Integrals 701 to 800

Sympy [F(-2)]

Exception generated. \[ \int x \arctan (c-(i-c) \coth (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x*atan(c-(I-c)*coth(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert _t0**2 - exp(2*a) of ty 
pe <class 'sympy.core.add.Add'> to QQ_I[x,b,_t0,exp(a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/276_5.3

Test file number \(276\)

Integral number in file \(107\)

Sympy [F(-2)]

Exception generated. \[ \int \arctan (c-(i-c) \coth (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(atan(c-(I-c)*coth(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert _t0**2 - exp(2*a) of ty 
pe <class 'sympy.core.add.Add'> to QQ_I[b,_t0,exp(a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/276_5.3

Test file number \(276\)

Integral number in file \(108\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {a+b \arctan (c x)}{x (d+i c d x)^3} \, dx=\text {Exception raised: RecursionError} \] Input:

integrate((a+b*atan(c*x))/x/(d+I*c*d*x)**3,x)
 

Output:

Exception raised: RecursionError >> maximum recursion depth exceeded in co 
mparison
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(63\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b \arctan (c x))^2}{x (d+i c d x)^3} \, dx=\text {Exception raised: RecursionError} \] Input:

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

Output:

Exception raised: RecursionError >> maximum recursion depth exceeded in co 
mparison
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(116\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\arctan (a x)}{\left (c+a^2 c x^2\right )^2} \, dx=\text {Exception raised: RecursionError} \] Input:

integrate(atan(a*x)/(a**2*c*x**2+c)**2,x)
 

Output:

Exception raised: RecursionError >> maximum recursion depth exceeded while 
 calling a Python object
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(187\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\arctan (a x)}{x \left (c+a^2 c x^2\right )^2} \, dx=\text {Exception raised: RecursionError} \] Input:

integrate(atan(a*x)/x/(a**2*c*x**2+c)**2,x)
 

Output:

Exception raised: RecursionError >> maximum recursion depth exceeded
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(188\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\arctan (a x)}{\left (c+a^2 c x^2\right )^3} \, dx=\text {Exception raised: RecursionError} \] Input:

integrate(atan(a*x)/(a**2*c*x**2+c)**3,x)
 

Output:

Exception raised: RecursionError >> maximum recursion depth exceeded in co 
mparison
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(195\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\arctan (a x)}{x \left (c+a^2 c x^2\right )^3} \, dx=\text {Exception raised: RecursionError} \] Input:

integrate(atan(a*x)/x/(a**2*c*x**2+c)**3,x)
 

Output:

Exception raised: RecursionError >> maximum recursion depth exceeded
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(196\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x \arctan (a x)}{\sqrt {c+a^2 c x^2}} \, dx=\text {Exception raised: TypeError} \] Input:

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

Output:

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

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(226\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x \arctan (a x)}{\left (c+a^2 c x^2\right )^{3/2}} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x*atan(a*x)/(a**2*c*x**2+c)**(3/2),x)
 

Output:

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

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(234\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\arctan (a x)}{x \left (c+a^2 c x^2\right )^{3/2}} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(atan(a*x)/x/(a**2*c*x**2+c)**(3/2),x)
 

Output:

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

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(236\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x \arctan (a x)}{\left (c+a^2 c x^2\right )^{5/2}} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x*atan(a*x)/(a**2*c*x**2+c)**(5/2),x)
 

Output:

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

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(244\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\arctan (a x)}{x \left (c+a^2 c x^2\right )^{5/2}} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(atan(a*x)/x/(a**2*c*x**2+c)**(5/2),x)
 

Output:

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

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(246\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b \arctan (c x)) \left (d+e \log \left (1+c^2 x^2\right )\right )}{x^2} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*atan(c*x))*(d+e*ln(c**2*x**2+1))/x**2,x)
 

Output:

