2.4.8 Integrals 701 to 800

2.4.8.1 Sympy [F(-2)]

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

[In]

integrate((((1-ln(x))*ln(4*x**2)**2+((-2*exp(4)+4)*ln(x)+2*exp(4)-4)*ln(4*x**2)+(-exp(4)**2+4*exp(4)+4)*ln(x)+
exp(4)**2-4*exp(4)+4)*exp(4/(ln(4*x**2)+exp(4)-2))+ln(x)**2*ln(4*x**2)**2+(2*exp(4)-4)*ln(x)**2*ln(4*x**2)+(ex
p(4)**2-4*exp(4)+4)*ln(x)**2)/(ln(x)**2*ln(4*x**2)**2+(2*exp(4)-4)*ln(x)**2*ln(4*x**2)+(exp(4)**2-4*exp(4)+4)*
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 \(3383\)

2.4.8.2 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-36 x^2+36 x \log (x)\right ) \log (x-\log (x))+\frac {e^x \left (-15+15 x+\left (-15 x-15 x^2+(15+15 x) \log (x)\right ) \log (x-\log (x))\right )}{\log (x-\log (x))}}{e^x \left (15 x^2-60 x^4+\left (-15 x+60 x^3\right ) \log (x)\right )+\frac {e^{2 x} \left (-25 x^3+25 x^2 \log (x)\right )}{\log (x-\log (x))}+\left (18 x^3-36 x^5+\left (-18 x^2+36 x^4\right ) \log (x)\right ) \log (x-\log (x))} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((((15*x+15)*ln(x)-15*x**2-15*x)*ln(x-ln(x))+15*x-15)*exp(-ln(ln(x-ln(x)))+x)+(36*x*ln(x)-36*x**2)*l
n(x-ln(x)))/((25*x**2*ln(x)-25*x**3)*ln(x-ln(x))*exp(-ln(ln(x-ln(x)))+x)**2+((60*x**3-15*x)*ln(x)-60*x**4+15*x
**2)*ln(x-ln(x))*exp(-ln(ln(x-ln(x)))+x)+((36*x**4-18*x**2)*ln(x)-36*x**5+18*x**3)*ln(x-ln(x))),x)

[Out]

Exception raised: PolynomialError >> 1/(-5*_t0*x**2 + 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 \(3431\)

2.4.8.3 Sympy [F(-2)]

Exception generated. \[ \int \frac {3 x+x^2+\left (6 x+2 x^2\right ) \log \left (\frac {3+x}{4}\right )+\left (3 x+x^2\right ) \log ^2\left (\frac {3+x}{4}\right )+\log ^2(x) \left (3+x-9 x^2+\left (6+2 x-9 x^2-3 x^3\right ) \log \left (\frac {3+x}{4}\right )+(3+x) \log ^2\left (\frac {3+x}{4}\right )\right )}{\log (x) \left (-3 x^2-x^3+\left (-6 x^2-2 x^3\right ) \log \left (\frac {3+x}{4}\right )+\left (-3 x^2-x^3\right ) \log ^2\left (\frac {3+x}{4}\right )\right )+\log ^2(x) \left (-3 x+2 x^2-8 x^3-3 x^4+\left (-6 x+4 x^2-7 x^3-3 x^4\right ) \log \left (\frac {3+x}{4}\right )+\left (-3 x+2 x^2+x^3\right ) \log ^2\left (\frac {3+x}{4}\right )\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((3+x)*ln(3/4+1/4*x)**2+(-3*x**3-9*x**2+2*x+6)*ln(3/4+1/4*x)-9*x**2+x+3)*ln(x)**2+(x**2+3*x)*ln(3/4
+1/4*x)**2+(2*x**2+6*x)*ln(3/4+1/4*x)+x**2+3*x)/(((x**3+2*x**2-3*x)*ln(3/4+1/4*x)**2+(-3*x**4-7*x**3+4*x**2-6*
x)*ln(3/4+1/4*x)-3*x**4-8*x**3+2*x**2-3*x)*ln(x)**2+((-x**3-3*x**2)*ln(3/4+1/4*x)**2+(-2*x**3-6*x**2)*ln(3/4+1
/4*x)-x**3-3*x**2)*ln(x)),x)

[Out]

Exception raised: PolynomialError >> 1/(_t0**2*x**3 + _t0**2*x**2 - 5*_t0**2*x + 3*_t0**2 - 2*_t0*x**3 - 4*_t0
*x**2 + 6*_t0*x + 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 \(3480\)

2.4.8.4 Sympy [F(-2)]

Exception generated. \[ \int \frac {9+x+(-27-4 x) \log (x)+(-3+5 x) \log ^2(x)+(6-2 x) \log ^3(x)}{\left (9 x+x^2\right ) \log (x)+\left (-3 x-2 x^2\right ) \log ^2(x)+\left (-6 x+x^2\right ) \log ^3(x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((6-2*x)*ln(x)**3+(5*x-3)*ln(x)**2+(-4*x-27)*ln(x)+x+9)/((x**2-6*x)*ln(x)**3+(-2*x**2-3*x)*ln(x)**2+
(x**2+9*x)*ln(x)),x)

[Out]

Exception raised: PolynomialError >> 1/(x**6 - 24*x**5 + 216*x**4 - 864*x**3 + 1296*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 \(3491\)

2.4.8.5 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: PolynomialError >> 1/(-2*x**4*log(5) + x**4 + x**4*log(5)**2 - 6*x**3 + 6*x**3*log(5) - 4*x*
*2*log(5) + 2*x**2*log(5)**2 + 11*x**2 - 12*x + 12*x*log(5) + 18) contains an element of the set of generators
.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(3538\)

2.4.8.6 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: PolynomialError >> 1/(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 \(3565\)

2.4.8.7 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (12 x+18 x^2+e^x \left (12+12 x+6 x^2\right )+\left (6 x+6 e^x x\right ) \log (x)\right ) \log \left (25 e^x x^2+25 x^3+\left (50 e^x x+50 x^2\right ) \log (x)+\left (25 e^x+25 x\right ) \log ^2(x)\right )+\left (3 e^x x+3 x^2+\left (3 e^x+3 x\right ) \log (x)\right ) \log ^2\left (25 e^x x^2+25 x^3+\left (50 e^x x+50 x^2\right ) \log (x)+\left (25 e^x+25 x\right ) \log ^2(x)\right )}{2 e^x x+2 x^2+\left (2 e^x+2 x\right ) \log (x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((3*exp(x)+3*x)*ln(x)+3*exp(x)*x+3*x**2)*ln((25*exp(x)+25*x)*ln(x)**2+(50*exp(x)*x+50*x**2)*ln(x)+2
5*exp(x)*x**2+25*x**3)**2+((6*exp(x)*x+6*x)*ln(x)+(6*x**2+12*x+12)*exp(x)+18*x**2+12*x)*ln((25*exp(x)+25*x)*ln
(x)**2+(50*exp(x)*x+50*x**2)*ln(x)+25*exp(x)*x**2+25*x**3))/((2*exp(x)+2*x)*ln(x)+2*exp(x)*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 \(3596\)

2.4.8.8 Sympy [F(-2)]

Exception generated. \[ \int \frac {-180 x^2+60 x^3+e^{\frac {1}{4} (3+4 x)} \left (-36 x^2+24 x^3-3 x^4\right )+e^x \left (36 x^2-24 x^3+3 x^4\right )}{25-10 e^x+e^{2 x}+e^{\frac {1}{2} (3+4 x)}+e^{\frac {1}{4} (3+4 x)} \left (10-2 e^x\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((-3*x**4+24*x**3-36*x**2)*exp(3/4+x)+(3*x**4-24*x**3+36*x**2)*exp(x)+60*x**3-180*x**2)/(exp(3/4+x)*
*2+(-2*exp(x)+10)*exp(3/4+x)+exp(x)**2-10*exp(x)+25),x)

[Out]

Exception raised: PolynomialError >> (-3*_t0*x**4*exp(3/4) + 3*_t0*x**4 - 24*_t0*x**3 + 24*_t0*x**3*exp(3/4) -
36*_t0*x**2*exp(3/4) + 36*_t0*x**2 + 60*x**3 - 180*x**2)/(-2*_t0**2*exp(3/4) + _t0**2 + _t0**2*exp(3/2) - 10*
_t0 + 10*_t0*exp(

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(3601\)

2.4.8.9 Sympy [F(-2)]

Exception generated. \[ \int \frac {96+e^4 (-8-2 x)+24 x+\left (96-8 e^4\right ) \log (x)-10 \log ^2(x)}{\left (-96 x-24 x^2+e^4 \left (8 x+2 x^2\right )\right ) \log (x)+\left (10 x+3 x^2\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((-10*ln(x)**2+(-8*exp(2)**2+96)*ln(x)+(-2*x-8)*exp(2)**2+24*x+96)/((3*x**2+10*x)*ln(x)**2+((2*x**2+8
*x)*exp(2)**2-24*x**2-96*x)*ln(x)),x)

[Out]

Exception raised: PolynomialError >> 1/(9*x**3 + 60*x**2 + 100*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 \(3760\)

2.4.8.10 Sympy [F(-2)]

Exception generated. \[ \int \frac {200 x^2+80 x^3+\left (-50 x^3-20 x^4\right ) \log (x)+\left (-400 x-160 x^2+\left (100 x^2+40 x^3\right ) \log (x)\right ) \log \left (x^2\right )+\left (200+80 x+\left (-50 x-20 x^2\right ) \log (x)\right ) \log ^2\left (x^2\right )+\left (\frac {4-x \log (x)}{x}\right )^{\frac {x}{-2 x+2 \log \left (x^2\right )}} \left (-100 x-85 x^2-5 x^3+10 x^3 \log (x)+\left (100+125 x+5 x^2-20 x^2 \log (x)\right ) \log \left (x^2\right )+(-40+10 x \log (x)) \log ^2\left (x^2\right )+\left (200+40 x+\left (-50 x-10 x^2\right ) \log (x)+\left (-100-20 x+\left (25 x+5 x^2\right ) \log (x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {4-x \log (x)}{x}\right )\right )}{-8 x^2+2 x^3 \log (x)+\left (16 x-4 x^2 \log (x)\right ) \log \left (x^2\right )+(-8+2 x \log (x)) \log ^2\left (x^2\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((((5*x**2+25*x)*ln(x)-20*x-100)*ln(x**2)+(-10*x**2-50*x)*ln(x)+40*x+200)*ln((-x*ln(x)+4)/x)+(10*x*
ln(x)-40)*ln(x**2)**2+(-20*x**2*ln(x)+5*x**2+125*x+100)*ln(x**2)+10*x**3*ln(x)-5*x**3-85*x**2-100*x)*exp(x*ln(
(-x*ln(x)+4)/x)/(2*ln(x**2)-2*x))+((-20*x**2-50*x)*ln(x)+80*x+200)*ln(x**2)**2+((40*x**3+100*x**2)*ln(x)-160*x
**2-400*x)*ln(x**2)+(-20*x**4-50*x**3)*ln(x)+80*x**3+200*x**2)/((2*x*ln(x)-8)*ln(x**2)**2+(-4*x**2*ln(x)+16*x)
*ln(x**2)+2*x**3*ln(x)-8*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 \(3909\)

2.4.8.11 Sympy [F(-2)]

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

[In]

integrate((((-x*exp(5)+2*x**2-x)*ln(3/2*x)*ln(exp(5)+1-2*x)-2*x**2*ln(3/2*x))*exp(x/ln(exp(5)+1-2*x))+(exp(5)+
1-2*x)*ln(exp(5)+1-2*x)**2)/(x*exp(5)-2*x**2+x)/ln(3/2*x)/ln(exp(5)+1-2*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 \(3922\)

