Exception generated. \[ \int \frac {(12+6 x) \log ^2\left (\frac {x}{2+x}\right )+e^{\frac {5 x}{\log \left (\frac {x}{2+x}\right )}} \left (-20+(20+10 x) \log \left (\frac {x}{2+x}\right )\right )}{(2+x) \log ^2\left (\frac {x}{2+x}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(598\)
Exception generated. \[ \int \frac {1-11 x+4 x^2+(-8-8 x) \log (2+2 x)+(-20-20 x) \log ^2(2+2 x)}{-15-4 x+9 x^2-2 x^3+\left (-60-28 x+28 x^2-4 x^3\right ) \log (2+2 x)+\left (-60-40 x+20 x^2\right ) \log ^2(2+2 x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(5*x + 5) contains an element of th e set of generators.
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(618\)
Exception generated. \[ \int \frac {\left (4-4 x^2\right ) \log (5)+\left (-1+x^2\right ) \log ^2(5) \log (-1+x)+\left (\left (-4+4 x^2+e^7 \left (-4-4 x+8 x^2\right )\right ) \log (5)+e^7 \left (-x-x^2\right ) \log ^2(5)+\left (1-x^2+e^7 \left (1+x-2 x^2\right )\right ) \log ^2(5) \log (-1+x)\right ) \log (x)+\left (\left (-4-4 x+8 x^2\right ) \log (5)+\left (-x-x^2\right ) \log ^2(5)+\left (1+x-2 x^2\right ) \log ^2(5) \log (-1+x)\right ) \log (x) \log \left (\frac {\log (x)}{x}\right )}{\left (-16 x^2-16 x^3+16 x^4+16 x^5+\left (8 x^2+8 x^3-8 x^4-8 x^5\right ) \log (5) \log (-1+x)+\left (-x^2-x^3+x^4+x^5\right ) \log ^2(5) \log ^2(-1+x)\right ) \log (x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(675\)
Exception generated. \[ \int \frac {8+(80-20 x) \log \left (\frac {324}{16-8 x+x^2}\right )+\left (-4+21 x-5 x^2\right ) \log ^2\left (\frac {324}{16-8 x+x^2}\right )}{(-80+20 x) \log \left (\frac {324}{16-8 x+x^2}\right )+\left (-20 x+5 x^2\right ) \log ^2\left (\frac {324}{16-8 x+x^2}\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(5*x**3 - 20*x**2) contains an elem ent of the set of generators.
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(694\)
Exception generated. \[ \int \frac {\left (-8 x^2+2 x^3-2 x^4\right ) \log (5) \log \left (\frac {1}{4} \left (-4 x+x^2-x^3\right )\right )+\left (16-8 x+12 x^2+\left (-4 x^2+2 x^3-3 x^4\right ) \log (5)\right ) \log \left (-4+x^2 \log (5)\right )+\left (8 x^2-2 x^3+2 x^4\right ) \log (5) \log \left (\frac {1}{4} \left (-4 x+x^2-x^3\right )\right ) \log \left (\log \left (\frac {1}{4} \left (-4 x+x^2-x^3\right )\right )\right )}{\left (-16 x+4 x^2-4 x^3+\left (4 x^3-x^4+x^5\right ) \log (5)\right ) \log \left (\frac {1}{4} \left (-4 x+x^2-x^3\right )\right ) \log ^2\left (-4+x^2 \log (5)\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(700\)
Exception generated. \[ \int \frac {3+x^2+e^4 x^2+\left (2 x+2 e^4 x\right ) \log (3)+\left (1+e^4\right ) \log ^2(3)+e^{2 x} \left (x^4+e^4 x^4\right ) \log ^2(3)+e^x \left (3 x^2+3 x^3+\left (-2 x^3-2 e^4 x^3\right ) \log (3)+\left (-2 x^2-2 e^4 x^2\right ) \log ^2(3)\right )}{-3 x-x^2+x^3+e^4 x^3+\left (-3-2 x+2 x^2+2 e^4 x^2\right ) \log (3)+\left (-1+x+e^4 x\right ) \log ^2(3)+e^x \left (3 x^3+\left (6 x^2+2 x^3-2 x^4-2 e^4 x^4\right ) \log (3)+\left (2 x^2-2 x^3-2 e^4 x^3\right ) \log ^2(3)\right )+e^{2 x} \left (-3 x^4 \log (3)+\left (-x^4+x^5+e^4 x^5\right ) \log ^2(3)\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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 )
Output:
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)*l og(3)**3 - 6*x**4*log(3)**2 - 2*x**4*log(3)**3 + x**3*log(3)**3 + 6*x**3*l og(3)**2 + 9*x*
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(702\)
Exception generated. \[ \int \frac {e^{-\frac {x}{\log (2 x)}} \left (e^{-4+x} x^2-e^{-4+x} x^2 \log (2 x)+e^{-4+x} \left (2 x+x^2\right ) \log ^2(2 x)\right )}{\log ^2(2 x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((x**2+2*x)*exp(-4+x)*ln(2*x)**2-x**2*exp(-4+x)*ln(2*x)+x**2*exp (-4+x))/ln(2*x)**2/exp(x/ln(2*x)),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(743\)
Exception generated. \[ \int \frac {-10+4 x+\left (-2+2 x-x^2\right ) \log (x)+(2-x) \log \left (-\frac {x}{-2+x}\right )}{-2 x+x^2+\left (-4 x+2 x^2\right ) \log (x)+\left (-2 x+x^2\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(778\)
Exception generated. \[ \int \frac {4^{\frac {-16-8 x-x^2}{-2-2 x+2 \log \left (\log \left (x^2\right )\right )}} \left (\left (32+48 x+18 x^2+2 x^3\right ) \log (4)+\left (2+8 x+10 x^2+4 x^3+\left (-8 x-6 x^2+3 x^3+x^4\right ) \log (4)\right ) \log \left (x^2\right )+\left (-4-12 x-8 x^2+\left (-8 x-10 x^2-2 x^3\right ) \log (4)\right ) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+(2+4 x) \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )\right )}{\left (2+4 x+2 x^2\right ) \log \left (x^2\right )+(-4-4 x) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+2 \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((2+4*x)*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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(835\)
Exception generated. \[ \int \frac {e^{5/4} (-360+72 x) \log ^3(x)+e^{5/4} (-90+36 x) \log ^4(x)+(180-72 x) \log ^5(x)}{-e^{25/4}+10 e^5 \log (x)-40 e^{15/4} \log ^2(x)+80 e^{5/2} \log ^3(x)-80 e^{5/4} \log ^4(x)+32 \log ^5(x)} \, dx=\text {Exception raised: AttributeError} \] Input:
integrate(((-72*x+180)*ln(x)**5+(36*x-90)*exp(5/4)*ln(x)**4+(72*x-360)*exp (5/4)*ln(x)**3)/(32*ln(x)**5-80*exp(5/4)*ln(x)**4+80*exp(5/4)**2*ln(x)**3- 40*exp(5/4)**3*ln(x)**2+10*exp(5/4)**4*ln(x)-exp(5/4)**5),x)
Output:
Exception raised: AttributeError >> 'NoneType' object has no attribute 'ex pr'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(852\)
Exception generated. \[ \int \frac {-8-2 x+\left (7+9 x-15 x^2-2 x^3\right ) \log (x)+\left (-x-2 x^2\right ) \log ^2(x)+(1+2 x) \log (x) \log (\log (x))}{\left (64 x+32 x^2+4 x^3\right ) \log (x)+\left (16 x+4 x^2\right ) \log ^2(x)+x \log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(917\)
Exception generated. \[ \int \frac {e^4 \left (-1+17 x-4 x^2-12 x^3+3 x^4\right )+e^4 \left (4 x-3 x^3\right ) \log (x)+\left (e^4 \left (20-5 x-12 x^2+3 x^3\right )+e^4 \left (5-3 x^2\right ) \log (x)\right ) \log (-4+x-\log (x))+\left (e^4 \left (-4 x+x^2\right )-e^4 x \log (x)+\left (e^4 (-4+x)-e^4 \log (x)\right ) \log (-4+x-\log (x))\right ) \log (x+\log (-4+x-\log (x)))}{4 x-x^2+x \log (x)+(4-x+\log (x)) \log (-4+x-\log (x))} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((-exp(4)*ln(x)+(-4+x)*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**4-12 *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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1003\)
Exception generated. \[ \int \frac {\left (\frac {x+4 \log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )}{\log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )}\right )^{\frac {1}{\log \left (x^2\right )}} \left (-x \log \left (x^2\right )+\left (-x+x^2\right ) \log \left (x^2\right ) \log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )+\left (\left (2 x-2 x^2\right ) \log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )+(8-8 x) \log ^2\left (\frac {(-4+4 x) \log (4)}{5 x}\right )\right ) \log \left (\frac {x+4 \log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )}{\log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )}\right )\right )}{\left (-x^2+x^3\right ) \log ^2\left (x^2\right ) \log \left (\frac {(-4+4 x) \log (4)}{5 x}\right )+\left (-4 x+4 x^2\right ) \log ^2\left (x^2\right ) \log ^2\left (\frac {(-4+4 x) \log (4)}{5 x}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1049\)
Exception generated. \[ \int \frac {4+4 \log \left (\frac {5 \log (3)}{e^2 x}\right )+(-4-8 x) \log ^2\left (\frac {5 \log (3)}{e^2 x}\right )+\left (-2-2 \log \left (\frac {5 \log (3)}{e^2 x}\right )+(2+4 x) \log ^2\left (\frac {5 \log (3)}{e^2 x}\right )\right ) \log \left (\frac {x+\left (-x-x^2\right ) \log \left (\frac {5 \log (3)}{e^2 x}\right )}{\log \left (\frac {5 \log (3)}{e^2 x}\right )}\right )}{-x \log \left (\frac {5 \log (3)}{e^2 x}\right )+\left (x+x^2\right ) \log ^2\left (\frac {5 \log (3)}{e^2 x}\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((((2+4*x)*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)
Output:
Exception raised: PolynomialError >> 1/(x**3 + 2*x**2 + x) contains an ele ment of the set of generators.
