56*x**3-39*x**2+45*x)*ln(x)),x)

[Out]

Exception raised: PolynomialError >> 1/(x**7 + 2*x**5 + x**3) contains an element of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1506\)

2.4.7.69 Sympy [F(-2)]

Exception generated. \[ \int \frac {x-21 x^2+20 x^3+e^5 \left (-20 x+20 x^2\right )+x \log (4 x)+\left (-2 x+2 x^2+e^5 (-2+2 x)+\left (-e^5-x\right ) \log (4 x)\right ) \log \left (e^5+x\right )}{20 x^3-40 x^4+20 x^5+e^5 \left (20 x^2-40 x^3+20 x^4\right )+\left (40 x^3-40 x^4+e^5 \left (40 x^2-40 x^3\right )\right ) \log (4 x)+\left (20 e^5 x^2+20 x^3\right ) \log ^2(4 x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-exp(5)-x)*ln(4*x)+(-2+2*x)*exp(5)+2*x**2-2*x)*ln(exp(5)+x)+x*ln(4*x)+(20*x**2-20*x)*exp(5)+20*x*
*3-21*x**2+x)/((20*x**2*exp(5)+20*x**3)*ln(4*x)**2+((-40*x**3+40*x**2)*exp(5)-40*x**4+40*x**3)*ln(4*x)+(20*x**
4-40*x**3+20*x**2)*exp(5)+20*x**5-40*x**4+20*x**3),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1587\)

2.4.7.70 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (5 x+4 e^3 x\right ) \log (x)+\left (-19+e^3 (8-4 x)-5 x\right ) \log \left (\frac {1}{5} \left (38+10 x+e^3 (-16+8 x)\right )\right )}{\left (19 x+5 x^2+e^3 \left (-8 x+4 x^2\right )\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-4*x+8)*exp(3)-5*x-19)*ln(1/5*(8*x-16)*exp(3)+2*x+38/5)+(4*x*exp(3)+5*x)*ln(x))/((4*x**2-8*x)*exp
(3)+5*x**2+19*x)/ln(x)**2,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1657\)

2.4.7.71 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-8 x+4 x^2\right ) \log (-2+x) \log \left (\frac {1}{2} (1+2 x)\right )+\left (-2 x-4 x^2+\left (2+3 x-2 x^2\right ) \log (-2+x)\right ) \log ^2\left (\frac {1}{2} (1+2 x)\right )}{\left (-2 x^2-3 x^3+2 x^4\right ) \log ^3(-2+x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-2*x**2+3*x+2)*ln(-2+x)-4*x**2-2*x)*ln(1/2+x)**2+(4*x**2-8*x)*ln(-2+x)*ln(1/2+x))/(2*x**4-3*x**3-
2*x**2)/ln(-2+x)**3,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1661\)

2.4.7.72 Sympy [F(-2)]

Exception generated. \[ \int \frac {4 x^5+x^3 \log (x)+\left (-32 x^3 \log \left (\frac {4}{x}\right )+64 x^3 \log \left (\frac {4}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {4}{x}\right )\right ) \log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right ) \log \left (\log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right )\right )+\left (2 x^3 \log \left (\frac {4}{x}\right )-4 x^3 \log \left (\frac {4}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {4}{x}\right )\right ) \log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right ) \log \left (\log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right )\right ) \log \left (\log \left (\log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right )\right )\right )}{\left (64 x^6 \log \left (\frac {4}{x}\right )+48 x^4 \log \left (\frac {4}{x}\right ) \log (x)+12 x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)+\log \left (\frac {4}{x}\right ) \log ^3(x)\right ) \log \left (\log \left (\frac {4}{x}\right )\right ) \log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right ) \log \left (\log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right )\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-4*x**3*ln(4/x)*ln(x)+2*x**3*ln(4/x))*ln(ln(4/x))*ln(ln(ln(4/x)))*ln(ln(ln(ln(4/x))))*ln(ln(ln(ln(
ln(4/x)))))+(64*x**3*ln(4/x)*ln(x)-32*x**3*ln(4/x))*ln(ln(4/x))*ln(ln(ln(4/x)))*ln(ln(ln(ln(4/x))))+x**3*ln(x)
+4*x**5)/(ln(4/x)*ln(x)**3+12*x**2*ln(4/x)*ln(x)**2+48*x**4*ln(4/x)*ln(x)+64*x**6*ln(4/x))/ln(ln(4/x))/ln(ln(l
n(4/x)))/ln(ln(ln(ln(4/x)))),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1705\)

2.4.7.73 Sympy [F(-2)]

Exception generated. \[ \int \frac {\log (x) \log ^2(\log (x))+e^{\frac {2 x^2}{\log (\log (x))}} (-2 x+4 x \log (x) \log (\log (x)))}{\log (x) \log ^2(\log (x))} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((4*x*ln(x)*ln(ln(x))-2*x)*exp(x**2/ln(ln(x)))**2+ln(x)*ln(ln(x))**2)/ln(x)/ln(ln(x))**2,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1820\)