2.4.8.12 Sympy [F(-2)]

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

[In]

integrate(((ln(x**3)-3)*exp(((-ln(3)+4)*ln(x**3)-x)/ln(x**3))-ln(x**3)**2)*exp(-exp(((-ln(3)+4)*ln(x**3)-x)/ln
(x**3))-x-2)/ln(x**3)**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 \(3939\)

2.4.8.13 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {4 x^2+x^2 \log (169)}{20 \log (50-x)}} \left (-4 x^2-x^2 \log (169)+\left (-400 x+8 x^2+\left (-100 x+2 x^2\right ) \log (169)\right ) \log (50-x)\right )}{(-1000+20 x) \log ^2(50-x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((2*(2*x**2-100*x)*ln(13)+8*x**2-400*x)*ln(-x+50)-2*x**2*ln(13)-4*x**2)*exp(1/20*(2*x**2*ln(13)+4*x*
*2)/ln(-x+50))/(20*x-1000)/ln(-x+50)**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 \(4051\)

2.4.8.14 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{15} \left (12+5 e^{\frac {2-16 x+4 x^2+4 x \log \left (25+10 x+x^2\right )}{-4 x+x^2+x \log \left (25+10 x+x^2\right )}} x\right )+\frac {2-16 x+4 x^2+4 x \log \left (25+10 x+x^2\right )}{-4 x+x^2+x \log \left (25+10 x+x^2\right )}} \left (40+64 x-28 x^2-3 x^3+x^4+\left (-10-42 x+2 x^2+2 x^3\right ) \log \left (25+10 x+x^2\right )+\left (5 x+x^2\right ) \log ^2\left (25+10 x+x^2\right )\right )}{240 x-72 x^2-9 x^3+3 x^4+\left (-120 x+6 x^2+6 x^3\right ) \log \left (25+10 x+x^2\right )+\left (15 x+3 x^2\right ) \log ^2\left (25+10 x+x^2\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((x**2+5*x)*ln(x**2+10*x+25)**2+(2*x**3+2*x**2-42*x-10)*ln(x**2+10*x+25)+x**4-3*x**3-28*x**2+64*x+40
)*exp((4*x*ln(x**2+10*x+25)+4*x**2-16*x+2)/(x*ln(x**2+10*x+25)+x**2-4*x))*exp(1/3*x*exp((4*x*ln(x**2+10*x+25)+
4*x**2-16*x+2)/(x*ln(x**2+10*x+25)+x**2-4*x))+4/5)/((3*x**2+15*x)*ln(x**2+10*x+25)**2+(6*x**3+6*x**2-120*x)*ln
(x**2+10*x+25)+3*x**4-9*x**3-72*x**2+240*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 \(4056\)

2.4.8.15 Sympy [F(-2)]

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

[In]

integrate(((-2*x-10)*ln(5+x)*ln(x*ln(5+x))**2+((((-2*x**2-10*x)*exp(x)+2*x**2+10*x)*ln(x)**2+((2*x+10)*exp(x)-
2*x**2-8*x+10)*ln(x))*ln(5+x)+2*x*ln(x))*ln(x*ln(5+x))+(((2*x**2+10*x)*exp(x)**2+(-2*x**3-12*x**2-10*x)*exp(x)
+2*x**3+12*x**2+10*x)*ln(x)**3+((-2*x-10)*exp(x)+2*x**2+10*x)*ln(x)**2)*ln(5+x)+(-2*exp(x)*x+2*x**2)*ln(x)**2)
/(x**2+5*x)/ln(x)**3/ln(5+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 \(4088\)

2.4.8.16 Sympy [F(-2)]

Exception generated. \[ \int \frac {30 x^2-10 x^4+\left (30-10 x^2+9 x^5-6 x^7+x^9-60 x^6 \log (3)\right ) \log (x)+\left (18 x^3-12 x^5+2 x^7-120 x^4 \log (3)\right ) \log ^2(x)+\left (9 x-6 x^3+x^5-60 x^2 \log (3)\right ) \log ^3(x)+\left (\left (-30-50 x^2+40 x^4\right ) \log (x)+20 x^2 \log ^2(x)\right ) \log (\log (x))}{\left (9 x^5-6 x^7+x^9\right ) \log (x)+\left (18 x^3-12 x^5+2 x^7\right ) \log ^2(x)+\left (9 x-6 x^3+x^5\right ) \log ^3(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((20*x**2*ln(x)**2+(40*x**4-50*x**2-30)*ln(x))*ln(ln(x))+(-60*x**2*ln(3)+x**5-6*x**3+9*x)*ln(x)**3+(
-120*x**4*ln(3)+2*x**7-12*x**5+18*x**3)*ln(x)**2+(-60*x**6*ln(3)+x**9-6*x**7+9*x**5-10*x**2+30)*ln(x)-10*x**4+
30*x**2)/((x**5-6*x**3+9*x)*ln(x)**3+(2*x**7-12*x**5+18*x**3)*ln(x)**2+(x**9-6*x**7+9*x**5)*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 \(4109\)

2.4.8.17 Sympy [F(-2)]

Exception generated. \[ \int \frac {-11 x+e^{\sqrt [4]{e}} \left (11 x+12 x^2\right )+\left (2 x+e^{\sqrt [4]{e}} \left (-2 x-2 x^2\right )\right ) \log \left (x+e^{\sqrt [4]{e}} \left (-x-x^2\right )\right )}{-25-5 x^2+e^{\sqrt [4]{e}} \left (25+25 x+5 x^2+5 x^3\right )+\left (10+x^2+e^{\sqrt [4]{e}} \left (-10-10 x-x^2-x^3\right )\right ) \log \left (x+e^{\sqrt [4]{e}} \left (-x-x^2\right )\right )+\left (-1+e^{\sqrt [4]{e}} (1+x)\right ) \log ^2\left (x+e^{\sqrt [4]{e}} \left (-x-x^2\right )\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((-2*x**2-2*x)*exp(exp(1/4))+2*x)*ln((-x**2-x)*exp(exp(1/4))+x)+(12*x**2+11*x)*exp(exp(1/4))-11*x)/
(((1+x)*exp(exp(1/4))-1)*ln((-x**2-x)*exp(exp(1/4))+x)**2+((-x**3-x**2-10*x-10)*exp(exp(1/4))+x**2+10)*ln((-x*
*2-x)*exp(exp(1/4))+x)+(5*x**3+5*x**2+25*x+25)*exp(exp(1/4))-5*x**2-25),x)

[Out]

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

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(4133\)

2.4.8.18 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} \left (15 x^3+12 x^4+3 x^5+e^x \left (-15-12 x-x^3\right )+\left (-15 x^2-12 x^3-2 x^4\right ) \log (15)+\left (9 x^4+e^x \left (-3 x-2 x^2\right )-7 x^3 \log (15)\right ) \log (x)+\left (-e^x x+3 x^3-2 x^2 \log (15)\right ) \log ^2(x)\right )}{2 x^3+4 x^2 \log (x)+2 x \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-exp(x)*x-2*x**2*ln(15)+3*x**3)*ln(x)**2+((-2*x**2-3*x)*exp(x)-7*x**3*ln(15)+9*x**4)*ln(x)+(-x**3-
12*x-15)*exp(x)+(-2*x**4-12*x**3-15*x**2)*ln(15)+3*x**5+12*x**4+15*x**3)*exp((3*x-15)/(x+ln(x)))/(2*x*ln(x)**2
+4*x**2*ln(x)+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 \(4134\)

2.4.8.19 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{-\frac {180 x^3}{(-1+x) \log (x)}} \left (-180 x^2+180 x^3+\left (540 x^2-360 x^3\right ) \log (x)\right )}{\left (1-2 x+x^2\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-360*x**3+540*x**2)*ln(x)+180*x**3-180*x**2)*exp(-180*x**3/(-1+x)/ln(x))/(x**2-2*x+1)/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 \(4177\)

2.4.8.20 Sympy [F(-2)]

Exception generated. \[ \int \frac {200 x+300 x^2+80 x^3+120 x^4+8 x^5+12 x^6+e^{\frac {10}{5+x^2}} \left (-50 x-20 x^3-2 x^5\right )+e^{\frac {5}{5+x^2}} \left (150 x-75 x^2+10 x^3-40 x^4+6 x^5-3 x^6\right )+e^x \left (-200 x-100 x^2-80 x^3-40 x^4-8 x^5-4 x^6+e^{\frac {5}{5+x^2}} \left (50 x+25 x^2+30 x^3+10 x^4+2 x^5+x^6\right )\right )}{800+420 x^2+100 x^3+72 x^4+40 x^5+4 x^6+4 x^7+e^{\frac {10}{5+x^2}} \left (50-5 x^2-8 x^4-x^6\right )+e^{\frac {5}{5+x^2}} \left (-400-85 x^2-25 x^3+14 x^4-10 x^5+3 x^6-x^7\right )+e^x \left (-100 x^2-40 x^4-4 x^6+e^{\frac {5}{5+x^2}} \left (25 x^2+10 x^4+x^6\right )\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((x**6+2*x**5+10*x**4+30*x**3+25*x**2+50*x)*exp(5/(x**2+5))-4*x**6-8*x**5-40*x**4-80*x**3-100*x**2-
200*x)*exp(x)+(-2*x**5-20*x**3-50*x)*exp(5/(x**2+5))**2+(-3*x**6+6*x**5-40*x**4+10*x**3-75*x**2+150*x)*exp(5/(
x**2+5))+12*x**6+8*x**5+120*x**4+80*x**3+300*x**2+200*x)/(((x**6+10*x**4+25*x**2)*exp(5/(x**2+5))-4*x**6-40*x*
*4-100*x**2)*exp(x)+(-x**6-8*x**4-5*x**2+50)*exp(5/(x**2+5))**2+(-x**7+3*x**6-10*x**5+14*x**4-25*x**3-85*x**2-
400)*exp(5/(x**2+5))+4*x**7+4*x**6+40*x**5+72*x**4+100*x**3+420*x**2+800),x)

[Out]

Exception raised: PolynomialError >> 1/(x**8 + 6*x**6 - 11*x**4 - 60*x**2 + 100) contains an element of the se
t of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(4191\)

2.4.8.21 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-128 x^3+256 x^4+\left (128 x^2-256 x^3\right ) \log (2)+\left (-128 x^2+256 x^3+\left (128 x-256 x^2\right ) \log (2)\right ) \log (x)\right ) \log \left (-12-x+x^2\right )+\left (768 x+64 x^2-64 x^3+\left (-768-832 x+64 x^3\right ) \log (2)+\left (-768 x-64 x^2+64 x^3\right ) \log (x)\right ) \log ^2\left (-12-x+x^2\right )}{-12 x^3-x^4+x^5+\left (-24 x^2-2 x^3+2 x^4\right ) \log (x)+\left (-12 x-x^2+x^3\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((64*x**3-64*x**2-768*x)*ln(x)+(64*x**3-832*x-768)*ln(2)-64*x**3+64*x**2+768*x)*ln(x**2-x-12)**2+((
(-256*x**2+128*x)*ln(2)+256*x**3-128*x**2)*ln(x)+(-256*x**3+128*x**2)*ln(2)+256*x**4-128*x**3)*ln(x**2-x-12))/
((x**3-x**2-12*x)*ln(x)**2+(2*x**4-2*x**3-24*x**2)*ln(x)+x**5-x**4-12*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 \(4204\)

2.4.8.22 Sympy [F(-2)]

Exception generated. \[ \int \frac {10 x-20 x \log (x)+\left (45+110 x+27 x^2\right ) \log ^2(x)}{-10 x^2 \log (x)+\left (45 x+55 x^2+9 x^3\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((27*x**2+110*x+45)*ln(x)**2-20*x*ln(x)+10*x)/((9*x**3+55*x**2+45*x)*ln(x)**2-10*x**2*ln(x)),x)

[Out]

Exception raised: PolynomialError >> 1/(81*x**5 + 990*x**4 + 3835*x**3 + 4950*x**2 + 2025*x) 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 \(4252\)