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1116\)
Exception generated. \[ \int \frac {e^{-\frac {x}{\log \left (\frac {48 x}{4+3 x}\right )}} \left (1036+(-1036-777 x) \log \left (\frac {48 x}{4+3 x}\right )\right )}{(4+3 x) \log ^2\left (\frac {48 x}{4+3 x}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1259\)
Exception generated. \[ \int \frac {e^{\frac {3-x+3 \log \left (\frac {-20-5 x-2 x^2}{6 x}\right )}{\log \left (\frac {-20-5 x-2 x^2}{6 x}\right )}} \left (60-20 x-6 x^2+2 x^3+\left (-20 x-5 x^2-2 x^3\right ) \log \left (\frac {-20-5 x-2 x^2}{6 x}\right )\right )}{\left (20 x+5 x^2+2 x^3\right ) \log ^2\left (\frac {-20-5 x-2 x^2}{6 x}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1276\)
Exception generated. \[ \int \frac {e^{2+2 x} (36-9 x)+4 x-x^2+e^{1+x} \left (8 x-6 x^2+x^3\right )+\left (-8 x+2 x^2+e^{1+x} (-72+18 x)\right ) \log (x)+(36-9 x) \log ^2(x)+\left (e^{2+2 x} (-48-9 x)-e^{1+x} x^2+\left (x^2+e^{1+x} (96+18 x)\right ) \log (x)+(-48-9 x) \log ^2(x)\right ) \log \left (\frac {x^2+e^{1+x} (48+9 x)+(-48-9 x) \log (x)}{-12 e^{1+x}+12 \log (x)}\right )}{e^{1+x} x^2+e^{2+2 x} (48+9 x)+\left (e^{1+x} (-96-18 x)-x^2\right ) \log (x)+(48+9 x) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((((-9*x-48)*ln(x)**2+((18*x+96)*exp(1+x)+x**2)*ln(x)+(-9*x-48)*e xp(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)*ln( 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)
Output:
Exception raised: PolynomialError >> 1/(27*x**3 + 288*x**2 + 768*x) contai ns an element of the set of generators.
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1296\)
Exception generated. \[ \int \frac {100+40 x+4 x^2+\left (-50-40 x-6 x^2\right ) \log (x)+\left (10 x+2 x^2\right ) \log ^2(x)-4 x \log ^3(x)+(-4+2 x) \log ^4(x)+2 \log ^5(x)+\left ((-100-20 x) \log (x)-20 \log ^3(x)\right ) \log (-2+\log (x))+\left (-200-40 x+(100+40 x) \log (x)-10 x \log ^2(x)\right ) \log ^2(-2+\log (x))+100 \log (x) \log ^3(-2+\log (x))+(100-50 \log (x)) \log ^4(-2+\log (x))}{-2 x \log ^3(x)+x \log ^4(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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-10 0)*ln(x))*ln(ln(x)-2)+2*ln(x)**5+(2*x-4)*ln(x)**4-4*x*ln(x)**3+(2*x**2+10* 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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1331\)
Exception generated. \[ \int \frac {(64-16 x) \log (x)+\left (-64 x+16 x^2\right ) \log (x) \log (2 x)+(64-16 x+(64-48 x) \log (x)) \log (2 x) \log \left (\frac {e^x}{\log (2 x)}\right )}{\left (-64 x^2+48 x^3-12 x^4+x^5\right ) \log ^2(x) \log (2 x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1387\)
Exception generated. \[ \int \frac {-240 x-48 x^2+\left (240 x+48 x^2\right ) \log (x)+\left (\left (240 x+96 x^2\right ) \log (x)+(45+18 x) \log ^2(x)\right ) \log \left (\frac {16 x+3 \log (x)}{\log (x)}\right ) \log \left (2 \log \left (\frac {16 x+3 \log (x)}{\log (x)}\right )\right )}{\left (16 x \log (x)+3 \log ^2(x)\right ) \log \left (\frac {16 x+3 \log (x)}{\log (x)}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1455\)
Exception generated. \[ \int \frac {-45+39 x-56 x^2+40 x^3-11 x^4+x^5+\left (-45+30 x-170 x^2+119 x^3-58 x^4+13 x^5-x^6\right ) \log (x)+\left (9 x^2-6 x^3+13 x^4-11 x^5-x^6-4 x^7-5 x^8+x^9\right ) \log ^2(x)}{\left (45 x-39 x^2+56 x^3-40 x^4+11 x^5-x^6\right ) \log (x)+\left (9 x^3-6 x^4+19 x^5-12 x^6+11 x^7-6 x^8+x^9\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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**3-170*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)
Output:
Exception raised: PolynomialError >> 1/(x**7 + 2*x**5 + x**3) contains an element of the set of generators.
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1506\)
Exception generated. \[ \int \frac {x-21 x^2+20 x^3+e^5 \left (-20 x+20 x^2\right )+x \log (4 x)+\left (-2 x+2 x^2+e^5 (-2+2 x)+\left (-e^5-x\right ) \log (4 x)\right ) \log \left (e^5+x\right )}{20 x^3-40 x^4+20 x^5+e^5 \left (20 x^2-40 x^3+20 x^4\right )+\left (40 x^3-40 x^4+e^5 \left (40 x^2-40 x^3\right )\right ) \log (4 x)+\left (20 e^5 x^2+20 x^3\right ) \log ^2(4 x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((-exp(5)-x)*ln(4*x)+(2*x-2)*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**4-4 0*x**3+20*x**2)*exp(5)+20*x**5-40*x**4+20*x**3),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1587\)
Exception generated. \[ \int \frac {\left (5 x+4 e^3 x\right ) \log (x)+\left (-19+e^3 (8-4 x)-5 x\right ) \log \left (\frac {1}{5} \left (38+10 x+e^3 (-16+8 x)\right )\right )}{\left (19 x+5 x^2+e^3 \left (-8 x+4 x^2\right )\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1657\)
Exception generated. \[ \int \frac {\left (-8 x+4 x^2\right ) \log (-2+x) \log \left (\frac {1}{2} (1+2 x)\right )+\left (-2 x-4 x^2+\left (2+3 x-2 x^2\right ) \log (-2+x)\right ) \log ^2\left (\frac {1}{2} (1+2 x)\right )}{\left (-2 x^2-3 x^3+2 x^4\right ) \log ^3(-2+x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1661\)
Exception generated. \[ \int \frac {4 x^5+x^3 \log (x)+\left (-32 x^3 \log \left (\frac {4}{x}\right )+64 x^3 \log \left (\frac {4}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {4}{x}\right )\right ) \log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right ) \log \left (\log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right )\right )+\left (2 x^3 \log \left (\frac {4}{x}\right )-4 x^3 \log \left (\frac {4}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {4}{x}\right )\right ) \log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right ) \log \left (\log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right )\right ) \log \left (\log \left (\log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right )\right )\right )}{\left (64 x^6 \log \left (\frac {4}{x}\right )+48 x^4 \log \left (\frac {4}{x}\right ) \log (x)+12 x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)+\log \left (\frac {4}{x}\right ) \log ^3(x)\right ) \log \left (\log \left (\frac {4}{x}\right )\right ) \log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right ) \log \left (\log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right )\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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(ln(4/x)))/ln(ln(ln(ln(4/x)))),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1705\)
Exception generated. \[ \int \frac {\log (x) \log ^2(\log (x))+e^{\frac {2 x^2}{\log (\log (x))}} (-2 x+4 x \log (x) \log (\log (x)))}{\log (x) \log ^2(\log (x))} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1820\)
Exception generated. \[ \int \frac {4+(1+x) \log \left (\frac {3}{x^2}\right ) \log ^2\left (\log ^2\left (\frac {3}{x^2}\right )\right )}{x \log \left (\frac {3}{x^2}\right ) \log \left (\log ^2\left (\frac {3}{x^2}\right )\right )+\left (\left (-x+x^2\right ) \log \left (\frac {3}{x^2}\right )+x \log \left (\frac {3}{x^2}\right ) \log (x)\right ) \log ^2\left (\log ^2\left (\frac {3}{x^2}\right )\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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 )
Output:
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)) contains an element of t
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1945\)
Exception generated. \[ \int \frac {2 x^3-4 x^4+\left (6 x-12 x^2-4 x^3+3 x^4+x^5\right ) \log \left (-x+x^2\right )+\left (-12 x+6 x^2+6 x^3\right ) \log ^2\left (-x+x^2\right )+\left (-10+9 x+x^2\right ) \log ^3\left (-x+x^2\right )}{\left (-x^4+x^5\right ) \log \left (-x+x^2\right )+\left (-6 x^2+6 x^3\right ) \log ^2\left (-x+x^2\right )+\left (-9+8 x+x^2\right ) \log ^3\left (-x+x^2\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)*l n(x**2-x)**3+(6*x**3-6*x**2)*ln(x**2-x)**2+(x**5-x**4)*ln(x**2-x)),x)
Output:
Exception raised: PolynomialError >> 1/(x**6 + 34*x**5 + 415*x**4 + 1980*x **3 + 1215*x**2 - 10206*x + 6561) contains an element of the set of genera tors.
