Exception generated. \[ \int \frac {e^{\frac {x^3}{4+2 x+\log (2+x)}} \left (16+16 x+28 x^2+19 x^3+4 x^4+\left (8+4 x+6 x^2+3 x^3\right ) \log (2+x)+\log ^2(2+x)\right )}{16+16 x+4 x^2+(8+4 x) \log (2+x)+\log ^2(2+x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((ln(2+x)**2+(3*x**3+6*x**2+4*x+8)*ln(2+x)+4*x**4+19*x**3+28*x**2 +16*x+16)*exp(x**3/(ln(2+x)+2*x+4))/(ln(2+x)**2+(4*x+8)*ln(2+x)+4*x**2+16* x+16),x)
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 \(2746\)
Exception generated. \[ \int \frac {-8 x+8 x^2+\left (8 x-16 x^2\right ) \log (x)+\frac {e^{-3+x^2} \left (-2 x+2 x^2+\left (6 x-4 x^2-8 x^3\right ) \log (x)\right )}{x}+\left (16 x-16 x \log (x)+\frac {e^{-3+x^2} \left (4 x+\left (4-4 x-8 x^2\right ) \log (x)\right )}{x}\right ) \log \left (4 \log (5)+\frac {e^{-3+x^2} \log (5)}{x}\right )+\left (8+\frac {2 e^{-3+x^2}}{x}\right ) \log ^2\left (4 \log (5)+\frac {e^{-3+x^2} \log (5)}{x}\right )}{e^{-3+x^2} \log ^2(x)+4 x \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((2*exp(-ln(x)+x**2-3)+8)*ln(ln(5)*exp(-ln(x)+x**2-3)+4*ln(5))** 2+(((-8*x**2-4*x+4)*ln(x)+4*x)*exp(-ln(x)+x**2-3)-16*x*ln(x)+16*x)*ln(ln(5 )*exp(-ln(x)+x**2-3)+4*ln(5))+((-8*x**3-4*x**2+6*x)*ln(x)+2*x**2-2*x)*exp( -ln(x)+x**2-3)+(-16*x**2+8*x)*ln(x)+8*x**2-8*x)/(x*ln(x)**2*exp(-ln(x)+x** 2-3)+4*x*ln(x)**2),x)
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 \(2942\)
Exception generated. \[ \int \frac {e \left (-30 x^4-5 x^5\right )+\left (x^3+30 x^5+5 x^6\right ) \log ^2(x)+\left (e \left (60 x^2+10 x^3\right )+\left (-x-60 x^3-10 x^4\right ) \log ^2(x)\right ) \log (2 x)+\left (e (-30-5 x)+\left (30 x+5 x^2\right ) \log ^2(x)\right ) \log ^2(2 x)+\left (6+x-12 x^2-2 x^3\right ) \log ^2(x) \log (6+x)}{\left (30 x^5+5 x^6\right ) \log ^2(x)+\left (-60 x^3-10 x^4\right ) \log ^2(x) \log (2 x)+\left (30 x+5 x^2\right ) \log ^2(x) \log ^2(2 x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((5*x**2+30*x)*ln(x)**2+(-5*x-30)*exp(1))*ln(2*x)**2+((-10*x**4 -60*x**3-x)*ln(x)**2+(10*x**3+60*x**2)*exp(1))*ln(2*x)+(-2*x**3-12*x**2+x+ 6)*ln(x)**2*ln(6+x)+(5*x**6+30*x**5+x**3)*ln(x)**2+(-5*x**5-30*x**4)*exp(1 ))/((5*x**2+30*x)*ln(x)**2*ln(2*x)**2+(-10*x**4-60*x**3)*ln(x)**2*ln(2*x)+ (5*x**6+30*x**5)*ln(x)**2),x)
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 \(2964\)
Exception generated. \[ \int \frac {\left (\frac {16}{e^{25}}+x\right ) \log \left (\frac {16}{e^{25}}+x\right )+\left (\frac {16 x}{e^{25}}+x^2\right ) \log (x) \log ^2\left (\frac {16}{e^{25}}+x\right )+\left (-x \log (x)+\left (-\frac {16}{e^{25}}-x\right ) \log (x) \log \left (\frac {16}{e^{25}}+x\right )\right ) \log (\log (x))}{\left (\frac {16 x^2}{e^{25}}+x^3\right ) \log (x) \log ^2\left (\frac {16}{e^{25}}+x\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((-exp(4*ln(2)-25)-x)*ln(x)*ln(exp(4*ln(2)-25)+x)-x*ln(x))*ln(l n(x))+(x*exp(4*ln(2)-25)+x**2)*ln(x)*ln(exp(4*ln(2)-25)+x)**2+(exp(4*ln(2) -25)+x)*ln(exp(4*ln(2)-25)+x))/(x**2*exp(4*ln(2)-25)+x**3)/ln(x)/ln(exp(4* ln(2)-25)+x)**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(25\)
Exception generated. \[ \int \frac {\left (8 x^2-50 x^3-2 x^4-16 x^5+100 x^6+4 x^7\right ) \log ^2\left (\frac {1}{x}\right )+\left (8-50 x-2 x^2\right ) \log \left (4-25 x-x^2\right )+\log \left (\frac {1}{x}\right ) \left (-50 x-4 x^2+\left (-8+50 x+2 x^2\right ) \log \left (4-25 x-x^2\right )\right )}{\left (-4 x^2+25 x^3+x^4\right ) \log ^2\left (\frac {1}{x}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((4*x**7+100*x**6-16*x**5-2*x**4-50*x**3+8*x**2)*ln(1/x)**2+((2* x**2+50*x-8)*ln(-x**2-25*x+4)-4*x**2-50*x)*ln(1/x)+(-2*x**2-50*x+8)*ln(-x* *2-25*x+4))/(x**4+25*x**3-4*x**2)/ln(1/x)**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(249\)
Exception generated. \[ \int \frac {\log (x) \log ^2(\log (x))+e^{\frac {3 x}{\log (\log (x))}} (-3+3 \log (x) \log (\log (x)))}{\log (x) \log ^2(\log (x))} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((3*ln(x)*ln(ln(x))-3)*exp(3/2*x/ln(ln(x)))**2+ln(x)*ln(ln(x))** 2)/ln(x)/ln(ln(x))**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(406\)
Exception generated. \[ \int \frac {2 x \log (x)+\left (-216 x^3+216 x^4-72 x^5+8 x^6\right ) \log ^3(x)+(6-2 x+(6-4 x) \log (x)) \log \left (9-6 x+x^2\right )}{\left (-27 x^3+27 x^4-9 x^5+x^6\right ) \log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((6-4*x)*ln(x)+6-2*x)*ln(x**2-6*x+9)+(8*x**6-72*x**5+216*x**4-2 16*x**3)*ln(x)**3+2*x*ln(x))/(x**6-9*x**5+27*x**4-27*x**3)/ln(x)**3,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(477\)
Exception generated. \[ \int \frac {\left (16 x-16 x^2+\left (96 x-48 x^2+\left (-32 x+16 x^2\right ) \log (x)\right ) \log (-3+\log (x))\right ) \log ^3\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )+\left (24 x-24 x^2+\left (-8 x+8 x^2\right ) \log (x)\right ) \log (-3+\log (x)) \log ^4\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )}{(3-3 x+(-1+x) \log (x)) \log (-3+\log (x))} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((8*x**2-8*x)*ln(x)-24*x**2+24*x)*ln(ln(x)-3)*ln(-x**2*ln(3)/(2 *x-2)/ln(ln(x)-3))**4+(((16*x**2-32*x)*ln(x)-48*x**2+96*x)*ln(ln(x)-3)-16* x**2+16*x)*ln(-x**2*ln(3)/(2*x-2)/ln(ln(x)-3))**3)/((-1+x)*ln(x)-3*x+3)/ln (ln(x)-3),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(591\)
Exception generated. \[ \int \frac {e^{7-e^{-\frac {x}{-x+\log (10+5 x)}}} \left (2 x^2+x^3+\left (-4 x-2 x^2\right ) \log (10+5 x)+(2+x) \log ^2(10+5 x)+e^{-\frac {x}{-x+\log (10+5 x)}} \left (-x^2+\left (2 x+x^2\right ) \log (10+5 x)\right )\right )}{2 x^2+x^3+\left (-4 x-2 x^2\right ) \log (10+5 x)+(2+x) \log ^2(10+5 x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((x**2+2*x)*ln(5*x+10)-x**2)*exp(-x/(ln(5*x+10)-x))+(2+x)*ln(5* x+10)**2+(-2*x**2-4*x)*ln(5*x+10)+x**3+2*x**2)/((2+x)*ln(5*x+10)**2+(-2*x* *2-4*x)*ln(5*x+10)+x**3+2*x**2)/exp(exp(-x/(ln(5*x+10)-x))-7),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(618\)
Exception generated. \[ \int \frac {e^{\frac {-8+x-2 \log (x)+10 x \log (4-2 x-\log (5))}{2 x \log (4-2 x-\log (5))}} \left (8 x-x^2+(-12+6 x+3 \log (5)) \log (4-2 x-\log (5))+\log (x) (2 x+(-4+2 x+\log (5)) \log (4-2 x-\log (5)))\right )}{\left (-4 x^2+2 x^3+x^2 \log (5)\right ) \log ^2(4-2 x-\log (5))} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((ln(5)+2*x-4)*ln(-ln(5)+4-2*x)+2*x)*ln(x)+(3*ln(5)+6*x-12)*ln( -ln(5)+4-2*x)-x**2+8*x)*exp(1/2*(-2*ln(x)+10*x*ln(-ln(5)+4-2*x)-8+x)/x/ln( -ln(5)+4-2*x))/(x**2*ln(5)+2*x**3-4*x**2)/ln(-ln(5)+4-2*x)**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(634\)
Exception generated. \[ \int \frac {2496 x \log (1-2 x)+(240-480 x) \log ^2(1-2 x)+\left (-768 x \log (1-2 x)+(-192+384 x) \log ^2(1-2 x)\right ) \log \left (x^2\right )}{-169 x^2+338 x^3+\left (104 x^2-208 x^3\right ) \log \left (x^2\right )+\left (-16 x^2+32 x^3\right ) \log ^2\left (x^2\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((384*x-192)*ln(1-2*x)**2-768*x*ln(1-2*x))*ln(x**2)+(-480*x+240 )*ln(1-2*x)**2+2496*x*ln(1-2*x))/((32*x**3-16*x**2)*ln(x**2)**2+(-208*x**3 +104*x**2)*ln(x**2)+338*x**3-169*x**2),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(685\)
Exception generated. \[ \int \frac {1-x}{\left (x^2+x \log \left (\frac {4}{x}\right )\right ) \log \left (x+\log \left (\frac {4}{x}\right )\right )+\left (2 x^2+2 x \log \left (\frac {4}{x}\right )\right ) \log ^2\left (x+\log \left (\frac {4}{x}\right )\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((1-x)/((2*x*ln(4/x)+2*x**2)*ln(ln(4/x)+x)**2+(x*ln(4/x)+x**2)*ln (ln(4/x)+x)),x)
Output:
Exception raised: PolynomialError >> 1/(_t0*x + x**2) contains an element of the set of generators.
