Integrals 6201 to 6300

Giac [F(-2)]

Exception generated. \[ \int \frac {-x^2+10 x^8}{\sqrt {-1+x^6} \left (-1+4 x^6\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((10*x^8-x^2)/(x^6-1)^(1/2)/(4*x^6-1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:rootof minimal polynomial must be u 
nitary Error: Bad Argument Valuerootof minimal polynomial must be unitary 
Error: Ba
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(851\)

Giac [F(-2)]

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

integrate((x^3-2)*(x^3+1)^(2/3)/x^3/(x^6+x^3+2),x, algorithm="giac")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument Valuein 
tegrate((sageVARx^6+sageVARx^3+2)^-1*((sageVARx^3+1)^(1/3))^2*(sageVARx^3- 
2)/sageVARx^
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(962\)

Giac [F(-2)]

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

integrate((x^3-2)*(x^3+1)^(2/3)/x^3/(x^6+x^3+2),x, algorithm="giac")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument Valuein 
tegrate((sageVARx^6+sageVARx^3+2)^-1*((sageVARx^3+1)^(1/3))^2*(sageVARx^3- 
2)/sageVARx^
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(963\)

Giac [F(-2)]

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

integrate(1/(x^3-1)/(x^3-x^2)^(1/3),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(969\)

Giac [F(-2)]

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

integrate(1/(x^3-1)/(x^3-x^2)^(1/3),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(970\)

Giac [F(-2)]

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

integrate((x^4-1)^(1/4)*(x^8-x^4+1)/x^6/(2*x^8+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1040\)

Giac [F(-2)]

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

integrate((x^4-1)^(1/4)*(x^8-x^4+1)/x^6/(2*x^8+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1041\)

Giac [F(-2)]

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

integrate((x^3-1)^(2/3)*(x^3+2)/x^6/(2*x^6+x^3+2),x, algorithm="giac")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument Valuein 
tegrate((2*sageVARx^6+sageVARx^3+2)^-1*(sageVARx^3+2)*((sageVARx^3-1)^(1/3 
))^2/sageVAR
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1052\)

Giac [F(-2)]

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

integrate((x^3-1)^(2/3)*(x^3+2)/x^6/(2*x^6+x^3+2),x, algorithm="giac")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument Valuein 
tegrate((2*sageVARx^6+sageVARx^3+2)^-1*(sageVARx^3+2)*((sageVARx^3-1)^(1/3 
))^2/sageVAR
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1053\)

Giac [F(-2)]

Exception generated. \[ \int \frac {1+x}{\sqrt {-7+4 x+14 x^2-12 x^3+x^4}} \, dx=\text {Exception raised: NotImplementedError} \] Input:

integrate((1+x)/(x^4-12*x^3+14*x^2+4*x-7)^(1/2),x, algorithm="giac")
 

Output:

Exception raised: NotImplementedError >> unable to parse Giac output: (-at 
an(i)+ln(4*sqrt(2)))*sign(sageVARx-1)+2*(1/2*atan(1/4*(-sageVARx+sqrt(sage 
VARx^2-10*sageVARx-7)+1))/sign(sageVARx-1)-1/2*ln(abs(-sageVARx+sqrt(sageV 
ARx^2-10*sageVARx-7
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1081\)

Giac [F(-2)]

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

integrate(1/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Not invertible Error: Bad Argument 
Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1092\)

Giac [F(-2)]

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

integrate(1/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Not invertible Error: Bad Argument 
Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1093\)

Giac [F(-2)]

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

integrate(1/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Not invertible Error: Bad Argument 
Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1105\)

Giac [F(-2)]

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

integrate(1/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Not invertible Error: Bad Argument 
Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1106\)

Giac [F(-2)]

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

integrate((x^6-1)^(1/2)*(2*x^6-1)^2/x^4/(4*x^6-1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:rootof minimal polynomial must be u 
nitary Error: Bad Argument Valuerootof minimal polynomial must be unitary 
Error: Ba
                                                                                    
                                                                                    
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1145\)

Giac [F(-2)]

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

integrate(1/(a*x^4+b*x^2)^(1/4)/(a*x^8-2*b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Not invertible Error: Bad Argument 
Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1149\)