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(1951\)
Exception generated. \[ \int \frac {e^{\frac {-2-x}{\left (-x+2 x^3\right ) \log (x)}} \left (-2-x+4 x^2+2 x^3+\left (-2+12 x^2+4 x^3\right ) \log (x)\right )}{\left (x^2-4 x^4+4 x^6\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2019\)
Exception generated. \[ \int \frac {4 x^3+4 x^2 \log (5)+\left (x-8 x^4+\left (1-8 x^2-8 x^3\right ) \log (5)\right ) \log (x) \log (\log (x))+\left (4 x^2+4 x \log (5)+\left (-12 x^3+\left (-8 x-12 x^2\right ) \log (5)\right ) \log (x) \log (\log (x))\right ) \log \left (\frac {x^2}{\left (x^2+2 x \log (5)+\log ^2(5)\right ) \log (\log (x))}\right )+\left (-4 x^2-4 x \log (5)\right ) \log (x) \log (\log (x)) \log ^2\left (\frac {x^2}{\left (x^2+2 x \log (5)+\log ^2(5)\right ) \log (\log (x))}\right )}{(2 x+2 \log (5)) \log (x) \log (\log (x))} \, dx=\text {Exception raised: TypeError} \] Input:
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*l n(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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2117\)
Exception generated. \[ \int \frac {\left (320+1264 x+1740 x^2+925 x^3+125 x^4\right ) \log \left (\frac {5+x}{5}\right )+\left (250 x+50 x^2+\left (250 x+50 x^2\right ) \log (2)\right ) \log ^2\left (\frac {5+x}{5}\right )+\log (x) \left (-64 x-240 x^2-300 x^3-125 x^4+\left (-250 x-50 x^2\right ) \log \left (\frac {5+x}{5}\right )\right )}{\left (320 x+1264 x^2+1740 x^3+925 x^4+125 x^5\right ) \log (x) \log \left (\frac {5+x}{5}\right )+\left (-320 x-1264 x^2-1740 x^3-925 x^4-125 x^5+\left (-320 x-1264 x^2-1740 x^3-925 x^4-125 x^5\right ) \log (2)\right ) \log ^2\left (\frac {5+x}{5}\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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+1264* 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)
Output:
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 test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2164\)
Exception generated. \[ \int \frac {e^{\frac {135 x}{-5 x^2+\log (x)}} \left (-270 x+1350 x^3+50 x^4+\left (270 x-20 x^2\right ) \log (x)+2 \log ^2(x)\right )}{375 x^4-150 x^2 \log (x)+15 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)**2-150*x**2*ln(x)+375*x**4),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2240\)
Exception generated. \[ \int \frac {8 x-16 x^3-16 x^4+e^8 \left (-48 x^3-48 x^4\right )+e^{12} \left (16 x^3+16 x^4\right )+e^4 \left (-8 x+48 x^3+48 x^4\right )+\left (-4+24 x^2+16 x^3-8 x^4+e^8 \left (24 x^2-24 x^4\right )+e^{12} \left (8 x^3+8 x^4\right )+e^4 \left (-48 x^2-24 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x+12 x^3+e^4 \left (12 x-12 x^2-24 x^3\right )+e^8 \left (12 x^2+12 x^3\right )\right ) \log ^2(x)+\left (2-4 x-6 x^2+e^4 \left (6 x+6 x^2\right )\right ) \log ^3(x)+(1+x) \log ^4(x)+\left (16-32 x+32 e^4 x+\left (8-16 x+16 e^4 x\right ) \log (x)\right ) \log (2+\log (x))}{-16 x^4+48 e^4 x^4-48 e^8 x^4+16 e^{12} x^4+\left (24 x^3-8 x^4+8 e^{12} x^4+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (-48 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x^2+12 x^3+12 e^8 x^3+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+\left (2 x-6 x^2+6 e^4 x^2\right ) \log ^3(x)+x \log ^4(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)*ln(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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2277\)
Exception generated. \[ \int \frac {x^2+2 x \log (x)+\log ^2(x)+e^{\frac {2 \left (25+e x^2+e x \log (x)\right )}{x^2+x \log (x)}} \left (-25-50 x+x^3+\left (-25+2 x^2\right ) \log (x)+x \log ^2(x)\right )}{x^2+2 x \log (x)+\log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2344\)
Exception generated. \[ \int \frac {-4 \log ^2(2 x)+e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x} \left ((1+2 x) \log ^2(2 x)+e^{\frac {6 x^2}{\log (2 x)}} \left (6 x^2-12 x^2 \log (2 x)\right )\right )}{\log ^2(2 x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2387\)
Exception generated. \[ \int \frac {-4 x \log (x)+4 e^{2 x+4 e^{2 x} x^2} x^2 (8+8 x) \log (x)+\left (2 x+e^{4 e^{2 x} x^2} (-2-2 \log (x))+2 x \log (x)\right ) \log \left (e^{8 e^{2 x} x^2}-2 e^{4 e^{2 x} x^2} x+x^2\right )}{e^{4 e^{2 x} x^2} x^2 \log ^2(x)-x^3 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2398\)
Exception generated. \[ \int \frac {e^{\frac {x^2+x \log (x)}{-x+\log \left (\frac {e^6 \left (9 x^2-6 x^3+x^4\right )+e^3 \left (-6 x+2 x^2\right ) \log (x)+\log ^2(x)}{e^6 x^2}\right )}} \left (-2 x+e^3 \left (3 x^2-x^4\right )+\left (-2+x-x^2-2 e^3 x^2\right ) \log (x)+2 \log ^2(x)+\left (e^3 \left (-3 x-5 x^2+2 x^3\right )+\left (1+2 x+e^3 \left (-3 x+x^2\right )\right ) \log (x)+\log ^2(x)\right ) \log \left (\frac {e^6 \left (9 x^2-6 x^3+x^4\right )+e^3 \left (-6 x+2 x^2\right ) \log (x)+\log ^2(x)}{e^6 x^2}\right )\right )}{e^3 \left (-3 x^3+x^4\right )+x^2 \log (x)+\left (e^3 \left (6 x^2-2 x^3\right )-2 x \log (x)\right ) \log \left (\frac {e^6 \left (9 x^2-6 x^3+x^4\right )+e^3 \left (-6 x+2 x^2\right ) \log (x)+\log ^2(x)}{e^6 x^2}\right )+\left (e^3 \left (-3 x+x^2\right )+\log (x)\right ) \log ^2\left (\frac {e^6 \left (9 x^2-6 x^3+x^4\right )+e^3 \left (-6 x+2 x^2\right ) \log (x)+\log ^2(x)}{e^6 x^2}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((ln(x)**2+((x**2-3*x)*exp(3)+2*x+1)*ln(x)+(2*x**3-5*x**2-3*x)*e xp(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)*ex p(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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2405\)
Exception generated. \[ \int \frac {\left (16-12 x^2+4 x^3+e^3 \left (-16 x^2-16 x^3+28 x^4-8 x^5\right )+e^3 \left (-16 x-16 x^2+28 x^3-8 x^4\right ) \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )+\left (-4 x^2+2 x^3+\left (-4 x+2 x^2\right ) \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{\left (x^2+x \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)/l n((x+ln(x))/exp((x**2+x+2)*exp(3))),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2423\)
Exception generated. \[ \int \frac {240 x^2+100 x^3+e^x \left (240 x+100 x^2\right )+\left (-120 x+50 x^2+e^x \left (-20 x-50 x^2\right )\right ) \log (x)+\left (e^x (-120-50 x)-120 x-50 x^2+\left (e^x (-120-50 x)-120 x-50 x^2\right ) \log (x)\right ) \log \left (\frac {144+120 x+25 x^2}{e^x+x}\right )}{\left (12 x^3+5 x^4+e^x \left (12 x^2+5 x^3\right )\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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+12* x**2)*exp(x)+5*x**4+12*x**3)/ln(x)**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2508\)