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(771\)
Exception generated. \[ \int \frac {(-3+x) \log (3-x)+\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (-e^3 x-x^2+\left (-3 x+x^2\right ) \log (3-x)\right )}{\log (3-x)}}{\left (-3 x+x^2\right ) \log (3-x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((x**2-3*x)*ln(3-x)-x*exp(3)-x**2)*exp(-ln(ln(3-x))+exp(exp(5)) )*exp((exp(3)+x)*exp(-ln(ln(3-x))+exp(exp(5))))+(-3+x)*ln(3-x))/(x**2-3*x) /ln(3-x),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(772\)
Exception generated. \[ \int \frac {e^5 \left (-10-2 x+10 x^2+2 x^3\right )+e^{10} \left (10-8 x-2 x^2\right ) \log ^2(5+x)+\log \left (\frac {3 e^x}{x}\right ) \left (e^5 \left (-10 x-2 x^2\right )+4 e^{10} x \log (5+x)\right )}{5 x+11 x^2+7 x^3+x^4+e^5 \left (-10 x-12 x^2-2 x^3\right ) \log ^2(5+x)+e^{10} \left (5 x+x^2\right ) \log ^4(5+x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((4*x*exp(5)**2*ln(5+x)+(-2*x**2-10*x)*exp(5))*ln(exp(ln(3)+x)/x )+(-2*x**2-8*x+10)*exp(5)**2*ln(5+x)**2+(2*x**3+10*x**2-2*x-10)*exp(5))/(( x**2+5*x)*exp(5)**2*ln(5+x)**4+(-2*x**3-12*x**2-10*x)*exp(5)*ln(5+x)**2+x* *4+7*x**3+11*x**2+5*x),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(869\)
Exception generated. \[ \int \frac {15\ 2^{1-2 e^{e^2}} e^{e^2} \left (6-2 e^6-3 x\right )^{2 e^{e^2}}}{-6+2 e^6+3 x} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(30*exp(exp(2))*exp(exp(exp(2))*ln(-exp(6)-3/2*x+3))**2/(2*exp(6) +3*x-6),x)
Output:
Exception raised: TypeError >> Invalid NaN comparison
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(875\)
Exception generated. \[ \int \frac {-2 x^2-4 x^3+x^4+\left (8 x+18 x^2-x^4\right ) \log (4+x)+\left (-8 x-18 x^2+x^4\right ) \log ^2(4+x)+\left (\left (-8 x-2 x^2-4 x^3-x^4\right ) \log (4+x)+\left (-8+6 x-2 x^2+3 x^3+x^4\right ) \log ^2(4+x)\right ) \log \left (\frac {2 x+(2-2 x) \log (4+x)}{\log (4+x)}\right )}{\left (-4 x^3-x^4\right ) \log (4+x)+\left (-4 x^2+3 x^3+x^4\right ) \log ^2(4+x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((((x**4+3*x**3-2*x**2+6*x-8)*ln(4+x)**2+(-x**4-4*x**3-2*x**2-8*x )*ln(4+x))*ln(((2-2*x)*ln(4+x)+2*x)/ln(4+x))+(x**4-18*x**2-8*x)*ln(4+x)**2 +(-x**4+18*x**2+8*x)*ln(4+x)+x**4-4*x**3-2*x**2)/((x**4+3*x**3-4*x**2)*ln( 4+x)**2+(-x**4-4*x**3)*ln(4+x)),x)
Output:
Exception raised: PolynomialError >> 1/(x**3 + 2*x**2 - 7*x + 4) contains an element of the set of generators.
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(957\)
Exception generated. \[ \int \frac {-x^2+3 x^2 \log (x)-5 \log (4) \log ^2(x)}{-x^3 \log (x)+(-5+5 x \log (4)) \log ^2(x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((-10*ln(2)*ln(x)**2+3*x**2*ln(x)-x**2)/((10*x*ln(2)-5)*ln(x)**2- x**3*ln(x)),x)
Output:
Exception raised: PolynomialError >> 1/(20*x**3*log(2)**2 - 20*x**2*log(2) + 5*x) contains an element of the set of generators.
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1148\)
Exception generated. \[ \int \frac {\left (-20 x+e^{3+2 x} \left (16 x+16 x^2+4 x^3\right )\right ) \log (x) \log \left (\frac {-5 x+e^{3+2 x} (2+x)}{2+x}\right )+\left (20 x+10 x^2+e^{3+2 x} \left (-8-8 x-2 x^2\right )+\left (-10 x-5 x^2+e^{3+2 x} \left (4+4 x+x^2\right )\right ) \log (x)\right ) \log ^2\left (\frac {-5 x+e^{3+2 x} (2+x)}{2+x}\right )}{\left (-10 x-5 x^2+e^{3+2 x} \left (4+4 x+x^2\right )\right ) \log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((((x**2+4*x+4)*exp(3+2*x)-5*x**2-10*x)*ln(x)+(-2*x**2-8*x-8)*ex p(3+2*x)+10*x**2+20*x)*ln(((2+x)*exp(3+2*x)-5*x)/(2+x))**2+((4*x**3+16*x** 2+16*x)*exp(3+2*x)-20*x)*ln(x)*ln(((2+x)*exp(3+2*x)-5*x)/(2+x)))/((x**2+4* x+4)*exp(3+2*x)-5*x**2-10*x)/ln(x)**3,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1164\)
Exception generated. \[ \int \frac {9 x+12 x^2+18 x^3-6 x^4-6 x^2 \log (x)+\left (24 x^2-12 x^4-12 x^2 \log (x)+\left (-36 x+18 x^3+18 x \log (x)\right ) \log \left (-2+x^2+\log (x)\right )\right ) \log \left (-2 x+3 \log \left (-2+x^2+\log (x)\right )\right )}{4 x-2 x^3-2 x \log (x)+\left (-6+3 x^2+3 \log (x)\right ) \log \left (-2+x^2+\log (x)\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((18*x*ln(x)+18*x**3-36*x)*ln(ln(x)+x**2-2)-12*x**2*ln(x)-12*x* *4+24*x**2)*ln(3*ln(ln(x)+x**2-2)-2*x)-6*x**2*ln(x)-6*x**4+18*x**3+12*x**2 +9*x)/((3*ln(x)+3*x**2-6)*ln(ln(x)+x**2-2)-2*x*ln(x)-2*x**3+4*x),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1265\)
Exception generated. \[ \int \frac {e^{\frac {20+5 x+x \log (x)+5 \log ^2(x)}{4+x+\log ^2(x)}} \left (-128-56 x-6 x^2+8 x \log (x)+(-64-18 x) \log ^2(x)+2 x \log ^3(x)-8 \log ^4(x)\right )}{16 x^5+8 x^6+x^7+\left (8 x^5+2 x^6\right ) \log ^2(x)+x^5 \log ^4(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((-8*ln(x)**4+2*x*ln(x)**3+(-18*x-64)*ln(x)**2+8*x*ln(x)-6*x**2-5 6*x-128)*exp((5*ln(x)**2+x*ln(x)+20+5*x)/(ln(x)**2+4+x))/(x**5*ln(x)**4+(2 *x**6+8*x**5)*ln(x)**2+x**7+8*x**6+16*x**5),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1313\)
Exception generated. \[ \int \frac {\left (\left (-320-16 x-1280 x^2-64 x^3\right ) \log \left (\frac {20+x}{4}\right )+\left (1280 x^2+64 x^3\right ) \log \left (x^2\right ) \log \left (\frac {20+x}{4}\right )\right ) \log \left (\frac {16+64 x^2}{\log \left (x^2\right )}\right )+\left (-4 x-16 x^3\right ) \log \left (x^2\right ) \log ^2\left (\frac {16+64 x^2}{\log \left (x^2\right )}\right )}{\left (20 x+x^2+80 x^3+4 x^4\right ) \log \left (x^2\right ) \log ^2\left (\frac {20+x}{4}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((-16*x**3-4*x)*ln(x**2)*ln((64*x**2+16)/ln(x**2))**2+((64*x**3+ 1280*x**2)*ln(5+1/4*x)*ln(x**2)+(-64*x**3-1280*x**2-16*x-320)*ln(5+1/4*x)) *ln((64*x**2+16)/ln(x**2)))/(4*x**4+80*x**3+x**2+20*x)/ln(5+1/4*x)**2/ln(x **2),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1350\)
Exception generated. \[ \int \frac {e^{\frac {12}{(-15+20 x) \log \left (x \log ^2(2)\right )}} \left (72-96 x-96 x \log \left (x \log ^2(2)\right )\right )}{\left (45 x-120 x^2+80 x^3\right ) \log ^2\left (x \log ^2(2)\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((-96*x*ln(x*ln(2)**2)-96*x+72)*exp(12/(20*x-15)/ln(x*ln(2)**2))/ (80*x**3-120*x**2+45*x)/ln(x*ln(2)**2)**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1422\)
Exception generated. \[ \int \frac {\left (-8 x+12 x^2+72 x^3+32 x^4\right ) \log (x)+\left (64-216 x-148 x^2-44 x^3-16 x^4+\left (224 x+284 x^2+60 x^3+32 x^4\right ) \log (x)\right ) \log \left (8+x+x^2\right )}{\left (8 x+x^2+x^3\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((32*x**4+60*x**3+284*x**2+224*x)*ln(x)-16*x**4-44*x**3-148*x** 2-216*x+64)*ln(x**2+x+8)+(32*x**4+72*x**3+12*x**2-8*x)*ln(x))/(x**3+x**2+8 *x)/ln(x)**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1508\)
Exception generated. \[ \int \frac {2358774 e^{2 x}+2358774 e^x x^2}{5 x^2+e^{2 x} (5+x)+e^x \left (10 x+x^2\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((2358774*exp(x)**2+2358774*exp(x)*x**2)/((5+x)*exp(x)**2+(x**2+1 0*x)*exp(x)+5*x**2),x)
Output:
Exception raised: PolynomialError >> 1/(x**2 + 10*x + 25) contains an elem ent of the set of generators.