2.4.7.74 Sympy [F(-2)]

Exception generated. \[ \int \frac {4+(1+x) \log \left (\frac {3}{x^2}\right ) \log ^2\left (\log ^2\left (\frac {3}{x^2}\right )\right )}{x \log \left (\frac {3}{x^2}\right ) \log \left (\log ^2\left (\frac {3}{x^2}\right )\right )+\left (\left (-x+x^2\right ) \log \left (\frac {3}{x^2}\right )+x \log \left (\frac {3}{x^2}\right ) \log (x)\right ) \log ^2\left (\log ^2\left (\frac {3}{x^2}\right )\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((1+x)*ln(3/x**2)*ln(ln(3/x**2)**2)**2+4)/((x*ln(3/x**2)*ln(x)+(x**2-x)*ln(3/x**2))*ln(ln(3/x**2)**2
)**2+x*ln(3/x**2)*ln(ln(3/x**2)**2)),x)

[Out]

Exception raised: PolynomialError >> 1/(2*_t0**3*x + 4*_t0**2*x**2 - 4*_t0**2*x - _t0**2*x*log(3) + 2*_t0*x**3
- 4*_t0*x**2 - 2*_t0*x**2*log(3) + 2*_t0*x + 2*_t0*x*log(3) - x**3*log(3) + 2*x**2*log(3) - x*log(3)) contain
s an element of t

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1945\)

2.4.7.75 Sympy [F(-2)]

Exception generated. \[ \int \frac {2 x^3-4 x^4+\left (6 x-12 x^2-4 x^3+3 x^4+x^5\right ) \log \left (-x+x^2\right )+\left (-12 x+6 x^2+6 x^3\right ) \log ^2\left (-x+x^2\right )+\left (-10+9 x+x^2\right ) \log ^3\left (-x+x^2\right )}{\left (-x^4+x^5\right ) \log \left (-x+x^2\right )+\left (-6 x^2+6 x^3\right ) \log ^2\left (-x+x^2\right )+\left (-9+8 x+x^2\right ) \log ^3\left (-x+x^2\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((x**2+9*x-10)*ln(x**2-x)**3+(6*x**3+6*x**2-12*x)*ln(x**2-x)**2+(x**5+3*x**4-4*x**3-12*x**2+6*x)*ln(
x**2-x)-4*x**4+2*x**3)/((x**2+8*x-9)*ln(x**2-x)**3+(6*x**3-6*x**2)*ln(x**2-x)**2+(x**5-x**4)*ln(x**2-x)),x)

[Out]

Exception raised: PolynomialError >> 1/(x**6 + 34*x**5 + 415*x**4 + 1980*x**3 + 1215*x**2 - 10206*x + 6561) co
ntains an element of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(1951\)

2.4.7.76 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {-2-x}{\left (-x+2 x^3\right ) \log (x)}} \left (-2-x+4 x^2+2 x^3+\left (-2+12 x^2+4 x^3\right ) \log (x)\right )}{\left (x^2-4 x^4+4 x^6\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((4*x**3+12*x**2-2)*ln(x)+2*x**3+4*x**2-x-2)*exp((-2-x)/(2*x**3-x)/ln(x))/(4*x**6-4*x**4+x**2)/ln(x)
**2,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2019\)

2.4.7.77 Sympy [F(-2)]

Exception generated. \[ \int \frac {4 x^3+4 x^2 \log (5)+\left (x-8 x^4+\left (1-8 x^2-8 x^3\right ) \log (5)\right ) \log (x) \log (\log (x))+\left (4 x^2+4 x \log (5)+\left (-12 x^3+\left (-8 x-12 x^2\right ) \log (5)\right ) \log (x) \log (\log (x))\right ) \log \left (\frac {x^2}{\left (x^2+2 x \log (5)+\log ^2(5)\right ) \log (\log (x))}\right )+\left (-4 x^2-4 x \log (5)\right ) \log (x) \log (\log (x)) \log ^2\left (\frac {x^2}{\left (x^2+2 x \log (5)+\log ^2(5)\right ) \log (\log (x))}\right )}{(2 x+2 \log (5)) \log (x) \log (\log (x))} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-4*x*ln(5)-4*x**2)*ln(x)*ln(ln(x))*ln(x**2/(ln(5)**2+2*x*ln(5)+x**2)/ln(ln(x)))**2+(((-12*x**2-8*x
)*ln(5)-12*x**3)*ln(x)*ln(ln(x))+4*x*ln(5)+4*x**2)*ln(x**2/(ln(5)**2+2*x*ln(5)+x**2)/ln(ln(x)))+((-8*x**3-8*x*
*2+1)*ln(5)-8*x**4+x)*ln(x)*ln(ln(x))+4*x**2*ln(5)+4*x**3)/(2*ln(5)+2*x)/ln(x)/ln(ln(x)),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2117\)