Giac [F(-2)]

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

integrate(1/(a*x^4+b*x^2)^(1/4)/(a*x^8-2*b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Not invertible Error: Bad Argument 
Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1150\)

Giac [F(-2)]

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

integrate((x^4-1)*(x^4+1)^(1/2)/(x^8+x^6+3*x^4+x^2+1),x, algorithm="giac")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Precision problem choosing root in common_EXT, current 
precision 14Precision problem choosing root in common_EXT, current precisi 
on 14Invalid
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1256\)

Giac [F(-2)]

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

integrate((x^8-1)/(x^4-x^2)^(1/4)/(x^8+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1309\)

Giac [F(-2)]

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

integrate((x^8-1)/(x^4-x^2)^(1/4)/(x^8+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1310\)

Giac [F(-2)]

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

integrate(1/x^6/(x^3+1)/(x^3+x^2)^(1/3),x, algorithm="giac")
                                                                                    
                                                                                    
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1413\)

Giac [F(-2)]

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

integrate(1/x^6/(x^3+1)/(x^3+x^2)^(1/3),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1414\)

Giac [F(-2)]

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

integrate((x^2-1)*(1+(1+x)^(1/2))^(1/2)/(x^2+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValuePrecision problem choosing root in common_EXT, current p 
recision
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1432\)

Giac [F(-2)]

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

integrate((x^2-1)*(1+(1+x)^(1/2))^(1/2)/(x^2+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValuePrecision problem choosing root in common_EXT, current p 
recision
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1433\)

Giac [F(-2)]

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

integrate((x^4-1)^(1/4)*(x^4+2)/x^2/(x^8+2*x^4+2),x, algorithm="giac")
 

Output:

Exception raised: NotImplementedError >> unable to parse Giac output: %%{p 
oly1[11728124029819/13521606404067752414158038073344*sin(1/4*atan(1/3))*at 
an((4123168604160*(sageVARx^4-1)^(1/4)/sageVARx-sin(1/4*atan(13/9))*exp(1/ 
4*ln(14450882888647
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1516\)

Giac [F(-2)]

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

integrate((x^4-1)^(1/4)*(x^4+2)/x^2/(x^8+2*x^4+2),x, algorithm="giac")
 

Output:

Exception raised: NotImplementedError >> unable to parse Giac output: %%{p 
oly1[11728124029819/13521606404067752414158038073344*sin(1/4*atan(1/3))*at 
an((4123168604160*(sageVARx^4-1)^(1/4)/sageVARx-sin(1/4*atan(13/9))*exp(1/ 
4*ln(14450882888647
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1517\)

Giac [F(-2)]

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

integrate((x^2-2)*(x^3+x)^(1/3)/x^2/(x^4-2*x^2+4),x, algorithm="giac")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument ValueIn 
valid _EXT in replace_ext Error: Bad Argument Value6*((1/sageVARx)^2+1)^(1 
/3)/8+integr
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1553\)

Giac [F(-2)]

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

integrate((x^2-2)*(x^3+x)^(1/3)/x^2/(x^4-2*x^2+4),x, algorithm="giac")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument ValueIn 
valid _EXT in replace_ext Error: Bad Argument Value6*((1/sageVARx)^2+1)^(1 
/3)/8+integr
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1554\)

Giac [F(-2)]

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

integrate((x^3+1)^(2/3)*(3*x^6+6*x^3+4)/x^6/(3*x^6+6*x^3+8),x, algorithm=" 
giac")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument Valuein 
tegrate((3*sageVARx^6+6*sageVARx^3+8)^-1*(3*sageVARx^6+6*sageVARx^3+4)*((s 
ageVARx^3+1)
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1674\)

Giac [F(-2)]

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

integrate((x^3+1)^(2/3)*(3*x^6+6*x^3+4)/x^6/(3*x^6+6*x^3+8),x, algorithm=" 
giac")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument Valuein 
tegrate((3*sageVARx^6+6*sageVARx^3+8)^-1*(3*sageVARx^6+6*sageVARx^3+4)*((s 
ageVARx^3+1)
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1675\)

Giac [F(-2)]