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1569\)
Exception generated. \[ \int \frac {16 x^2+\left (160 x+32 x^2\right ) \log (2)+e^x \left (-8 x^2+\left (-40 x-36 x^2\right ) \log (2)+(40 x+(100+180 x) \log (2)) \log (5)\right )+e^{2 x} \left (x^2+2 x^2 \log (2)+(-10 x-20 x \log (2)) \log (5)+(25+50 \log (2)) \log ^2(5)\right )}{16 x^3+\left (80 x^2+32 x^3\right ) \log (2)+e^x \left (-8 x^3+\left (-20 x^2-16 x^3\right ) \log (2)+\left (40 x^2+\left (100 x+80 x^2\right ) \log (2)\right ) \log (5)\right )+e^{2 x} \left (x^3+2 x^3 \log (2)+\left (-10 x^2-20 x^2 \log (2)\right ) \log (5)+(25 x+50 x \log (2)) \log ^2(5)\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((((50*ln(2)+25)*ln(5)**2+(-20*x*ln(2)-10*x)*ln(5)+2*x**2*ln(2)+x **2)*exp(x)**2+(((180*x+100)*ln(2)+40*x)*ln(5)+(-36*x**2-40*x)*ln(2)-8*x** 2)*exp(x)+(32*x**2+160*x)*ln(2)+16*x**2)/(((50*x*ln(2)+25*x)*ln(5)**2+(-20 *x**2*ln(2)-10*x**2)*ln(5)+2*x**3*ln(2)+x**3)*exp(x)**2+(((80*x**2+100*x)* ln(2)+40*x**2)*ln(5)+(-16*x**3-20*x**2)*ln(2)-8*x**3)*exp(x)+(32*x**3+80*x **2)*ln(2)+16*x**3),x)
Output:
Exception raised: PolynomialError >> 1/(x**2 + 2*x**2*log(2) - 20*x*log(2) *log(5) - 10*x*log(5) + 25*log(5)**2 + 50*log(2)*log(5)**2) contains an el ement of the set of generators.
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1573\)
Exception generated. \[ \int \frac {e^4 \left (4-4 x+9 x^2-9 x^3\right )+\left (36 x^3-36 x^2 \log (x)\right ) \log \left (48+108 x^2\right )+\left (4-4 x+9 x^2-9 x^3\right ) \log ^2\left (48+108 x^2\right )}{e^8 \left (4 x+9 x^3\right )+e^4 \left (-4 x^2-9 x^4\right )+e^4 \left (4 x+9 x^3\right ) \log (x)+\left (-4 x^2-9 x^4+e^4 \left (8 x+18 x^3\right )+\left (4 x+9 x^3\right ) \log (x)\right ) \log ^2\left (48+108 x^2\right )+\left (4 x+9 x^3\right ) \log ^4\left (48+108 x^2\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate(((-9*x**3+9*x**2-4*x+4)*ln(108*x**2+48)**2+(-36*x**2*ln(x)+36*x* *3)*ln(108*x**2+48)+(-9*x**3+9*x**2-4*x+4)*exp(4))/((9*x**3+4*x)*ln(108*x* *2+48)**4+((9*x**3+4*x)*ln(x)+(18*x**3+8*x)*exp(4)-9*x**4-4*x**2)*ln(108*x **2+48)**2+(9*x**3+4*x)*exp(4)*ln(x)+(9*x**3+4*x)*exp(4)**2+(-9*x**4-4*x** 2)*exp(4)),x)
Output:
Exception raised: PolynomialError >> 1/(81*x**6 + 72*x**4 + 16*x**2) conta ins an element of the set of generators.
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1592\)
Exception generated. \[ \int \frac {-25 x+\left (100 e^{2 e^{\frac {4 e^5+\log (5)}{e^5}}}-25 x\right ) \log \left (4 e^{2 e^{\frac {4 e^5+\log (5)}{e^5}}}-x\right ) \log \left (\log \left (4 e^{2 e^{\frac {4 e^5+\log (5)}{e^5}}}-x\right )\right )}{\left (4 e^{2 e^{\frac {4 e^5+\log (5)}{e^5}}}-x\right ) \log \left (4 e^{2 e^{\frac {4 e^5+\log (5)}{e^5}}}-x\right )} \, dx=\text {Exception raised: CoercionFailed} \] Input:
integrate(((100*exp(exp((ln(5)+4*exp(5))/exp(5)))**2-25*x)*ln(4*exp(exp((l n(5)+4*exp(5))/exp(5)))**2-x)*ln(ln(4*exp(exp((ln(5)+4*exp(5))/exp(5)))**2 -x))-25*x)/(4*exp(exp((ln(5)+4*exp(5))/exp(5)))**2-x)/ln(4*exp(exp((ln(5)+ 4*exp(5))/exp(5)))**2-x),x)
Output:
Exception raised: CoercionFailed >> Cannot convert x - 4*exp(2*5**exp(-5)* exp(4)) of type <class 'sympy.core.add.Add'> to QQ[x,exp(5**exp(-5)*exp(4) )]
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1616\)
Exception generated. \[ \int \frac {-9+e^{e^x} \left (-3-3 e^x x-6 \log (5)\right )+e^{2 e^x} \left (-\log (5)-\log ^2(5)\right )}{-90+45 x+e^{e^x} (15 x+(-60+30 x) \log (5))+e^{2 e^x} \left (5 x \log (5)+(-10+5 x) \log ^2(5)\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate(((-ln(5)**2-ln(5))*exp(exp(x))**2+(-3*exp(x)*x-6*ln(5)-3)*exp(ex p(x))-9)/(((5*x-10)*ln(5)**2+5*x*ln(5))*exp(exp(x))**2+((30*x-60)*ln(5)+15 *x)*exp(exp(x))+45*x-90),x)
Output:
Exception raised: PolynomialError >> 1/(5*x**2*log(5) + 5*x**2*log(5)**3 + 10*x**2*log(5)**2 - 20*x*log(5)**3 - 20*x*log(5)**2 + 20*log(5)**3) conta ins an element of the set of generators.
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1679\)
Exception generated. \[ \int \frac {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}} \left (2+\left (-1-x^2\right ) \log (x)+3 x^2 \log ^2(x)\right )}{\log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((3*x**2*ln(x)**2+(-x**2-1)*ln(x)+2)*exp((-x**3*ln(x)+x)/ln(x)**2 )/ln(x)**3,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1742\)
Exception generated. \[ \int \frac {e^{\frac {-e+\log (3)}{-20-x+x \log (x)}} (e-\log (3)) \log (x)}{400+40 x+x^2+\left (-40 x-2 x^2\right ) \log (x)+x^2 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((-ln(3)+exp(1))*ln(x)*exp((ln(3)-exp(1))/(x*ln(x)-x-20))/(x**2*l n(x)**2+(-2*x**2-40*x)*ln(x)+x**2+40*x+400),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1758\)
Exception generated. \[ \int \frac {390625 \log (x)-x \log ^2(x)+\left (390625+x \log ^2(x)\right ) \log (x \log (3))+x \log ^2(x) \log ^2(x \log (3))}{\left (-390625 x \log (x)+x^2 \log ^2(x)\right ) \log (x \log (3))+\left (x+x^2\right ) \log ^2(x) \log ^2(x \log (3))} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((x*ln(x)**2*ln(x*ln(3))**2+(x*ln(x)**2+390625)*ln(x*ln(3))-x*ln( x)**2+390625*ln(x))/((x**2+x)*ln(x)**2*ln(x*ln(3))**2+(x**2*ln(x)**2-39062 5*x*ln(x))*ln(x*ln(3))),x)
Output:
Exception raised: PolynomialError >> 1/(x**6 + 4*x**5 + 6*x**4 + 4*x**3 + x**2) contains an element of the set of generators.
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1784\)
Exception generated. \[ \int \frac {e^2 \left (2 x+2 x^2\right )+e \left (52 x+4 x^2\right ) \log (x)+\left (50 x+2 x^2\right ) \log ^2(x)+\left (e (96+48 x)+e^2 \left (2 x+x^2\right )+e \left (4 x+2 x^2\right ) \log (x)+\left (2 x+x^2\right ) \log ^2(x)\right ) \log (2+x)}{e^2 \left (2 x+x^2\right )+e \left (4 x+2 x^2\right ) \log (x)+\left (2 x+x^2\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((x**2+2*x)*ln(x)**2+(2*x**2+4*x)*exp(1)*ln(x)+(x**2+2*x)*exp(1 )**2+(48*x+96)*exp(1))*ln(2+x)+(2*x**2+50*x)*ln(x)**2+(4*x**2+52*x)*exp(1) *ln(x)+(2*x**2+2*x)*exp(1)**2)/((x**2+2*x)*ln(x)**2+(2*x**2+4*x)*exp(1)*ln (x)+(x**2+2*x)*exp(1)**2),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(1935\)
