Integrals 701 to 800

Sympy [F(-2)]

Exception generated. $$\int x\arctan (c-(i-c)\coth (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int \arctan (c-(i-c)\coth (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int \frac{a+b\arctan (cx)}{x(d+icdx{)}^3}dx=\text{Exception raised: RecursionError}$$ 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. $$\int \frac{(a+b\arctan (cx){)}^2}{x(d+icdx{)}^3}dx=\text{Exception raised: RecursionError}$$ 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. $$\int \frac{\arctan (ax)}{{(c+a^{2}c{x}^2)}^2}dx=\text{Exception raised: RecursionError}$$ 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. $$\int \frac{\arctan (ax)}{x{(c+a^{2}c{x}^2)}^2}dx=\text{Exception raised: RecursionError}$$ 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. $$\int \frac{\arctan (ax)}{{(c+a^{2}c{x}^2)}^3}dx=\text{Exception raised: RecursionError}$$ 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. $$\int \frac{\arctan (ax)}{x{(c+a^{2}c{x}^2)}^3}dx=\text{Exception raised: RecursionError}$$ 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. $$\int \frac{x\arctan (ax)}{\sqrt{c+a^{2}c{x}^2}}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{x\arctan (ax)}{{(c+a^{2}c{x}^2)}^{3/2}}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{\arctan (ax)}{x{(c+a^{2}c{x}^2)}^{3/2}}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{x\arctan (ax)}{{(c+a^{2}c{x}^2)}^{5/2}}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{\arctan (ax)}{x{(c+a^{2}c{x}^2)}^{5/2}}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{(a+b\arctan (cx))(d+e\log (1+c^2{x}^2))}{x^2}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{(a+b\arctan (cx))(d+e\log (1+c^2{x}^2))}{x^4}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{(a+b\arctan (cx))(d+e\log (1+c^2{x}^2))}{x^6}dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{-1+n}{\cot }^{-1}(a+b{x}^n)dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int x^2{\cot }^{-1}(c+(1+ic)\tan (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x{\cot }^{-1}(c+(1+ic)\tan (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int {\cot }^{-1}(c+(1+ic)\tan (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x^2{\cot }^{-1}(c-(1-ic)\tan (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x{\cot }^{-1}(c-(1-ic)\tan (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int {\cot }^{-1}(c-(1-ic)\tan (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x^2{\cot }^{-1}(c+(1-ic)\cot (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x{\cot }^{-1}(c+(1-ic)\cot (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int {\cot }^{-1}(c+(1-ic)\cot (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x^2{\cot }^{-1}(c-(1+ic)\cot (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x{\cot }^{-1}(c-(1+ic)\cot (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int {\cot }^{-1}(c-(1+ic)\cot (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x^2{\cot }^{-1}(c+(i+c)\tanh (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x{\cot }^{-1}(c+(i+c)\tanh (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int {\cot }^{-1}(c+(i+c)\tanh (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x^2{\cot }^{-1}(c-(i-c)\tanh (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x{\cot }^{-1}(c-(i-c)\tanh (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int {\cot }^{-1}(c-(i-c)\tanh (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x^2{\cot }^{-1}(c+(i+c)\coth (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x{\cot }^{-1}(c+(i+c)\coth (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int {\cot }^{-1}(c+(i+c)\coth (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x^2{\cot }^{-1}(c-(i-c)\coth (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int x{\cot }^{-1}(c-(i-c)\coth (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int {\cot }^{-1}(c-(i-c)\coth (a+bx))dx=\text{Exception raised: CoercionFailed}$$ 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. $$\int \frac{{\cot }^{-1}(x)}{{(1+x^2)}^2}dx=\text{Exception raised: RecursionError}$$ 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. $$\int x^m\cosh (a+bx)\sinh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m\sinh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{3+m}\sinh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{2+m}\sinh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{1+m}\sinh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^m\sinh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{-1+m}\sinh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{-2+m}\sinh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{-3+m}\sinh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m(a+ia\sinh (e+fx){)}^{3}dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m(a+ia\sinh (e+fx){)}^{2}dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m(a+ia\sinh (e+fx))dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m(a+b\sinh (e+fx){)}^{3}dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m(a+b\sinh (e+fx){)}^{2}dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m(a+b\sinh (e+fx))dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m\cosh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{3+m}\cosh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{2+m}\cosh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{1+m}\cosh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^m\cosh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{-1+m}\cosh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{-2+m}\cosh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{-3+m}\cosh (a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m(a+a\cosh (e+fx){)}^{3}dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m(a+a\cosh (e+fx){)}^{2}dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m(a+a\cosh (e+fx))dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m(a+b\cosh (e+fx){)}^{3}dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m(a+b\cosh (e+fx){)}^{2}dx=\text{Exception raised: TypeError}$$ 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. $$\int (c+dx{)}^m(a+b\cosh (e+fx))dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{(c+dx{)}^3}{(a+b\coth (e+fx){)}^2}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{(c+dx{)}^2}{(a+b\coth (e+fx){)}^2}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{c+dx}{(a+b\coth (e+fx){)}^2}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{1}{(a+b\coth (c+dx){)}^2}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{1}{(a+b\coth (c+dx){)}^3}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{1}{(a+b\coth (c+dx){)}^4}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{{\coth }^3(a+b\log \left(c{x}^n\right))}{x}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{{\coth }^4(a+b\log \left(c{x}^n\right))}{x}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{{\coth }^5(a+b\log \left(c{x}^n\right))}{x}dx=\text{Exception raised: TypeError}$$ 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. $$\int x^{-1+n}\text{arctanh}(a+b{x}^n)dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int x^{-1+n}{\coth }^{-1}(a+b{x}^n)dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int (c+dx{)}^m\mathrm{\Gamma }(2,a+bx)dx=\text{Exception raised: TypeError}$$ 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. $$\int e^{-a-bx}(c+dx{)}^{m}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{(-8-3x){\log }^2(x)+(-4-x){\log }^2(x)\log (4x^2+x^3)+(-8-2x+(-8-2x)\log (x)+(20x^2+5x^3){\log }^2(x)){\log }^2(4x^2+x^3)}{(4x+x^2){\log }^2(x)\log (4x^2+x^3)+((8x+2x^2)\log (x)+(8x^2+22x^3+5x^4){\log }^2(x)){\log }^2(4x^2+x^3)}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{e^2(100+40x+4x^2)+e^2(100+40x+4x^2)\log (x)+(20x^3-4e^5{x}^3){\log }^3(x)}{e^2(-25x-10x^2-x^3)\log (x)+(10x^4+2x^5+e^5(10x^3+2x^4)){\log }^3(x)}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{e^{\frac{18}{2x^2+x^2\log (x)}}(-90+4x^2+(-36+4x^2)\log (x)+x^2{\log }^2(x))}{4x^2+4x^2\log (x)+x^2{\log }^2(x)}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{e^{14x/5}(-360-165x-15x^2)+(45x+15x^2+e^{14x/5}(888x+447x^2+42x^3))\log (x)+(-360-165x-15x^2+(-120x-15x^2)\log (x))\log (8+x)}{(360x+285x^2+70x^3+5x^4){\log }^2(x)}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{100-105x+31x^2+3e^{2x}{x}^2+e^x(-30x+24x^2-x^3)+(30x-19x^2-6e^x{x}^2)\log (x)+3x^2{\log }^2(x)}{75+10x-83x^2+30x^3+e^{2x}(3x^2+3x^3)+e^x(-30x-17x^2+19x^3)+(30x+17x^2-19x^3+e^x(-6x^2-6x^3))\log (x)+(3x^2+3x^3){\log }^2(x)}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{e^{\frac{4x^3}{11x-2e^{2}x-2x^2+2\log (x)}}(-8x^2+88x^3-16e^2{x}^3-8x^4+24x^2\log (x))}{121x^2+4e^4{x}^2-44x^3+4x^4+e^2(-44x^2+8x^3)+(44x-8e^{2}x-8x^2)\log (x)+4{\log }^2(x)}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{3-3x+(-12+3x-3\log (x))\log (4-x+\log (x))+(64+e^2(32-8x)+e^4(4-x)-16x+(16+8e^2+e^4)\log (x)){\log }^2(4-x+\log (x))}{(-12x+3x^2-3x\log (x))\log (4-x+\log (x))+(64x-16x^2+e^2(32x-8x^2)+e^4(4x-x^2)+(16x+8e^{2}x+e^{4}x)\log (x)){\log }^2(4-x+\log (x))}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{-2x+2\log (x)+(x-\log (x))\log \left(2x^2\right)+(1-x)\log \left(2x^2\right)\log \left(\frac{x}{\log \left(2x^2\right)}\right)}{(x^3-2x^2\log (x)+x{\log }^2(x))\log \left(2x^2\right)}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{3750x+300x^2+6x^3+(4000x^2+300x^3+6x^4)\log (x)+((4000x^2+310x^3+6x^4)\log (x)+(3750x+300x^2+6x^3)\log (x)\log (\log (x)))\log \left(\frac{6400x^2+480x^3+9x^4+(12000x+930x^2+18x^3)\log (\log (x))+(5625+450x+9x^2){\log }^2(\log (x))}{5625+450x+9x^2}\right)}{(2000x+155x^2+3x^3)\log (x)+(1875+150x+3x^2)\log (x)\log (\log (x))}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{x^3\log (2)+(18x^2-3x^3)\log (2)\log (6-x)+(12x-2x^2+(-12+2x)\log (2)){\log }^2(6-x)}{(6x^3-x^4)\log (2)\log (6-x)+(6x^2-x^3+(6-13x+2x^2)\log (2)){\log }^2(6-x)}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{e^x(e^{1+\frac{1}{4}(-2+x)}(36-27x+3x^2)+e(144-144x+16x^2))}{192x^2+96e^{\frac{1}{4}(-2+x)}{x}^2+12e^{\frac{1}{2}(-2+x)}{x}^2}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{4x+(-4x+x^3)\log (x)+(-4x+3x^2)\log (x)\log \left(\frac{\log (x)}{x}\right)+3x\log (x){\log }^2\left(\frac{\log (x)}{x}\right)+\log (x){\log }^3\left(\frac{\log (x)}{x}\right)}{(-7x^3+x^4)\log (x)+(-17x^2+3x^3)\log (x)\log \left(\frac{\log (x)}{x}\right)+(-15x+3x^2)\log (x){\log }^2\left(\frac{\log (x)}{x}\right)+(-5+x)\log (x){\log }^3\left(\frac{\log (x)}{x}\right)}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{e^{\frac{x}{4+2x+2\log \left(x^2\right)}}(-16+8x+20x^2+6x^3+(-16+17x+11x^2)\log \left(x^2\right)+(-4+6x){\log }^2\left(x^2\right))}{8x^3-8x^4-6x^5+4x^6+2x^7+(8x^3-12x^4+4x^6)\log \left(x^2\right)+(2x^3-4x^4+2x^5){\log }^2\left(x^2\right)}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{e^3(-3+5x-x^2)+e^6(-12+20x-4x^2)\log (x)+(e^6(-12x+4x^2)+e^6(12-4x)\log (3x-x^2))\log (-x+\log (3x-x^2))}{30x^2-10x^3+(-30x+10x^2)\log (3x-x^2)+\log (x)(e^3(240x^2-80x^3)+e^3(-240x+80x^2)\log (3x-x^2))+{\log }^2(x)(e^6(480x^2-160x^3)+e^6(-480x+160x^2)\log (3x-x^2))}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{e^{\frac{5}{-4x^2+x^2\log (\log (x))}}(-5+40\log (x)-10\log (x)\log (\log (x)))}{16x^3\log (x)-8x^3\log (x)\log (\log (x))+x^3\log (x){\log }^2(\log (x))}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{4x^3\log (x){\log }^2(\log (x))+e^{\frac{-8x-5e^{3}x+x^2-10\log (\log (x))}{\log (\log (x))}}(8+5e^3-x+(-8-5e^3+2x)\log (x)\log (\log (x)))+e^{\frac{-8x-5e^{3}x+x^2-10\log (\log (x))}{2\log (\log (x))}}(8x^2+5e^3{x}^2-x^3+(-8x^2-5e^3{x}^2+2x^3)\log (x)\log (\log (x))+4x\log (x){\log }^2(\log (x)))}{\log (x){\log }^2(\log (x))}dx=\text{Exception raised: TypeError}$$ 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 $473$