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

integrate(x^4/(x^4+x^2)^(1/4)/(x^8+x^4+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:proot error [1,0,0,0,1,0,0,0,1]proo 
t error [1,0,0,0,-1,0,0,0,1]proot error [1,0,-10,0,1]proot error [1,0,-10, 
0,1]proot
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1692\)

Giac [F(-2)]

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

integrate(x^4/(x^4+x^2)^(1/4)/(x^8+x^4+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:proot error [1,0,0,0,1,0,0,0,1]proo 
t error [1,0,0,0,-1,0,0,0,1]proot error [1,0,-10,0,1]proot error [1,0,-10, 
0,1]proot
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1693\)

Giac [F(-2)]

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

integrate((2*x^2+1)*(2*x^3+x)^(1/3)/x^4/(2*x^4+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1711\)

Giac [F(-2)]

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

integrate((2*x^3+x)^(1/3)*(x^4-1)/x^4/(x^4-x^2+2),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1764\)

Giac [F(-2)]

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

integrate((x^3-x)^(1/3)*(x^4-10*x^2+8)/x^4/(x^4-2*x^2+4),x, algorithm="gia 
c")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument Value(3 
072*(-(1/sageVARx)^2+1)^(1/3)*(-(1/sageVARx)^2+1)+9216*(-(1/sageVARx)^2+1) 
^(1/3))/4096
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1778\)

Giac [F(-2)]

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

integrate((x^3-x)^(1/3)*(x^4-10*x^2+8)/x^4/(x^4-2*x^2+4),x, algorithm="gia 
c")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument Value(3 
072*(-(1/sageVARx)^2+1)^(1/3)*(-(1/sageVARx)^2+1)+9216*(-(1/sageVARx)^2+1) 
^(1/3))/4096
                                                                                    
                                                                                    
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1779\)

Giac [F(-2)]

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

integrate((x^4+1)*(x^4-x^2)^(1/4)/(x^8+x^4+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:proot error [1,0,0,0,1,0,0,0,1]proo 
t error [1,0,0,0,-1,0,0,0,1]proot error [1,0,-10,0,1]proot error [1,0,-10, 
0,1]proot
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1793\)

Giac [F(-2)]

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

integrate((x^4+1)*(x^4-x^2)^(1/4)/(x^8+x^4+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:proot error [1,0,0,0,1,0,0,0,1]proo 
t error [1,0,0,0,-1,0,0,0,1]proot error [1,0,-10,0,1]proot error [1,0,-10, 
0,1]proot
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1794\)

Giac [F(-2)]

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

integrate((1+k^(3/2)*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(-1+k^(3/2)*x^3),x 
, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const 
index_m & i,const vecteur & l) Error: Bad Argument Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1824\)

Giac [F(-2)]

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

integrate((-1+k^(3/2)*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(1+k^(3/2)*x^3),x 
, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const 
index_m & i,const vecteur & l) Error: Bad Argument Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1837\)

Giac [F(-2)]

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

integrate((x^4+2)/(x^4+x^2)^(1/4)/(2*x^8-x^4-1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1851\)

Giac [F(-2)]

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

integrate((x^4+2)/(x^4+x^2)^(1/4)/(2*x^8-x^4-1),x, algorithm="giac")
                                                                                    
                                                                                    
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1852\)

Giac [F(-2)]

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

integrate((x^4-1)*(1+(1+x)^(1/2))^(1/2)/(x^4+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1877\)

Giac [F(-2)]

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

integrate((x^4-1)*(1+(1+x)^(1/2))^(1/2)/(x^4+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1878\)

Giac [F(-2)]

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

integrate((1+x)^(1/2)*(x^2-1)/(x^2+1)/(1+(1+x)^(1/2))^(1/2),x, algorithm=" 
giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueInvalid _EXT in replace_ext Error: Bad Argument ValueDon 
e
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1882\)

Giac [F(-2)]

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

integrate((1+x)^(1/2)*(x^2-1)/(x^2+1)/(1+(1+x)^(1/2))^(1/2),x, algorithm=" 
giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueInvalid _EXT in replace_ext Error: Bad Argument ValueDon 
e
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1883\)

Giac [F(-2)]