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

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(1290\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b \arctan (c x)) \left (d+e \log \left (1+c^2 x^2\right )\right )}{x^4} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*atan(c*x))*(d+e*ln(c**2*x**2+1))/x**4,x)
 

Output:

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

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(1292\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b \arctan (c x)) \left (d+e \log \left (1+c^2 x^2\right )\right )}{x^6} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*atan(c*x))*(d+e*ln(c**2*x**2+1))/x**6,x)
 

Output:

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

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.3_Inverse_tangent/279_5.3.4

Test file number \(279\)

Integral number in file \(1294\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(2\)

Sympy [F(-2)]

Exception generated. \[ \int x^2 \cot ^{-1}(c+(1+i c) \tan (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x**2*acot(c+(1+I*c)*tan(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert 2*_t0**2*c*exp(2*I*a) - 
 _t0**2*I*exp(2*I*a) + I of type <class 'sympy.core.add.Add'> to QQ_I[x,b, 
c,_t0,exp(I*a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(14\)

Sympy [F(-2)]

Exception generated. \[ \int x \cot ^{-1}(c+(1+i c) \tan (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x*acot(c+(1+I*c)*tan(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert 2*_t0**2*c*exp(2*I*a) - 
 _t0**2*I*exp(2*I*a) + I of type <class 'sympy.core.add.Add'> to QQ_I[x,b, 
c,_t0,exp(I*a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(15\)

Sympy [F(-2)]

Exception generated. \[ \int \cot ^{-1}(c+(1+i c) \tan (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(acot(c+(1+I*c)*tan(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert 2*_t0**2*c*exp(2*I*a) - 
 _t0**2*I*exp(2*I*a) + I of type <class 'sympy.core.add.Add'> to QQ_I[b,c, 
_t0,exp(I*a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(16\)

Sympy [F(-2)]

Exception generated. \[ \int x^2 \cot ^{-1}(c-(1-i c) \tan (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x**2*acot(c-(1-I*c)*tan(b*x+a)),x)
                                                                                    
                                                                                    
 

Output:

Exception raised: CoercionFailed >> Cannot convert 2*_t0**4*c**2*exp(4*I*a 
) + _t0**4*I*c*exp(4*I*a) - 3*_t0**2*I*c*exp(2*I*a) + _t0**2*exp(2*I*a) - 
1 of type <class 'sympy.core.add.Add'> to QQ_I[x,b,c,_t0,exp(I*a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(18\)

Sympy [F(-2)]

Exception generated. \[ \int x \cot ^{-1}(c-(1-i c) \tan (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x*acot(c-(1-I*c)*tan(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert 2*_t0**4*c**2*exp(4*I*a 
) + _t0**4*I*c*exp(4*I*a) - 3*_t0**2*I*c*exp(2*I*a) + _t0**2*exp(2*I*a) - 
1 of type <class 'sympy.core.add.Add'> to QQ_I[x,b,c,_t0,exp(I*a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(19\)

Sympy [F(-2)]

Exception generated. \[ \int \cot ^{-1}(c-(1-i c) \tan (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(acot(c-(1-I*c)*tan(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert 2*_t0**4*c**2*exp(4*I*a 
) + _t0**4*I*c*exp(4*I*a) - 3*_t0**2*I*c*exp(2*I*a) + _t0**2*exp(2*I*a) - 
1 of type <class 'sympy.core.add.Add'> to QQ_I[b,c,_t0,exp(I*a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(20\)

Sympy [F(-2)]

Exception generated. \[ \int x^2 \cot ^{-1}(c+(1-i c) \cot (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x**2*(pi-acot(-c-(1-I*c)*cot(b*x+a))),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert 2*_t0**4*c**2*exp(4*I*a 
) + _t0**4*I*c*exp(4*I*a) + 3*_t0**2*I*c*exp(2*I*a) - _t0**2*exp(2*I*a) - 
1 of type <class 'sympy.core.add.Add'> to QQ_I[x,b,c,_t0,exp(I*a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(27\)