Exception generated. \[ \int \frac {-8 e^{2 x}+e^{e^{e^5}+2 x} \left (10-30 x+10 x^2\right )+\left (-16 e^{2 x}+e^{e^{e^5}+2 x} \left (70-80 x+20 x^2\right )\right ) \log \left (\frac {1}{5} \left (4+e^{e^{e^5}} \left (-30+25 x-5 x^2\right )\right )\right )+\left (-8 e^{2 x}+e^{e^{e^5}+2 x} \left (60-50 x+10 x^2\right )\right ) \log ^2\left (\frac {1}{5} \left (4+e^{e^{e^5}} \left (-30+25 x-5 x^2\right )\right )\right )}{-4+e^{e^{e^5}} \left (30-25 x+5 x^2\right )} \, dx=\text {Exception raised: CoercionFailed} \] Input:
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)
Output:
Exception raised: CoercionFailed >> Cannot convert 5*exp(exp(exp(5))) of t ype <class 'sympy.core.mul.Mul'> to ZZ[exp(exp(exp(5))/2),sqrt(16 + 5*exp( exp(exp(5))))]
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2531\)
Exception generated. \[ \int \frac {16 \log ^2\left (x^2\right )+e^{2 e^{e^{\frac {x}{\log \left (x^2\right )}}}+4 x} \left ((1+4 x) \log ^2\left (x^2\right )+e^{e^{\frac {x}{\log \left (x^2\right )}}+\frac {x}{\log \left (x^2\right )}} \left (-4 x+2 x \log \left (x^2\right )\right )\right )+e^{e^{e^{\frac {x}{\log \left (x^2\right )}}}+2 x} \left ((8+16 x) \log ^2\left (x^2\right )+e^{e^{\frac {x}{\log \left (x^2\right )}}+\frac {x}{\log \left (x^2\right )}} \left (-16 x+8 x \log \left (x^2\right )\right )\right )}{\log ^2\left (x^2\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2569\)
Exception generated. \[ \int \frac {e^{\frac {-15+5 x}{\left (39 x-8 x^2-4 x^3+x^4\right ) \log (x)}} \left (-585+315 x+20 x^2-35 x^3+5 x^4+\left (-585+240 x+140 x^2-100 x^3+15 x^4\right ) \log (x)\right )}{\left (1521 x^2-624 x^3-248 x^4+142 x^5-8 x^7+x^8\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2570\)
Exception generated. \[ \int \frac {-6-24 x+(-1-6 x) \log (2 x)+(24 x+4 \log (x)+(6 x+\log (x)) \log (2 x)+(8+2 \log (2 x)) \log (4+\log (2 x))) \log \left (\frac {8}{6 x+\log (x)+2 \log (4+\log (2 x))}\right )}{24 x+4 \log (x)+(6 x+\log (x)) \log (2 x)+(8+2 \log (2 x)) \log (4+\log (2 x))} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2849\)
Exception generated. \[ \int \frac {1+\log \left (\frac {3}{2 x}\right )+\log ^2\left (\frac {3}{2 x}\right )}{x \log \left (\frac {3}{2 x}\right )+(28+x+\log (2)) \log ^2\left (\frac {3}{2 x}\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(x**3 + 2*x**2*log(2) + 56*x**2 + x *log(2)**2 + 56*x*log(2) + 784*x) contains an element of the set of genera tors.
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2865\)
Exception generated. \[ \int \frac {15-21 x-36 x^2+(12+12 x) \log (x)+(2+4 x+(2+4 x) \log (x)) \log \left (x+x^2\right )+\left (-8+16 x+24 x^2+(-7-7 x) \log (x)\right ) \log ^2\left (x+x^2\right )+\left (1-3 x-4 x^2+(1+x) \log (x)\right ) \log ^4\left (x+x^2\right )+\left (3-15 x-18 x^2+(12+12 x) \log (x)+\left (-1+11 x+12 x^2+(-7-7 x) \log (x)\right ) \log ^2\left (x+x^2\right )+\left (-2 x-2 x^2+(1+x) \log (x)\right ) \log ^4\left (x+x^2\right )\right ) \log \left (\frac {-1+6 x-4 \log (x)+(-2 x+\log (x)) \log ^2\left (x+x^2\right )}{-3+\log ^2\left (x+x^2\right )}\right )}{3-15 x-18 x^2+(12+12 x) \log (x)+\left (-1+11 x+12 x^2+(-7-7 x) \log (x)\right ) \log ^2\left (x+x^2\right )+\left (-2 x-2 x^2+(1+x) \log (x)\right ) \log ^4\left (x+x^2\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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+((2+4*x)*ln(x)+4 *x+2)*ln(x**2+x)+(12*x+12)*ln(x)-36*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)
Output:
Exception raised: PolynomialError >> 1/(36*_t0**4*x**4 + 72*_t0**4*x**3 + 36*_t0**4*x**2 - 288*_t0**3*x**5 - 576*_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 test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2875\)
Exception generated. \[ \int \frac {20 x+129 x^2+50 x^3+5 x^4+\left (60+730 x+171 x^2-20 x^3-5 x^4\right ) \log (x)+\left (-60-387 x-150 x^2-15 x^3\right ) \log \left (\frac {4 x+25 x^2+5 x^3}{75+15 x}\right )}{\left (20 x+129 x^2+50 x^3+5 x^4\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2893\)
Exception generated. \[ \int \frac {\left (-40 x^2+40 x^3-10 x^4\right ) \log ^2(x)+\left (2-3 x+x^2\right ) \log \left (x-x^2\right )+\log (x) \left (-2+5 x-2 x^2+\left (2-2 x+x^2\right ) \log \left (x-x^2\right )\right )}{\left (120 x^2-120 x^3+30 x^4\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)/l n(x)**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2907\)
Exception generated. \[ \int \frac {-50 x^4+\left (-450+300 x-50 x^2-150 x^4\right ) \log (x)+\left (450-150 x-150 x^4\right ) \log ^2(x)+\left (450-150 x-50 x^4\right ) \log ^3(x)}{-x^3+25 x^5+\left (-3 x^3+75 x^5\right ) \log (x)+\left (225 x-150 x^2+22 x^3+75 x^5\right ) \log ^2(x)+\left (225 x-150 x^2+24 x^3+25 x^5\right ) \log ^3(x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)*ln( x)+25*x**5-x**3),x)
Output:
Exception raised: PolynomialError >> 1/(390625*x**18 + 1500000*x**16 - 937 5000*x**15 + 16222500*x**14 - 27000000*x**13 + 126257400*x**12 - 279045000 *x**11 + 391055526*x**10 - 831794400*x**9 + 1973451600*x**8 - 2835405000*x **7 + 327827250
input file name test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2918\)
Exception generated. \[ \int \frac {2 x+e^4 x^2+x^4+e^2 \left (-1-2 x^3\right )+e^{2-x} \left (3 x+e^4 x^2+x^4+e^2 \left (-2-2 x^3\right )\right )+\left (-1-2 e^4 x+4 e^2 x^2-2 x^3+e^{2-x} \left (-1-2 e^4 x+4 e^2 x^2-2 x^3\right )\right ) \log \left (1+e^{2-x}\right )+\left (e^4-2 e^2 x+x^2+e^{2-x} \left (e^4-2 e^2 x+x^2\right )\right ) \log ^2\left (1+e^{2-x}\right )}{-x^2+e^4 x^3+x^5+e^2 \left (x-2 x^4\right )+e^{2-x} \left (-x^2+e^4 x^3+x^5+e^2 \left (x-2 x^4\right )\right )+\left (x-2 e^4 x^2-2 x^4+e^2 \left (-1+4 x^3\right )+e^{2-x} \left (x-2 e^4 x^2-2 x^4+e^2 \left (-1+4 x^3\right )\right )\right ) \log \left (1+e^{2-x}\right )+\left (e^4 x-2 e^2 x^2+x^3+e^{2-x} \left (e^4 x-2 e^2 x^2+x^3\right )\right ) \log ^2\left (1+e^{2-x}\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
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 test_cases/extra_tests/361_Hebisch_1
Test file number \(361\)
Integral number in file \(2965\)
Exception generated. \[ \int \frac {-5 \log (3)+\left (x-12 x^6-9 x^9\right ) \log ^2(x)}{-5 x \log (3) \log (x)+\left (-x^2+2 x^7+x^{10}\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(x**18 + 4*x**15 + 4*x**12 - 2*x**1 0 - 4*x**7 + x**2) contains an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(23\)
Exception generated. \[ \int \frac {-2 x-x^2+\left (-2-x-2 x^2-2 x^3-x^4\right ) \log (x)+\left (-2 x-4 x^2-2 x^3\right ) \log ^2(x)+\left (-2 x-x^2\right ) \log ^3(x)+\left (2+3 x+x^2\right ) \log (x) \log \left (\left (8+8 x+2 x^2\right ) \log (x)\right )}{\left (2 x^3+x^4\right ) \log (x)+\left (4 x^2+2 x^3\right ) \log ^2(x)+\left (2 x+x^2\right ) \log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(63\)