Exception generated. \[ \int \frac {e^x \left (10 x^3-10 x^4+e^3 \left (-10 x^2+10 x^3\right )\right )+e^x \left (20 e^3 x^2-20 x^3\right ) \log \left (e^3-x\right )+e^x \left (10 e^3 x-10 x^2\right ) \log ^2\left (e^3-x\right )+\log \left (-9+5 e^x\right ) \left (-54 x^3+e^3 \left (-36 x+54 x^2\right )+e^x \left (30 x^3+e^3 \left (20 x-30 x^2\right )\right )+\left (-36 x+72 e^3 x-72 x^2+e^x \left (20 x-40 e^3 x+40 x^2\right )\right ) \log \left (e^3-x\right )+\left (18 e^3-18 x+e^x \left (-10 e^3+10 x\right )\right ) \log ^2\left (e^3-x\right )\right )}{9 x^5-18 x^6+9 x^7+e^3 \left (-9 x^4+18 x^5-9 x^6\right )+e^x \left (-5 x^5+10 x^6-5 x^7+e^3 \left (5 x^4-10 x^5+5 x^6\right )\right )+\left (-36 x^5+36 x^6+e^3 \left (36 x^4-36 x^5\right )+e^x \left (20 x^5-20 x^6+e^3 \left (-20 x^4+20 x^5\right )\right )\right ) \log \left (e^3-x\right )+\left (-18 x^4+54 x^5+e^3 \left (18 x^3-54 x^4\right )+e^x \left (10 x^4-30 x^5+e^3 \left (-10 x^3+30 x^4\right )\right )\right ) \log ^2\left (e^3-x\right )+\left (-36 e^3 x^3+36 x^4+e^x \left (20 e^3 x^3-20 x^4\right )\right ) \log ^3\left (e^3-x\right )+\left (-9 e^3 x^2+9 x^3+e^x \left (5 e^3 x^2-5 x^3\right )\right ) \log ^4\left (e^3-x\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((((-10*exp(3)+10*x)*exp(x)+18*exp(3)-18*x)*ln(-x+exp(3))**2+((- 40*x*exp(3)+40*x**2+20*x)*exp(x)+72*x*exp(3)-72*x**2-36*x)*ln(-x+exp(3))+( (-30*x**2+20*x)*exp(3)+30*x**3)*exp(x)+(54*x**2-36*x)*exp(3)-54*x**3)*ln(5 *exp(x)-9)+(10*x*exp(3)-10*x**2)*exp(x)*ln(-x+exp(3))**2+(20*x**2*exp(3)-2 0*x**3)*exp(x)*ln(-x+exp(3))+((10*x**3-10*x**2)*exp(3)-10*x**4+10*x**3)*ex p(x))/(((5*x**2*exp(3)-5*x**3)*exp(x)-9*x**2*exp(3)+9*x**3)*ln(-x+exp(3))* *4+((20*x**3*exp(3)-20*x**4)*exp(x)-36*x**3*exp(3)+36*x**4)*ln(-x+exp(3))* *3+(((30*x**4-10*x**3)*exp(3)-30*x**5+10*x**4)*exp(x)+(-54*x**4+18*x**3)*e xp(3)+54*x**5-18*x**4)*ln(-x+exp(3))**2+(((20*x**5-20*x**4)*exp(3)-20*x**6 +20*x**5)*exp(x)+(-36*x**5+36*x**4)*exp(3)+36*x**6-36*x**5)*ln(-x+exp(3))+ ((5*x**6-10*x**5+5*x**4)*exp(3)-5*x**7+10*x**6-5*x**5)*exp(x)+(-9*x**6+18* x**5-9*x**4)*exp(3)+9*x**7-18*x**6+9*x**5),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2068\)
Exception generated. \[ \int \frac {(-6 x+3 \log (4)) \log \left (\frac {x}{2}\right )+\left (-2 x^2+x \log (4)\right ) \log ^2\left (\frac {x}{2}\right )+\left (3 x-3 \log (4)+\left (-x^2+x \log (4)\right ) \log ^2\left (\frac {x}{2}\right )\right ) \log \left (-x^2+x \log (4)\right )}{\left (-x^2+x \log (4)\right ) \log ^2\left (\frac {x}{2}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((2*x*ln(2)-x**2)*ln(1/2*x)**2-6*ln(2)+3*x)*ln(2*x*ln(2)-x**2)+ (2*x*ln(2)-2*x**2)*ln(1/2*x)**2+(6*ln(2)-6*x)*ln(1/2*x))/(2*x*ln(2)-x**2)/ ln(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/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2168\)
Exception generated. \[ \int \frac {(1+9 x) \log (x)+(-22-9 x-\log (x)) \log \left (\frac {1}{2} (22+9 x+\log (x))\right )}{\left (22 x+9 x^2\right ) \log ^2(x)+x \log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((-ln(x)-9*x-22)*ln(1/2*ln(x)+9/2*x+11)+(9*x+1)*ln(x))/(x*ln(x)* *3+(9*x**2+22*x)*ln(x)**2),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2247\)
Exception generated. \[ \int \frac {e^{\frac {1}{3} \left (9-x \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )} \left (100 x^2-50 x^3-25 x^4+\left (20-12 x-7 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (4-2 x-x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )+\left (100 x^2-50 x^3-25 x^4+\left (-20+10 x+5 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (-4+2 x+x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )\right ) \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )}{-300 x^2+150 x^3+75 x^4+\left (60-30 x-15 x^2\right ) \log (5)+\left (-120 x^2+60 x^3+30 x^4+\left (12-6 x-3 x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (-12 x^2+6 x^3+3 x^4\right ) \log ^2\left (-4+2 x+x^2\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((((-x**4-2*x**3+4*x**2)*ln(x**2+2*x-4)**2+((x**2+2*x-4)*ln(5)-10 *x**4-20*x**3+40*x**2)*ln(x**2+2*x-4)+(5*x**2+10*x-20)*ln(5)-25*x**4-50*x* *3+100*x**2)*ln((-x**2*ln(x**2+2*x-4)+ln(5)-5*x**2)/(x*ln(x**2+2*x-4)+5*x) )+(-x**4-2*x**3+4*x**2)*ln(x**2+2*x-4)**2+((-x**2-2*x+4)*ln(5)-10*x**4-20* x**3+40*x**2)*ln(x**2+2*x-4)+(-7*x**2-12*x+20)*ln(5)-25*x**4-50*x**3+100*x **2)*exp(-1/3*x*ln((-x**2*ln(x**2+2*x-4)+ln(5)-5*x**2)/(x*ln(x**2+2*x-4)+5 *x))+3)/((3*x**4+6*x**3-12*x**2)*ln(x**2+2*x-4)**2+((-3*x**2-6*x+12)*ln(5) +30*x**4+60*x**3-120*x**2)*ln(x**2+2*x-4)+(-15*x**2-30*x+60)*ln(5)+75*x**4 +150*x**3-300*x**2),x)
Output:
Exception raised: PolynomialError >> 1/(9*x**5 + 18*x**4 - 36*x**3) contai ns an element of the set of generators.
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2263\)
Exception generated. \[ \int \frac {e^{e^{\frac {9 x}{6+e^3+\log \left (\frac {5}{3}\right )+3 \log (x)}}+\frac {9 x}{6+e^3+\log \left (\frac {5}{3}\right )+3 \log (x)}} \left (27+9 e^3+9 \log \left (\frac {5}{3}\right )+27 \log (x)\right )}{36+12 e^3+e^6-\left (-12-2 e^3\right ) \log \left (\frac {5}{3}\right )+\log ^2\left (\frac {5}{3}\right )+\left (36+6 e^3+6 \log \left (\frac {5}{3}\right )\right ) \log (x)+9 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((27*ln(x)-9*ln(3/5)+9*exp(3)+27)*exp(9*x/(3*ln(x)-ln(3/5)+exp(3) +6))*exp(exp(9*x/(3*ln(x)-ln(3/5)+exp(3)+6)))/(9*ln(x)**2+(-6*ln(3/5)+6*ex p(3)+36)*ln(x)+ln(3/5)**2+(-2*exp(3)-12)*ln(3/5)+exp(3)**2+12*exp(3)+36),x )
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2305\)
Exception generated. \[ \int \frac {\left (-16 x+28 x^2-8 x^3\right ) \log (x)+\left (8 x-4 x^2+\left (8 x-28 x^2+12 x^3\right ) \log (x)\right ) \log \left (e^{-2 x} \left (-2 x^2+x^3\right )\right )+\left (-16 x+8 x^2\right ) \log (x) \log \left (e^{-2 x} \left (-2 x^2+x^3\right )\right ) \log \left (\frac {\log \left (e^{-2 x} \left (-2 x^2+x^3\right )\right )}{x \log (x)}\right )}{(-2+x) \log (x) \log \left (e^{-2 x} \left (-2 x^2+x^3\right )\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((8*x**2-16*x)*ln(x)*ln((x**3-2*x**2)/exp(x)**2)*ln(ln((x**3-2*x **2)/exp(x)**2)/x/ln(x))+((12*x**3-28*x**2+8*x)*ln(x)-4*x**2+8*x)*ln((x**3 -2*x**2)/exp(x)**2)+(-8*x**3+28*x**2-16*x)*ln(x))/(-2+x)/ln(x)/ln((x**3-2* x**2)/exp(x)**2),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2314\)
Exception generated. \[ \int \frac {\left (600-160 x-136 x^2-16 x^3\right ) \log ^2(2 x)+e^{\frac {x}{(40+8 x) \log (2 x)}} \left (-5 x-x^2+5 x \log (2 x)+\left (200+80 x+8 x^2\right ) \log ^2(2 x)\right )}{\left (200+80 x+8 x^2\right ) \log ^2(2 x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((8*x**2+80*x+200)*ln(2*x)**2+5*x*ln(2*x)-x**2-5*x)*exp(x/(8*x+ 40)/ln(2*x))+(-16*x**3-136*x**2-160*x+600)*ln(2*x)**2)/(8*x**2+80*x+200)/l n(2*x)**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2325\)
Exception generated. \[ \int \frac {-720+540 x+3 e^{4+x} x^3+\left (180 x-6 e^{4+x} x^2\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} x \log ^2\left (\frac {x}{\log (5)}\right )+\left (-720 x-180 x^2+3 e^{4+x} x^2+\left (720+180 x-6 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )\right ) \log \left (\frac {-240-60 x+e^{4+x} x-e^{4+x} \log \left (\frac {x}{\log (5)}\right )}{-x+\log \left (\frac {x}{\log (5)}\right )}\right )}{-240 x-60 x^2+e^{4+x} x^2+\left (240+60 x-2 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((3*exp(4+x)*ln(x/ln(5))**2+(-6*x*exp(4+x)+180*x+720)*ln(x/ln(5) )+3*x**2*exp(4+x)-180*x**2-720*x)*ln((-exp(4+x)*ln(x/ln(5))+x*exp(4+x)-60* x-240)/(ln(x/ln(5))-x))+3*x*exp(4+x)*ln(x/ln(5))**2+(-6*x**2*exp(4+x)+180* x)*ln(x/ln(5))+3*x**3*exp(4+x)+540*x-720)/(exp(4+x)*ln(x/ln(5))**2+(-2*x*e xp(4+x)+60*x+240)*ln(x/ln(5))+x**2*exp(4+x)-60*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/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2392\)
Exception generated. \[ \int \frac {1+(5-x) \log (5-x)+e^3 (-100+20 x) \log ^2(5-x)}{(5-x) \log (5-x)+e^3 (-100+20 x) \log ^2(5-x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate(((20*x-100)*exp(3)*ln(5-x)**2+(5-x)*ln(5-x)+1)/((20*x-100)*exp(3 )*ln(5-x)**2+(5-x)*ln(5-x)),x)
Output:
Exception raised: PolynomialError >> 1/(x - 5) contains an element of the set of generators.