2.4.7.78 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (320+1264 x+1740 x^2+925 x^3+125 x^4\right ) \log \left (\frac {5+x}{5}\right )+\left (250 x+50 x^2+\left (250 x+50 x^2\right ) \log (2)\right ) \log ^2\left (\frac {5+x}{5}\right )+\log (x) \left (-64 x-240 x^2-300 x^3-125 x^4+\left (-250 x-50 x^2\right ) \log \left (\frac {5+x}{5}\right )\right )}{\left (320 x+1264 x^2+1740 x^3+925 x^4+125 x^5\right ) \log (x) \log \left (\frac {5+x}{5}\right )+\left (-320 x-1264 x^2-1740 x^3-925 x^4-125 x^5+\left (-320 x-1264 x^2-1740 x^3-925 x^4-125 x^5\right ) \log (2)\right ) \log ^2\left (\frac {5+x}{5}\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((-50*x**2-250*x)*ln(1+1/5*x)-125*x**4-300*x**3-240*x**2-64*x)*ln(x)+((50*x**2+250*x)*ln(2)+50*x**2
+250*x)*ln(1+1/5*x)**2+(125*x**4+925*x**3+1740*x**2+1264*x+320)*ln(1+1/5*x))/((125*x**5+925*x**4+1740*x**3+126
4*x**2+320*x)*ln(1+1/5*x)*ln(x)+((-125*x**5-925*x**4-1740*x**3-1264*x**2-320*x)*ln(2)-125*x**5-925*x**4-1740*x
**3-1264*x**2-320*x)*ln(1+1/5*x)**2),x)

[Out]

Exception raised: PolynomialError >> 1/(x**2*log(2) + x**2 + 5*x*log(2) + 5*x) contains an element of the set
of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2164\)

2.4.7.79 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {135 x}{-5 x^2+\log (x)}} \left (-270 x+1350 x^3+50 x^4+\left (270 x-20 x^2\right ) \log (x)+2 \log ^2(x)\right )}{375 x^4-150 x^2 \log (x)+15 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((2*ln(x)**2+(-20*x**2+270*x)*ln(x)+50*x**4+1350*x**3-270*x)*exp(135*x/(ln(x)-5*x**2))/(15*ln(x)**2-1
50*x**2*ln(x)+375*x**4),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2240\)

2.4.7.80 Sympy [F(-2)]

Exception generated. \[ \int \frac {8 x-16 x^3-16 x^4+e^8 \left (-48 x^3-48 x^4\right )+e^{12} \left (16 x^3+16 x^4\right )+e^4 \left (-8 x+48 x^3+48 x^4\right )+\left (-4+24 x^2+16 x^3-8 x^4+e^8 \left (24 x^2-24 x^4\right )+e^{12} \left (8 x^3+8 x^4\right )+e^4 \left (-48 x^2-24 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x+12 x^3+e^4 \left (12 x-12 x^2-24 x^3\right )+e^8 \left (12 x^2+12 x^3\right )\right ) \log ^2(x)+\left (2-4 x-6 x^2+e^4 \left (6 x+6 x^2\right )\right ) \log ^3(x)+(1+x) \log ^4(x)+\left (16-32 x+32 e^4 x+\left (8-16 x+16 e^4 x\right ) \log (x)\right ) \log (2+\log (x))}{-16 x^4+48 e^4 x^4-48 e^8 x^4+16 e^{12} x^4+\left (24 x^3-8 x^4+8 e^{12} x^4+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (-48 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x^2+12 x^3+12 e^8 x^3+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+\left (2 x-6 x^2+6 e^4 x^2\right ) \log ^3(x)+x \log ^4(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((16*x*exp(4)-16*x+8)*ln(x)+32*x*exp(4)-32*x+16)*ln(ln(x)+2)+(1+x)*ln(x)**4+((6*x**2+6*x)*exp(4)-6*
x**2-4*x+2)*ln(x)**3+((12*x**3+12*x**2)*exp(4)**2+(-24*x**3-12*x**2+12*x)*exp(4)+12*x**3-12*x)*ln(x)**2+((8*x*
*4+8*x**3)*exp(4)**3+(-24*x**4+24*x**2)*exp(4)**2+(24*x**4-24*x**3-48*x**2)*exp(4)-8*x**4+16*x**3+24*x**2-4)*l
n(x)+(16*x**4+16*x**3)*exp(4)**3+(-48*x**4-48*x**3)*exp(4)**2+(48*x**4+48*x**3-8*x)*exp(4)-16*x**4-16*x**3+8*x
)/(x*ln(x)**4+(6*x**2*exp(4)-6*x**2+2*x)*ln(x)**3+(12*x**3*exp(4)**2+(-24*x**3+12*x**2)*exp(4)+12*x**3-12*x**2
)*ln(x)**2+(8*x**4*exp(4)**3+(-24*x**4+24*x**3)*exp(4)**2+(24*x**4-48*x**3)*exp(4)-8*x**4+24*x**3)*ln(x)+16*x*
*4*exp(4)**3-48*x**4*exp(4)**2+48*x**4*exp(4)-16*x**4),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2277\)

2.4.7.81 Sympy [F(-2)]

Exception generated. \[ \int \frac {x^2+2 x \log (x)+\log ^2(x)+e^{\frac {2 \left (25+e x^2+e x \log (x)\right )}{x^2+x \log (x)}} \left (-25-50 x+x^3+\left (-25+2 x^2\right ) \log (x)+x \log ^2(x)\right )}{x^2+2 x \log (x)+\log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((x*ln(x)**2+(2*x**2-25)*ln(x)+x**3-50*x-25)*exp((x*exp(1)*ln(x)+x**2*exp(1)+25)/(x*ln(x)+x**2))**2+
ln(x)**2+2*x*ln(x)+x**2)/(ln(x)**2+2*x*ln(x)+x**2),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2344\)