2.4.8.23 Sympy [F(-2)]

Exception generated. \[ \int \frac {-28+16 x+60000 x^4-10000 x^5+\left (24-12 x-30000 x^4+5000 x^5\right ) \log (x)+\left (-4+2 x+3750 x^4-625 x^5\right ) \log ^2(x)}{-16 x+10000 x^5+\left (12 x-5000 x^5\right ) \log (x)+\left (-2 x+625 x^5\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((-625*x**5+3750*x**4+2*x-4)*ln(x)**2+(5000*x**5-30000*x**4-12*x+24)*ln(x)-10000*x**5+60000*x**4+16*
x-28)/((625*x**5-2*x)*ln(x)**2+(-5000*x**5+12*x)*ln(x)+10000*x**5-16*x),x)

[Out]

Exception raised: PolynomialError >> 1/(390625*x**9 - 2500*x**5 + 4*x) contains an element of the set of gener
ators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(4295\)

2.4.8.24 Sympy [F(-2)]

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

[In]

integrate((4*x*exp(x)**2+(8*x**2-8*x-12)*exp(x)+12*x**2-24*x)/((1+x)*exp(x)**2+(x**2+3*x+3)*exp(x)+3*x**2),x)

[Out]

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

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(4316\)

2.4.8.25 Sympy [F(-2)]

Exception generated. \[ \int \frac {-5 x-x^2-6 x^3+10 x^4-4 x^5+(-10+2 x) \log (2 x)+\left (-2 x-12 x^2+20 x^3-8 x^4\right ) \log ^2(2 x)+\left (-6 x+10 x^2-4 x^3\right ) \log ^4(2 x)+\left (-x^2-3 x^3-x^5+\left (-x-6 x^2-2 x^4\right ) \log ^2(2 x)+\left (-3 x-x^3\right ) \log ^4(2 x)\right ) \log \left (\frac {1+3 x+x^3+\left (3+x^2\right ) \log ^2(2 x)}{x+\log ^2(2 x)}\right )}{x^2+3 x^3+x^5+\left (x+6 x^2+2 x^4\right ) \log ^2(2 x)+\left (3 x+x^3\right ) \log ^4(2 x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((-x**3-3*x)*ln(2*x)**4+(-2*x**4-6*x**2-x)*ln(2*x)**2-x**5-3*x**3-x**2)*ln(((x**2+3)*ln(2*x)**2+x**
3+3*x+1)/(ln(2*x)**2+x))+(-4*x**3+10*x**2-6*x)*ln(2*x)**4+(-8*x**4+20*x**3-12*x**2-2*x)*ln(2*x)**2+(2*x-10)*ln
(2*x)-4*x**5+10*x**4-6*x**3-x**2-5*x)/((x**3+3*x)*ln(2*x)**4+(2*x**4+6*x**2+x)*ln(2*x)**2+x**5+3*x**3+x**2),x)

[Out]

Exception raised: PolynomialError >> 1/(x**10 + 12*x**8 + 54*x**6 + 108*x**4 + 81*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 \(4389\)

2.4.8.26 Sympy [F(-2)]

Exception generated. \[ \int \frac {15+27 x+12 x^2-3 x^3-3 x^4+\left (27 x+24 x^2-9 x^3-12 x^4\right ) \log (x)+\left (25 x+40 x^2+16 x^3-10 x^4-8 x^5+x^7\right ) \log ^2(x)}{\left (-15 x-27 x^2-12 x^3+3 x^4+3 x^5\right ) \log (x)+\left (475 x+1735 x^2+2364 x^3+1234 x^4-222 x^5-512 x^6-141 x^7+39 x^8+20 x^9\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((x**7-8*x**5-10*x**4+16*x**3+40*x**2+25*x)*ln(x)**2+(-12*x**4-9*x**3+24*x**2+27*x)*ln(x)-3*x**4-3*x
**3+12*x**2+27*x+15)/((20*x**9+39*x**8-141*x**7-512*x**6-222*x**5+1234*x**4+2364*x**3+1735*x**2+475*x)*ln(x)**
2+(3*x**5+3*x**4-12*x**3-27*x**2-15*x)*ln(x)),x)

[Out]

Exception raised: PolynomialError >> 1/(400*x**9 + 760*x**8 - 2839*x**7 - 10080*x**6 - 4088*x**5 + 24550*x**4
+ 46176*x**3 + 33440*x**2 + 9025*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 \(4411\)

2.4.8.27 Sympy [F(-2)]

Exception generated. \[ \int \frac {12 x+16 x^2+\left (-14 x-8 x^2\right ) \log (x)+\left (3 x+10 x^2+8 x^3\right ) \log ^3(x)+(12+16 x) \log (3+4 x)}{\left (3 x+4 x^2\right ) \log ^3(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((16*x+12)*ln(3+4*x)+(8*x**3+10*x**2+3*x)*ln(x)**3+(-8*x**2-14*x)*ln(x)+16*x**2+12*x)/(4*x**2+3*x)/l
n(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 \(4469\)

2.4.8.28 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-x^3-x^4\right ) \log (x)+\left (5 x^2+6 x^3+x^4+\left (5 x^2+6 x^3+x^4\right ) \log (x)\right ) \log (5+x)+\left (-500-600 x-100 x^2\right ) \log ^2(5+x)+\left (\left (5 x^2+11 x^3+2 x^4\right ) \log (x) \log (5+x)+\left (500+1225 x+475 x^2+50 x^3\right ) \log ^2(5+x)\right ) \log \left (\frac {x^2 \log (x)+(100+25 x) \log (5+x)}{25 x \log (5+x)}\right )}{\left (5 x^2+x^3\right ) \log (x) \log (5+x)+\left (500+225 x+25 x^2\right ) \log ^2(5+x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((50*x**3+475*x**2+1225*x+500)*ln(5+x)**2+(2*x**4+11*x**3+5*x**2)*ln(x)*ln(5+x))*ln(1/25*((25*x+100
)*ln(5+x)+x**2*ln(x))/x/ln(5+x))+(-100*x**2-600*x-500)*ln(5+x)**2+((x**4+6*x**3+5*x**2)*ln(x)+x**4+6*x**3+5*x*
*2)*ln(5+x)+(-x**4-x**3)*ln(x))/((25*x**2+225*x+500)*ln(5+x)**2+(x**3+5*x**2)*ln(x)*ln(5+x)),x)

[Out]

Exception raised: PolynomialError >> 1/(75*x**3 + 975*x**2 + 4200*x + 6000) contains an element of the set of
generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(4480\)

2.4.8.29 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: GeneratorsError >> polynomial ring and it's ground domain share generators

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(4529\)

2.4.8.30 Sympy [F(-2)]

Exception generated. \[ \int \frac {2+2 x+2 \log (16)-2 x \log (x)+\left (26 x+2 x^2\right ) \log ^2(x)}{\left (-2 x-2 x^2-2 x \log (16)\right ) \log (x)+\left (x+26 x^2+x^3+x \log (16)\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((2*x**2+26*x)*ln(x)**2-2*x*ln(x)+8*ln(2)+2*x+2)/((4*x*ln(2)+x**3+26*x**2+x)*ln(x)**2+(-8*x*ln(2)-2*
x**2-2*x)*ln(x)),x)

[Out]

Exception raised: PolynomialError >> 1/(x**5 + 52*x**4 + 8*x**3*log(2) + 678*x**3 + 52*x**2 + 208*x**2*log(2)
+ x + 8*x*log(2) + 16*x*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 \(4541\)

2.4.8.31 Sympy [F(-2)]

Exception generated. \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((x**4*ln(x)**2+(-18*x**2*ln(2)-2*x**5-18*x**3-6*x**2)*ln(x)+81*ln(2)**2+(18*x**3+162*x)*ln(2)+x**6+
18*x**4+9*x**3+78*x**2+27*x)*exp(-3/(x**2*ln(x)-9*ln(2)-x**3-9*x))-x**4*ln(x)**3+(18*x**2*ln(2)+2*x**5+x**4+18
*x**3)*ln(x)**2+(-81*ln(2)**2+(-18*x**3-18*x**2-162*x)*ln(2)-x**6-2*x**5-18*x**4-18*x**3-81*x**2)*ln(x)+81*ln(
2)**2+(18*x**3+162*x)*ln(2)+x**6+18*x**4+81*x**2)/(x**6*ln(x)**2+(-18*x**4*ln(2)-2*x**7-18*x**5)*ln(x)+81*x**2
*ln(2)**2+(18*x**5+162*x**3)*ln(2)+x**8+18*x**6+81*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 \(4629\)

2.4.8.32 Sympy [F(-2)]

Exception generated. \[ \int \frac {5-25 x-108 x^2-180 x^3+36 x^2 \log (x)+\left (15-11 x-60 x^2+(-5+12 x) \log (x)\right ) \log (3+5 x-\log (x))+(-3-5 x+\log (x)) \log ^2(3+5 x-\log (x))}{360 x^2+168 x^3-720 x^4+\left (-120 x^2+144 x^3\right ) \log (x)+\left (60 x-44 x^2-240 x^3+\left (-20 x+48 x^2\right ) \log (x)\right ) \log (3+5 x-\log (x))+\left (-12 x-20 x^2+4 x \log (x)\right ) \log ^2(3+5 x-\log (x))} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((ln(x)-5*x-3)*ln(-ln(x)+5*x+3)**2+((12*x-5)*ln(x)-60*x**2-11*x+15)*ln(-ln(x)+5*x+3)+36*x**2*ln(x)-1
80*x**3-108*x**2-25*x+5)/((4*x*ln(x)-20*x**2-12*x)*ln(-ln(x)+5*x+3)**2+((48*x**2-20*x)*ln(x)-240*x**3-44*x**2+
60*x)*ln(-ln(x)+5*x+3)+(144*x**3-120*x**2)*ln(x)-720*x**4+168*x**3+360*x**2),x)

[Out]

Exception raised: PolynomialError >> 1/(-_t0*x + 5*x**2 + 3*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 \(4738\)

2.4.8.33 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{2 x} \left (15 x^2+20 x^3-4 x^4\right )+e^{2 x} \left (24 x+19 x^2-2 x^3\right ) \log (4-x)+e^{2 x} \left (2 x+2 x^2\right ) \log ^2(4-x)}{-2 x^2+e^{2 x} \left (12 x^3-2 x^4\right )+\left (-4 x+e^{2 x} \left (12 x^2-x^3\right )\right ) \log (4-x)+\left (-2+e^{2 x} x^2\right ) \log ^2(4-x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((2*x**2+2*x)*exp(x)**2*ln(-x+4)**2+(-2*x**3+19*x**2+24*x)*exp(x)**2*ln(-x+4)+(-4*x**4+20*x**3+15*x*
*2)*exp(x)**2)/((exp(x)**2*x**2-2)*ln(-x+4)**2+((-x**3+12*x**2)*exp(x)**2-4*x)*ln(-x+4)+(-2*x**4+12*x**3)*exp(
x)**2-2*x**2),x)

[Out]

Exception raised: PolynomialError >> 1/(x - 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 \(4777\)

2.4.8.34 Sympy [F(-2)]

Exception generated. \[ \int \frac {-e^{5 x} x^5+e^{10 x} \left (-3 x^4+x^5-x^6\right )+\left (e^{10 x} \left (15 x^4-4 x^5+3 x^6\right )+e^{5 x} \left (4 x^5+5 x^6\right )\right ) \log (x)}{\left (e^{5 x} x^6+e^{10 x} \left (3 x^5-x^6+x^7\right )\right ) \log (x)+\left (2 x^2+e^{5 x} \left (12 x-4 x^2+4 x^3\right )+e^{10 x} \left (18-12 x+14 x^2-4 x^3+2 x^4\right )\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((3*x**6-4*x**5+15*x**4)*exp(5*x)**2+(5*x**6+4*x**5)*exp(5*x))*ln(x)+(-x**6+x**5-3*x**4)*exp(5*x)**
2-x**5*exp(5*x))/(((2*x**4-4*x**3+14*x**2-12*x+18)*exp(5*x)**2+(4*x**3-4*x**2+12*x)*exp(5*x)+2*x**2)*ln(x)**2+
((x**7-x**6+3*x**5)*exp(5*x)**2+x**6*exp(5*x))*ln(x)),x)