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2411\)
Exception generated. \[ \int \frac {75+90 x+3 x^2+\left (120 x-24 x^2+\left (75-30 x+3 x^2\right ) \log \left (\frac {x}{e}\right )\right ) \log \left (\frac {-8 x+(-5+x) \log \left (\frac {x}{e}\right )}{-5+x}\right ) \log \left (-\log \left (\frac {-8 x+(-5+x) \log \left (\frac {x}{e}\right )}{-5+x}\right )\right )}{\left (40 x-8 x^2+\left (25-10 x+x^2\right ) \log \left (\frac {x}{e}\right )\right ) \log \left (\frac {-8 x+(-5+x) \log \left (\frac {x}{e}\right )}{-5+x}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((3*x**2-30*x+75)*ln(x/exp(1))-24*x**2+120*x)*ln(((-5+x)*ln(x/e xp(1))-8*x)/(-5+x))*ln(-ln(((-5+x)*ln(x/exp(1))-8*x)/(-5+x)))+3*x**2+90*x+ 75)/((x**2-10*x+25)*ln(x/exp(1))-8*x**2+40*x)/ln(((-5+x)*ln(x/exp(1))-8*x) /(-5+x)),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2435\)
Exception generated. \[ \int \frac {4 x-x^2+e^x \left (-4 x+x^2\right )+e^{e^x} \left (-x^2+e^{2 x} \left (-4 x+x^2\right )+e^x \left (x+4 x^2-x^3\right )\right )+\left (-2 e^x+2 x\right ) \log \left (\frac {x}{5}\right )+\left (e^x x-x^2\right ) \log \left (-e^x+x\right )}{e^x x-x^2} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((exp(x)*x-x**2)*ln(x-exp(x))+((x**2-4*x)*exp(x)**2+(-x**3+4*x** 2+x)*exp(x)-x**2)*exp(exp(x))+(-2*exp(x)+2*x)*ln(1/5*x)+(x**2-4*x)*exp(x)- x**2+4*x)/(exp(x)*x-x**2),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2519\)
Exception generated. \[ \int \frac {\left (80-40 x-2 x^2+x^3\right ) \log (-2+x)+e^{3 e^x+x} \left (-60 x^2+30 x^3\right ) \log (-2+x)+\left (-40 x-10 e^{3 e^x} x^2-x^3\right ) \log \left (\frac {40+10 e^{3 e^x} x+x^2}{x}\right )}{e^{3 e^x} \left (-20 x^2+10 x^3\right ) \log ^2(-2+x)+\left (-80 x+40 x^2-2 x^3+x^4\right ) \log ^2(-2+x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((-10*x**2*exp(3*exp(x))-x**3-40*x)*ln((10*x*exp(3*exp(x))+x**2+ 40)/x)+(30*x**3-60*x**2)*exp(x)*ln(-2+x)*exp(3*exp(x))+(x**3-2*x**2-40*x+8 0)*ln(-2+x))/((10*x**3-20*x**2)*ln(-2+x)**2*exp(3*exp(x))+(x**4-2*x**3+40* x**2-80*x)*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/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2523\)
Exception generated. \[ \int \frac {e^{2 x} (-3-6 x)+9 x^2+e^{-3+e^x} \left (-3-3 e^x x-3 \log (x)\right )+\left (-3 e^{2 x}+3 x^2\right ) \log (x)+\left (-3 e^{-3+e^x}-3 e^{2 x}+3 x^2\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )}{\left (-3 e^{2 x} x+3 x^3\right ) \log (x)+\left (e^{2 x} x^2-x^4\right ) \log ^2(x)+e^{-3+e^x} \left (-3 x \log (x)+x^2 \log ^2(x)\right )+\left (-3 e^{2 x} x+3 x^3+\left (2 e^{2 x} x^2-2 x^4\right ) \log (x)+e^{-3+e^x} \left (-3 x+2 x^2 \log (x)\right )\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )+\left (e^{-3+e^x} x^2+e^{2 x} x^2-x^4\right ) \log ^2\left (-e^{-3+e^x}-e^{2 x}+x^2\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate(((-3*exp(exp(x)-3)-3*exp(x)**2+3*x**2)*ln(-exp(exp(x)-3)-exp(x)* *2+x**2)+(-3*ln(x)-3*exp(x)*x-3)*exp(exp(x)-3)+(-3*exp(x)**2+3*x**2)*ln(x) +(-6*x-3)*exp(x)**2+9*x**2)/((x**2*exp(exp(x)-3)+exp(x)**2*x**2-x**4)*ln(- exp(exp(x)-3)-exp(x)**2+x**2)**2+((2*x**2*ln(x)-3*x)*exp(exp(x)-3)+(2*exp( x)**2*x**2-2*x**4)*ln(x)-3*x*exp(x)**2+3*x**3)*ln(-exp(exp(x)-3)-exp(x)**2 +x**2)+(x**2*ln(x)**2-3*x*ln(x))*exp(exp(x)-3)+(exp(x)**2*x**2-x**4)*ln(x) **2+(-3*x*exp(x)**2+3*x**3)*ln(x)),x)
Output:
Exception raised: PolynomialError >> 1/(-_t1**2*x**2 - _t2*x**2 + x**4) co ntains an element of the set of generators.
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2581\)
Exception generated. \[ \int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{\left (3 x^2+x^3\right ) \log ^2(5) \log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((3*x+9)*ln(5)**2*ln(x)**3+(6*x**4+18*x**3)*ln(x)-6*x**4-18*x** 3)*ln(3+x)+(-x**2-9*x-18)*ln(5)**2*ln(x)**3+(-9*x**4-36*x**3)*ln(x)+12*x** 4+36*x**3)/(x**3+3*x**2)/ln(5)**2/ln(x)**3,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2610\)
Exception generated. \[ \int \frac {\left (6 x+12 x^2+4 x^3\right ) \log ^2(3 x)+e^{\frac {2 \left (-x^2+x^3\right )}{\log (3 x)}} \left (6 x^2+2 x^3-6 x^4-2 x^5+\left (-12 x^2+2 x^3+20 x^4+6 x^5\right ) \log (3 x)+\left (3+8 x+3 x^2\right ) \log ^2(3 x)\right )}{\log ^2(3 x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((3*x**2+8*x+3)*ln(3*x)**2+(6*x**5+20*x**4+2*x**3-12*x**2)*ln(3 *x)-2*x**5-6*x**4+2*x**3+6*x**2)*exp((x**3-x**2)/ln(3*x))**2+(4*x**3+12*x* *2+6*x)*ln(3*x)**2)/ln(3*x)**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2617\)
Exception generated. \[ \int \frac {e^{-\frac {5}{x^4 \log \left (-3 x+2 x^5\right )}} \left (-45+150 x^4+\left (-180+120 x^4\right ) \log \left (-3 x+2 x^5\right )\right )}{\left (-3 x^5+2 x^9\right ) \log ^2\left (-3 x+2 x^5\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((120*x**4-180)*ln(2*x**5-3*x)+150*x**4-45)/(2*x**9-3*x**5)/ln(2 *x**5-3*x)**2/exp(5/x**4/ln(2*x**5-3*x)),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2620\)
Exception generated. \[ \int \frac {x \log (4)+\log ^2(4)+e^x \left (-x^2 \log (4)-x \log ^2(4)\right )+\left (-x \log (4)+\log ^2(4)+e^x \left (x^3 \log (4)+x^2 \log ^2(4)\right )\right ) \log \left (\frac {x}{4}\right )+\left (x \log (4)+\log ^2(4)+\left (x \log (4)+\log ^2(4)\right ) \log \left (\frac {x}{4}\right )\right ) \log \left (x^2+2 x \log (4)+\log ^2(4)\right )}{\left (x^3+x^2 \log (4)\right ) \log ^2\left (\frac {x}{4}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((4*ln(2)**2+2*x*ln(2))*ln(1/4*x)+4*ln(2)**2+2*x*ln(2))*ln(4*ln (2)**2+4*x*ln(2)+x**2)+((4*x**2*ln(2)**2+2*x**3*ln(2))*exp(x)+4*ln(2)**2-2 *x*ln(2))*ln(1/4*x)+(-4*x*ln(2)**2-2*x**2*ln(2))*exp(x)+4*ln(2)**2+2*x*ln( 2))/(2*x**2*ln(2)+x**3)/ln(1/4*x)**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2793\)
Exception generated. \[ \int \frac {-4 \log (5) \log ^2\left (\frac {16}{x^2}\right )+e^{\frac {x}{\log \left (\frac {16}{x^2}\right )}} \left (8 x-8 x^2+\left (4 x-4 x^2\right ) \log \left (\frac {16}{x^2}\right )-4 \log ^2\left (\frac {16}{x^2}\right )\right )}{3 x^2 \log ^2\left (\frac {16}{x^2}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(1/3*((-4*ln(16/x**2)**2+(-4*x**2+4*x)*ln(16/x**2)-8*x**2+8*x)*ex p(x/ln(16/x**2))-4*ln(5)*ln(16/x**2)**2)/x**2/ln(16/x**2)**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2800\)
Exception generated. \[ \int \frac {e^{\frac {e^{\frac {2}{x^2}} x+x^2+\log \left (\frac {5}{3}\right )}{x}} \left (-4 e^{\frac {2}{x^2}}+x^3-x \log \left (\frac {5}{3}\right )\right )}{x^3} \, dx=\text {Exception raised: IndexError} \] Input:
integrate((-4*exp(2/x**2)+x*ln(3/5)+x**3)*exp((x*exp(2/x**2)-ln(3/5)+x**2) /x)/x**3,x)
Output:
Exception raised: IndexError >> Index out of range: a[1]
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2858\)
Exception generated. \[ \int \frac {e^{\frac {1}{-400 x^5+\left (2000 x^4+400 x^5\right ) \log (x)}} (-5+4 x+(-20-5 x) \log (x))}{200 x^7+\left (-2000 x^6-400 x^7\right ) \log (x)+\left (5000 x^5+2000 x^6+200 x^7\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((-5*x-20)*ln(x)+4*x-5)/((200*x**7+2000*x**6+5000*x**5)*ln(x)**2 +(-400*x**7-2000*x**6)*ln(x)+200*x**7)/exp(-1/((400*x**5+2000*x**4)*ln(x)- 400*x**5)),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2869\)
Exception generated. \[ \int \frac {4 e^5 x^2 \log ^2(x)+e^{\frac {3}{e^5 x^2 \log (x)}} \log \left (2+e^2\right ) \left (6+12 \log (x)-4 e^5 x^2 \log ^2(x)\right )+e^{\frac {6}{e^5 x^2 \log (x)}} \log ^2\left (2+e^2\right ) \left (-3-6 \log (x)+e^5 x^2 \log ^2(x)\right )}{2 e^5 x \log ^2\left (2+e^2\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(1/2*((x**2*ln(x)**2*exp(5)-6*ln(x)-3)*ln(exp(2)+2)**2*exp(3/x**2 /exp(5)/ln(x))**2+(-4*x**2*ln(x)**2*exp(5)+12*ln(x)+6)*ln(exp(2)+2)*exp(3/ x**2/exp(5)/ln(x))+4*x**2*ln(x)**2*exp(5))/x/exp(5)/ln(x)**2/ln(exp(2)+2)* *2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2893\)