2.4.7.82 Sympy [F(-2)]

Exception generated. \[ \int \frac {-4 \log ^2(2 x)+e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x} \left ((1+2 x) \log ^2(2 x)+e^{\frac {6 x^2}{\log (2 x)}} \left (6 x^2-12 x^2 \log (2 x)\right )\right )}{\log ^2(2 x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-12*x**2*ln(2*x)+6*x**2)*exp(6*x**2/ln(2*x))+(1+2*x)*ln(2*x)**2)*exp(-exp(6*x**2/ln(2*x))+2*x)-4*
ln(2*x)**2)/ln(2*x)**2,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2387\)

2.4.7.83 Sympy [F(-2)]

Exception generated. \[ \int \frac {-4 x \log (x)+4 e^{2 x+4 e^{2 x} x^2} x^2 (8+8 x) \log (x)+\left (2 x+e^{4 e^{2 x} x^2} (-2-2 \log (x))+2 x \log (x)\right ) \log \left (e^{8 e^{2 x} x^2}-2 e^{4 e^{2 x} x^2} x+x^2\right )}{e^{4 e^{2 x} x^2} x^2 \log ^2(x)-x^3 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-2*ln(x)-2)*exp(exp(ln(2*x)+x)**2)+2*x*ln(x)+2*x)*ln(exp(exp(ln(2*x)+x)**2)**2-2*x*exp(exp(ln(2*x
)+x)**2)+x**2)+(8*x+8)*ln(x)*exp(ln(2*x)+x)**2*exp(exp(ln(2*x)+x)**2)-4*x*ln(x))/(x**2*ln(x)**2*exp(exp(ln(2*x
)+x)**2)-x**3*ln(x)**2),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2398\)

2.4.7.84 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {x^2+x \log (x)}{-x+\log \left (\frac {e^6 \left (9 x^2-6 x^3+x^4\right )+e^3 \left (-6 x+2 x^2\right ) \log (x)+\log ^2(x)}{e^6 x^2}\right )}} \left (-2 x+e^3 \left (3 x^2-x^4\right )+\left (-2+x-x^2-2 e^3 x^2\right ) \log (x)+2 \log ^2(x)+\left (e^3 \left (-3 x-5 x^2+2 x^3\right )+\left (1+2 x+e^3 \left (-3 x+x^2\right )\right ) \log (x)+\log ^2(x)\right ) \log \left (\frac {e^6 \left (9 x^2-6 x^3+x^4\right )+e^3 \left (-6 x+2 x^2\right ) \log (x)+\log ^2(x)}{e^6 x^2}\right )\right )}{e^3 \left (-3 x^3+x^4\right )+x^2 \log (x)+\left (e^3 \left (6 x^2-2 x^3\right )-2 x \log (x)\right ) \log \left (\frac {e^6 \left (9 x^2-6 x^3+x^4\right )+e^3 \left (-6 x+2 x^2\right ) \log (x)+\log ^2(x)}{e^6 x^2}\right )+\left (e^3 \left (-3 x+x^2\right )+\log (x)\right ) \log ^2\left (\frac {e^6 \left (9 x^2-6 x^3+x^4\right )+e^3 \left (-6 x+2 x^2\right ) \log (x)+\log ^2(x)}{e^6 x^2}\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((ln(x)**2+((x**2-3*x)*exp(3)+2*x+1)*ln(x)+(2*x**3-5*x**2-3*x)*exp(3))*ln((ln(x)**2+(2*x**2-6*x)*exp
(3)*ln(x)+(x**4-6*x**3+9*x**2)*exp(3)**2)/x**2/exp(3)**2)+2*ln(x)**2+(-2*x**2*exp(3)-x**2+x-2)*ln(x)+(-x**4+3*
x**2)*exp(3)-2*x)*exp((x*ln(x)+x**2)/(ln((ln(x)**2+(2*x**2-6*x)*exp(3)*ln(x)+(x**4-6*x**3+9*x**2)*exp(3)**2)/x
**2/exp(3)**2)-x))/((ln(x)+(x**2-3*x)*exp(3))*ln((ln(x)**2+(2*x**2-6*x)*exp(3)*ln(x)+(x**4-6*x**3+9*x**2)*exp(
3)**2)/x**2/exp(3)**2)**2+(-2*x*ln(x)+(-2*x**3+6*x**2)*exp(3))*ln((ln(x)**2+(2*x**2-6*x)*exp(3)*ln(x)+(x**4-6*
x**3+9*x**2)*exp(3)**2)/x**2/exp(3)**2)+x**2*ln(x)+(x**4-3*x**3)*exp(3)),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2405\)