Sympy [F(-2)]

Exception generated. \[ \int x \cot ^{-1}(c+(1-i c) \cot (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x*(pi-acot(-c-(1-I*c)*cot(b*x+a))),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert 2*_t0**4*c**2*exp(4*I*a 
) + _t0**4*I*c*exp(4*I*a) + 3*_t0**2*I*c*exp(2*I*a) - _t0**2*exp(2*I*a) - 
1 of type <class 'sympy.core.add.Add'> to QQ_I[x,b,c,_t0,exp(I*a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(28\)

Sympy [F(-2)]

Exception generated. \[ \int \cot ^{-1}(c+(1-i c) \cot (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(pi-acot(-c-(1-I*c)*cot(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert 2*_t0**4*c**2*exp(4*I*a 
) + _t0**4*I*c*exp(4*I*a) + 3*_t0**2*I*c*exp(2*I*a) - _t0**2*exp(2*I*a) - 
1 of type <class 'sympy.core.add.Add'> to QQ_I[b,c,_t0,exp(I*a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(29\)

Sympy [F(-2)]

Exception generated. \[ \int x^2 \cot ^{-1}(c-(1+i c) \cot (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x**2*(pi-acot(-c+(1+I*c)*cot(b*x+a))),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert 2*_t0**2*c*exp(2*I*a) - 
 _t0**2*I*exp(2*I*a) - I of type <class 'sympy.core.add.Add'> to QQ_I[x,b, 
c,_t0,exp(I*a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(31\)

Sympy [F(-2)]

Exception generated. \[ \int x \cot ^{-1}(c-(1+i c) \cot (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x*(pi-acot(-c+(1+I*c)*cot(b*x+a))),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert 2*_t0**2*c*exp(2*I*a) - 
 _t0**2*I*exp(2*I*a) - I of type <class 'sympy.core.add.Add'> to QQ_I[x,b, 
c,_t0,exp(I*a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(32\)

Sympy [F(-2)]

Exception generated. \[ \int \cot ^{-1}(c-(1+i c) \cot (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(pi-acot(-c+(1+I*c)*cot(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert 2*_t0**2*c*exp(2*I*a) - 
 _t0**2*I*exp(2*I*a) - I of type <class 'sympy.core.add.Add'> to QQ_I[b,c, 
_t0,exp(I*a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(33\)

Sympy [F(-2)]

Exception generated. \[ \int x^2 \cot ^{-1}(c+(i+c) \tanh (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x**2*acot(c+(I+c)*tanh(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert -_t0**4 - 3*_t0**2*I*c* 
exp(2*a) + _t0**2*exp(2*a) + 2*c**2*exp(4*a) + I*c*exp(4*a) of type <class 
 'sympy.core.add.Add'> to QQ_I[x,b,c,_t0,exp(a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(44\)

Sympy [F(-2)]

Exception generated. \[ \int x \cot ^{-1}(c+(i+c) \tanh (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x*acot(c+(I+c)*tanh(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert -_t0**4 - 3*_t0**2*I*c* 
exp(2*a) + _t0**2*exp(2*a) + 2*c**2*exp(4*a) + I*c*exp(4*a) of type <class 
 'sympy.core.add.Add'> to QQ_I[x,b,c,_t0,exp(a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(45\)

Sympy [F(-2)]

Exception generated. \[ \int \cot ^{-1}(c+(i+c) \tanh (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(acot(c+(I+c)*tanh(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert -_t0**4 - 3*_t0**2*I*c* 
exp(2*a) + _t0**2*exp(2*a) + 2*c**2*exp(4*a) + I*c*exp(4*a) of type <class 
 'sympy.core.add.Add'> to QQ_I[b,c,_t0,exp(a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(46\)

Sympy [F(-2)]