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

integrate((x^6-1)*(x^6+1)^(2/3)/x^3/(2*x^6-x^3+2),x, algorithm="giac")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument Valuein 
tegrate((2*sageVARx^6-sageVARx^3+2)^-1*((sageVARx^6+1)^(1/3))^2*(sageVARx^ 
6-1)/sageVAR
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1919\)

Giac [F(-2)]

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

integrate((a*x^8-b)/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Not invertible Error: Bad Argument 
Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1967\)

Giac [F(-2)]

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

integrate((a*x^8-b)/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Not invertible Error: Bad Argument 
Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1968\)

Giac [F(-2)]

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

integrate((a*x^8+b)/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Not invertible Error: Bad Argument 
Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1982\)

Giac [F(-2)]

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

integrate((a*x^8+b)/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Not invertible Error: Bad Argument 
Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(1983\)

Giac [F(-2)]

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

integrate((x^2+x+2)/(x^2+2*x+3)/(x^3+x^2)^(1/3),x, algorithm="giac")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument Value-l 
n(abs((1/sageVARx+1)^(1/3)-1))+1/2*ln(((1/sageVARx+1)^(1/3))^2+(1/sageVARx 
+1)^(1/3)+1)
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2047\)

Giac [F(-2)]

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

integrate((x^2+x+2)/(x^2+2*x+3)/(x^3+x^2)^(1/3),x, algorithm="giac")
 

Output:

Exception raised: RuntimeError >> an error occurred running a Giac command 
:INPUT:sage2OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument Value-l 
n(abs((1/sageVARx+1)^(1/3)-1))+1/2*ln(((1/sageVARx+1)^(1/3))^2+(1/sageVARx 
+1)^(1/3)+1)
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2048\)

Giac [F(-2)]

Exception generated. \[ \int \frac {\sqrt [4]{-b+a x^4} \left (-8 b+a x^8\right )}{x^{10} \left (b+a x^4\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a*x^4-b)^(1/4)*(a*x^8-8*b)/x^10/(a*x^4+b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro 
unding error%%%{-8,[0,1,8,2,0]%%%}+%%%{8,[0,1,4,1,1]%%%}+%%%{1,[0,1,0,1,1] 
%%%}+%%%{
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2134\)

Giac [F(-2)]

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

integrate((x^2-1)/(1+x)^(1/2)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x, algorithm=" 
giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueInvalid _EXT in replace_ext Error: Bad Argument ValueInv 
alid _EXT
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2152\)

Giac [F(-2)]

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

integrate((x^2-1)/(1+x)^(1/2)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x, algorithm=" 
giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueInvalid _EXT in replace_ext Error: Bad Argument ValueInv 
alid _EXT
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2153\)

Giac [F(-2)]

Exception generated. \[ \int \frac {x (-4 a+3 x)}{\sqrt [3]{x^2 (-a+x)} \left (a-x+d x^4\right )} \, dx=\text {Exception raised: NotImplementedError} \] Input:

integrate(x*(-4*a+3*x)/(x^2*(-a+x))^(1/3)/(d*x^4+a-x),x, algorithm="giac")
 

Output:

Exception raised: NotImplementedError >> unable to parse Giac output: 1/2* 
(-1/sageVARd)^(1/3)*ln((sqrt(3)*(abs(sageVARd)^(1/3))^2*sqrt(3)/2*(-sageVA 
Ra/sageVARx+1)^(1/3)*(-sageVARa/sageVARx+1)-sqrt(3)*(abs(sageVARd)^(1/3))^ 
2*sqrt(3)/2*(-sageV
                                                                                    
                                                                                    
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2162\)

Giac [F(-2)]

Exception generated. \[ \int \frac {\sqrt {1+\sqrt {1-\sqrt {1+\frac {1}{x^2}}}}}{x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((1+(1-(1+1/x^2)^(1/2))^(1/2))^(1/2)/x,x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Error index.cc index_gcd Error: Bad 
 Argument ValueError index.cc index_gcd Error: Bad Argument ValueError ind 
ex.cc ind
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2171\)

Giac [F(-2)]

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

integrate((x^3+1)*(x^6-x^3-2)^(1/2)/x^4/(x^6-2*x^3-1),x, algorithm="giac")
 

Output:

Exception raised: AttributeError >> type
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2203\)