Exception generated. \[ \int \frac {108 x^3+30 x^4+2 x^5+\left (-108 x^3-21 x^4-x^5\right ) \log (x)+\left (27 x^3+3 x^4\right ) \log ^2(x)+\left (\left (432 x^3+105 x^4+7 x^5\right ) \log (x)+\left (-432 x^3-87 x^4-4 x^5\right ) \log ^2(x)+\left (108 x^3+15 x^4\right ) \log ^3(x)\right ) \log (\log (x))}{\left (36+12 x+x^2\right ) \log (x)+(-36-6 x) \log ^2(x)+9 \log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(87\)
Exception generated. \[ \int \frac {16 x^2-112 x^3-128 x^2 \log (x)+\left (-64 x^2+32 x^3+\left (-64 x+32 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-8 x+12 x^2+(-8+12 x) \log (x)\right ) \log ^2(x+\log (x))+\left (8 x^2-88 x^3-96 x^2 \log (x)+\left (-48 x^2+24 x^3+\left (-48 x+24 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-6 x+8 x^2+(-6+8 x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log \left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )+\left (-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )}{-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))} \, dx=\text {Exception raised: TypeError} \] Input:
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+((24* 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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(89\)
Exception generated. \[ \int \frac {\left (4-4 e^4+e^8\right ) \log ^2(x)+\left (-4+2 e^4\right ) \log ^2(x) \log \left (4 x^2\right )+\log ^2(x) \log ^2\left (4 x^2\right )+e^{\frac {4}{-2+e^4+\log \left (4 x^2\right )}} \left (4-4 e^4+e^8+\left (4+4 e^4-e^8\right ) \log (x)+\left (-4+2 e^4+\left (4-2 e^4\right ) \log (x)\right ) \log \left (4 x^2\right )+(1-\log (x)) \log ^2\left (4 x^2\right )\right )}{\left (4-4 e^4+e^8\right ) \log ^2(x)+\left (-4+2 e^4\right ) \log ^2(x) \log \left (4 x^2\right )+\log ^2(x) \log ^2\left (4 x^2\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)+(exp( 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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(383\)
Exception generated. \[ \int \frac {\left (-36 x^2+36 x \log (x)\right ) \log (x-\log (x))+\frac {e^x \left (-15+15 x+\left (-15 x-15 x^2+(15+15 x) \log (x)\right ) \log (x-\log (x))\right )}{\log (x-\log (x))}}{e^x \left (15 x^2-60 x^4+\left (-15 x+60 x^3\right ) \log (x)\right )+\frac {e^{2 x} \left (-25 x^3+25 x^2 \log (x)\right )}{\log (x-\log (x))}+\left (18 x^3-36 x^5+\left (-18 x^2+36 x^4\right ) \log (x)\right ) \log (x-\log (x))} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)*ln(x-ln(x)))/((25*x**2*ln(x)-25*x**3)*l n(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)
Output:
Exception raised: PolynomialError >> 1/(-5*_t0*x**2 + 5*x**3) contains an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(431\)
Exception generated. \[ \int \frac {3 x+x^2+\left (6 x+2 x^2\right ) \log \left (\frac {3+x}{4}\right )+\left (3 x+x^2\right ) \log ^2\left (\frac {3+x}{4}\right )+\log ^2(x) \left (3+x-9 x^2+\left (6+2 x-9 x^2-3 x^3\right ) \log \left (\frac {3+x}{4}\right )+(3+x) \log ^2\left (\frac {3+x}{4}\right )\right )}{\log (x) \left (-3 x^2-x^3+\left (-6 x^2-2 x^3\right ) \log \left (\frac {3+x}{4}\right )+\left (-3 x^2-x^3\right ) \log ^2\left (\frac {3+x}{4}\right )\right )+\log ^2(x) \left (-3 x+2 x^2-8 x^3-3 x^4+\left (-6 x+4 x^2-7 x^3-3 x^4\right ) \log \left (\frac {3+x}{4}\right )+\left (-3 x+2 x^2+x^3\right ) \log ^2\left (\frac {3+x}{4}\right )\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
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) conta ins an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(480\)
Exception generated. \[ \int \frac {9+x+(-27-4 x) \log (x)+(-3+5 x) \log ^2(x)+(6-2 x) \log ^3(x)}{\left (9 x+x^2\right ) \log (x)+\left (-3 x-2 x^2\right ) \log ^2(x)+\left (-6 x+x^2\right ) \log ^3(x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
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 test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(491\)
Exception generated. \[ \int \frac {4 x^5+\left (-4 x^3-2 x^5\right ) \log \left (4+4 x^2+x^4\right )+\left (-6-3 x^2\right ) \log ^2\left (4+4 x^2+x^4\right )}{\left (-2 x^4-x^6\right ) \log \left (4+4 x^2+x^4\right )+\left (6 x-2 x^2+3 x^3-x^4+\left (2 x^2+x^4\right ) \log (5)\right ) \log ^2\left (4+4 x^2+x^4\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
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 test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(538\)
Exception generated. \[ \int \frac {(4+4 x) \log (1+x)+(-4-8 x) \log ^2(1+x)+\log (3 x) (-4 x+(4+8 x) \log (1+x))}{\left (x+x^2\right ) \log (3 x) \log (1+x)+\left (-x-x^2\right ) \log ^2(1+x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(x**2 + x) contains an element of t he set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(565\)
Exception generated. \[ \int \frac {\left (12 x+18 x^2+e^x \left (12+12 x+6 x^2\right )+\left (6 x+6 e^x x\right ) \log (x)\right ) \log \left (25 e^x x^2+25 x^3+\left (50 e^x x+50 x^2\right ) \log (x)+\left (25 e^x+25 x\right ) \log ^2(x)\right )+\left (3 e^x x+3 x^2+\left (3 e^x+3 x\right ) \log (x)\right ) \log ^2\left (25 e^x x^2+25 x^3+\left (50 e^x x+50 x^2\right ) \log (x)+\left (25 e^x+25 x\right ) \log ^2(x)\right )}{2 e^x x+2 x^2+\left (2 e^x+2 x\right ) \log (x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)+25*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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(596\)
Exception generated. \[ \int \frac {-180 x^2+60 x^3+e^{\frac {1}{4} (3+4 x)} \left (-36 x^2+24 x^3-3 x^4\right )+e^x \left (36 x^2-24 x^3+3 x^4\right )}{25-10 e^x+e^{2 x}+e^{\frac {1}{2} (3+4 x)}+e^{\frac {1}{4} (3+4 x)} \left (10-2 e^x\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate(((-3*x**4+24*x**3-36*x**2)*exp(3/4+x)+(3*x**4-24*x**3+36*x**2)*e xp(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)
Output:
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*_t 0 + 10*_t0*exp(
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(601\)
Exception generated. \[ \int \frac {96+e^4 (-8-2 x)+24 x+\left (96-8 e^4\right ) \log (x)-10 \log ^2(x)}{\left (-96 x-24 x^2+e^4 \left (8 x+2 x^2\right )\right ) \log (x)+\left (10 x+3 x^2\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(9*x**3 + 60*x**2 + 100*x) contains an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(760\)