Exception generated. \[ \int x^2 \cot ^{-1}(c-(i-c) \tanh (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x**2*acot(c-(I-c)*tanh(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert _t0**2*I + 2*c*exp(2*a) 
 - I*exp(2*a) of type <class 'sympy.core.add.Add'> to QQ_I[x,b,c,_t0,exp(a 
)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(48\)

Sympy [F(-2)]

Exception generated. \[ \int x \cot ^{-1}(c-(i-c) \tanh (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x*acot(c-(I-c)*tanh(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert _t0**2*I + 2*c*exp(2*a) 
 - I*exp(2*a) of type <class 'sympy.core.add.Add'> to QQ_I[x,b,c,_t0,exp(a 
)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(49\)

Sympy [F(-2)]

Exception generated. \[ \int \cot ^{-1}(c-(i-c) \tanh (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(acot(c-(I-c)*tanh(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert _t0**2*I + 2*c*exp(2*a) 
 - I*exp(2*a) of type <class 'sympy.core.add.Add'> to QQ_I[b,c,_t0,exp(a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(50\)

Sympy [F(-2)]

Exception generated. \[ \int x^2 \cot ^{-1}(c+(i+c) \coth (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x**2*acot(c+(I+c)*coth(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert -_t0**4 + 3*_t0**2*I*c* 
exp(2*a) - _t0**2*exp(2*a) + 2*c**2*exp(4*a) + I*c*exp(4*a) of type <class 
 'sympy.core.add.Add'> to QQ_I[x,b,c,_t0,exp(a)]
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(61\)

Sympy [F(-2)]

Exception generated. \[ \int x \cot ^{-1}(c+(i+c) \coth (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x*acot(c+(I+c)*coth(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert -_t0**4 + 3*_t0**2*I*c* 
exp(2*a) - _t0**2*exp(2*a) + 2*c**2*exp(4*a) + I*c*exp(4*a) of type <class 
 'sympy.core.add.Add'> to QQ_I[x,b,c,_t0,exp(a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(62\)

Sympy [F(-2)]

Exception generated. \[ \int \cot ^{-1}(c+(i+c) \coth (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(acot(c+(I+c)*coth(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert -_t0**4 + 3*_t0**2*I*c* 
exp(2*a) - _t0**2*exp(2*a) + 2*c**2*exp(4*a) + I*c*exp(4*a) of type <class 
 'sympy.core.add.Add'> to QQ_I[b,c,_t0,exp(a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(63\)

Sympy [F(-2)]

Exception generated. \[ \int x^2 \cot ^{-1}(c-(i-c) \coth (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x**2*acot(c-(I-c)*coth(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert -_t0**2*I + 2*c*exp(2*a 
) - I*exp(2*a) of type <class 'sympy.core.add.Add'> to QQ_I[x,b,c,_t0,exp( 
a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(65\)

Sympy [F(-2)]

Exception generated. \[ \int x \cot ^{-1}(c-(i-c) \coth (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(x*acot(c-(I-c)*coth(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert -_t0**2*I + 2*c*exp(2*a 
) - I*exp(2*a) of type <class 'sympy.core.add.Add'> to QQ_I[x,b,c,_t0,exp( 
a)]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(66\)

Sympy [F(-2)]

Exception generated. \[ \int \cot ^{-1}(c-(i-c) \coth (a+b x)) \, dx=\text {Exception raised: CoercionFailed} \] Input:

integrate(acot(c-(I-c)*coth(b*x+a)),x)
 

Output:

Exception raised: CoercionFailed >> Cannot convert -_t0**2*I + 2*c*exp(2*a 
) - I*exp(2*a) of type <class 'sympy.core.add.Add'> to QQ_I[b,c,_t0,exp(a) 
]
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/281_5.4

Test file number \(281\)

Integral number in file \(67\)

Sympy [F(-2)]

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

integrate(acot(x)/(x**2+1)**2,x)
                                                                                    