Giac [F(-2)]

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

integrate((-a/b^2+a^2*x^2/b^2)^(1/2)*(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2) 
)^(1/2),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const 
index_m & i,const vecteur & l) Error: Bad Argument Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2210\)

Giac [F(-2)]

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

integrate((x^3-x^2)^(1/3)/(x^2+x+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2338\)

Giac [F(-2)]

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

integrate((x^3-x^2)^(1/3)/(x^2+x+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2339\)

Giac [F(-2)]

Exception generated. \[ \int \frac {x^4 \sqrt [4]{-x^2+x^4}}{1+x^4+x^8} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x^4*(x^4-x^2)^(1/4)/(x^8+x^4+1),x, algorithm="giac")
                                                                                    
                                                                                    
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:proot error [1,0,0,0,1,0,0,0,1]proo 
t error [1,0,0,0,-1,0,0,0,1]proot error [1,0,-10,0,1]proot error [1,0,-10, 
0,1]proot
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2371\)

Giac [F(-2)]

Exception generated. \[ \int \frac {x^4 \sqrt [4]{-x^2+x^4}}{1+x^4+x^8} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x^4*(x^4-x^2)^(1/4)/(x^8+x^4+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:proot error [1,0,0,0,1,0,0,0,1]proo 
t error [1,0,0,0,-1,0,0,0,1]proot error [1,0,-10,0,1]proot error [1,0,-10, 
0,1]proot
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2372\)

Giac [F(-2)]

Exception generated. \[ \int \frac {2 x^4-x^9}{\sqrt {-1+x^5} \left (a-a x^5+x^{10}\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((-x^9+2*x^4)/(x^5-1)^(1/2)/(x^10-a*x^5+a),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Limit: Max order reached or unable 
to make series expansion Error: Bad Argument Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2456\)

Giac [F(-2)]

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

integrate(1/(1-x*(a*x^2+b*x+c)^(1/2)),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const 
index_m & i,const vecteur & l) Error: Bad Argument Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2476\)

Giac [F(-2)]

Exception generated. \[ \int \frac {\sqrt [4]{b+a x^4} \left (2 b+3 a x^4\right )}{x^6 \left (b+a x^8\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a*x^4+b)^(1/4)*(3*a*x^4+2*b)/x^6/(a*x^8+b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro 
unding error%%%{2,[0,1,4,1,0]%%%}+%%%{3,[0,1,0,0,1]%%%} / %%%{1,[0,0,0,1,0 
]%%%} Err
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2482\)

Giac [F(-2)]

Exception generated. \[ \int \frac {\sqrt [4]{b+a x^4} \left (2 b+3 a x^4\right )}{x^6 \left (b+a x^8\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a*x^4+b)^(1/4)*(3*a*x^4+2*b)/x^6/(a*x^8+b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro 
unding error%%%{2,[0,1,4,1,0]%%%}+%%%{3,[0,1,0,0,1]%%%} / %%%{1,[0,0,0,1,0 
]%%%} Err
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2483\)

Giac [F(-2)]

Exception generated. \[ \int \frac {\sqrt {x+\sqrt {1+x}}}{1+x^2} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((x+(1+x)^(1/2))^(1/2)/(x^2+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Precision problem choosing root in 
common_EXT, current precision 14Precision problem choosing root in common_ 
EXT, curr
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2484\)

Giac [F(-2)]

Exception generated. \[ \int \frac {\sqrt {x+\sqrt {1+x}}}{1+x^2} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((x+(1+x)^(1/2))^(1/2)/(x^2+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Precision problem choosing root in 
common_EXT, current precision 14Precision problem choosing root in common_ 
EXT, curr
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2485\)

Giac [F(-2)]

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

integrate((x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2)/(x^2+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueInvalid _EXT in replace_ext Error: Bad Argument ValueDon 
e
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2511\)

Giac [F(-2)]

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

integrate((x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2)/(x^2+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueInvalid _EXT in replace_ext Error: Bad Argument ValueDon 
e
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2512\)

Giac [F(-2)]

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

integrate((x^2-1)*(x^4+x^3)^(1/4)/(x^4+x^2+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:proot error [1,0,0,0,1,0,0,0,1]proo 
t error [1,0,0,0,-1,0,0,0,1]proot error [1,0,-10,0,1]proot error [1,0,-10, 
0,1]proot
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2523\)