Exception generated. \[ \int \frac {e^{\frac {x}{2+\log (-18-2 x+\log (4)+3 \log (25))}} (-36-2 x+2 \log (4)+6 \log (25)+(-18-2 x+\log (4)+3 \log (25)) \log (-18-2 x+\log (4)+3 \log (25)))}{-72-8 x+4 \log (4)+12 \log (25)+(-72-8 x+4 \log (4)+12 \log (25)) \log (-18-2 x+\log (4)+3 \log (25))+(-18-2 x+\log (4)+3 \log (25)) \log ^2(-18-2 x+\log (4)+3 \log (25))} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((6*ln(5)+2*ln(2)-2*x-18)*ln(6*ln(5)+2*ln(2)-2*x-18)+12*ln(5)+4* ln(2)-2*x-36)*exp(x/(ln(6*ln(5)+2*ln(2)-2*x-18)+2))/((6*ln(5)+2*ln(2)-2*x- 18)*ln(6*ln(5)+2*ln(2)-2*x-18)**2+(24*ln(5)+8*ln(2)-8*x-72)*ln(6*ln(5)+2*l n(2)-2*x-18)+24*ln(5)+8*ln(2)-8*x-72),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/363_Hebisch_3
Test file number \(363\)
Integral number in file \(2900\)
Exception generated. \[ \int \frac {e^{\frac {2 x}{\log (x)}} \left (-2 x^2+2 x^2 \log (x)+2 x \log ^2(x)+e^{-30+2 x-2 x \log (2 x)} \left (-2+2 \log (x)-2 \log ^2(x) \log (2 x)\right )+e^{-15+x-x \log (2 x)} \left (4 x-4 x \log (x)-2 \log ^2(x)+2 x \log ^2(x) \log (2 x)\right )\right )}{5 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(1/5*((-2*ln(x)**2*ln(2*x)+2*ln(x)-2)*exp(-x*ln(2*x)+x-15)**2+(2* x*ln(x)**2*ln(2*x)-2*ln(x)**2-4*x*ln(x)+4*x)*exp(-x*ln(2*x)+x-15)+2*x*ln(x )**2+2*x**2*ln(x)-2*x**2)*exp(x/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/364_Hebisch_4
Test file number \(364\)
Integral number in file \(1\)
Exception generated. \[ \int \frac {e^{\frac {3+e^{10} \left (-x^2-x^3\right )}{-e^{10} x^2+e^{10} x^2 \log \left (\frac {x}{5 \log (x)}\right )}} \left (3+e^{10} \left (-x^2-x^3\right )+\left (3+e^{10} \left (x^2+2 x^3\right )\right ) \log (x)+\left (-6-e^{10} x^3\right ) \log (x) \log \left (\frac {x}{5 \log (x)}\right )\right )}{e^{10} x^3 \log (x)-2 e^{10} x^3 \log (x) \log \left (\frac {x}{5 \log (x)}\right )+e^{10} x^3 \log (x) \log ^2\left (\frac {x}{5 \log (x)}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((-x**3*exp(5)**2-6)*ln(x)*ln(1/5*x/ln(x))+((2*x**3+x**2)*exp(5) **2+3)*ln(x)+(-x**3-x**2)*exp(5)**2+3)*exp(((-x**3-x**2)*exp(5)**2+3)/(x** 2*exp(5)**2*ln(1/5*x/ln(x))-x**2*exp(5)**2))/(x**3*exp(5)**2*ln(x)*ln(1/5* x/ln(x))**2-2*x**3*exp(5)**2*ln(x)*ln(1/5*x/ln(x))+x**3*exp(5)**2*ln(x)),x )
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(11\)
Exception generated. \[ \int \frac {30+30 x+e^4 \left (10+25 x+15 x^2\right )+\left (3 x+e^4 \left (-15 x-15 x^2\right )\right ) \log (x)+e^4 (15+15 x) \log ^2(x)+(-3-3 x) \log (1+x)}{e^4 \left (15 x+15 x^2\right ) \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((-3*x-3)*ln(1+x)+(15*x+15)*exp(4)*ln(x)**2+((-15*x**2-15*x)*exp (4)+3*x)*ln(x)+(15*x**2+25*x+10)*exp(4)+30*x+30)/(15*x**2+15*x)/exp(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/364_Hebisch_4
Test file number \(364\)
Integral number in file \(95\)
Exception generated. \[ \int \frac {2 x \log (x)+\left (-x+\left (x+x^2-x^3\right ) \log (x)\right ) \log \left (2 x^2\right )+\left (-2 \log (x)+\left (-1+x^2\right ) \log (x) \log \left (2 x^2\right )\right ) \log (\log (x))+\left (2 x^2 \log (x)-2 x \log (x) \log (\log (x))\right ) \log \left (\frac {e^x}{-x+\log (\log (x))}\right )}{-x^3 \log (5) \log (x) \log ^2\left (2 x^2\right )+x^2 \log (5) \log (x) \log ^2\left (2 x^2\right ) \log (\log (x))} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((-2*x*ln(x)*ln(ln(x))+2*x**2*ln(x))*ln(exp(x)/(ln(ln(x))-x))+(( x**2-1)*ln(x)*ln(2*x**2)-2*ln(x))*ln(ln(x))+((-x**3+x**2+x)*ln(x)-x)*ln(2* x**2)+2*x*ln(x))/(x**2*ln(5)*ln(x)*ln(2*x**2)**2*ln(ln(x))-x**3*ln(5)*ln(x )*ln(2*x**2)**2),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(101\)
Exception generated. \[ \int \frac {-36 x+36 x^2+\left (3 x-3 x^2\right ) \log (x)+\left (33 x-108 x^2+\left (-3 x+9 x^2\right ) \log (x)\right ) \log (2 x)+(-36 x+3 x \log (x)+(72 x-6 x \log (x)) \log (2 x)) \log \left (\frac {-12+\log (x)}{8 x}\right )}{(-12+\log (x)) \log ^2(2 x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((-6*x*ln(x)+72*x)*ln(2*x)+3*x*ln(x)-36*x)*ln(1/8*(ln(x)-12)/x) +((9*x**2-3*x)*ln(x)-108*x**2+33*x)*ln(2*x)+(-3*x**2+3*x)*ln(x)+36*x**2-36 *x)/(ln(x)-12)/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/364_Hebisch_4
Test file number \(364\)
Integral number in file \(111\)
Exception generated. \[ \int \frac {e^x x^3+\left (324+324 x+e^{e^{4 x}} (324+324 x)\right ) \log \left (1+e^{e^{4 x}}\right )+2 e^x x^2 \log (x)+e^x x \log ^2(x)+e^{e^{4 x}} \left (-1296 e^{4 x} x^2+e^x x^3+\left (-1296 e^{4 x} x+2 e^x x^2\right ) \log (x)+e^x x \log ^2(x)\right )}{x^3+2 x^2 \log (x)+x \log ^2(x)+e^{e^{4 x}} \left (x^3+2 x^2 \log (x)+x \log ^2(x)\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((324*x+324)*exp(exp(4*x))+324*x+324)*ln(exp(exp(4*x))+1)+(x*ex p(x)*ln(x)**2+(-1296*x*exp(4*x)+2*exp(x)*x**2)*ln(x)-1296*x**2*exp(4*x)+ex p(x)*x**3)*exp(exp(4*x))+x*exp(x)*ln(x)**2+2*x**2*exp(x)*ln(x)+exp(x)*x**3 )/((x*ln(x)**2+2*x**2*ln(x)+x**3)*exp(exp(4*x))+x*ln(x)**2+2*x**2*ln(x)+x* *3),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(277\)
Exception generated. \[ \int \frac {\left (8+2 x-2 x^2+e \left (16 x+4 x^2-4 x^3\right )\right ) \log (x)+\left (-4+8 x+e \left (-4 x+8 x^2\right )\right ) \log ^2(x) \log \left (\frac {x+e x^2}{e}\right )+\left (-8-2 x+2 x^2+e \left (-8 x-2 x^2+2 x^3\right )+\left (8+4 x-6 x^2+e \left (8 x+4 x^2-6 x^3\right )\right ) \log (x)\right ) \log \left (\frac {x+e x^2}{e}\right ) \log \left (\log \left (\frac {x+e x^2}{e}\right )\right )}{(1+e x) \log ^2(x) \log \left (\frac {x+e x^2}{e}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((((-6*x**3+4*x**2+8*x)*exp(1)-6*x**2+4*x+8)*ln(x)+(2*x**3-2*x** 2-8*x)*exp(1)+2*x**2-2*x-8)*ln((x**2*exp(1)+x)/exp(1))*ln(ln((x**2*exp(1)+ x)/exp(1)))+((8*x**2-4*x)*exp(1)+8*x-4)*ln(x)**2*ln((x**2*exp(1)+x)/exp(1) )+((-4*x**3+4*x**2+16*x)*exp(1)-2*x**2+2*x+8)*ln(x))/(exp(1)*x+1)/ln(x)**2 /ln((x**2*exp(1)+x)/exp(1)),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(310\)
Exception generated. \[ \int \frac {16 e^4+e^{4+2 x} x^2+e^{4+x} (-4+4 x)}{-32+16 x+e^x \left (-20 x+8 x^2\right )+e^{2 x} \left (-3 x^2+x^3\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((x**2*exp(4)*exp(x)**2+(-4+4*x)*exp(4)*exp(x)+16*exp(4))/((x**3- 3*x**2)*exp(x)**2+(8*x**2-20*x)*exp(x)+16*x-32),x)
Output:
Exception raised: PolynomialError >> 1/(x**4 - 6*x**3 + 9*x**2) contains a n element of the set of generators.
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(366\)
Exception generated. \[ \int \frac {e^{\frac {9+123 x+30 x^2}{10 \log \left (\frac {2+x^2}{x}\right )}} \left (18+246 x+51 x^2-123 x^3-30 x^4+\left (246 x+120 x^2+123 x^3+60 x^4\right ) \log \left (\frac {2+x^2}{x}\right )+\left (20+10 x^2\right ) \log ^2\left (\frac {2+x^2}{x}\right )\right )}{\left (20+10 x^2\right ) \log ^2\left (\frac {2+x^2}{x}\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((10*x**2+20)*ln((x**2+2)/x)**2+(60*x**4+123*x**3+120*x**2+246*x )*ln((x**2+2)/x)-30*x**4-123*x**3+51*x**2+246*x+18)*exp(1/10*(30*x**2+123* x+9)/ln((x**2+2)/x))/(10*x**2+20)/ln((x**2+2)/x)**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(541\)
Exception generated. \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((((3*x**2+2*x)*ln(x)**4+(12*x+8)*ln(x)**3-15*x**2-10*x)*ln(2+3*x )**3+((-9*x**3-6*x**2)*ln(x)**4+(-36*x**2-24*x)*ln(x)**3+(-36*x**2-24*x)*l n(x)**2+(-72*x-48)*ln(x)+45*x**3+30*x**2)*ln(2+3*x)**2+((9*x**4+6*x**3)*ln (x)**4+(36*x**3+24*x**2)*ln(x)**3+(72*x**3+12*x**2+12*x)*ln(x)**2+(144*x** 2+96*x)*ln(x)-45*x**4-30*x**3+108*x**2+72*x)*ln(2+3*x)+(-3*x**5-2*x**4)*ln (x)**4+(-12*x**4-8*x**3)*ln(x)**3+(-36*x**4+12*x**3-12*x**2)*ln(x)**2+(-72 *x**3-48*x**2)*ln(x)+15*x**5+10*x**4-108*x**3+144*x**2-72*x)/(((3*x**2+2*x )*ln(x)**4-15*x**2-10*x)*ln(2+3*x)**3+((-9*x**3-6*x**2)*ln(x)**4+(-36*x**2 -24*x)*ln(x)**2+45*x**3+30*x**2)*ln(2+3*x)**2+((9*x**4+6*x**3)*ln(x)**4+(7 2*x**3+48*x**2)*ln(x)**2-45*x**4-30*x**3+108*x**2+72*x)*ln(2+3*x)+(-3*x**5 -2*x**4)*ln(x)**4+(-36*x**4-24*x**3)*ln(x)**2+15*x**5+10*x**4-108*x**3-72* x**2),x)
Output:
Exception raised: PolynomialError >> 1/(9*_t0**16*x**4 + 12*_t0**16*x**3 + 4*_t0**16*x**2 - 180*_t0**12*x**4 - 240*_t0**12*x**3 - 80*_t0**12*x**2 + 1350*_t0**8*x**4 + 1800*_t0**8*x**3 + 600*_t0**8*x**2 - 4500*_t0**4*x**4 - 6000*_t0**4*x*