2.4.7.85 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (16-12 x^2+4 x^3+e^3 \left (-16 x^2-16 x^3+28 x^4-8 x^5\right )+e^3 \left (-16 x-16 x^2+28 x^3-8 x^4\right ) \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )+\left (-4 x^2+2 x^3+\left (-4 x+2 x^2\right ) \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{\left (x^2+x \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((2*x**2-4*x)*ln(x)+2*x**3-4*x**2)*ln((x+ln(x))/exp((x**2+x+2)*exp(3)))*ln(ln((x+ln(x))/exp((x**2+x
+2)*exp(3)))**2)**2+((-8*x**4+28*x**3-16*x**2-16*x)*exp(3)*ln(x)+(-8*x**5+28*x**4-16*x**3-16*x**2)*exp(3)+4*x*
*3-12*x**2+16)*ln(ln((x+ln(x))/exp((x**2+x+2)*exp(3)))**2))/(x*ln(x)+x**2)/ln((x+ln(x))/exp((x**2+x+2)*exp(3))
),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2423\)

2.4.7.86 Sympy [F(-2)]

Exception generated. \[ \int \frac {240 x^2+100 x^3+e^x \left (240 x+100 x^2\right )+\left (-120 x+50 x^2+e^x \left (-20 x-50 x^2\right )\right ) \log (x)+\left (e^x (-120-50 x)-120 x-50 x^2+\left (e^x (-120-50 x)-120 x-50 x^2\right ) \log (x)\right ) \log \left (\frac {144+120 x+25 x^2}{e^x+x}\right )}{\left (12 x^3+5 x^4+e^x \left (12 x^2+5 x^3\right )\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((((-50*x-120)*exp(x)-50*x**2-120*x)*ln(x)+(-50*x-120)*exp(x)-50*x**2-120*x)*ln((25*x**2+120*x+144)/
(exp(x)+x))+((-50*x**2-20*x)*exp(x)+50*x**2-120*x)*ln(x)+(100*x**2+240*x)*exp(x)+100*x**3+240*x**2)/((5*x**3+1
2*x**2)*exp(x)+5*x**4+12*x**3)/ln(x)**2,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2508\)

2.4.7.87 Sympy [F(-2)]

Exception generated. \[ \int \frac {-8 e^{2 x}+e^{e^{e^5}+2 x} \left (10-30 x+10 x^2\right )+\left (-16 e^{2 x}+e^{e^{e^5}+2 x} \left (70-80 x+20 x^2\right )\right ) \log \left (\frac {1}{5} \left (4+e^{e^{e^5}} \left (-30+25 x-5 x^2\right )\right )\right )+\left (-8 e^{2 x}+e^{e^{e^5}+2 x} \left (60-50 x+10 x^2\right )\right ) \log ^2\left (\frac {1}{5} \left (4+e^{e^{e^5}} \left (-30+25 x-5 x^2\right )\right )\right )}{-4+e^{e^{e^5}} \left (30-25 x+5 x^2\right )} \, dx=\text {Exception raised: CoercionFailed} \]

[In]

integrate((((10*x**2-50*x+60)*exp(x)**2*exp(exp(exp(5)))-8*exp(x)**2)*ln(1/5*(-5*x**2+25*x-30)*exp(exp(exp(5))
)+4/5)**2+((20*x**2-80*x+70)*exp(x)**2*exp(exp(exp(5)))-16*exp(x)**2)*ln(1/5*(-5*x**2+25*x-30)*exp(exp(exp(5))
)+4/5)+(10*x**2-30*x+10)*exp(x)**2*exp(exp(exp(5)))-8*exp(x)**2)/((5*x**2-25*x+30)*exp(exp(exp(5)))-4),x)

[Out]

Exception raised: CoercionFailed >> Cannot convert 5*exp(exp(exp(5))) of type <class 'sympy.core.mul.Mul'> to
ZZ[exp(exp(exp(5))/2),sqrt(16 + 5*exp(exp(exp(5))))]

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2531\)

2.4.7.88 Sympy [F(-2)]

Exception generated. \[ \int \frac {16 \log ^2\left (x^2\right )+e^{2 e^{e^{\frac {x}{\log \left (x^2\right )}}}+4 x} \left ((1+4 x) \log ^2\left (x^2\right )+e^{e^{\frac {x}{\log \left (x^2\right )}}+\frac {x}{\log \left (x^2\right )}} \left (-4 x+2 x \log \left (x^2\right )\right )\right )+e^{e^{e^{\frac {x}{\log \left (x^2\right )}}}+2 x} \left ((8+16 x) \log ^2\left (x^2\right )+e^{e^{\frac {x}{\log \left (x^2\right )}}+\frac {x}{\log \left (x^2\right )}} \left (-16 x+8 x \log \left (x^2\right )\right )\right )}{\log ^2\left (x^2\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((2*x*ln(x**2)-4*x)*exp(x/ln(x**2))*exp(exp(x/ln(x**2)))+(1+4*x)*ln(x**2)**2)*exp(exp(exp(x/ln(x**2
)))+2*x)**2+((8*x*ln(x**2)-16*x)*exp(x/ln(x**2))*exp(exp(x/ln(x**2)))+(16*x+8)*ln(x**2)**2)*exp(exp(exp(x/ln(x
**2)))+2*x)+16*ln(x**2)**2)/ln(x**2)**2,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2569\)