[Out]

Exception raised: PolynomialError >> 1/(4*_t0**2*x**8 - 16*_t0**2*x**7 + 72*_t0**2*x**6 - 160*_t0**2*x**5 + 36
4*_t0**2*x**4 - 480*_t0**2*x**3 + 648*_t0**2*x**2 - 432*_t0**2*x + 324*_t0**2 + 4*_t0*x**11 - 12*_t0*x**10 + 4
8*_t0*x**9 - 76*_

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(4845\)

2.4.8.35 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{4 x} (-256+64 x)+(16-5 x) \log (2)+(-256+64 x) \log ^2(2)+e^{2 x} \left (-16+37 x-8 x^2+(512-128 x) \log (2)\right )+\left (e^{4 x} (-128+32 x)+(4-x) \log (2)+(-128+32 x) \log ^2(2)+e^{2 x} \left (-4+9 x-2 x^2+(256-64 x) \log (2)\right )\right ) \log \left (-\frac {4}{-4+x}\right )+\left (e^{4 x} (-16+4 x)+e^{2 x} (32-8 x) \log (2)+(-16+4 x) \log ^2(2)\right ) \log ^2\left (-\frac {4}{-4+x}\right )}{e^{4 x} \left (-256-192 x+64 x^2\right )+\left (16 x-4 x^2\right ) \log (2)+\left (-256-192 x+64 x^2\right ) \log ^2(2)+e^{2 x} \left (-16 x+4 x^2+\left (512+384 x-128 x^2\right ) \log (2)\right )+\left (e^{4 x} \left (-128-96 x+32 x^2\right )+\left (4 x-x^2\right ) \log (2)+\left (-128-96 x+32 x^2\right ) \log ^2(2)+e^{2 x} \left (-4 x+x^2+\left (256+192 x-64 x^2\right ) \log (2)\right )\right ) \log \left (-\frac {4}{-4+x}\right )+\left (e^{4 x} \left (-16-12 x+4 x^2\right )+e^{2 x} \left (32+24 x-8 x^2\right ) \log (2)+\left (-16-12 x+4 x^2\right ) \log ^2(2)\right ) \log ^2\left (-\frac {4}{-4+x}\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((4*x-16)*exp(x)**4+(-8*x+32)*ln(2)*exp(x)**2+(4*x-16)*ln(2)**2)*ln(-4/(x-4))**2+((32*x-128)*exp(x)
**4+((-64*x+256)*ln(2)-2*x**2+9*x-4)*exp(x)**2+(32*x-128)*ln(2)**2+(-x+4)*ln(2))*ln(-4/(x-4))+(64*x-256)*exp(x
)**4+((-128*x+512)*ln(2)-8*x**2+37*x-16)*exp(x)**2+(64*x-256)*ln(2)**2+(-5*x+16)*ln(2))/(((4*x**2-12*x-16)*exp
(x)**4+(-8*x**2+24*x+32)*ln(2)*exp(x)**2+(4*x**2-12*x-16)*ln(2)**2)*ln(-4/(x-4))**2+((32*x**2-96*x-128)*exp(x)
**4+((-64*x**2+192*x+256)*ln(2)+x**2-4*x)*exp(x)**2+(32*x**2-96*x-128)*ln(2)**2+(-x**2+4*x)*ln(2))*ln(-4/(x-4)
)+(64*x**2-192*x-256)*exp(x)**4+((-128*x**2+384*x+512)*ln(2)+4*x**2-16*x)*exp(x)**2+(64*x**2-192*x-256)*ln(2)*
*2+(-4*x**2+16*x)*ln(2)),x)

[Out]

Exception raised: PolynomialError >> 1/(4*_t0**2*x**3 - 8*_t0**2*x**2 - 28*_t0**2*x - 16*_t0**2 + 32*_t0*x**3
- 64*_t0*x**2 - 224*_t0*x - 128*_t0 + 64*x**3 - 128*x**2 - 448*x - 256) contains an element of the set of gene
rators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(4911\)

2.4.8.36 Sympy [F(-2)]

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

[In]

integrate((((x**2-x)*ln(1-x)**2+(2*x**2+6*x)*ln(1-x))*ln(x)+(-4*x**2+x+3)*ln(1-x)**2+(2*x**3+6*x**2)*ln(1-x))/
((x**2-x)*ln(x)**2+(2*x**3-2*x**2)*ln(x)+x**4-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 \(4944\)

2.4.8.37 Sympy [F(-2)]

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

[In]

integrate(((-exp(x)*exp(exp(3/exp(x)))-exp(x)*x)*ln(exp(exp(3/exp(x)))+x)+(-3*x*ln(x)*exp(3/exp(x))+x*exp(x)*l
n(x)**2)*exp(exp(3/exp(x)))+x**2*exp(x)*ln(x)**2+x*exp(x)*ln(x))/(x*exp(x)*ln(x)**2*exp(exp(3/exp(x)))+x**2*ex
p(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 \(5357\)

2.4.8.38 Sympy [F(-2)]

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

[In]

integrate(((2*x*ln(x)+2*x-6)*ln(ln(1/3*ln(x)*(-3+x)+8/3))**3+((-x**2+3*x)*ln(x)-8*x)*ln(1/3*ln(x)*(-3+x)+8/3)*
ln(ln(1/3*ln(x)*(-3+x)+8/3))**2+((-2*x**2+2*x)*ln(x)-2*x**2+8*x-6)*ln(ln(1/3*ln(x)*(-3+x)+8/3))+((x**3-4*x**2+
3*x)*ln(x)+8*x**2-8*x)*ln(1/3*ln(x)*(-3+x)+8/3))/((2*x**2-6*x)*ln(x)+16*x)/ln(1/3*ln(x)*(-3+x)+8/3),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 \(5388\)

2.4.8.39 Sympy [F(-2)]

Exception generated. \[ \int \frac {-2 x^3+x^5+\left (2 x^3-x^5\right ) \log \left (\frac {x}{3}\right )+\left (320-240 x-160 x^2+62 x^3-20 x^4+29 x^5+10 x^6\right ) \log ^2\left (\frac {x}{3}\right )+\left (-2 x^5 \log \left (\frac {x}{3}\right )+\left (160 x^2-240 x^3+10 x^4+58 x^5+10 x^6\right ) \log ^2\left (\frac {x}{3}\right )\right ) \log \left (\frac {x^3+\left (-80+120 x-5 x^2-29 x^3-5 x^4\right ) \log \left (\frac {x}{3}\right )}{x^2 \log \left (\frac {x}{3}\right )}\right )}{-x^4 \log \left (\frac {x}{3}\right )+\left (80 x-120 x^2+5 x^3+29 x^4+5 x^5\right ) \log ^2\left (\frac {x}{3}\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((10*x**6+58*x**5+10*x**4-240*x**3+160*x**2)*ln(1/3*x)**2-2*x**5*ln(1/3*x))*ln(((-5*x**4-29*x**3-5*
x**2+120*x-80)*ln(1/3*x)+x**3)/x**2/ln(1/3*x))+(10*x**6+29*x**5-20*x**4+62*x**3-160*x**2-240*x+320)*ln(1/3*x)*
*2+(-x**5+2*x**3)*ln(1/3*x)+x**5-2*x**3)/((5*x**5+29*x**4+5*x**3-120*x**2+80*x)*ln(1/3*x)**2-x**4*ln(1/3*x)),x
)

[Out]

Exception raised: PolynomialError >> 1/(25*x**9 + 290*x**8 + 891*x**7 - 910*x**6 - 6135*x**5 + 3440*x**4 + 152
00*x**3 - 19200*x**2 + 6400*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 \(5392\)

2.4.8.40 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{-\frac {1250}{x \log (2 x)}} (-2500-2500 \log (2 x))+e^{-\frac {2500}{x \log (2 x)}} (2500+2500 \log (2 x))}{x^2 \log ^2(2 x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((2500*ln(2*x)+2500)*exp(-1250/x/ln(2*x))**2+(-2500*ln(2*x)-2500)*exp(-1250/x/ln(2*x)))/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 \(5539\)

2.4.8.41 Sympy [F(-2)]

Exception generated. \[ \int \frac {50-9 x+\left (-3 x+2 x^2\right ) \log \left (\frac {5}{x}\right )+\left (-7 x-2 x^2\right ) \log ^2\left (\frac {5}{x}\right )+\left (-x+2 x^2\right ) \log ^3\left (\frac {5}{x}\right )}{-27 x+x^2+\left (31 x+7 x^2\right ) \log \left (\frac {5}{x}\right )+\left (-6 x-7 x^2-x^3\right ) \log ^2\left (\frac {5}{x}\right )+\left (2 x-x^2+x^3\right ) \log ^3\left (\frac {5}{x}\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((2*x**2-x)*ln(5/x)**3+(-2*x**2-7*x)*ln(5/x)**2+(2*x**2-3*x)*ln(5/x)-9*x+50)/((x**3-x**2+2*x)*ln(5/x
)**3+(-x**3-7*x**2-6*x)*ln(5/x)**2+(7*x**2+31*x)*ln(5/x)+x**2-27*x),x)

[Out]

Exception raised: PolynomialError >> 1/(x**10 - 4*x**9 + 14*x**8 - 28*x**7 + 49*x**6 - 56*x**5 + 56*x**4 - 32*
x**3 + 16*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 \(5561\)

2.4.8.42 Sympy [F(-2)]

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

[In]

integrate(((-10*x*ln(5)**2-5*ln(5))*ln(x)-5*x*ln(5)**2-5*ln(5))*exp(5*ln(5)/(x**2*ln(5)+x)/ln(x))*exp(exp(5*ln
(5)/(x**2*ln(5)+x)/ln(x))-4)/(x**4*ln(5)**2+2*x**3*ln(5)+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 \(5630\)

2.4.8.43 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-30-12 x^2-6 x^3+6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\log \left (\frac {2}{x}\right ) \left (\left (60-6 x^3+12 x^4\right ) \log \left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\left (30+12 x^2+6 x^3-6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )\right )}{\left (-5 x^3-2 x^5-x^6+x^7\right ) \log ^3\left (\frac {2}{x}\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-6*x**4+6*x**3+12*x**2+30)*ln((-x**4+x**3+2*x**2+5)/x**2)**2+(12*x**4-6*x**3+60)*ln((-x**4+x**3+2
*x**2+5)/x**2))*ln(2/x)+(6*x**4-6*x**3-12*x**2-30)*ln((-x**4+x**3+2*x**2+5)/x**2)**2)/(x**7-x**6-2*x**5-5*x**3
)/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 \(5647\)

2.4.8.44 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{3} (-4-15 x)} \left (-75 \log ^2(x)+e^{\frac {2}{3} \left (-1+e^{\frac {x}{\log (x)}}\right )} \left (-75 \log ^2(x)+e^{\frac {x}{\log (x)}} (-10+10 \log (x))\right )\right )}{\log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((10*ln(x)-10)*exp(x/ln(x))-75*ln(x)**2)*exp(1/3*exp(x/ln(x))-1/3)**2-75*ln(x)**2)/exp(5*x+4/3)/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 \(5655\)