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(659\)
Exception generated. \[ \int \frac {-50 x-20 e^4 x-2 e^8 x+\left (-20 x-4 e^4 x\right ) \log (x)-2 x \log ^2(x)+e^{\frac {x^3+x^2 \log (4)}{5+e^4+\log (x)}} \left (25+e^8+14 x^3+e^4 \left (10+3 x^3\right )+\left (9 x^2+2 e^4 x^2\right ) \log (4)+\left (10+2 e^4+3 x^3+2 x^2 \log (4)\right ) \log (x)+\log ^2(x)\right )}{25+10 e^4+e^8+\left (10+2 e^4\right ) \log (x)+\log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((ln(x)**2+(4*x**2*ln(2)+2*exp(4)+3*x**3+10)*ln(x)+2*(2*x**2*exp (4)+9*x**2)*ln(2)+exp(4)**2+(3*x**3+10)*exp(4)+14*x**3+25)*exp((2*x**2*ln( 2)+x**3)/(ln(x)+5+exp(4)))-2*x*ln(x)**2+(-4*x*exp(4)-20*x)*ln(x)-2*x*exp(4 )**2-20*x*exp(4)-50*x)/(ln(x)**2+(2*exp(4)+10)*ln(x)+exp(4)**2+10*exp(4)+2 5),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(749\)
Exception generated. \[ \int \frac {\left (e^{10}-e^5 x\right ) \log ^2\left (e^{10}-2 e^5 x+x^2\right )+e^{\frac {4 x^3}{e^5 \log \left (e^{10}-2 e^5 x+x^2\right )}} \left (8 x^3+\left (12 e^5 x^2-12 x^3\right ) \log \left (e^{10}-2 e^5 x+x^2\right )\right )}{\left (e^{10}-e^5 x\right ) \log ^2\left (e^{10}-2 e^5 x+x^2\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((12*x**2*exp(5)-12*x**3)*ln(exp(5)**2-2*x*exp(5)+x**2)+8*x**3) *exp(4*x**3/exp(5)/ln(exp(5)**2-2*x*exp(5)+x**2))+(exp(5)**2-x*exp(5))*ln( exp(5)**2-2*x*exp(5)+x**2)**2)/(exp(5)**2-x*exp(5))/ln(exp(5)**2-2*x*exp(5 )+x**2)**2,x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(775\)
Exception generated. \[ \int \frac {e^{\frac {3 x^2+5 x^3+2 x^4}{(4+8 x) \log \left (x^2\right )}} \left (-6 x^2-22 x^3-24 x^4-8 x^5+\left (6 x^2+21 x^3+28 x^4+12 x^5\right ) \log \left (x^2\right )+\left (-8-32 x-32 x^2\right ) \log ^2\left (x^2\right )\right )}{\left (4 x^3+16 x^4+16 x^5\right ) \log ^2\left (x^2\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((-32*x**2-32*x-8)*ln(x**2)**2+(12*x**5+28*x**4+21*x**3+6*x**2)* ln(x**2)-8*x**5-24*x**4-22*x**3-6*x**2)*exp((2*x**4+5*x**3+3*x**2)/(8*x+4) /ln(x**2))/(16*x**5+16*x**4+4*x**3)/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/364_Hebisch_4
Test file number \(364\)
Integral number in file \(947\)
Exception generated. \[ \int \frac {e^{9 e^{\frac {2 \left (-4 x-x^2\right )}{6-3 x+3 \log (x)}}+\frac {2 \left (-4 x-x^2\right )}{6-3 x+3 \log (x)}} \left (-24-18 x+6 x^2+(-24-12 x) \log (x)\right )}{4-4 x+x^2+(4-2 x) \log (x)+\log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((-12*x-24)*ln(x)+6*x**2-18*x-24)*exp((-x**2-4*x)/(3*ln(x)-3*x+6 ))**2*exp(9*exp((-x**2-4*x)/(3*ln(x)-3*x+6))**2)/(ln(x)**2+(4-2*x)*ln(x)+x **2-4*x+4),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(1034\)
Exception generated. \[ \int \frac {7 x^2+(12+4 x) \log ^3(5 x) \log (3+x)+\log ^4(5 x) (-x+(-3-x) \log (3+x))}{147 x^2+49 x^3+\left (-42 x-14 x^2\right ) \log ^4(5 x)+(3+x) \log ^8(5 x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((-3-x)*ln(3+x)-x)*ln(5*x)**4+(4*x+12)*ln(3+x)*ln(5*x)**3+7*x** 2)/((3+x)*ln(5*x)**8+(-14*x**2-42*x)*ln(5*x)**4+49*x**3+147*x**2),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(1123\)
Exception generated. \[ \int \frac {e^{-\frac {-5 x+e^5 x+\left (-5+e^5\right ) \log (x)+\log \left (\frac {x}{\log (x)}\right )}{x+\log (x)}} \left (e^{\frac {-5 x+e^5 x+\left (-5+e^5\right ) \log (x)+\log \left (\frac {x}{\log (x)}\right )}{x+\log (x)}} \left (x^2 \log (x)+2 x \log ^2(x)+\log ^3(x)\right )+e^{e^{-\frac {-5 x+e^5 x+\left (-5+e^5\right ) \log (x)+\log \left (\frac {x}{\log (x)}\right )}{x+\log (x)}} \left (-2 e^{\frac {-5 x+e^5 x+\left (-5+e^5\right ) \log (x)+\log \left (\frac {x}{\log (x)}\right )}{x+\log (x)}}+x\right )} \left (x+\left (1-x+x^2\right ) \log (x)+(-1+2 x) \log ^2(x)+\log ^3(x)+(1+x) \log (x) \log \left (\frac {x}{\log (x)}\right )\right )\right )}{x^2 \log (x)+2 x \log ^2(x)+\log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((1+x)*ln(x)*ln(x/ln(x))+ln(x)**3+(-1+2*x)*ln(x)**2+(x**2-x+1)* ln(x)+x)*exp((-2*exp((ln(x/ln(x))+(exp(5)-5)*ln(x)+x*exp(5)-5*x)/(x+ln(x)) )+x)/exp((ln(x/ln(x))+(exp(5)-5)*ln(x)+x*exp(5)-5*x)/(x+ln(x))))+(ln(x)**3 +2*x*ln(x)**2+x**2*ln(x))*exp((ln(x/ln(x))+(exp(5)-5)*ln(x)+x*exp(5)-5*x)/ (x+ln(x))))/(ln(x)**3+2*x*ln(x)**2+x**2*ln(x))/exp((ln(x/ln(x))+(exp(5)-5) *ln(x)+x*exp(5)-5*x)/(x+ln(x))),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(1148\)
Exception generated. \[ \int \frac {128-32 x+64 x^2-16 x^3+8 x^4-2 x^5+\left (40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7\right ) \log (x)+\left (2-296 x+82 x^2-258 x^3+64 x^4-48 x^5+12 x^6\right ) \log ^2(x)+\left (-49 x+4 x^2-32 x^3-6 x^5\right ) \log ^3(x)-2 x \log ^4(x)+\left (\left (52-x+88 x^2-16 x^3+19 x^4-4 x^5\right ) \log (x)+\left (20+24 x^2+5 x^4\right ) \log ^2(x)+\log ^3(x)\right ) \log \left (\log ^2(x)\right )}{\left (16-8 x+x^2\right ) \log (x)+(8-2 x) \log ^2(x)+\log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((ln(x)**3+(5*x**4+24*x**2+20)*ln(x)**2+(-4*x**5+19*x**4-16*x**3 +88*x**2-x+52)*ln(x))*ln(ln(x)**2)-2*x*ln(x)**4+(-6*x**5-32*x**3+4*x**2-49 *x)*ln(x)**3+(12*x**6-48*x**5+64*x**4-258*x**3+82*x**2-296*x+2)*ln(x)**2+( -6*x**7+48*x**6-128*x**5+258*x**4-545*x**3+280*x**2-530*x+40)*ln(x)-2*x**5 +8*x**4-16*x**3+64*x**2-32*x+128)/(ln(x)**3+(-2*x+8)*ln(x)**2+(x**2-8*x+16 )*ln(x)),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(1161\)
Exception generated. \[ \int \frac {-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )+e^{\frac {1}{13 x-4 x^2+3 x \log \left (81-108 x+54 x^2-12 x^3+x^4\right )}} \left (39-49 x+8 x^2+(9-3 x) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )\right )}{-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((-3*x+9)*ln(x**4-12*x**3+54*x**2-108*x+81)+8*x**2-49*x+39)*exp (1/(3*x*ln(x**4-12*x**3+54*x**2-108*x+81)-4*x**2+13*x))+(9*x**3-27*x**2)*l n(x**4-12*x**3+54*x**2-108*x+81)**2+(-24*x**4+150*x**3-234*x**2)*ln(x**4-1 2*x**3+54*x**2-108*x+81)+16*x**5-152*x**4+481*x**3-507*x**2)/((9*x**3-27*x **2)*ln(x**4-12*x**3+54*x**2-108*x+81)**2+(-24*x**4+150*x**3-234*x**2)*ln( x**4-12*x**3+54*x**2-108*x+81)+16*x**5-152*x**4+481*x**3-507*x**2),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
input file name test_cases/extra_tests/364_Hebisch_4
Test file number \(364\)
Integral number in file \(1263\)
Exception generated. \[ \int \frac {\left (-208 x-60 x^2+108 x^3-36 x^4+4 x^5\right ) \log (2 x)+\left (-60+164 x-57 x^2-15 x^3+9 x^4-x^5\right ) \log \left (\frac {400-1920 x+2424 x^2-48 x^3-607 x^4+132 x^5+30 x^6-12 x^7+x^8}{81-108 x+54 x^2-12 x^3+x^4}\right )}{\left (60 x-164 x^2+57 x^3+15 x^4-9 x^5+x^6\right ) \log ^2(2 x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((-x**5+9*x**4-15*x**3-57*x**2+164*x-60)*ln((x**8-12*x**7+30*x** 6+132*x**5-607*x**4-48*x**3+2424*x**2-1920*x+400)/(x**4-12*x**3+54*x**2-10 8*x+81))+(4*x**5-36*x**4+108*x**3-60*x**2-208*x)*ln(2*x))/(x**6-9*x**5+15* x**4+57*x**3-164*x**2+60*x)/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/364_Hebisch_4
Test file number \(364\)
Integral number in file \(1318\)
Exception generated. \[ \int \frac {5-5 e^x+5 x-5 x^2+\left (5+4 x^2+x^3+e^x (-5+6 x)\right ) \log (x)+\left (-x^3+e^x \left (x-x^2\right )\right ) \log ^2(x)+\left (5+(5-x) \log (x)-x \log ^2(x)\right ) \log \left (\frac {1}{2} (-5+x \log (x))\right )}{-5 x^2 \log ^2(x)+x^3 \log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((-x*ln(x)**2+ln(x)*(5-x)+5)*ln(1/2*x*ln(x)-5/2)+((-x**2+x)*exp( x)-x**3)*ln(x)**2+((6*x-5)*exp(x)+x**3+4*x**2+5)*ln(x)-5*exp(x)-5*x**2+5*x +5)/(x**3*ln(x)**3-5*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/364_Hebisch_4
Test file number \(364\)
Integral number in file \(1323\)
Exception generated. \[ \int \frac {2 a \left (-b^3+2 \sqrt {2} a^2 b x^2\right )}{b^4-a^2 b^2 x^2+\sqrt {2} a^4 x^4} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate(2*a*(-b**3+2*2**(1/2)*a**2*b*x**2)/(b**4-a**2*b**2*x**2+2**(1/2) *a**4*x**4),x)
Output:
Exception raised: PolynomialError >> 1/(_t**4 - 4*sqrt(2)*_t**2 + 8) conta ins an element of the set of generators.