                                                                                    
 

Output:

Exception raised: RecursionError >> maximum recursion depth exceeded in co 
mparison
 

input file name test_cases/rubi_tests/5_Inverse_trig_functions/5.4_Inverse_cotangent/284_5.4.4

Test file number \(284\)

Integral number in file \(7\)

Sympy [F(-2)]

Exception generated. \[ \int x^m \cosh (a+b x) \sinh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**m*cosh(b*x+a)*sinh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6_Miscellaneous/290_6

Test file number \(290\)

Integral number in file \(252\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m \sinh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*sinh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(75\)

Sympy [F(-2)]

Exception generated. \[ \int x^{3+m} \sinh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(3+m)*sinh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(78\)

Sympy [F(-2)]

Exception generated. \[ \int x^{2+m} \sinh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(2+m)*sinh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(79\)

Sympy [F(-2)]

Exception generated. \[ \int x^{1+m} \sinh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(1+m)*sinh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(80\)

Sympy [F(-2)]

Exception generated. \[ \int x^m \sinh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**m*sinh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(81\)

Sympy [F(-2)]

Exception generated. \[ \int x^{-1+m} \sinh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(-1+m)*sinh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(82\)

Sympy [F(-2)]

Exception generated. \[ \int x^{-2+m} \sinh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(-2+m)*sinh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(83\)

Sympy [F(-2)]

Exception generated. \[ \int x^{-3+m} \sinh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(-3+m)*sinh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(84\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m (a+i a \sinh (e+f x))^3 \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*(a+I*a*sinh(f*x+e))**3,x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(152\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m (a+i a \sinh (e+f x))^2 \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*(a+I*a*sinh(f*x+e))**2,x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(153\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m (a+i a \sinh (e+f x)) \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*(a+I*a*sinh(f*x+e)),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(154\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m (a+b \sinh (e+f x))^3 \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*(a+b*sinh(f*x+e))**3,x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(182\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m (a+b \sinh (e+f x))^2 \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*(a+b*sinh(f*x+e))**2,x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(183\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m (a+b \sinh (e+f x)) \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*(a+b*sinh(f*x+e)),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.1_Hyperbolic_sine/293_6.1.1

Test file number \(293\)

Integral number in file \(184\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m \cosh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*cosh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(78\)

Sympy [F(-2)]

Exception generated. \[ \int x^{3+m} \cosh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(3+m)*cosh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(81\)

Sympy [F(-2)]

Exception generated. \[ \int x^{2+m} \cosh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(2+m)*cosh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(82\)

Sympy [F(-2)]

Exception generated. \[ \int x^{1+m} \cosh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(1+m)*cosh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(83\)

Sympy [F(-2)]

Exception generated. \[ \int x^m \cosh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**m*cosh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(84\)

Sympy [F(-2)]

Exception generated. \[ \int x^{-1+m} \cosh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(-1+m)*cosh(b*x+a),x)
                                                                                    
                                                                                    
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(85\)

Sympy [F(-2)]

Exception generated. \[ \int x^{-2+m} \cosh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(-2+m)*cosh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(86\)

Sympy [F(-2)]

Exception generated. \[ \int x^{-3+m} \cosh (a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(-3+m)*cosh(b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(87\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m (a+a \cosh (e+f x))^3 \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*(a+a*cosh(f*x+e))**3,x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(151\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m (a+a \cosh (e+f x))^2 \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*(a+a*cosh(f*x+e))**2,x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(152\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m (a+a \cosh (e+f x)) \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*(a+a*cosh(f*x+e)),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(153\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m (a+b \cosh (e+f x))^3 \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*(a+b*cosh(f*x+e))**3,x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(179\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m (a+b \cosh (e+f x))^2 \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*(a+b*cosh(f*x+e))**2,x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(180\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m (a+b \cosh (e+f x)) \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*(a+b*cosh(f*x+e)),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.2_Hyperbolic_cosine/299_6.2.1