2.4.8.45 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-250 x^2+50 x^3\right ) \log (x) \log (3+x)+\left (375 x+50 x^2-25 x^3+\left (-750 x-250 x^2\right ) \log (x)\right ) \log ^2(3+x)}{\left (-54000+14400 x+4320 x^2-1728 x^3+144 x^4\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-250*x**2-750*x)*ln(x)-25*x**3+50*x**2+375*x)*ln(3+x)**2+(50*x**3-250*x**2)*ln(x)*ln(3+x))/(144*x
**4-1728*x**3+4320*x**2+14400*x-54000)/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 \(5656\)

2.4.8.46 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {x}{4 \log (x)}} \left (-e^{\frac {625-1000 x+100 x^2+440 x^3-71 x^4-88 x^5+4 x^6+8 x^7+x^8}{x^4}} x^5-x^6-x^7+\left (e^{\frac {625-1000 x+100 x^2+440 x^3-71 x^4-88 x^5+4 x^6+8 x^7+x^8}{x^4}} x^5+x^6+x^7\right ) \log (x)+\left (4 x^5+8 x^6+e^{\frac {625-1000 x+100 x^2+440 x^3-71 x^4-88 x^5+4 x^6+8 x^7+x^8}{x^4}} \left (-10000+12000 x-800 x^2-1760 x^3-352 x^5+32 x^6+96 x^7+16 x^8\right )\right ) \log ^2(x)\right )}{4 x^5 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/4*(((16*x**8+96*x**7+32*x**6-352*x**5-1760*x**3-800*x**2+12000*x-10000)*exp((x**8+8*x**7+4*x**6-88
*x**5-71*x**4+440*x**3+100*x**2-1000*x+625)/x**4)+8*x**6+4*x**5)*ln(x)**2+(x**5*exp((x**8+8*x**7+4*x**6-88*x**
5-71*x**4+440*x**3+100*x**2-1000*x+625)/x**4)+x**7+x**6)*ln(x)-x**5*exp((x**8+8*x**7+4*x**6-88*x**5-71*x**4+44
0*x**3+100*x**2-1000*x+625)/x**4)-x**7-x**6)*exp(1/4*x/ln(x))/x**5/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 \(5688\)

2.4.8.47 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (3+12 x^2\right ) \log ^2(x)+e^{\frac {4+4 x \log (x)}{x \log (x)}} \left (-80 x-80 x \log (x)+60 x^2 \log ^2(x)\right )+e^{\frac {2 (4+4 x \log (x))}{x \log (x)}} \left (-200 x-200 x \log (x)+75 x^2 \log ^2(x)\right )}{\log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((75*x**2*ln(x)**2-200*x*ln(x)-200*x)*exp((4*x*ln(x)+4)/x/ln(x))**2+(60*x**2*ln(x)**2-80*x*ln(x)-80*
x)*exp((4*x*ln(x)+4)/x/ln(x))+(12*x**2+3)*ln(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 \(5709\)

2.4.8.48 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {x^3}{4+2 x+\log (2+x)}} \left (16+16 x+28 x^2+19 x^3+4 x^4+\left (8+4 x+6 x^2+3 x^3\right ) \log (2+x)+\log ^2(2+x)\right )}{16+16 x+4 x^2+(8+4 x) \log (2+x)+\log ^2(2+x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((ln(2+x)**2+(3*x**3+6*x**2+4*x+8)*ln(2+x)+4*x**4+19*x**3+28*x**2+16*x+16)*exp(x**3/(ln(2+x)+2*x+4))/
(ln(2+x)**2+(4*x+8)*ln(2+x)+4*x**2+16*x+16),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 \(5746\)

2.4.8.49 Sympy [F(-2)]

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

[In]

integrate(((2*exp(-ln(x)+x**2-3)+8)*ln(ln(5)*exp(-ln(x)+x**2-3)+4*ln(5))**2+(((-8*x**2-4*x+4)*ln(x)+4*x)*exp(-
ln(x)+x**2-3)-16*x*ln(x)+16*x)*ln(ln(5)*exp(-ln(x)+x**2-3)+4*ln(5))+((-8*x**3-4*x**2+6*x)*ln(x)+2*x**2-2*x)*ex
p(-ln(x)+x**2-3)+(-16*x**2+8*x)*ln(x)+8*x**2-8*x)/(x*ln(x)**2*exp(-ln(x)+x**2-3)+4*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 \(5942\)

2.4.8.50 Sympy [F(-2)]

Exception generated. \[ \int \frac {e \left (-30 x^4-5 x^5\right )+\left (x^3+30 x^5+5 x^6\right ) \log ^2(x)+\left (e \left (60 x^2+10 x^3\right )+\left (-x-60 x^3-10 x^4\right ) \log ^2(x)\right ) \log (2 x)+\left (e (-30-5 x)+\left (30 x+5 x^2\right ) \log ^2(x)\right ) \log ^2(2 x)+\left (6+x-12 x^2-2 x^3\right ) \log ^2(x) \log (6+x)}{\left (30 x^5+5 x^6\right ) \log ^2(x)+\left (-60 x^3-10 x^4\right ) \log ^2(x) \log (2 x)+\left (30 x+5 x^2\right ) \log ^2(x) \log ^2(2 x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((5*x**2+30*x)*ln(x)**2+(-5*x-30)*exp(1))*ln(2*x)**2+((-10*x**4-60*x**3-x)*ln(x)**2+(10*x**3+60*x**
2)*exp(1))*ln(2*x)+(-2*x**3-12*x**2+x+6)*ln(x)**2*ln(6+x)+(5*x**6+30*x**5+x**3)*ln(x)**2+(-5*x**5-30*x**4)*exp
(1))/((5*x**2+30*x)*ln(x)**2*ln(2*x)**2+(-10*x**4-60*x**3)*ln(x)**2*ln(2*x)+(5*x**6+30*x**5)*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 \(5964\)

2.4.8.51 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (\frac {16}{e^{25}}+x\right ) \log \left (\frac {16}{e^{25}}+x\right )+\left (\frac {16 x}{e^{25}}+x^2\right ) \log (x) \log ^2\left (\frac {16}{e^{25}}+x\right )+\left (-x \log (x)+\left (-\frac {16}{e^{25}}-x\right ) \log (x) \log \left (\frac {16}{e^{25}}+x\right )\right ) \log (\log (x))}{\left (\frac {16 x^2}{e^{25}}+x^3\right ) \log (x) \log ^2\left (\frac {16}{e^{25}}+x\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-exp(4*ln(2)-25)-x)*ln(x)*ln(exp(4*ln(2)-25)+x)-x*ln(x))*ln(ln(x))+(x*exp(4*ln(2)-25)+x**2)*ln(x)
*ln(exp(4*ln(2)-25)+x)**2+(exp(4*ln(2)-25)+x)*ln(exp(4*ln(2)-25)+x))/(x**2*exp(4*ln(2)-25)+x**3)/ln(x)/ln(exp(
4*ln(2)-25)+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 \(6025\)

2.4.8.52 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (8 x^2-50 x^3-2 x^4-16 x^5+100 x^6+4 x^7\right ) \log ^2\left (\frac {1}{x}\right )+\left (8-50 x-2 x^2\right ) \log \left (4-25 x-x^2\right )+\log \left (\frac {1}{x}\right ) \left (-50 x-4 x^2+\left (-8+50 x+2 x^2\right ) \log \left (4-25 x-x^2\right )\right )}{\left (-4 x^2+25 x^3+x^4\right ) \log ^2\left (\frac {1}{x}\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((4*x**7+100*x**6-16*x**5-2*x**4-50*x**3+8*x**2)*ln(1/x)**2+((2*x**2+50*x-8)*ln(-x**2-25*x+4)-4*x**2
-50*x)*ln(1/x)+(-2*x**2-50*x+8)*ln(-x**2-25*x+4))/(x**4+25*x**3-4*x**2)/ln(1/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 \(6249\)

2.4.8.53 Sympy [F(-2)]

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

[In]

integrate(((3*ln(x)*ln(ln(x))-3)*exp(3/2*x/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 \(6406\)

2.4.8.54 Sympy [F(-2)]

Exception generated. \[ \int \frac {2 x \log (x)+\left (-216 x^3+216 x^4-72 x^5+8 x^6\right ) \log ^3(x)+(6-2 x+(6-4 x) \log (x)) \log \left (9-6 x+x^2\right )}{\left (-27 x^3+27 x^4-9 x^5+x^6\right ) \log ^3(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((6-4*x)*ln(x)+6-2*x)*ln(x**2-6*x+9)+(8*x**6-72*x**5+216*x**4-216*x**3)*ln(x)**3+2*x*ln(x))/(x**6-9
*x**5+27*x**4-27*x**3)/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 \(6477\)

2.4.8.55 Sympy [F(-2)]

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

[In]

integrate((((8*x**2-8*x)*ln(x)-24*x**2+24*x)*ln(ln(x)-3)*ln(-x**2*ln(3)/(-2+2*x)/ln(ln(x)-3))**4+(((16*x**2-32
*x)*ln(x)-48*x**2+96*x)*ln(ln(x)-3)-16*x**2+16*x)*ln(-x**2*ln(3)/(-2+2*x)/ln(ln(x)-3))**3)/((-1+x)*ln(x)-3*x+3
)/ln(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 \(6591\)

2.4.8.56 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{7-e^{-\frac {x}{-x+\log (10+5 x)}}} \left (2 x^2+x^3+\left (-4 x-2 x^2\right ) \log (10+5 x)+(2+x) \log ^2(10+5 x)+e^{-\frac {x}{-x+\log (10+5 x)}} \left (-x^2+\left (2 x+x^2\right ) \log (10+5 x)\right )\right )}{2 x^2+x^3+\left (-4 x-2 x^2\right ) \log (10+5 x)+(2+x) \log ^2(10+5 x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((x**2+2*x)*ln(5*x+10)-x**2)*exp(-x/(ln(5*x+10)-x))+(2+x)*ln(5*x+10)**2+(-2*x**2-4*x)*ln(5*x+10)+x*
*3+2*x**2)/((2+x)*ln(5*x+10)**2+(-2*x**2-4*x)*ln(5*x+10)+x**3+2*x**2)/exp(exp(-x/(ln(5*x+10)-x))-7),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 \(6618\)

2.4.8.57 Sympy [F(-2)]

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

[In]

integrate((((ln(5)+2*x-4)*ln(-ln(5)+4-2*x)+2*x)*ln(x)+(3*ln(5)+6*x-12)*ln(-ln(5)+4-2*x)-x**2+8*x)*exp(1/2*(-2*
ln(x)+10*x*ln(-ln(5)+4-2*x)-8+x)/x/ln(-ln(5)+4-2*x))/(x**2*ln(5)+2*x**3-4*x**2)/ln(-ln(5)+4-2*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 \(6634\)

2.4.8.58 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-6-60 x+24 x^2+e^x \left (-12 x-12 x^2\right )\right ) \log ^2(x)+\left (\left (2+20 x-8 x^2+e^x \left (4 x+4 x^2\right )\right ) \log (x)+\left (\left (60 x+12 e^x x-12 x^2\right ) \log (x)+6 \log ^2(x)\right ) \log \left (10 x+2 e^x x-2 x^2+\log (x)\right )\right ) \log \left (\log \left (10 x+2 e^x x-2 x^2+\log (x)\right )\right )+\left (-20 x-4 e^x x+4 x^2-2 \log (x)\right ) \log \left (10 x+2 e^x x-2 x^2+\log (x)\right ) \log ^2\left (\log \left (10 x+2 e^x x-2 x^2+\log (x)\right )\right )}{\left (\left (10 x^2+2 e^x x^2-2 x^3\right ) \log ^3(x)+x \log ^4(x)\right ) \log \left (10 x+2 e^x x-2 x^2+\log (x)\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-2*ln(x)-4*exp(x)*x+4*x**2-20*x)*ln(ln(x)+2*exp(x)*x-2*x**2+10*x)*ln(ln(ln(x)+2*exp(x)*x-2*x**2+10
*x))**2+((6*ln(x)**2+(12*exp(x)*x-12*x**2+60*x)*ln(x))*ln(ln(x)+2*exp(x)*x-2*x**2+10*x)+((4*x**2+4*x)*exp(x)-8
*x**2+20*x+2)*ln(x))*ln(ln(ln(x)+2*exp(x)*x-2*x**2+10*x))+((-12*x**2-12*x)*exp(x)+24*x**2-60*x-6)*ln(x)**2)/(x
*ln(x)**4+(2*exp(x)*x**2-2*x**3+10*x**2)*ln(x)**3)/ln(ln(x)+2*exp(x)*x-2*x**2+10*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 \(6684\)