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(1\)
Exception generated. \[ \int \frac {-\sqrt {3} b-2 a x+4 \sqrt {2} a x+3 b^2 x+2 \sqrt {3} a b x^2-2 \sqrt {6} a b x^2+2 \sqrt {2} a^2 x^3}{1-2 \sqrt {3} b x-a x^2+3 b^2 x^2+\sqrt {3} a b x^3+\sqrt {2} a^2 x^4} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((-3**(1/2)*b-2*a*x+4*2**(1/2)*a*x+3*b**2*x+2*3**(1/2)*a*b*x**2-2 *6**(1/2)*a*b*x**2+2*2**(1/2)*a**2*x**3)/(1-2*3**(1/2)*b*x-a*x**2+3*b**2*x **2+3**(1/2)*a*b*x**3+2**(1/2)*a**2*x**4),x)
Output:
Exception raised: PolynomialError >> 1/(128*_t**4*a**2 - 768*_t**4*a*b**2 + 144*sqrt(2)*_t**4*a*b**2 - 432*sqrt(2)*_t**4*b**4 + 1233*_t**4*b**4 - 51 2*sqrt(2)*_t**3*a**2 - 128*_t**3*a**2 + 192*_t**3*a*b**2 + 1368*sqrt(2)*_t **3*a*b**2 - 12
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(3\)
Exception generated. \[ \int \frac {-\sqrt {3}+x+4 \sqrt {2} x+2 \sqrt {3} x^2-2 \sqrt {6} x^2+2 \sqrt {2} x^3}{1-2 \sqrt {3} x+2 x^2+\sqrt {3} x^3+\sqrt {2} x^4} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((-3**(1/2)+x+4*2**(1/2)*x+2*3**(1/2)*x**2-2*6**(1/2)*x**2+2*2**( 1/2)*x**3)/(1-2*3**(1/2)*x+2*x**2+3**(1/2)*x**3+2**(1/2)*x**4),x)
Output:
Exception raised: PolynomialError >> 1/(-593*_t**4 + 288*sqrt(2)*_t**4 - 1 360*sqrt(2)*_t**3 + 1196*_t**3 - 1044*_t**2 + 244*sqrt(2)*_t**2 - 800*_t + 584*sqrt(2)*_t - 136 + 96*sqrt(2)) contains an element of the set of gene rators.
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(8\)
Exception generated. \[ \int \frac {-1-x+4 \sqrt {2} x+2 x^2-2 \sqrt {2} x^2+2 \sqrt {2} x^3}{1-2 x+x^3+\sqrt {2} x^4} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((-1-x+4*2**(1/2)*x+2*x**2-2*2**(1/2)*x**2+2*2**(1/2)*x**3)/(1-2* x+x**3+2**(1/2)*x**4),x)
Output:
Exception raised: PolynomialError >> 1/(9*_t**4 - 204*_t**3 + 12*sqrt(2)*_ t**2 + 1204*_t**2 - 544*_t - 136*sqrt(2)*_t + 32*sqrt(2) + 72) contains an element of the set of generators.
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(9\)
Exception generated. \[ \int \frac {1+b x^3}{x^4 \left (-\sqrt {2} a^3 b+x^6\right )^2} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((b*x**3+1)/x**4/(-2**(1/2)*a**3*b+x**6)**2,x)
Output:
Exception raised: PolynomialError >> 1/(606928896*sqrt(2)*_t**6*a**45*b**1 5 + 151732224*sqrt(2)*_t**5*a**39*b**14 + 12644352*sqrt(2)*_t**4*a**33*b** 13 - 24385536*_t**4*a**30*b**10 + 351232*sqrt(2)*_t**3*a**27*b**12 - 40642 56*_t**3*a**24*
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(19\)
Exception generated. \[ \int \frac {\left (3-2 \sqrt {2}+x^2\right )^2 \left (-3+2 \sqrt {2}+x^2\right )}{577-408 \sqrt {2}+328 x^2-232 \sqrt {2} x^2+78 x^4-56 \sqrt {2} x^4+8 x^6-8 \sqrt {2} x^6+x^8} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((3-2*2**(1/2)+x**2)**2*(-3+2*2**(1/2)+x**2)/(577-408*2**(1/2)+32 8*x**2-232*2**(1/2)*x**2+78*x**4-56*2**(1/2)*x**4+8*x**6-8*x**6*2**(1/2)+x **8),x)
Output:
Exception raised: PolynomialError >> 1/(-489331912114255602061892417478047 2498117708482611714912381696*_t**4 + 3460099133069698398004476359279702930 052248019321310378430976*sqrt(2)*_t**4 - 159769239484575670917838951113184 628965915778476
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(47\)
Exception generated. \[ \int \frac {\sqrt {5} \left (-24-2 \sqrt {21}\right )+\sqrt {5} \left (-105+15 \sqrt {21}\right ) x^2}{-16+\left (-48 \sqrt {5}+4 \sqrt {105}\right ) x+\left (50+60 \sqrt {21}\right ) x^2+\left (-210 \sqrt {5}-30 \sqrt {105}\right ) x^3+525 x^4} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((5**(1/2)*(-24-2*21**(1/2))+5**(1/2)*(-105+15*21**(1/2))*x**2)/( -16+(-48*5**(1/2)+4*105**(1/2))*x+(50+60*21**(1/2))*x**2+(-210*5**(1/2)-30 *105**(1/2))*x**3+525*x**4),x)
Output:
Exception raised: PolynomialError >> 1/(-11312*_t**4 + 1680*sqrt(21)*_t**4 - 3360*_t**3 + 288*sqrt(21)*_t**3 - 600*sqrt(21)*_t**2 + 2568*_t**2 - 72* sqrt(21)*_t + 360*_t - 207 + 45*sqrt(21)) contains an element of the set o f generators.
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(48\)
Exception generated. \[ \int \frac {3 \sqrt {7}+6 \sqrt {11}+\left (-121 \sqrt {105}-98 \sqrt {165}\right ) x^4}{-12 \sqrt {15}+10200 x^4-118580 \sqrt {15} x^8} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((3*7**(1/2)+6*11**(1/2)+(-121*105**(1/2)-98*165**(1/2))*x**4)/(- 12*15**(1/2)+10200*x**4-118580*15**(1/2)*x**8),x)
Output:
Exception raised: PolynomialError >> 1/(8876619644311361811449478210059404 03892090960648942070894847733907374495278002081072424698386397863110524278 65545878613259174768870299313417544282422774969138741079283023024302083445 868952121128899
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(50\)
Exception generated. \[ \int \frac {8 \sqrt {11}-2 \sqrt {165}-14 \sqrt {15} x+\left (-70 \sqrt {11}-14 \sqrt {165}\right ) x^2+770 x^3+245 \sqrt {11} x^4}{8 \left (-30+8 \sqrt {15}\right )+8 \left (-650+40 \sqrt {15}\right ) x^2+8 \left (3850+1015 \sqrt {15}\right ) x^4-107800 x^6} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((8*11**(1/2)-2*165**(1/2)-14*15**(1/2)*x+(-70*11**(1/2)-14*165** (1/2))*x**2+770*x**3+245*11**(1/2)*x**4)/(-240+64*15**(1/2)+8*(-650+40*15* *(1/2))*x**2+8*(3850+1015*15**(1/2))*x**4-107800*x**6),x)
Output:
Exception raised: PolynomialError >> 1/(8026406129722253778490365429016317 86571585667051597111057095382995817099486707204483301622083173133484870882 512219322449920000000000000000000000000000000000*_t**48 + 2072409151354094 443219300735040
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(51\)
Exception generated. \[ \int \frac {12 \left (-420+1999 \sqrt {3}\right ) x}{\left (-1999+140 \sqrt {3}\right ) \left (-4-2 \sqrt {3}-6 x^2+6 \sqrt {3} x^2-9 x^4\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate(12*(-420+1999*3**(1/2))*x/(-1999+140*3**(1/2))/(-4-2*3**(1/2)-6* x**2+6*3**(1/2)*x**2-9*x**4),x)
Output:
Exception raised: PolynomialError >> 1/(-173135830797577185636502362255200 6976*_t**2 + 987143636854743804260619971714841888*sqrt(3)*_t**2 - 45428740 085141256258642586775496*_t + 27842854251208551842166254171016*sqrt(3)*_t - 3639190287298
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(54\)
Exception generated. \[ \int \frac {-2 \left (-1-\sqrt {3}\right )-8 \sqrt {3} x-4 x^2}{2-2 \sqrt {3}+\left (4+4 \sqrt {3}\right ) x-4 \sqrt {3} x^2-8 x^3+4 x^4} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((2+2*3**(1/2)-8*3**(1/2)*x-4*x**2)/(2-2*3**(1/2)+(4+4*3**(1/2))* x-4*3**(1/2)*x**2-8*x**3+4*x**4),x)
Output:
Exception raised: PolynomialError >> 1/(192*sqrt(3)*_t**4 + 336*_t**4 - 48 0*_t**3 - 256*sqrt(3)*_t**3 + 48*sqrt(3)*_t**2 + 184*_t**2 + 8*_t + 16*sqr t(3)*_t + 1) contains an element of the set of generators.
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(59\)
Exception generated. \[ \int \frac {\left (3-2 \sqrt {2}+x^2\right )^2 \left (-3+2 \sqrt {2}+x^2\right )}{577-408 \sqrt {2}+328 x^2-232 \sqrt {2} x^2+78 x^4-56 \sqrt {2} x^4+8 x^6-8 \sqrt {2} x^6+x^8} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((3-2*2**(1/2)+x**2)**2*(-3+2*2**(1/2)+x**2)/(577-408*2**(1/2)+32 8*x**2-232*2**(1/2)*x**2+78*x**4-56*2**(1/2)*x**4+8*x**6-8*x**6*2**(1/2)+x **8),x)
Output:
Exception raised: PolynomialError >> 1/(-489331912114255602061892417478047 2498117708482611714912381696*_t**4 + 3460099133069698398004476359279702930 052248019321310378430976*sqrt(2)*_t**4 - 159769239484575670917838951113184 628965915778476
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(83\)
Exception generated. \[ \int \frac {-36-2 \sqrt {6} x^2}{9 \sqrt {3}+3 \sqrt {2} x^2-x^4} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((-36-2*6**(1/2)*x**2)/(9*3**(1/2)+3*2**(1/2)*x**2-x**4),x)
Output:
Exception raised: PolynomialError >> 1/(2*_t**4 - 2*sqrt(2)*_t**2 + 1) con tains an element of the set of generators.
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(98\)