Giac [F(-2)]

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

integrate((x^2-1)*(x^4+x^3)^(1/4)/(x^4+x^2+1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:proot error [1,0,0,0,1,0,0,0,1]proo 
t error [1,0,0,0,-1,0,0,0,1]proot error [1,0,-10,0,1]proot error [1,0,-10, 
0,1]proot
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2524\)

Giac [F(-2)]

Exception generated. \[ \int \frac {\sqrt [4]{-b+a x^4} \left (b+c x^4+a x^8\right )}{x^6 \left (b+2 a x^8\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a*x^4-b)^(1/4)*(a*x^8+c*x^4+b)/x^6/(2*a*x^8+b),x, algorithm="gi 
ac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro 
unding error%%%{1,[0,1,4,1,0]%%%}+%%%{1,[0,1,0,0,1]%%%} / %%%{1,[0,0,0,1,0 
]%%%} Err
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2554\)

Giac [F(-2)]

Exception generated. \[ \int \frac {\sqrt [4]{-b+a x^4} \left (b+c x^4+a x^8\right )}{x^6 \left (b+2 a x^8\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a*x^4-b)^(1/4)*(a*x^8+c*x^4+b)/x^6/(2*a*x^8+b),x, algorithm="gi 
ac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro 
unding error%%%{1,[0,1,4,1,0]%%%}+%%%{1,[0,1,0,0,1]%%%} / %%%{1,[0,0,0,1,0 
]%%%} Err
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2555\)

Giac [F(-2)]

Exception generated. \[ \int \frac {\left (-4 b+a x^4\right ) \sqrt [4]{-b+a x^4}}{x^6 \left (-8 b+a x^8\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a*x^4-4*b)*(a*x^4-b)^(1/4)/x^6/(a*x^8-8*b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro 
unding error%%%{4,[0,1,4,1,0]%%%}+%%%{-1,[0,1,0,0,1]%%%} / %%%{8,[0,0,0,1, 
0]%%%} Er
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2567\)

Giac [F(-2)]

Exception generated. \[ \int \frac {\left (-4 b+a x^4\right ) \sqrt [4]{-b+a x^4}}{x^6 \left (-8 b+a x^8\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a*x^4-4*b)*(a*x^4-b)^(1/4)/x^6/(a*x^8-8*b),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro 
unding error%%%{4,[0,1,4,1,0]%%%}+%%%{-1,[0,1,0,0,1]%%%} / %%%{8,[0,0,0,1, 
0]%%%} Er
                                                                                    
                                                                                    
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2568\)

Giac [F(-2)]

Exception generated. \[ \int \frac {x^3 \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}{\sqrt {a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x^3*(-a/b^2+a^2*x^2/b^2)^(1/2)/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^( 
1/2))^(1/2),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const 
index_m & i,const vecteur & l) Error: Bad Argument Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2638\)

Giac [F(-2)]

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

integrate(x^2*(x^8-2)*(x^8-2*x^4+2)^(1/4)/(x^8+2)/(2*x^8-x^4+4),x, algorit 
hm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueDone
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2711\)

Giac [F(-2)]

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

integrate((x^2-1)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueInvalid _EXT in replace_ext Error: Bad Argument ValueInv 
alid _EXT
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2712\)

Giac [F(-2)]

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

integrate((x^2-1)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueInvalid _EXT in replace_ext Error: Bad Argument ValueInv 
alid _EXT
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2713\)

Giac [F(-2)]

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

integrate(x^3/(x^3-x^2)^(1/3)/(x^6-1),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:proot error [1,0,0,1,0,0,1]proot er 
ror [1,0,0,-1,0,0,1]Invalid _EXT in replace_ext Error: Bad Argument Valuep 
root erro
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2752\)

Giac [F(-2)]

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

integrate((x^2-1)^2*(x^3+x)/(x^4+1)^(1/2)/(x^8-2*x^6+4*x^4-2*x^2+1),x, alg 
orithm="giac")
                                                                                    
                                                                                    
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueNot invertible Error: Bad Argument Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2761\)

Giac [F(-2)]