2.4.8.59 Sympy [F(-2)]

Exception generated. \[ \int \frac {2496 x \log (1-2 x)+(240-480 x) \log ^2(1-2 x)+\left (-768 x \log (1-2 x)+(-192+384 x) \log ^2(1-2 x)\right ) \log \left (x^2\right )}{-169 x^2+338 x^3+\left (104 x^2-208 x^3\right ) \log \left (x^2\right )+\left (-16 x^2+32 x^3\right ) \log ^2\left (x^2\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((384*x-192)*ln(1-2*x)**2-768*x*ln(1-2*x))*ln(x**2)+(-480*x+240)*ln(1-2*x)**2+2496*x*ln(1-2*x))/((3
2*x**3-16*x**2)*ln(x**2)**2+(-208*x**3+104*x**2)*ln(x**2)+338*x**3-169*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 \(6685\)

2.4.8.60 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: PolynomialError >> 1/(_t0*x + 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 \(6771\)

2.4.8.61 Sympy [F(-2)]

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

[In]

integrate((((x**2-3*x)*ln(-x+3)-x*exp(3)-x**2)*exp(-ln(ln(-x+3))+exp(exp(5)))*exp((exp(3)+x)*exp(-ln(ln(-x+3))
+exp(exp(5))))+(-3+x)*ln(-x+3))/(x**2-3*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 \(6772\)

2.4.8.62 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^5 \left (-10-2 x+10 x^2+2 x^3\right )+e^{10} \left (10-8 x-2 x^2\right ) \log ^2(5+x)+\log \left (\frac {3 e^x}{x}\right ) \left (e^5 \left (-10 x-2 x^2\right )+4 e^{10} x \log (5+x)\right )}{5 x+11 x^2+7 x^3+x^4+e^5 \left (-10 x-12 x^2-2 x^3\right ) \log ^2(5+x)+e^{10} \left (5 x+x^2\right ) \log ^4(5+x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((4*x*exp(5)**2*ln(5+x)+(-2*x**2-10*x)*exp(5))*ln(exp(ln(3)+x)/x)+(-2*x**2-8*x+10)*exp(5)**2*ln(5+x)
**2+(2*x**3+10*x**2-2*x-10)*exp(5))/((x**2+5*x)*exp(5)**2*ln(5+x)**4+(-2*x**3-12*x**2-10*x)*exp(5)*ln(5+x)**2+
x**4+7*x**3+11*x**2+5*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 \(6869\)

2.4.8.63 Sympy [F(-2)]

Exception generated. \[ \int \frac {15\ 2^{1-2 e^{e^2}} e^{e^2} \left (6-2 e^6-3 x\right )^{2 e^{e^2}}}{-6+2 e^6+3 x} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(30*exp(exp(2))*exp(exp(exp(2))*ln(-exp(6)-3/2*x+3))**2/(2*exp(6)+3*x-6),x)

[Out]

Exception raised: TypeError >> Invalid NaN comparison

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(6875\)

2.4.8.64 Sympy [F(-2)]

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

[In]

integrate((((x**4+3*x**3-2*x**2+6*x-8)*ln(4+x)**2+(-x**4-4*x**3-2*x**2-8*x)*ln(4+x))*ln(((2-2*x)*ln(4+x)+2*x)/
ln(4+x))+(x**4-18*x**2-8*x)*ln(4+x)**2+(-x**4+18*x**2+8*x)*ln(4+x)+x**4-4*x**3-2*x**2)/((x**4+3*x**3-4*x**2)*l
n(4+x)**2+(-x**4-4*x**3)*ln(4+x)),x)

[Out]

Exception raised: PolynomialError >> 1/(x**3 + 2*x**2 - 7*x + 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 \(6957\)

2.4.8.65 Sympy [F(-2)]

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

[In]

integrate((-10*ln(2)*ln(x)**2+3*x**2*ln(x)-x**2)/((10*x*ln(2)-5)*ln(x)**2-x**3*ln(x)),x)

[Out]

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

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(7148\)

2.4.8.66 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-20 x+e^{3+2 x} \left (16 x+16 x^2+4 x^3\right )\right ) \log (x) \log \left (\frac {-5 x+e^{3+2 x} (2+x)}{2+x}\right )+\left (20 x+10 x^2+e^{3+2 x} \left (-8-8 x-2 x^2\right )+\left (-10 x-5 x^2+e^{3+2 x} \left (4+4 x+x^2\right )\right ) \log (x)\right ) \log ^2\left (\frac {-5 x+e^{3+2 x} (2+x)}{2+x}\right )}{\left (-10 x-5 x^2+e^{3+2 x} \left (4+4 x+x^2\right )\right ) \log ^3(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((((x**2+4*x+4)*exp(3+2*x)-5*x**2-10*x)*ln(x)+(-2*x**2-8*x-8)*exp(3+2*x)+10*x**2+20*x)*ln(((2+x)*exp
(3+2*x)-5*x)/(2+x))**2+((4*x**3+16*x**2+16*x)*exp(3+2*x)-20*x)*ln(x)*ln(((2+x)*exp(3+2*x)-5*x)/(2+x)))/((x**2+
4*x+4)*exp(3+2*x)-5*x**2-10*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 \(7164\)

2.4.8.67 Sympy [F(-2)]

Exception generated. \[ \int \frac {9 x+12 x^2+18 x^3-6 x^4-6 x^2 \log (x)+\left (24 x^2-12 x^4-12 x^2 \log (x)+\left (-36 x+18 x^3+18 x \log (x)\right ) \log \left (-2+x^2+\log (x)\right )\right ) \log \left (-2 x+3 \log \left (-2+x^2+\log (x)\right )\right )}{4 x-2 x^3-2 x \log (x)+\left (-6+3 x^2+3 \log (x)\right ) \log \left (-2+x^2+\log (x)\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((18*x*ln(x)+18*x**3-36*x)*ln(ln(x)+x**2-2)-12*x**2*ln(x)-12*x**4+24*x**2)*ln(3*ln(ln(x)+x**2-2)-2*
x)-6*x**2*ln(x)-6*x**4+18*x**3+12*x**2+9*x)/((3*ln(x)+3*x**2-6)*ln(ln(x)+x**2-2)-2*x*ln(x)-2*x**3+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 \(7265\)

2.4.8.68 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {20+5 x+x \log (x)+5 \log ^2(x)}{4+x+\log ^2(x)}} \left (-128-56 x-6 x^2+8 x \log (x)+(-64-18 x) \log ^2(x)+2 x \log ^3(x)-8 \log ^4(x)\right )}{16 x^5+8 x^6+x^7+\left (8 x^5+2 x^6\right ) \log ^2(x)+x^5 \log ^4(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((-8*ln(x)**4+2*x*ln(x)**3+(-18*x-64)*ln(x)**2+8*x*ln(x)-6*x**2-56*x-128)*exp((5*ln(x)**2+x*ln(x)+20+
5*x)/(ln(x)**2+4+x))/(x**5*ln(x)**4+(2*x**6+8*x**5)*ln(x)**2+x**7+8*x**6+16*x**5),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 \(7313\)

2.4.8.69 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (\left (-320-16 x-1280 x^2-64 x^3\right ) \log \left (\frac {20+x}{4}\right )+\left (1280 x^2+64 x^3\right ) \log \left (x^2\right ) \log \left (\frac {20+x}{4}\right )\right ) \log \left (\frac {16+64 x^2}{\log \left (x^2\right )}\right )+\left (-4 x-16 x^3\right ) \log \left (x^2\right ) \log ^2\left (\frac {16+64 x^2}{\log \left (x^2\right )}\right )}{\left (20 x+x^2+80 x^3+4 x^4\right ) \log \left (x^2\right ) \log ^2\left (\frac {20+x}{4}\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-16*x**3-4*x)*ln(x**2)*ln((64*x**2+16)/ln(x**2))**2+((64*x**3+1280*x**2)*ln(5+1/4*x)*ln(x**2)+(-64
*x**3-1280*x**2-16*x-320)*ln(5+1/4*x))*ln((64*x**2+16)/ln(x**2)))/(4*x**4+80*x**3+x**2+20*x)/ln(5+1/4*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 \(7350\)

2.4.8.70 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {12}{(-15+20 x) \log \left (x \log ^2(2)\right )}} \left (72-96 x-96 x \log \left (x \log ^2(2)\right )\right )}{\left (45 x-120 x^2+80 x^3\right ) \log ^2\left (x \log ^2(2)\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((-96*x*ln(x*ln(2)**2)-96*x+72)*exp(12/(20*x-15)/ln(x*ln(2)**2))/(80*x**3-120*x**2+45*x)/ln(x*ln(2)**
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 \(7422\)

2.4.8.71 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-8 x+12 x^2+72 x^3+32 x^4\right ) \log (x)+\left (64-216 x-148 x^2-44 x^3-16 x^4+\left (224 x+284 x^2+60 x^3+32 x^4\right ) \log (x)\right ) \log \left (8+x+x^2\right )}{\left (8 x+x^2+x^3\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((32*x**4+60*x**3+284*x**2+224*x)*ln(x)-16*x**4-44*x**3-148*x**2-216*x+64)*ln(x**2+x+8)+(32*x**4+72
*x**3+12*x**2-8*x)*ln(x))/(x**3+x**2+8*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 \(7508\)

2.4.8.72 Sympy [F(-2)]

Exception generated. \[ \int \frac {2358774 e^{2 x}+2358774 e^x x^2}{5 x^2+e^{2 x} (5+x)+e^x \left (10 x+x^2\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((2358774*exp(x)**2+2358774*exp(x)*x**2)/((5+x)*exp(x)**2+(x**2+10*x)*exp(x)+5*x**2),x)

[Out]

Exception raised: PolynomialError >> 1/(x**2 + 10*x + 25) contains an element of the set of generators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(7569\)

2.4.8.73 Sympy [F(-2)]

Exception generated. \[ \int \frac {16 x^2+\left (160 x+32 x^2\right ) \log (2)+e^x \left (-8 x^2+\left (-40 x-36 x^2\right ) \log (2)+(40 x+(100+180 x) \log (2)) \log (5)\right )+e^{2 x} \left (x^2+2 x^2 \log (2)+(-10 x-20 x \log (2)) \log (5)+(25+50 \log (2)) \log ^2(5)\right )}{16 x^3+\left (80 x^2+32 x^3\right ) \log (2)+e^x \left (-8 x^3+\left (-20 x^2-16 x^3\right ) \log (2)+\left (40 x^2+\left (100 x+80 x^2\right ) \log (2)\right ) \log (5)\right )+e^{2 x} \left (x^3+2 x^3 \log (2)+\left (-10 x^2-20 x^2 \log (2)\right ) \log (5)+(25 x+50 x \log (2)) \log ^2(5)\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((50*ln(2)+25)*ln(5)**2+(-20*x*ln(2)-10*x)*ln(5)+2*x**2*ln(2)+x**2)*exp(x)**2+(((180*x+100)*ln(2)+4
0*x)*ln(5)+(-36*x**2-40*x)*ln(2)-8*x**2)*exp(x)+(32*x**2+160*x)*ln(2)+16*x**2)/(((50*x*ln(2)+25*x)*ln(5)**2+(-
20*x**2*ln(2)-10*x**2)*ln(5)+2*x**3*ln(2)+x**3)*exp(x)**2+(((80*x**2+100*x)*ln(2)+40*x**2)*ln(5)+(-16*x**3-20*
x**2)*ln(2)-8*x**3)*exp(x)+(32*x**3+80*x**2)*ln(2)+16*x**3),x)