2.4.7.89 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {-15+5 x}{\left (39 x-8 x^2-4 x^3+x^4\right ) \log (x)}} \left (-585+315 x+20 x^2-35 x^3+5 x^4+\left (-585+240 x+140 x^2-100 x^3+15 x^4\right ) \log (x)\right )}{\left (1521 x^2-624 x^3-248 x^4+142 x^5-8 x^7+x^8\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((15*x**4-100*x**3+140*x**2+240*x-585)*ln(x)+5*x**4-35*x**3+20*x**2+315*x-585)*exp((5*x-15)/(x**4-4*
x**3-8*x**2+39*x)/ln(x))/(x**8-8*x**7+142*x**5-248*x**4-624*x**3+1521*x**2)/ln(x)**2,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2570\)

2.4.7.90 Sympy [F(-2)]

Exception generated. \[ \int \frac {-6-24 x+(-1-6 x) \log (2 x)+(24 x+4 \log (x)+(6 x+\log (x)) \log (2 x)+(8+2 \log (2 x)) \log (4+\log (2 x))) \log \left (\frac {8}{6 x+\log (x)+2 \log (4+\log (2 x))}\right )}{24 x+4 \log (x)+(6 x+\log (x)) \log (2 x)+(8+2 \log (2 x)) \log (4+\log (2 x))} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((2*ln(2*x)+8)*ln(ln(2*x)+4)+(ln(x)+6*x)*ln(2*x)+4*ln(x)+24*x)*ln(8/(2*ln(ln(2*x)+4)+ln(x)+6*x))+(-
6*x-1)*ln(2*x)-24*x-6)/((2*ln(2*x)+8)*ln(ln(2*x)+4)+(ln(x)+6*x)*ln(2*x)+4*ln(x)+24*x),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2849\)

2.4.7.91 Sympy [F(-2)]

Exception generated. \[ \int \frac {1+\log \left (\frac {3}{2 x}\right )+\log ^2\left (\frac {3}{2 x}\right )}{x \log \left (\frac {3}{2 x}\right )+(28+x+\log (2)) \log ^2\left (\frac {3}{2 x}\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((ln(3/2/x)**2+ln(3/2/x)+1)/((ln(2)+x+28)*ln(3/2/x)**2+x*ln(3/2/x)),x)

[Out]

Exception raised: PolynomialError >> 1/(x**3 + 2*x**2*log(2) + 56*x**2 + x*log(2)**2 + 56*x*log(2) + 784*x) co
ntains an element of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2865\)

2.4.7.92 Sympy [F(-2)]

Exception generated. \[ \int \frac {15-21 x-36 x^2+(12+12 x) \log (x)+(2+4 x+(2+4 x) \log (x)) \log \left (x+x^2\right )+\left (-8+16 x+24 x^2+(-7-7 x) \log (x)\right ) \log ^2\left (x+x^2\right )+\left (1-3 x-4 x^2+(1+x) \log (x)\right ) \log ^4\left (x+x^2\right )+\left (3-15 x-18 x^2+(12+12 x) \log (x)+\left (-1+11 x+12 x^2+(-7-7 x) \log (x)\right ) \log ^2\left (x+x^2\right )+\left (-2 x-2 x^2+(1+x) \log (x)\right ) \log ^4\left (x+x^2\right )\right ) \log \left (\frac {-1+6 x-4 \log (x)+(-2 x+\log (x)) \log ^2\left (x+x^2\right )}{-3+\log ^2\left (x+x^2\right )}\right )}{3-15 x-18 x^2+(12+12 x) \log (x)+\left (-1+11 x+12 x^2+(-7-7 x) \log (x)\right ) \log ^2\left (x+x^2\right )+\left (-2 x-2 x^2+(1+x) \log (x)\right ) \log ^4\left (x+x^2\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((ln(x)*(1+x)-2*x**2-2*x)*ln(x**2+x)**4+((-7*x-7)*ln(x)+12*x**2+11*x-1)*ln(x**2+x)**2+(12*x+12)*ln(
x)-18*x**2-15*x+3)*ln(((ln(x)-2*x)*ln(x**2+x)**2-4*ln(x)+6*x-1)/(ln(x**2+x)**2-3))+(ln(x)*(1+x)-4*x**2-3*x+1)*
ln(x**2+x)**4+((-7*x-7)*ln(x)+24*x**2+16*x-8)*ln(x**2+x)**2+((4*x+2)*ln(x)+4*x+2)*ln(x**2+x)+(12*x+12)*ln(x)-3
6*x**2-21*x+15)/((ln(x)*(1+x)-2*x**2-2*x)*ln(x**2+x)**4+((-7*x-7)*ln(x)+12*x**2+11*x-1)*ln(x**2+x)**2+(12*x+12
)*ln(x)-18*x**2-15*x+3),x)

[Out]

Exception raised: PolynomialError >> 1/(36*_t0**4*x**4 + 72*_t0**4*x**3 + 36*_t0**4*x**2 - 288*_t0**3*x**5 - 5
76*_t0**3*x**4 - 288*_t0**3*x**3 + 864*_t0**2*x**6 + 1728*_t0**2*x**5 + 864*_t0**2*x**4 - 1152*_t0*x**7 - 2304
*_t0*x**6 - 1152*

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2875\)