Test file number \(299\)

Integral number in file \(181\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(c+d x)^3}{(a+b \coth (e+f x))^2} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**3/(a+b*coth(f*x+e))**2,x)
 

Output:

Exception raised: TypeError >> Invalid NaN comparison
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.4_Hyperbolic_cotangent/309_6.4.1

Test file number \(309\)

Integral number in file \(57\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(c+d x)^2}{(a+b \coth (e+f x))^2} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**2/(a+b*coth(f*x+e))**2,x)
 

Output:

Exception raised: TypeError >> Invalid NaN comparison
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.4_Hyperbolic_cotangent/309_6.4.1

Test file number \(309\)

Integral number in file \(58\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {c+d x}{(a+b \coth (e+f x))^2} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)/(a+b*coth(f*x+e))**2,x)
 

Output:

Exception raised: TypeError >> Invalid NaN comparison
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.4_Hyperbolic_cotangent/309_6.4.1

Test file number \(309\)

Integral number in file \(59\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(a+b \coth (c+d x))^2} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(1/(a+b*coth(d*x+c))**2,x)
 

Output:

Exception raised: TypeError >> Invalid NaN comparison
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.4_Hyperbolic_cotangent/310_6.4.2

Test file number \(310\)

Integral number in file \(82\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(a+b \coth (c+d x))^3} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(1/(a+b*coth(d*x+c))**3,x)
 

Output:

Exception raised: TypeError >> Invalid NaN comparison
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.4_Hyperbolic_cotangent/310_6.4.2

Test file number \(310\)

Integral number in file \(83\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(a+b \coth (c+d x))^4} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(1/(a+b*coth(d*x+c))**4,x)
 

Output:

Exception raised: TypeError >> Invalid NaN comparison
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.4_Hyperbolic_cotangent/310_6.4.2

Test file number \(310\)

Integral number in file \(84\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\coth ^3\left (a+b \log \left (c x^n\right )\right )}{x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(coth(a+b*ln(c*x**n))**3/x,x)
 

Output:

Exception raised: TypeError >> Invalid NaN comparison
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.4_Hyperbolic_cotangent/310_6.4.2

Test file number \(310\)

Integral number in file \(196\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\coth ^4\left (a+b \log \left (c x^n\right )\right )}{x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(coth(a+b*ln(c*x**n))**4/x,x)
 

Output:

Exception raised: TypeError >> Invalid NaN comparison
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.4_Hyperbolic_cotangent/310_6.4.2

Test file number \(310\)

Integral number in file \(197\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\coth ^5\left (a+b \log \left (c x^n\right )\right )}{x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(coth(a+b*ln(c*x**n))**5/x,x)
 

Output:

Exception raised: TypeError >> Invalid NaN comparison
 

input file name test_cases/rubi_tests/6_Hyperbolic_functions/6.4_Hyperbolic_cotangent/310_6.4.2

Test file number \(310\)

Integral number in file \(198\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/7_Inverse_hyperbolic_functions/7.3_Inverse_hyperbolic_tangent/336_7.3

Test file number \(336\)

Integral number in file \(29\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/7_Inverse_hyperbolic_functions/7.4_Inverse_hyperbolic_cotangent/341_7.4

Test file number \(341\)

Integral number in file \(173\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^m \Gamma (2,a+b x) \, dx=\text {Exception raised: TypeError} \] Input:

integrate((d*x+c)**m*uppergamma(2,b*x+a),x)
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/8_Special_functions/355_8.6

Test file number \(355\)

Integral number in file \(180\)

Sympy [F(-2)]

Exception generated. \[ \int e^{-a-b x} (c+d x)^m \, dx=\text {Exception raised: TypeError} \] Input:

integrate(exp(-b*x-a)*(d*x+c)**m,x)
                                                                                    
                                                                                    
 

Output:

Exception raised: TypeError >> cannot determine truth value of Relational
 

input file name test_cases/rubi_tests/8_Special_functions/355_8.6

Test file number \(355\)

Integral number in file \(181\)

Sympy [F(-2)]

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

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

Output:

Exception raised: PolynomialError >> 1/(25*_t0**2*x**6 + 120*_t0**2*x**5 + 
 84*_t0**2*x**4 + 16*_t0**2*x**3 + 20*_t0*x**4 + 88*_t0*x**3 + 32*_t0*x**2 
 + 4*x**2 + 16*x) contains an element of the set of generators.
 

input file name test_cases/extra_tests/361_Hebisch_1

Test file number \(361\)

Integral number in file \(8\)

Sympy [F(-2)]

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

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

Output:

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

input file name test_cases/extra_tests/361_Hebisch_1

Test file number \(361\)

Integral number in file \(21\)

Sympy [F(-2)]

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

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

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 \(86\)

Sympy [F(-2)]

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

integrate((((-15*x**2-120*x)*ln(x)-15*x**2-165*x-360)*ln(x+8)+((42*x**3+44 
7*x**2+888*x)*exp(2/5*x)**2*exp(x)**2+15*x**2+45*x)*ln(x)+(-15*x**2-165*x- 
360)*exp(2/5*x)**2*exp(x)**2)/(5*x**4+70*x**3+285*x**2+360*x)/ln(x)**2,x)
 

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 \(89\)

Sympy [F(-2)]

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

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

Output:

Exception raised: PolynomialError >> 1/(3*x**4 + 6*x**3 + 3*x**2) 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 \(99\)

Sympy [F(-2)]

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

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

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 \(152\)

Sympy [F(-2)]

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

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

Output:

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

input file name test_cases/extra_tests/361_Hebisch_1

Test file number \(361\)

Integral number in file \(211\)

Sympy [F(-2)]

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

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

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 \(222\)

Sympy [F(-2)]

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

integrate((((6*x**3+300*x**2+3750*x)*ln(x)*ln(ln(x))+(6*x**4+310*x**3+4000 
*x**2)*ln(x))*ln(((9*x**2+450*x+5625)*ln(ln(x))**2+(18*x**3+930*x**2+12000 
*x)*ln(ln(x))+9*x**4+480*x**3+6400*x**2)/(9*x**2+450*x+5625))+(6*x**4+300* 
x**3+4000*x**2)*ln(x)+6*x**3+300*x**2+3750*x)/((3*x**2+150*x+1875)*ln(x)*l 
n(ln(x))+(3*x**3+155*x**2+2000*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 \(255\)

Sympy [F(-2)]

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

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

Output:

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

input file name test_cases/extra_tests/361_Hebisch_1

Test file number \(361\)

Integral number in file \(256\)

Sympy [F(-2)]

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

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

Output:

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

input file name test_cases/extra_tests/361_Hebisch_1

Test file number \(361\)

Integral number in file \(275\)

Sympy [F(-2)]

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

integrate((ln(x)*ln(ln(x)/x)**3+3*x*ln(x)*ln(ln(x)/x)**2+(3*x**2-4*x)*ln(x 
)*ln(ln(x)/x)+(x**3-4*x)*ln(x)+4*x)/((-5+x)*ln(x)*ln(ln(x)/x)**3+(3*x**2-1 
5*x)*ln(x)*ln(ln(x)/x)**2+(3*x**3-17*x**2)*ln(x)*ln(ln(x)/x)+(x**4-7*x**3) 
*ln(x)),x)
 

Output:

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

input file name test_cases/extra_tests/361_Hebisch_1

Test file number \(361\)

Integral number in file \(280\)

Sympy [F(-2)]

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

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

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 \(284\)

Sympy [F(-2)]

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

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

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 \(307\)

Sympy [F(-2)]

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

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

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 \(330\)

Sympy [F(-2)]

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

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

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 \(473\)