[Out]

Exception raised: PolynomialError >> 1/(x**2 + 2*x**2*log(2) - 20*x*log(2)*log(5) - 10*x*log(5) + 25*log(5)**2
+ 50*log(2)*log(5)**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 \(7573\)

2.4.8.74 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^4 \left (4-4 x+9 x^2-9 x^3\right )+\left (36 x^3-36 x^2 \log (x)\right ) \log \left (48+108 x^2\right )+\left (4-4 x+9 x^2-9 x^3\right ) \log ^2\left (48+108 x^2\right )}{e^8 \left (4 x+9 x^3\right )+e^4 \left (-4 x^2-9 x^4\right )+e^4 \left (4 x+9 x^3\right ) \log (x)+\left (-4 x^2-9 x^4+e^4 \left (8 x+18 x^3\right )+\left (4 x+9 x^3\right ) \log (x)\right ) \log ^2\left (48+108 x^2\right )+\left (4 x+9 x^3\right ) \log ^4\left (48+108 x^2\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((-9*x**3+9*x**2-4*x+4)*ln(108*x**2+48)**2+(-36*x**2*ln(x)+36*x**3)*ln(108*x**2+48)+(-9*x**3+9*x**2-
4*x+4)*exp(4))/((9*x**3+4*x)*ln(108*x**2+48)**4+((9*x**3+4*x)*ln(x)+(18*x**3+8*x)*exp(4)-9*x**4-4*x**2)*ln(108
*x**2+48)**2+(9*x**3+4*x)*exp(4)*ln(x)+(9*x**3+4*x)*exp(4)**2+(-9*x**4-4*x**2)*exp(4)),x)

[Out]

Exception raised: PolynomialError >> 1/(81*x**6 + 72*x**4 + 16*x**2) contains an element of the set of generat
ors.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(7592\)

2.4.8.75 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: CoercionFailed >> Cannot convert x - 4*exp(2*5**exp(-5)*exp(4)) of type <class 'sympy.core.a
dd.Add'> to QQ[x,exp(5**exp(-5)*exp(4))]

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(7616\)

2.4.8.76 Sympy [F(-2)]

Exception generated. \[ \int \frac {-9+e^{e^x} \left (-3-3 e^x x-6 \log (5)\right )+e^{2 e^x} \left (-\log (5)-\log ^2(5)\right )}{-90+45 x+e^{e^x} (15 x+(-60+30 x) \log (5))+e^{2 e^x} \left (5 x \log (5)+(-10+5 x) \log ^2(5)\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((-ln(5)**2-ln(5))*exp(exp(x))**2+(-3*exp(x)*x-6*ln(5)-3)*exp(exp(x))-9)/(((5*x-10)*ln(5)**2+5*x*ln(
5))*exp(exp(x))**2+((30*x-60)*ln(5)+15*x)*exp(exp(x))+45*x-90),x)

[Out]

Exception raised: PolynomialError >> 1/(5*x**2*log(5) + 5*x**2*log(5)**3 + 10*x**2*log(5)**2 - 20*x*log(5)**3
- 20*x*log(5)**2 + 20*log(5)**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 \(7679\)

2.4.8.77 Sympy [F(-2)]

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

[In]

integrate((3*x**2*ln(x)**2+(-x**2-1)*ln(x)+2)*exp((-x**3*ln(x)+x)/ln(x)**2)/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 \(7742\)

2.4.8.78 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {-e+\log (3)}{-20-x+x \log (x)}} (e-\log (3)) \log (x)}{400+40 x+x^2+\left (-40 x-2 x^2\right ) \log (x)+x^2 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((-ln(3)+exp(1))*ln(x)*exp((ln(3)-exp(1))/(x*ln(x)-x-20))/(x**2*ln(x)**2+(-2*x**2-40*x)*ln(x)+x**2+40
*x+400),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 \(7758\)

2.4.8.79 Sympy [F(-2)]

Exception generated. \[ \int \frac {390625 \log (x)-x \log ^2(x)+\left (390625+x \log ^2(x)\right ) \log (x \log (3))+x \log ^2(x) \log ^2(x \log (3))}{\left (-390625 x \log (x)+x^2 \log ^2(x)\right ) \log (x \log (3))+\left (x+x^2\right ) \log ^2(x) \log ^2(x \log (3))} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((x*ln(x)**2*ln(x*ln(3))**2+(x*ln(x)**2+390625)*ln(x*ln(3))-x*ln(x)**2+390625*ln(x))/((x**2+x)*ln(x)*
*2*ln(x*ln(3))**2+(x**2*ln(x)**2-390625*x*ln(x))*ln(x*ln(3))),x)

[Out]

Exception raised: PolynomialError >> 1/(x**6 + 4*x**5 + 6*x**4 + 4*x**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 \(7784\)

2.4.8.80 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^2 \left (2 x+2 x^2\right )+e \left (52 x+4 x^2\right ) \log (x)+\left (50 x+2 x^2\right ) \log ^2(x)+\left (e (96+48 x)+e^2 \left (2 x+x^2\right )+e \left (4 x+2 x^2\right ) \log (x)+\left (2 x+x^2\right ) \log ^2(x)\right ) \log (2+x)}{e^2 \left (2 x+x^2\right )+e \left (4 x+2 x^2\right ) \log (x)+\left (2 x+x^2\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((x**2+2*x)*ln(x)**2+(2*x**2+4*x)*exp(1)*ln(x)+(x**2+2*x)*exp(1)**2+(48*x+96)*exp(1))*ln(2+x)+(2*x*
*2+50*x)*ln(x)**2+(4*x**2+52*x)*exp(1)*ln(x)+(2*x**2+2*x)*exp(1)**2)/((x**2+2*x)*ln(x)**2+(2*x**2+4*x)*exp(1)*
ln(x)+(x**2+2*x)*exp(1)**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 \(7935\)

2.4.8.81 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^x \left (10 x^3-10 x^4+e^3 \left (-10 x^2+10 x^3\right )\right )+e^x \left (20 e^3 x^2-20 x^3\right ) \log \left (e^3-x\right )+e^x \left (10 e^3 x-10 x^2\right ) \log ^2\left (e^3-x\right )+\log \left (-9+5 e^x\right ) \left (-54 x^3+e^3 \left (-36 x+54 x^2\right )+e^x \left (30 x^3+e^3 \left (20 x-30 x^2\right )\right )+\left (-36 x+72 e^3 x-72 x^2+e^x \left (20 x-40 e^3 x+40 x^2\right )\right ) \log \left (e^3-x\right )+\left (18 e^3-18 x+e^x \left (-10 e^3+10 x\right )\right ) \log ^2\left (e^3-x\right )\right )}{9 x^5-18 x^6+9 x^7+e^3 \left (-9 x^4+18 x^5-9 x^6\right )+e^x \left (-5 x^5+10 x^6-5 x^7+e^3 \left (5 x^4-10 x^5+5 x^6\right )\right )+\left (-36 x^5+36 x^6+e^3 \left (36 x^4-36 x^5\right )+e^x \left (20 x^5-20 x^6+e^3 \left (-20 x^4+20 x^5\right )\right )\right ) \log \left (e^3-x\right )+\left (-18 x^4+54 x^5+e^3 \left (18 x^3-54 x^4\right )+e^x \left (10 x^4-30 x^5+e^3 \left (-10 x^3+30 x^4\right )\right )\right ) \log ^2\left (e^3-x\right )+\left (-36 e^3 x^3+36 x^4+e^x \left (20 e^3 x^3-20 x^4\right )\right ) \log ^3\left (e^3-x\right )+\left (-9 e^3 x^2+9 x^3+e^x \left (5 e^3 x^2-5 x^3\right )\right ) \log ^4\left (e^3-x\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((((-10*exp(3)+10*x)*exp(x)+18*exp(3)-18*x)*ln(-x+exp(3))**2+((-40*x*exp(3)+40*x**2+20*x)*exp(x)+72*
x*exp(3)-72*x**2-36*x)*ln(-x+exp(3))+((-30*x**2+20*x)*exp(3)+30*x**3)*exp(x)+(54*x**2-36*x)*exp(3)-54*x**3)*ln
(5*exp(x)-9)+(10*x*exp(3)-10*x**2)*exp(x)*ln(-x+exp(3))**2+(20*x**2*exp(3)-20*x**3)*exp(x)*ln(-x+exp(3))+((10*
x**3-10*x**2)*exp(3)-10*x**4+10*x**3)*exp(x))/(((5*x**2*exp(3)-5*x**3)*exp(x)-9*x**2*exp(3)+9*x**3)*ln(-x+exp(
3))**4+((20*x**3*exp(3)-20*x**4)*exp(x)-36*x**3*exp(3)+36*x**4)*ln(-x+exp(3))**3+(((30*x**4-10*x**3)*exp(3)-30
*x**5+10*x**4)*exp(x)+(-54*x**4+18*x**3)*exp(3)+54*x**5-18*x**4)*ln(-x+exp(3))**2+(((20*x**5-20*x**4)*exp(3)-2
0*x**6+20*x**5)*exp(x)+(-36*x**5+36*x**4)*exp(3)+36*x**6-36*x**5)*ln(-x+exp(3))+((5*x**6-10*x**5+5*x**4)*exp(3
)-5*x**7+10*x**6-5*x**5)*exp(x)+(-9*x**6+18*x**5-9*x**4)*exp(3)+9*x**7-18*x**6+9*x**5),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 \(8068\)

2.4.8.82 Sympy [F(-2)]

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

[In]

integrate((((2*x*ln(2)-x**2)*ln(1/2*x)**2-6*ln(2)+3*x)*ln(2*x*ln(2)-x**2)+(2*x*ln(2)-2*x**2)*ln(1/2*x)**2+(6*l
n(2)-6*x)*ln(1/2*x))/(2*x*ln(2)-x**2)/ln(1/2*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 \(8168\)

2.4.8.83 Sympy [F(-2)]

Exception generated. \[ \int \frac {(1+9 x) \log (x)+(-22-9 x-\log (x)) \log \left (\frac {1}{2} (22+9 x+\log (x))\right )}{\left (22 x+9 x^2\right ) \log ^2(x)+x \log ^3(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-ln(x)-9*x-22)*ln(1/2*ln(x)+9/2*x+11)+(9*x+1)*ln(x))/(x*ln(x)**3+(9*x**2+22*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 \(8247\)

2.4.8.84 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{3} \left (9-x \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )} \left (100 x^2-50 x^3-25 x^4+\left (20-12 x-7 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (4-2 x-x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )+\left (100 x^2-50 x^3-25 x^4+\left (-20+10 x+5 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (-4+2 x+x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )\right ) \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )}{-300 x^2+150 x^3+75 x^4+\left (60-30 x-15 x^2\right ) \log (5)+\left (-120 x^2+60 x^3+30 x^4+\left (12-6 x-3 x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (-12 x^2+6 x^3+3 x^4\right ) \log ^2\left (-4+2 x+x^2\right )} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((((-x**4-2*x**3+4*x**2)*ln(x**2+2*x-4)**2+((x**2+2*x-4)*ln(5)-10*x**4-20*x**3+40*x**2)*ln(x**2+2*x-4
)+(5*x**2+10*x-20)*ln(5)-25*x**4-50*x**3+100*x**2)*ln((-x**2*ln(x**2+2*x-4)+ln(5)-5*x**2)/(x*ln(x**2+2*x-4)+5*
x))+(-x**4-2*x**3+4*x**2)*ln(x**2+2*x-4)**2+((-x**2-2*x+4)*ln(5)-10*x**4-20*x**3+40*x**2)*ln(x**2+2*x-4)+(-7*x
**2-12*x+20)*ln(5)-25*x**4-50*x**3+100*x**2)*exp(-1/3*x*ln((-x**2*ln(x**2+2*x-4)+ln(5)-5*x**2)/(x*ln(x**2+2*x-
4)+5*x))+3)/((3*x**4+6*x**3-12*x**2)*ln(x**2+2*x-4)**2+((-3*x**2-6*x+12)*ln(5)+30*x**4+60*x**3-120*x**2)*ln(x*
*2+2*x-4)+(-15*x**2-30*x+60)*ln(5)+75*x**4+150*x**3-300*x**2),x)