2.4.7.93 Sympy [F(-2)]

Exception generated. \[ \int \frac {20 x+129 x^2+50 x^3+5 x^4+\left (60+730 x+171 x^2-20 x^3-5 x^4\right ) \log (x)+\left (-60-387 x-150 x^2-15 x^3\right ) \log \left (\frac {4 x+25 x^2+5 x^3}{75+15 x}\right )}{\left (20 x+129 x^2+50 x^3+5 x^4\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-15*x**3-150*x**2-387*x-60)*ln((5*x**3+25*x**2+4*x)/(15*x+75))+(-5*x**4-20*x**3+171*x**2+730*x+60)
*ln(x)+5*x**4+50*x**3+129*x**2+20*x)/(5*x**4+50*x**3+129*x**2+20*x)/ln(x)**2,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2893\)

2.4.7.94 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-40 x^2+40 x^3-10 x^4\right ) \log ^2(x)+\left (2-3 x+x^2\right ) \log \left (x-x^2\right )+\log (x) \left (-2+5 x-2 x^2+\left (2-2 x+x^2\right ) \log \left (x-x^2\right )\right )}{\left (120 x^2-120 x^3+30 x^4\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-10*x**4+40*x**3-40*x**2)*ln(x)**2+((x**2-2*x+2)*ln(-x**2+x)-2*x**2+5*x-2)*ln(x)+(x**2-3*x+2)*ln(-
x**2+x))/(30*x**4-120*x**3+120*x**2)/ln(x)**2,x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2907\)

2.4.7.95 Sympy [F(-2)]

Exception generated. \[ \int \frac {-50 x^4+\left (-450+300 x-50 x^2-150 x^4\right ) \log (x)+\left (450-150 x-150 x^4\right ) \log ^2(x)+\left (450-150 x-50 x^4\right ) \log ^3(x)}{-x^3+25 x^5+\left (-3 x^3+75 x^5\right ) \log (x)+\left (225 x-150 x^2+22 x^3+75 x^5\right ) \log ^2(x)+\left (225 x-150 x^2+24 x^3+25 x^5\right ) \log ^3(x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((-50*x**4-150*x+450)*ln(x)**3+(-150*x**4-150*x+450)*ln(x)**2+(-150*x**4-50*x**2+300*x-450)*ln(x)-50
*x**4)/((25*x**5+24*x**3-150*x**2+225*x)*ln(x)**3+(75*x**5+22*x**3-150*x**2+225*x)*ln(x)**2+(75*x**5-3*x**3)*l
n(x)+25*x**5-x**3),x)

[Out]

Exception raised: PolynomialError >> 1/(390625*x**18 + 1500000*x**16 - 9375000*x**15 + 16222500*x**14 - 270000
00*x**13 + 126257400*x**12 - 279045000*x**11 + 391055526*x**10 - 831794400*x**9 + 1973451600*x**8 - 2835405000
*x**7 + 327827250

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2918\)

2.4.7.96 Sympy [F(-2)]

Exception generated. \[ \int \frac {2 x+e^4 x^2+x^4+e^2 \left (-1-2 x^3\right )+e^{2-x} \left (3 x+e^4 x^2+x^4+e^2 \left (-2-2 x^3\right )\right )+\left (-1-2 e^4 x+4 e^2 x^2-2 x^3+e^{2-x} \left (-1-2 e^4 x+4 e^2 x^2-2 x^3\right )\right ) \log \left (1+e^{2-x}\right )+\left (e^4-2 e^2 x+x^2+e^{2-x} \left (e^4-2 e^2 x+x^2\right )\right ) \log ^2\left (1+e^{2-x}\right )}{-x^2+e^4 x^3+x^5+e^2 \left (x-2 x^4\right )+e^{2-x} \left (-x^2+e^4 x^3+x^5+e^2 \left (x-2 x^4\right )\right )+\left (x-2 e^4 x^2-2 x^4+e^2 \left (-1+4 x^3\right )+e^{2-x} \left (x-2 e^4 x^2-2 x^4+e^2 \left (-1+4 x^3\right )\right )\right ) \log \left (1+e^{2-x}\right )+\left (e^4 x-2 e^2 x^2+x^3+e^{2-x} \left (e^4 x-2 e^2 x^2+x^3\right )\right ) \log ^2\left (1+e^{2-x}\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((exp(2)**2-2*exp(2)*x+x**2)*exp(2-x)+exp(2)**2-2*exp(2)*x+x**2)*ln(exp(2-x)+1)**2+((-2*x*exp(2)**2
+4*x**2*exp(2)-2*x**3-1)*exp(2-x)-2*x*exp(2)**2+4*x**2*exp(2)-2*x**3-1)*ln(exp(2-x)+1)+(x**2*exp(2)**2+(-2*x**
3-2)*exp(2)+x**4+3*x)*exp(2-x)+x**2*exp(2)**2+(-2*x**3-1)*exp(2)+x**4+2*x)/(((x*exp(2)**2-2*x**2*exp(2)+x**3)*
exp(2-x)+x*exp(2)**2-2*x**2*exp(2)+x**3)*ln(exp(2-x)+1)**2+((-2*x**2*exp(2)**2+(4*x**3-1)*exp(2)-2*x**4+x)*exp
(2-x)-2*x**2*exp(2)**2+(4*x**3-1)*exp(2)-2*x**4+x)*ln(exp(2-x)+1)+(x**3*exp(2)**2+(-2*x**4+x)*exp(2)+x**5-x**2
)*exp(2-x)+x**3*exp(2)**2+(-2*x**4+x)*exp(2)+x**5-x**2),x)