Exception generated. \[ \int \frac {200 x^2+80 x^3+\left (-50 x^3-20 x^4\right ) \log (x)+\left (-400 x-160 x^2+\left (100 x^2+40 x^3\right ) \log (x)\right ) \log \left (x^2\right )+\left (200+80 x+\left (-50 x-20 x^2\right ) \log (x)\right ) \log ^2\left (x^2\right )+\left (\frac {4-x \log (x)}{x}\right )^{\frac {x}{-2 x+2 \log \left (x^2\right )}} \left (-100 x-85 x^2-5 x^3+10 x^3 \log (x)+\left (100+125 x+5 x^2-20 x^2 \log (x)\right ) \log \left (x^2\right )+(-40+10 x \log (x)) \log ^2\left (x^2\right )+\left (200+40 x+\left (-50 x-10 x^2\right ) \log (x)+\left (-100-20 x+\left (25 x+5 x^2\right ) \log (x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {4-x \log (x)}{x}\right )\right )}{-8 x^2+2 x^3 \log (x)+\left (16 x-4 x^2 \log (x)\right ) \log \left (x^2\right )+(-8+2 x \log (x)) \log ^2\left (x^2\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)*l n(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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(909\)
Exception generated. \[ \int \frac {\left (1+e^5-2 x\right ) \log ^2\left (1+e^5-2 x\right )+e^{\frac {x}{\log \left (1+e^5-2 x\right )}} \left (-2 x^2 \log \left (\frac {3 x}{2}\right )+\left (-x-e^5 x+2 x^2\right ) \log \left (1+e^5-2 x\right ) \log \left (\frac {3 x}{2}\right )\right )}{\left (x+e^5 x-2 x^2\right ) \log ^2\left (1+e^5-2 x\right ) \log \left (\frac {3 x}{2}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(922\)
Exception generated. \[ \int \frac {e^{-2-e^{\frac {-x+(4-\log (3)) \log \left (x^3\right )}{\log \left (x^3\right )}}-x} \left (e^{\frac {-x+(4-\log (3)) \log \left (x^3\right )}{\log \left (x^3\right )}} \left (-3+\log \left (x^3\right )\right )-\log ^2\left (x^3\right )\right )}{\log ^2\left (x^3\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(939\)
Exception generated. \[ \int \frac {e^{\frac {4 x^2+x^2 \log (169)}{20 \log (50-x)}} \left (-4 x^2-x^2 \log (169)+\left (-400 x+8 x^2+\left (-100 x+2 x^2\right ) \log (169)\right ) \log (50-x)\right )}{(-1000+20 x) \log ^2(50-x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1051\)
Exception generated. \[ \int \frac {e^{\frac {1}{15} \left (12+5 e^{\frac {2-16 x+4 x^2+4 x \log \left (25+10 x+x^2\right )}{-4 x+x^2+x \log \left (25+10 x+x^2\right )}} x\right )+\frac {2-16 x+4 x^2+4 x \log \left (25+10 x+x^2\right )}{-4 x+x^2+x \log \left (25+10 x+x^2\right )}} \left (40+64 x-28 x^2-3 x^3+x^4+\left (-10-42 x+2 x^2+2 x^3\right ) \log \left (25+10 x+x^2\right )+\left (5 x+x^2\right ) \log ^2\left (25+10 x+x^2\right )\right )}{240 x-72 x^2-9 x^3+3 x^4+\left (-120 x+6 x^2+6 x^3\right ) \log \left (25+10 x+x^2\right )+\left (15 x+3 x^2\right ) \log ^2\left (25+10 x+x^2\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1056\)
Exception generated. \[ \int \frac {\left (-2 e^x x+2 x^2\right ) \log ^2(x)+\left (\left (e^x (-10-2 x)+10 x+2 x^2\right ) \log ^2(x)+\left (10 x+12 x^2+2 x^3+e^{2 x} \left (10 x+2 x^2\right )+e^x \left (-10 x-12 x^2-2 x^3\right )\right ) \log ^3(x)\right ) \log (5+x)+\left (2 x \log (x)+\left (\left (10-8 x-2 x^2+e^x (10+2 x)\right ) \log (x)+\left (10 x+2 x^2+e^x \left (-10 x-2 x^2\right )\right ) \log ^2(x)\right ) \log (5+x)\right ) \log (x \log (5+x))+(-10-2 x) \log (5+x) \log ^2(x \log (5+x))}{\left (5 x+x^2\right ) \log ^3(x) \log (5+x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1088\)
Exception generated. \[ \int \frac {30 x^2-10 x^4+\left (30-10 x^2+9 x^5-6 x^7+x^9-60 x^6 \log (3)\right ) \log (x)+\left (18 x^3-12 x^5+2 x^7-120 x^4 \log (3)\right ) \log ^2(x)+\left (9 x-6 x^3+x^5-60 x^2 \log (3)\right ) \log ^3(x)+\left (\left (-30-50 x^2+40 x^4\right ) \log (x)+20 x^2 \log ^2(x)\right ) \log (\log (x))}{\left (9 x^5-6 x^7+x^9\right ) \log (x)+\left (18 x^3-12 x^5+2 x^7\right ) \log ^2(x)+\left (9 x-6 x^3+x^5\right ) \log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1109\)
Exception generated. \[ \int \frac {-11 x+e^{\sqrt [4]{e}} \left (11 x+12 x^2\right )+\left (2 x+e^{\sqrt [4]{e}} \left (-2 x-2 x^2\right )\right ) \log \left (x+e^{\sqrt [4]{e}} \left (-x-x^2\right )\right )}{-25-5 x^2+e^{\sqrt [4]{e}} \left (25+25 x+5 x^2+5 x^3\right )+\left (10+x^2+e^{\sqrt [4]{e}} \left (-10-10 x-x^2-x^3\right )\right ) \log \left (x+e^{\sqrt [4]{e}} \left (-x-x^2\right )\right )+\left (-1+e^{\sqrt [4]{e}} (1+x)\right ) \log ^2\left (x+e^{\sqrt [4]{e}} \left (-x-x^2\right )\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(x**2*exp(exp(1/4)) - x + x*exp(exp (1/4))) contains an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1133\)
Exception generated. \[ \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} \left (15 x^3+12 x^4+3 x^5+e^x \left (-15-12 x-x^3\right )+\left (-15 x^2-12 x^3-2 x^4\right ) \log (15)+\left (9 x^4+e^x \left (-3 x-2 x^2\right )-7 x^3 \log (15)\right ) \log (x)+\left (-e^x x+3 x^3-2 x^2 \log (15)\right ) \log ^2(x)\right )}{2 x^3+4 x^2 \log (x)+2 x \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1134\)
Exception generated. \[ \int \frac {e^{-\frac {180 x^3}{(-1+x) \log (x)}} \left (-180 x^2+180 x^3+\left (540 x^2-360 x^3\right ) \log (x)\right )}{\left (1-2 x+x^2\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1177\)
Exception generated. \[ \int \frac {200 x+300 x^2+80 x^3+120 x^4+8 x^5+12 x^6+e^{\frac {10}{5+x^2}} \left (-50 x-20 x^3-2 x^5\right )+e^{\frac {5}{5+x^2}} \left (150 x-75 x^2+10 x^3-40 x^4+6 x^5-3 x^6\right )+e^x \left (-200 x-100 x^2-80 x^3-40 x^4-8 x^5-4 x^6+e^{\frac {5}{5+x^2}} \left (50 x+25 x^2+30 x^3+10 x^4+2 x^5+x^6\right )\right )}{800+420 x^2+100 x^3+72 x^4+40 x^5+4 x^6+4 x^7+e^{\frac {10}{5+x^2}} \left (50-5 x^2-8 x^4-x^6\right )+e^{\frac {5}{5+x^2}} \left (-400-85 x^2-25 x^3+14 x^4-10 x^5+3 x^6-x^7\right )+e^x \left (-100 x^2-40 x^4-4 x^6+e^{\frac {5}{5+x^2}} \left (25 x^2+10 x^4+x^6\right )\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)*e xp(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)
Output:
Exception raised: PolynomialError >> 1/(x**8 + 6*x**6 - 11*x**4 - 60*x**2 + 100) contains an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1191\)
Exception generated. \[ \int \frac {\left (-128 x^3+256 x^4+\left (128 x^2-256 x^3\right ) \log (2)+\left (-128 x^2+256 x^3+\left (128 x-256 x^2\right ) \log (2)\right ) \log (x)\right ) \log \left (-12-x+x^2\right )+\left (768 x+64 x^2-64 x^3+\left (-768-832 x+64 x^3\right ) \log (2)+\left (-768 x-64 x^2+64 x^3\right ) \log (x)\right ) \log ^2\left (-12-x+x^2\right )}{-12 x^3-x^4+x^5+\left (-24 x^2-2 x^3+2 x^4\right ) \log (x)+\left (-12 x-x^2+x^3\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1204\)
Exception generated. \[ \int \frac {10 x-20 x \log (x)+\left (45+110 x+27 x^2\right ) \log ^2(x)}{-10 x^2 \log (x)+\left (45 x+55 x^2+9 x^3\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate(((27*x**2+110*x+45)*ln(x)**2-20*x*ln(x)+10*x)/((9*x**3+55*x**2+4 5*x)*ln(x)**2-10*x**2*ln(x)),x)
Output:
Exception raised: PolynomialError >> 1/(81*x**5 + 990*x**4 + 3835*x**3 + 4 950*x**2 + 2025*x) contains an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1252\)
Exception generated. \[ \int \frac {-28+16 x+60000 x^4-10000 x^5+\left (24-12 x-30000 x^4+5000 x^5\right ) \log (x)+\left (-4+2 x+3750 x^4-625 x^5\right ) \log ^2(x)}{-16 x+10000 x^5+\left (12 x-5000 x^5\right ) \log (x)+\left (-2 x+625 x^5\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(390625*x**9 - 2500*x**5 + 4*x) con tains an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1295\)
Exception generated. \[ \int \frac {-24 x+4 e^{2 x} x+12 x^2+e^x \left (-12-8 x+8 x^2\right )}{3 x^2+e^{2 x} (1+x)+e^x \left (3+3 x+x^2\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(x**2 + 2*x + 1) contains an elemen t of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1316\)
Exception generated. \[ \int \frac {-5 x-x^2-6 x^3+10 x^4-4 x^5+(-10+2 x) \log (2 x)+\left (-2 x-12 x^2+20 x^3-8 x^4\right ) \log ^2(2 x)+\left (-6 x+10 x^2-4 x^3\right ) \log ^4(2 x)+\left (-x^2-3 x^3-x^5+\left (-x-6 x^2-2 x^4\right ) \log ^2(2 x)+\left (-3 x-x^3\right ) \log ^4(2 x)\right ) \log \left (\frac {1+3 x+x^3+\left (3+x^2\right ) \log ^2(2 x)}{x+\log ^2(2 x)}\right )}{x^2+3 x^3+x^5+\left (x+6 x^2+2 x^4\right ) \log ^2(2 x)+\left (3 x+x^3\right ) \log ^4(2 x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
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 test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1389\)
Exception generated. \[ \int \frac {15+27 x+12 x^2-3 x^3-3 x^4+\left (27 x+24 x^2-9 x^3-12 x^4\right ) \log (x)+\left (25 x+40 x^2+16 x^3-10 x^4-8 x^5+x^7\right ) \log ^2(x)}{\left (-15 x-27 x^2-12 x^3+3 x^4+3 x^5\right ) \log (x)+\left (475 x+1735 x^2+2364 x^3+1234 x^4-222 x^5-512 x^6-141 x^7+39 x^8+20 x^9\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
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) co ntains an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1411\)
Exception generated. \[ \int \frac {12 x+16 x^2+\left (-14 x-8 x^2\right ) \log (x)+\left (3 x+10 x^2+8 x^3\right ) \log ^3(x)+(12+16 x) \log (3+4 x)}{\left (3 x+4 x^2\right ) \log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)/ln(x)**3,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1469\)
Exception generated. \[ \int \frac {\left (-x^3-x^4\right ) \log (x)+\left (5 x^2+6 x^3+x^4+\left (5 x^2+6 x^3+x^4\right ) \log (x)\right ) \log (5+x)+\left (-500-600 x-100 x^2\right ) \log ^2(5+x)+\left (\left (5 x^2+11 x^3+2 x^4\right ) \log (x) \log (5+x)+\left (500+1225 x+475 x^2+50 x^3\right ) \log ^2(5+x)\right ) \log \left (\frac {x^2 \log (x)+(100+25 x) \log (5+x)}{25 x \log (5+x)}\right )}{\left (5 x^2+x^3\right ) \log (x) \log (5+x)+\left (500+225 x+25 x^2\right ) \log ^2(5+x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(75*x**3 + 975*x**2 + 4200*x + 6000 ) contains an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1480\)
Exception generated. \[ \int \frac {e^{e^{\frac {1}{x^2 \log ^2(2+\log (4))}}} \left (-2 e^{x+\frac {1}{x^2 \log ^2(2+\log (4))}}+e^x \left (x^2+x^3\right ) \log ^2(2+\log (4))\right )}{8 x^2 \log ^2(2+\log (4))} \, dx=\text {Exception raised: GeneratorsError} \] Input:
integrate(1/8*(-2*exp(x)*exp(1/x**2/ln(2+2*ln(2))**2)+(x**3+x**2)*exp(x)*l n(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 )
Output:
Exception raised: GeneratorsError >> polynomial ring and it's ground domai n share generators
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1529\)
Exception generated. \[ \int \frac {2+2 x+2 \log (16)-2 x \log (x)+\left (26 x+2 x^2\right ) \log ^2(x)}{\left (-2 x-2 x^2-2 x \log (16)\right ) \log (x)+\left (x+26 x^2+x^3+x \log (16)\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(x**5 + 52*x**4 + 8*x**3*log(2) + 6 78*x**3 + 52*x**2 + 208*x**2*log(2) + x + 8*x*log(2) + 16*x*log(2)**2) con tains an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1541\)
Exception generated. \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1629\)
Exception generated. \[ \int \frac {5-25 x-108 x^2-180 x^3+36 x^2 \log (x)+\left (15-11 x-60 x^2+(-5+12 x) \log (x)\right ) \log (3+5 x-\log (x))+(-3-5 x+\log (x)) \log ^2(3+5 x-\log (x))}{360 x^2+168 x^3-720 x^4+\left (-120 x^2+144 x^3\right ) \log (x)+\left (60 x-44 x^2-240 x^3+\left (-20 x+48 x^2\right ) \log (x)\right ) \log (3+5 x-\log (x))+\left (-12 x-20 x^2+4 x \log (x)\right ) \log ^2(3+5 x-\log (x))} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)-180*x**3-108*x**2-25*x+5)/((4*x*ln(x)-2 0*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)
Output:
Exception raised: PolynomialError >> 1/(-_t0*x + 5*x**2 + 3*x) contains an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1738\)
Exception generated. \[ \int \frac {e^{2 x} \left (15 x^2+20 x^3-4 x^4\right )+e^{2 x} \left (24 x+19 x^2-2 x^3\right ) \log (4-x)+e^{2 x} \left (2 x+2 x^2\right ) \log ^2(4-x)}{-2 x^2+e^{2 x} \left (12 x^3-2 x^4\right )+\left (-4 x+e^{2 x} \left (12 x^2-x^3\right )\right ) \log (4-x)+\left (-2+e^{2 x} x^2\right ) \log ^2(4-x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(x - 4) contains an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1777\)
Exception generated. \[ \int \frac {-e^{5 x} x^5+e^{10 x} \left (-3 x^4+x^5-x^6\right )+\left (e^{10 x} \left (15 x^4-4 x^5+3 x^6\right )+e^{5 x} \left (4 x^5+5 x^6\right )\right ) \log (x)}{\left (e^{5 x} x^6+e^{10 x} \left (3 x^5-x^6+x^7\right )\right ) \log (x)+\left (2 x^2+e^{5 x} \left (12 x-4 x^2+4 x^3\right )+e^{10 x} \left (18-12 x+14 x^2-4 x^3+2 x^4\right )\right ) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(4*_t0**2*x**8 - 16*_t0**2*x**7 + 7 2*_t0**2*x**6 - 160*_t0**2*x**5 + 364*_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 + 48* _t0*x**9 - 76*_
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1845\)
Exception generated. \[ \int \frac {e^{4 x} (-256+64 x)+(16-5 x) \log (2)+(-256+64 x) \log ^2(2)+e^{2 x} \left (-16+37 x-8 x^2+(512-128 x) \log (2)\right )+\left (e^{4 x} (-128+32 x)+(4-x) \log (2)+(-128+32 x) \log ^2(2)+e^{2 x} \left (-4+9 x-2 x^2+(256-64 x) \log (2)\right )\right ) \log \left (-\frac {4}{-4+x}\right )+\left (e^{4 x} (-16+4 x)+e^{2 x} (32-8 x) \log (2)+(-16+4 x) \log ^2(2)\right ) \log ^2\left (-\frac {4}{-4+x}\right )}{e^{4 x} \left (-256-192 x+64 x^2\right )+\left (16 x-4 x^2\right ) \log (2)+\left (-256-192 x+64 x^2\right ) \log ^2(2)+e^{2 x} \left (-16 x+4 x^2+\left (512+384 x-128 x^2\right ) \log (2)\right )+\left (e^{4 x} \left (-128-96 x+32 x^2\right )+\left (4 x-x^2\right ) \log (2)+\left (-128-96 x+32 x^2\right ) \log ^2(2)+e^{2 x} \left (-4 x+x^2+\left (256+192 x-64 x^2\right ) \log (2)\right )\right ) \log \left (-\frac {4}{-4+x}\right )+\left (e^{4 x} \left (-16-12 x+4 x^2\right )+e^{2 x} \left (32+24 x-8 x^2\right ) \log (2)+\left (-16-12 x+4 x^2\right ) \log ^2(2)\right ) \log ^2\left (-\frac {4}{-4+x}\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((((4*x-16)*exp(x)**4+(-8*x+32)*ln(2)*exp(x)**2+(4*x-16)*ln(2)**2 )*ln(-4/(-4+x))**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/(-4+x))+(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/(-4+x))**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/(-4+x))+(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)