[Out]

Exception raised: PolynomialError >> 1/(9*x**5 + 18*x**4 - 36*x**3) 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 \(8263\)

2.4.8.85 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{e^{\frac {9 x}{6+e^3+\log \left (\frac {5}{3}\right )+3 \log (x)}}+\frac {9 x}{6+e^3+\log \left (\frac {5}{3}\right )+3 \log (x)}} \left (27+9 e^3+9 \log \left (\frac {5}{3}\right )+27 \log (x)\right )}{36+12 e^3+e^6-\left (-12-2 e^3\right ) \log \left (\frac {5}{3}\right )+\log ^2\left (\frac {5}{3}\right )+\left (36+6 e^3+6 \log \left (\frac {5}{3}\right )\right ) \log (x)+9 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((27*ln(x)-9*ln(3/5)+9*exp(3)+27)*exp(9*x/(3*ln(x)-ln(3/5)+exp(3)+6))*exp(exp(9*x/(3*ln(x)-ln(3/5)+ex
p(3)+6)))/(9*ln(x)**2+(-6*ln(3/5)+6*exp(3)+36)*ln(x)+ln(3/5)**2+(-2*exp(3)-12)*ln(3/5)+exp(3)**2+12*exp(3)+36)
,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 \(8305\)

2.4.8.86 Sympy [F(-2)]

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

[In]

integrate(((8*x**2-16*x)*ln(x)*ln((x**3-2*x**2)/exp(x)**2)*ln(ln((x**3-2*x**2)/exp(x)**2)/x/ln(x))+((12*x**3-2
8*x**2+8*x)*ln(x)-4*x**2+8*x)*ln((x**3-2*x**2)/exp(x)**2)+(-8*x**3+28*x**2-16*x)*ln(x))/(-2+x)/ln(x)/ln((x**3-
2*x**2)/exp(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 \(8314\)

2.4.8.87 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (600-160 x-136 x^2-16 x^3\right ) \log ^2(2 x)+e^{\frac {x}{(40+8 x) \log (2 x)}} \left (-5 x-x^2+5 x \log (2 x)+\left (200+80 x+8 x^2\right ) \log ^2(2 x)\right )}{\left (200+80 x+8 x^2\right ) \log ^2(2 x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((8*x**2+80*x+200)*ln(2*x)**2+5*x*ln(2*x)-x**2-5*x)*exp(x/(8*x+40)/ln(2*x))+(-16*x**3-136*x**2-160*
x+600)*ln(2*x)**2)/(8*x**2+80*x+200)/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 \(8325\)

2.4.8.88 Sympy [F(-2)]

Exception generated. \[ \int \frac {-100 x^2+50 x^3+25 x^4+e^{2+2 x} \left (-4+2 x+x^2\right )+e^{1+x} \left (40 x-20 x^2-10 x^3\right )+3^x \left (\left (-25 x^2-50 x^3-25 x^4\right ) \log (3)+e^{1+x} \left (5+5 x-5 x^2-5 x^3+\left (5 x+10 x^2+5 x^3\right ) \log (3)\right )\right )}{125 x^2+250 x^3+125 x^4+e^{2+2 x} \left (5+10 x+5 x^2\right )+e^{1+x} \left (-50 x-100 x^2-50 x^3\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate(((((5*x**3+10*x**2+5*x)*ln(3)-5*x**3-5*x**2+5*x+5)*exp(1+x)+(-25*x**4-50*x**3-25*x**2)*ln(3))*exp(x*
ln(3))+(x**2+2*x-4)*exp(1+x)**2+(-10*x**3-20*x**2+40*x)*exp(1+x)+25*x**4+50*x**3-100*x**2)/((5*x**2+10*x+5)*ex
p(1+x)**2+(-50*x**3-100*x**2-50*x)*exp(1+x)+125*x**4+250*x**3+125*x**2),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(8381\)

2.4.8.89 Sympy [F(-2)]

Exception generated. \[ \int \frac {-720+540 x+3 e^{4+x} x^3+\left (180 x-6 e^{4+x} x^2\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} x \log ^2\left (\frac {x}{\log (5)}\right )+\left (-720 x-180 x^2+3 e^{4+x} x^2+\left (720+180 x-6 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )\right ) \log \left (\frac {-240-60 x+e^{4+x} x-e^{4+x} \log \left (\frac {x}{\log (5)}\right )}{-x+\log \left (\frac {x}{\log (5)}\right )}\right )}{-240 x-60 x^2+e^{4+x} x^2+\left (240+60 x-2 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((3*exp(4+x)*ln(x/ln(5))**2+(-6*x*exp(4+x)+180*x+720)*ln(x/ln(5))+3*x**2*exp(4+x)-180*x**2-720*x)*ln
((-exp(4+x)*ln(x/ln(5))+x*exp(4+x)-60*x-240)/(ln(x/ln(5))-x))+3*x*exp(4+x)*ln(x/ln(5))**2+(-6*x**2*exp(4+x)+18
0*x)*ln(x/ln(5))+3*x**3*exp(4+x)+540*x-720)/(exp(4+x)*ln(x/ln(5))**2+(-2*x*exp(4+x)+60*x+240)*ln(x/ln(5))+x**2
*exp(4+x)-60*x**2-240*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 \(8392\)

2.4.8.90 Sympy [F(-2)]

Exception generated. \[ \int \frac {1+(5-x) \log (5-x)+e^3 (-100+20 x) \log ^2(5-x)}{(5-x) \log (5-x)+e^3 (-100+20 x) \log ^2(5-x)} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate(((20*x-100)*exp(3)*ln(5-x)**2+(5-x)*ln(5-x)+1)/((20*x-100)*exp(3)*ln(5-x)**2+(5-x)*ln(5-x)),x)

[Out]

Exception raised: PolynomialError >> 1/(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 \(8411\)

2.4.8.91 Sympy [F(-2)]

Exception generated. \[ \int \frac {75+90 x+3 x^2+\left (120 x-24 x^2+\left (75-30 x+3 x^2\right ) \log \left (\frac {x}{e}\right )\right ) \log \left (\frac {-8 x+(-5+x) \log \left (\frac {x}{e}\right )}{-5+x}\right ) \log \left (-\log \left (\frac {-8 x+(-5+x) \log \left (\frac {x}{e}\right )}{-5+x}\right )\right )}{\left (40 x-8 x^2+\left (25-10 x+x^2\right ) \log \left (\frac {x}{e}\right )\right ) \log \left (\frac {-8 x+(-5+x) \log \left (\frac {x}{e}\right )}{-5+x}\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((3*x**2-30*x+75)*ln(x/exp(1))-24*x**2+120*x)*ln(((-5+x)*ln(x/exp(1))-8*x)/(-5+x))*ln(-ln(((-5+x)*l
n(x/exp(1))-8*x)/(-5+x)))+3*x**2+90*x+75)/((x**2-10*x+25)*ln(x/exp(1))-8*x**2+40*x)/ln(((-5+x)*ln(x/exp(1))-8*
x)/(-5+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 \(8435\)

2.4.8.92 Sympy [F(-2)]

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

[In]

integrate(((exp(x)*x-x**2)*ln(x-exp(x))+((x**2-4*x)*exp(x)**2+(-x**3+4*x**2+x)*exp(x)-x**2)*exp(exp(x))+(-2*ex
p(x)+2*x)*ln(1/5*x)+(x**2-4*x)*exp(x)-x**2+4*x)/(exp(x)*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 \(8519\)

2.4.8.93 Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (80-40 x-2 x^2+x^3\right ) \log (-2+x)+e^{3 e^x+x} \left (-60 x^2+30 x^3\right ) \log (-2+x)+\left (-40 x-10 e^{3 e^x} x^2-x^3\right ) \log \left (\frac {40+10 e^{3 e^x} x+x^2}{x}\right )}{e^{3 e^x} \left (-20 x^2+10 x^3\right ) \log ^2(-2+x)+\left (-80 x+40 x^2-2 x^3+x^4\right ) \log ^2(-2+x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-10*x**2*exp(3*exp(x))-x**3-40*x)*ln((10*x*exp(3*exp(x))+x**2+40)/x)+(30*x**3-60*x**2)*exp(x)*ln(-
2+x)*exp(3*exp(x))+(x**3-2*x**2-40*x+80)*ln(-2+x))/((10*x**3-20*x**2)*ln(-2+x)**2*exp(3*exp(x))+(x**4-2*x**3+4
0*x**2-80*x)*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 \(8523\)

2.4.8.94 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: PolynomialError >> 1/(-_t1**2*x**2 - _t2*x**2 + x**4) contains an element of the set of gene
rators.

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(8581\)

2.4.8.95 Sympy [F(-2)]

Exception generated. \[ \int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{\left (3 x^2+x^3\right ) \log ^2(5) \log ^3(x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((3*x+9)*ln(5)**2*ln(x)**3+(6*x**4+18*x**3)*ln(x)-6*x**4-18*x**3)*ln(3+x)+(-x**2-9*x-18)*ln(5)**2*l
n(x)**3+(-9*x**4-36*x**3)*ln(x)+12*x**4+36*x**3)/(x**3+3*x**2)/ln(5)**2/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 \(8610\)

2.4.8.96 Sympy [F(-2)]

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

[In]

integrate((((3*x**2+8*x+3)*ln(3*x)**2+(6*x**5+20*x**4+2*x**3-12*x**2)*ln(3*x)-2*x**5-6*x**4+2*x**3+6*x**2)*exp
((x**3-x**2)/ln(3*x))**2+(4*x**3+12*x**2+6*x)*ln(3*x)**2)/ln(3*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 \(8617\)

2.4.8.97 Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{-\frac {5}{x^4 \log \left (-3 x+2 x^5\right )}} \left (-45+150 x^4+\left (-180+120 x^4\right ) \log \left (-3 x+2 x^5\right )\right )}{\left (-3 x^5+2 x^9\right ) \log ^2\left (-3 x+2 x^5\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((120*x**4-180)*ln(2*x**5-3*x)+150*x**4-45)/(2*x**9-3*x**5)/ln(2*x**5-3*x)**2/exp(5/x**4/ln(2*x**5-3
*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 \(8620\)

2.4.8.98 Sympy [F(-2)]

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

[In]

integrate((((4*ln(2)**2+2*x*ln(2))*ln(1/4*x)+4*ln(2)**2+2*x*ln(2))*ln(4*ln(2)**2+4*x*ln(2)+x**2)+((4*x**2*ln(2
)**2+2*x**3*ln(2))*exp(x)+4*ln(2)**2-2*x*ln(2))*ln(1/4*x)+(-4*x*ln(2)**2-2*x**2*ln(2))*exp(x)+4*ln(2)**2+2*x*l
n(2))/(2*x**2*ln(2)+x**3)/ln(1/4*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 \(8793\)

2.4.8.99 Sympy [F(-2)]

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

[In]

integrate(1/3*((-4*ln(16/x**2)**2+(-4*x**2+4*x)*ln(16/x**2)-8*x**2+8*x)*exp(x/ln(16/x**2))-4*ln(5)*ln(16/x**2)
**2)/x**2/ln(16/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 \(8800\)

2.4.8.100 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: IndexError >> Index out of range: a[1]

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(8858\)