[Out]

Exception raised: PolynomialError >> 1/(_t0*x**4 - 2*_t0*x**3*exp(2) + _t0*x**2*exp(4) + x**4 - 2*x**3*exp(2)
+ x**2*exp(4)) contains an element of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2965\)

2.4.7.97 Sympy [F(-2)]

Exception generated. \[ \int \frac {-5 \log (3)+\left (x-12 x^6-9 x^9\right ) \log ^2(x)}{-5 x \log (3) \log (x)+\left (-x^2+2 x^7+x^{10}\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((-9*x**9-12*x**6+x)*ln(x)**2-5*ln(3))/((x**10+2*x**7-x**2)*ln(x)**2-5*x*ln(3)*ln(x)),x)

[Out]

Exception raised: PolynomialError >> 1/(x**18 + 4*x**15 + 4*x**12 - 2*x**10 - 4*x**7 + x**2) contains an eleme
nt of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(3023\)

2.4.7.98 Sympy [F(-2)]

Exception generated. \[ \int \frac {-2 x-x^2+\left (-2-x-2 x^2-2 x^3-x^4\right ) \log (x)+\left (-2 x-4 x^2-2 x^3\right ) \log ^2(x)+\left (-2 x-x^2\right ) \log ^3(x)+\left (2+3 x+x^2\right ) \log (x) \log \left (\left (8+8 x+2 x^2\right ) \log (x)\right )}{\left (2 x^3+x^4\right ) \log (x)+\left (4 x^2+2 x^3\right ) \log ^2(x)+\left (2 x+x^2\right ) \log ^3(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((x**2+3*x+2)*ln(x)*ln((2*x**2+8*x+8)*ln(x))+(-x**2-2*x)*ln(x)**3+(-2*x**3-4*x**2-2*x)*ln(x)**2+(-x*
*4-2*x**3-2*x**2-x-2)*ln(x)-x**2-2*x)/((x**2+2*x)*ln(x)**3+(2*x**3+4*x**2)*ln(x)**2+(x**4+2*x**3)*ln(x)),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(3063\)

2.4.7.99 Sympy [F(-2)]

Exception generated. \[ \int \frac {108 x^3+30 x^4+2 x^5+\left (-108 x^3-21 x^4-x^5\right ) \log (x)+\left (27 x^3+3 x^4\right ) \log ^2(x)+\left (\left (432 x^3+105 x^4+7 x^5\right ) \log (x)+\left (-432 x^3-87 x^4-4 x^5\right ) \log ^2(x)+\left (108 x^3+15 x^4\right ) \log ^3(x)\right ) \log (\log (x))}{\left (36+12 x+x^2\right ) \log (x)+(-36-6 x) \log ^2(x)+9 \log ^3(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((15*x**4+108*x**3)*ln(x)**3+(-4*x**5-87*x**4-432*x**3)*ln(x)**2+(7*x**5+105*x**4+432*x**3)*ln(x))*
ln(ln(x))+(3*x**4+27*x**3)*ln(x)**2+(-x**5-21*x**4-108*x**3)*ln(x)+2*x**5+30*x**4+108*x**3)/(9*ln(x)**3+(-6*x-
36)*ln(x)**2+(x**2+12*x+36)*ln(x)),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(3087\)

2.4.7.100 Sympy [F(-2)]

Exception generated. \[ \int \frac {16 x^2-112 x^3-128 x^2 \log (x)+\left (-64 x^2+32 x^3+\left (-64 x+32 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-8 x+12 x^2+(-8+12 x) \log (x)\right ) \log ^2(x+\log (x))+\left (8 x^2-88 x^3-96 x^2 \log (x)+\left (-48 x^2+24 x^3+\left (-48 x+24 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-6 x+8 x^2+(-6+8 x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log \left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )+\left (-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )}{-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((((-1+x)*ln(x)+x**2-x)*ln(x+ln(x))**2+((4*x**2-8*x)*ln(x)+4*x**3-8*x**2)*ln(x+ln(x))-16*x**2*ln(x)-
16*x**3)*ln(((x**2-x)*ln(x+ln(x))-4*x**2)/(ln(x+ln(x))+4*x))**2+(((8*x-6)*ln(x)+8*x**2-6*x)*ln(x+ln(x))**2+((2
4*x**2-48*x)*ln(x)+24*x**3-48*x**2)*ln(x+ln(x))-96*x**2*ln(x)-88*x**3+8*x**2)*ln(((x**2-x)*ln(x+ln(x))-4*x**2)
/(ln(x+ln(x))+4*x))+((12*x-8)*ln(x)+12*x**2-8*x)*ln(x+ln(x))**2+((32*x**2-64*x)*ln(x)+32*x**3-64*x**2)*ln(x+ln
(x))-128*x**2*ln(x)-112*x**3+16*x**2)/(((-1+x)*ln(x)+x**2-x)*ln(x+ln(x))**2+((4*x**2-8*x)*ln(x)+4*x**3-8*x**2)
*ln(x+ln(x))-16*x**2*ln(x)-16*x**3),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(3089\)