Exception generated. \[ \int \frac {\sqrt [4]{2 b+a x^4} \left (-4 b+a x^8\right )}{x^6 \left (-4 b+c x^4+a x^8\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a*x^4+2*b)^(1/4)*(a*x^8-4*b)/x^6/(a*x^8+c*x^4-4*b),x, algorithm 
="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro 
unding error%%%{4,[0,1,4,1,0]%%%}+%%%{1,[0,1,0,0,1]%%%} / %%%{4,[0,0,0,1,0 
]%%%} Err
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2795\)

Giac [F(-2)]

Exception generated. \[ \int \frac {\sqrt [4]{2 b+a x^4} \left (-4 b+a x^8\right )}{x^6 \left (-4 b+c x^4+a x^8\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a*x^4+2*b)^(1/4)*(a*x^8-4*b)/x^6/(a*x^8+c*x^4-4*b),x, algorithm 
="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro 
unding error%%%{4,[0,1,4,1,0]%%%}+%%%{1,[0,1,0,0,1]%%%} / %%%{4,[0,0,0,1,0 
]%%%} Err
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2796\)

Giac [F(-2)]

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

integrate(1/(1-(1+x)*(a*x^2+b*x+c)^(1/2)),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const 
index_m & i,const vecteur & l) Error: Bad Argument Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2798\)

Giac [F(-2)]

Exception generated. \[ \int \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}} \sqrt [3]{a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((-a/b^2+a^2*x^2/b^2)^(1/2)*(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2) 
)^(1/3),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const 
index_m & i,const vecteur & l) Error: Bad Argument Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2917\)

Giac [F(-2)]

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

integrate((a*x^2+b*x+c)^(5/2)/(b*x+c),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const 
index_m & i,const vecteur & l) Error: Bad Argument Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2921\)

Giac [F(-2)]

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

integrate((1+x)^(1/2)*(x^2-1)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x, algorithm=" 
giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueInvalid _EXT in replace_ext Error: Bad Argument ValueInv 
alid _EXT
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2924\)

Giac [F(-2)]

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

integrate((1+x)^(1/2)*(x^2-1)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x, algorithm=" 
giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Invalid _EXT in replace_ext Error: 
Bad Argument ValueInvalid _EXT in replace_ext Error: Bad Argument ValueInv 
alid _EXT
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2925\)

Giac [F(-2)]

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

integrate((a^2*x^2+a*b*c-b^2*x)/(a*x^2+b*x+c)^(1/2)/(b*x^2+c),x, algorithm 
="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Error: Bad Argument Type
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(2931\)

Giac [F(-2)]

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

integrate((a*x^2+b*x+c)^(3/2)/(1-x*(a*x^2+b*x+c)^(1/2)),x, algorithm="giac 
")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const 
index_m & i,const vecteur & l) Error: Bad Argument Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(3031\)

Giac [F(-2)]

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

integrate(1/(a*x^2+b*x+c)^(1/2)/(a^3*b^3*x^3+c^3),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const 
index_m & i,const vecteur & l) Error: Bad Argument Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(3052\)

Giac [F(-2)]

Exception generated. \[ \int \sqrt {\frac {-1+a x-2 x^2+2 a x^3-x^4+a x^5}{1+a x-2 x^2-2 a x^3+x^4+a x^5}} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(((a*x^5+2*a*x^3-x^4+a*x-2*x^2-1)/(a*x^5-2*a*x^3+x^4+a*x-2*x^2+1) 
)^(1/2),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const 
index_m & i,const vecteur & l) Error: Bad Argument Value
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(3055\)

Giac [F(-2)]

Exception generated. \[ \int \frac {x \left (2 x^3 c_3-c_4\right )}{\left (-x+x^3 c_3+c_4\right ) \sqrt [3]{\frac {x c_0+x^3 c_3+c_4}{x c_1+x^3 c_3+c_4}} \left (x^2+x^4 c_3+x^6 c_3{}^2+x c_4+2 x^3 c_3 c_4+c_4{}^2\right )} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(x*(2*_C3*x^3-_C4)/(_C3*x^3+_C4-x)/((_C3*x^3+_C0*x+_C4)/(_C3*x^3+ 
_C1*x+_C4))^(1/3)/(_C3^2*x^6+2*_C3*_C4*x^3+_C3*x^4+_C4^2+_C4*x+x^2),x, alg 
orithm="giac")
 