Output:
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 genera tors.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1911\)
Exception generated. \[ \int \frac {\left (6 x^2+2 x^3\right ) \log (1-x)+\left (3+x-4 x^2\right ) \log ^2(1-x)+\left (\left (6 x+2 x^2\right ) \log (1-x)+\left (-x+x^2\right ) \log ^2(1-x)\right ) \log (x)}{-x^3+x^4+\left (-2 x^2+2 x^3\right ) \log (x)+\left (-x+x^2\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(1944\)
Exception generated. \[ \int \frac {e^x x \log (x)+e^x x^2 \log ^2(x)+e^{e^{3 e^{-x}}} \left (-3 e^{3 e^{-x}} x \log (x)+e^x x \log ^2(x)\right )+\left (-e^{e^{3 e^{-x}}+x}-e^x x\right ) \log \left (e^{e^{3 e^{-x}}}+x\right )}{e^{e^{3 e^{-x}}+x} x \log ^2(x)+e^x x^2 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)*ln(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*exp( x)*ln(x)**2),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(2357\)
Exception generated. \[ \int \frac {\left (-8 x+8 x^2+\left (3 x-4 x^2+x^3\right ) \log (x)\right ) \log \left (\frac {1}{3} (8+(-3+x) \log (x))\right )+\left (-6+8 x-2 x^2+\left (2 x-2 x^2\right ) \log (x)\right ) \log \left (\log \left (\frac {1}{3} (8+(-3+x) \log (x))\right )\right )+\left (-8 x+\left (3 x-x^2\right ) \log (x)\right ) \log \left (\frac {1}{3} (8+(-3+x) \log (x))\right ) \log ^2\left (\log \left (\frac {1}{3} (8+(-3+x) \log (x))\right )\right )+(-6+2 x+2 x \log (x)) \log ^3\left (\log \left (\frac {1}{3} (8+(-3+x) \log (x))\right )\right )}{\left (16 x+\left (-6 x+2 x^2\right ) \log (x)\right ) \log \left (\frac {1}{3} (8+(-3+x) \log (x))\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)/l n(1/3*ln(x)*(-3+x)+8/3),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(2388\)
Exception generated. \[ \int \frac {-2 x^3+x^5+\left (2 x^3-x^5\right ) \log \left (\frac {x}{3}\right )+\left (320-240 x-160 x^2+62 x^3-20 x^4+29 x^5+10 x^6\right ) \log ^2\left (\frac {x}{3}\right )+\left (-2 x^5 \log \left (\frac {x}{3}\right )+\left (160 x^2-240 x^3+10 x^4+58 x^5+10 x^6\right ) \log ^2\left (\frac {x}{3}\right )\right ) \log \left (\frac {x^3+\left (-80+120 x-5 x^2-29 x^3-5 x^4\right ) \log \left (\frac {x}{3}\right )}{x^2 \log \left (\frac {x}{3}\right )}\right )}{-x^4 \log \left (\frac {x}{3}\right )+\left (80 x-120 x^2+5 x^3+29 x^4+5 x^5\right ) \log ^2\left (\frac {x}{3}\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
Exception raised: PolynomialError >> 1/(25*x**9 + 290*x**8 + 891*x**7 - 91 0*x**6 - 6135*x**5 + 3440*x**4 + 15200*x**3 - 19200*x**2 + 6400*x) contain s an element of the set of generators.
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(2392\)
Exception generated. \[ \int \frac {e^{-\frac {1250}{x \log (2 x)}} (-2500-2500 \log (2 x))+e^{-\frac {2500}{x \log (2 x)}} (2500+2500 \log (2 x))}{x^2 \log ^2(2 x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(2539\)
Exception generated. \[ \int \frac {50-9 x+\left (-3 x+2 x^2\right ) \log \left (\frac {5}{x}\right )+\left (-7 x-2 x^2\right ) \log ^2\left (\frac {5}{x}\right )+\left (-x+2 x^2\right ) \log ^3\left (\frac {5}{x}\right )}{-27 x+x^2+\left (31 x+7 x^2\right ) \log \left (\frac {5}{x}\right )+\left (-6 x-7 x^2-x^3\right ) \log ^2\left (\frac {5}{x}\right )+\left (2 x-x^2+x^3\right ) \log ^3\left (\frac {5}{x}\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
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)
Output:
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 test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(2561\)
Exception generated. \[ \int \frac {5^{\frac {5}{\left (x+x^2 \log (5)\right ) \log (x)}} e^{-4+5^{\frac {5}{\left (x+x^2 \log (5)\right ) \log (x)}}} \left (-5 \log (5)-5 x \log ^2(5)+\left (-5 \log (5)-10 x \log ^2(5)\right ) \log (x)\right )}{\left (x^2+2 x^3 \log (5)+x^4 \log ^2(5)\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(2630\)
Exception generated. \[ \int \frac {\left (-30-12 x^2-6 x^3+6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\log \left (\frac {2}{x}\right ) \left (\left (60-6 x^3+12 x^4\right ) \log \left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\left (30+12 x^2+6 x^3-6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )\right )}{\left (-5 x^3-2 x^5-x^6+x^7\right ) \log ^3\left (\frac {2}{x}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(2647\)
Exception generated. \[ \int \frac {e^{\frac {1}{3} (-4-15 x)} \left (-75 \log ^2(x)+e^{\frac {2}{3} \left (-1+e^{\frac {x}{\log (x)}}\right )} \left (-75 \log ^2(x)+e^{\frac {x}{\log (x)}} (-10+10 \log (x))\right )\right )}{\log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(2655\)
Exception generated. \[ \int \frac {\left (-250 x^2+50 x^3\right ) \log (x) \log (3+x)+\left (375 x+50 x^2-25 x^3+\left (-750 x-250 x^2\right ) \log (x)\right ) \log ^2(3+x)}{\left (-54000+14400 x+4320 x^2-1728 x^3+144 x^4\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(2656\)
Exception generated. \[ \int \frac {e^{\frac {x}{4 \log (x)}} \left (-e^{\frac {625-1000 x+100 x^2+440 x^3-71 x^4-88 x^5+4 x^6+8 x^7+x^8}{x^4}} x^5-x^6-x^7+\left (e^{\frac {625-1000 x+100 x^2+440 x^3-71 x^4-88 x^5+4 x^6+8 x^7+x^8}{x^4}} x^5+x^6+x^7\right ) \log (x)+\left (4 x^5+8 x^6+e^{\frac {625-1000 x+100 x^2+440 x^3-71 x^4-88 x^5+4 x^6+8 x^7+x^8}{x^4}} \left (-10000+12000 x-800 x^2-1760 x^3-352 x^5+32 x^6+96 x^7+16 x^8\right )\right ) \log ^2(x)\right )}{4 x^5 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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+440*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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(2688\)
Exception generated. \[ \int \frac {\left (3+12 x^2\right ) \log ^2(x)+e^{\frac {4+4 x \log (x)}{x \log (x)}} \left (-80 x-80 x \log (x)+60 x^2 \log ^2(x)\right )+e^{\frac {2 (4+4 x \log (x))}{x \log (x)}} \left (-200 x-200 x \log (x)+75 x^2 \log ^2(x)\right )}{\log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
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)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/362_Hebisch_2
Test file number \(362\)
Integral number in file \(2709\)