Output:

Exception raised: AttributeError >> type
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(3125\)

Giac [F(-2)]

Exception generated. \[ \int \frac {c_8+x c_9}{\sqrt {c_4+\sqrt {\frac {c_0+x c_1}{c_2+x c_3}} c_5} (c_6+x c_7)} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((_C9*x+_C8)/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2)/(_C7 
*x+_C6),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Warning, need to choose a branch fo 
r the root of a polynomial with parameters. This might be wrong.Non regula 
r value [
 

input file name test_cases/extra_tests/366_Blake_1

Test file number \(366\)

Integral number in file \(3150\)

Giac [F(-2)]

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

integrate(2*a*(-b^3+2*2^(1/2)*a^2*b*x^2)/(b^4-a^2*b^2*x^2+2^(1/2)*a^4*x^4) 
,x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro 
unding error%%%{1,[16]%%%}+%%%{%%%{%%{[-681148277399173791970,584447570846 
596707587
 

input file name test_cases/extra_tests/367_Blake_2

Test file number \(367\)

Integral number in file \(1\)

Giac [F(-2)]

Exception generated. \[ \int \frac {3 x^3 \left (-16+20\ 2^{3/4} \sqrt [4]{3}-8 \sqrt [4]{2} 3^{3/4}-12 \sqrt {6}+\left (36+12\ 2^{3/4} \sqrt [4]{3}+18 \sqrt [4]{2} 3^{3/4}-30 \sqrt {6}\right ) x^2+\left (-54-18\ 2^{3/4} \sqrt [4]{3}+30 \sqrt [4]{2} 3^{3/4}-12 \sqrt {6}\right ) x^4+\left (-30+9\ 2^{3/4} \sqrt [4]{3}+4 \sqrt [4]{2} 3^{3/4}+6 \sqrt {6}\right ) x^6\right )}{19 \left (\sqrt {6}-\sqrt [4]{2} 3^{3/4} x^2+3 x^4\right )^3} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(3/19*x^3*(-16+20*2^(3/4)*3^(1/4)-8*2^(1/4)*3^(3/4)-12*6^(1/2)+(3 
6+12*2^(3/4)*3^(1/4)+18*2^(1/4)*3^(3/4)-30*6^(1/2))*x^2+(-54-18*2^(3/4)*3^ 
(1/4)+30*2^(1/4)*3^(3/4)-12*6^(1/2))*x^4+(-30+9*2^(3/4)*3^(1/4)+4*2^(1/4)* 
3^(3/4)+6*6^(1/2))*x^6)/(6^(1/2)-2^(1/4)*3^(3/4)*x^2+3*x^4)^3,x, algorithm 
="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro 
unding error%%%{133056,[12]%%%}+%%%{%%{[-459,0,0,0,12717,0,0,0,193023,0,0, 
0,360639]
                                                                                    
                                                                                    
 

input file name test_cases/extra_tests/367_Blake_2

Test file number \(367\)

Integral number in file \(5\)

Giac [F(-2)]

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

integrate(2*3^(1/2)*x*(-4*6^(1/2)+4*2^(1/2)-8*(3^(1/2)-1)*x^2-6*2^(1/2)*x^ 
4+2*6^(1/2)*x^4+12*(1/2*6^(1/2)-1/2*2^(1/2))*x^4+4*(3/2*2^(1/2)-1/2*6^(1/2 
))*x^4-4*(3^(1/2)-1)*x^6+(1/2*6^(1/2)-1/2*2^(1/2))*x^8)/(2+2*3^(1/2)-2*2^( 
1/2)*x^2+x^4)^2/(-4*3^(1/2)+4*(3/2*2^(1/2)-1/2*6^(1/2))*x^2-3*x^4+3^(1/2)* 
x^4),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:  ***   Warning: increasing stack s 
ize to 4096000.  ***   Warning: increasing stack size to 4096000.  ***   W 
arning: i
 

input file name test_cases/extra_tests/367_Blake_2

Test file number \(367\)

Integral number in file \(7\)