Exception generated. \[ \int \frac {-\sqrt {3}+x+4 \sqrt {2} x+2 \sqrt {3} x^2-2 \sqrt {6} x^2+2 \sqrt {2} x^3}{1-2 \sqrt {3} x+2 x^2+\sqrt {3} x^3+\sqrt {2} x^4} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((-3^(1/2)+x+4*2^(1/2)*x+2*3^(1/2)*x^2-2*6^(1/2)*x^2+2*2^(1/2)*x^ 3)/(1-2*3^(1/2)*x+2*x^2+3^(1/2)*x^3+2^(1/2)*x^4),x, 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/367_Blake_2
Test file number \(367\)
Integral number in file \(8\)
Exception generated. \[ \int \frac {-1-x+4 \sqrt {2} x+2 x^2-2 \sqrt {2} x^2+2 \sqrt {2} x^3}{1-2 x+x^3+\sqrt {2} x^4} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((-1-x+4*2^(1/2)*x+2*x^2-2*2^(1/2)*x^2+2*2^(1/2)*x^3)/(1-2*x+x^3+ 2^(1/2)*x^4),x, 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%%%{%%{[1,0]:[1,0,-2]%%},[4]%%%}+%%%{1,[3]%%%}+%%%{-2,[1]%%%}+ %%%{1,[0]
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(9\)
Exception generated. \[ \int \frac {-10-7 x+4 x^2}{x-3 x^2+3 x^3+2 x^4} \, dx=\text {Exception raised: NotImplementedError} \] Input:
integrate((4*x^2-7*x-10)/(2*x^4+3*x^3-3*x^2+x),x, algorithm="giac")
Output:
Exception raised: NotImplementedError >> unable to parse Giac output: -10* ln(abs(sageVARx))+((7/221184*rootof([[-3,0,8640,0,-5308416],[1,0,-3456,0,2 985984,0,254803968]])-162)/(6*(1/2654208*rootof([[-3,0,8640,0,-5308416],[1 ,0,-3456,0,2985984,
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(16\)
Exception generated. \[ \int \frac {-16 \left (105-10 \sqrt {21}\right ) x-2352 \sqrt {21} x^3-2352 \sqrt {21} x^5}{16+\left (896-480 \sqrt {21}\right ) x^2+\left (1708-560 \sqrt {21}\right ) x^4-588 \left (14+5 \sqrt {21}\right ) x^6+21609 x^8} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((-16*(105-10*21^(1/2))*x-2352*21^(1/2)*x^3-2352*21^(1/2)*x^5)/(1 6+(896-480*21^(1/2))*x^2+(1708-560*21^(1/2))*x^4-588*(14+5*21^(1/2))*x^6+2 1609*x^8),x, algorithm="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to find common minimal polyn omial Error: Bad Argument ValueUnable to find common minimal polynomial Er ror: Bad
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(34\)
Exception generated. \[ \int \frac {-43-27 \sqrt {3}+\left (110+73 \sqrt {3}\right ) x^2+\left (67+46 \sqrt {3}\right ) x^4+\left (19+8 \sqrt {3}\right ) x^6}{\left (1+\left (2+\sqrt {3}\right ) x^2+x^4\right )^2} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((-43-27*3^(1/2)+(110+73*3^(1/2))*x^2+(67+46*3^(1/2))*x^4+(19+8*3 ^(1/2))*x^6)/(1+(2+3^(1/2))*x^2+x^4)^2,x, algorithm="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to find common minimal polyn omial Error: Bad Argument ValueFrancis algorithm failure for[-1.0,0.0,infi nity,infi
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(37\)
Exception generated. \[ \int \frac {-43-27 \sqrt {3}+\left (110+73 \sqrt {3}\right ) x^2+\left (67+46 \sqrt {3}\right ) x^4+\left (19+8 \sqrt {3}\right ) x^6}{\left (1+\left (2+\sqrt {3}\right ) x^2+x^4\right )^2} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((-43-27*3^(1/2)+(110+73*3^(1/2))*x^2+(67+46*3^(1/2))*x^4+(19+8*3 ^(1/2))*x^6)/(1+(2+3^(1/2))*x^2+x^4)^2,x, algorithm="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to find common minimal polyn omial Error: Bad Argument ValueFrancis algorithm failure for[-1.0,0.0,infi nity,infi
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(39\)
Exception generated. \[ \int \frac {27 \sqrt {3}+\left (-108-54 \sqrt {3}\right ) x+\left (81+54 \sqrt {3}\right ) x^2-36 x^3+\left (18+3 \sqrt {3}\right ) x^4-18 \sqrt {3} x^5+\left (9-12 \sqrt {3}\right ) x^6+3 \sqrt {3} x^8+2 \sqrt {3} x^9+x^{10}}{\left (3 \sqrt {3}-6 x+\sqrt {3} x^2+x^4\right )^3} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((27*3^(1/2)+(-108-54*3^(1/2))*x+(81+54*3^(1/2))*x^2-36*x^3+(18+3 *3^(1/2))*x^4-18*3^(1/2)*x^5+(9-12*3^(1/2))*x^6+3*3^(1/2)*x^8+2*3^(1/2)*x^ 9+x^10)/(3*3^(1/2)-6*x+3^(1/2)*x^2+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%%%{%%{[1084716759416832,13101256450146816]:[1,0,-3]%%},[4]%%% }+%%%{%%{
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(40\)
Exception generated. \[ \int \frac {-500+192 \sqrt {7}+952 x+360 \sqrt {7} x+672 x^2+252 \sqrt {7} x^2+196 x^3+84 \sqrt {7} x^3+49 x^4}{\left (16-6 \sqrt {7}+14 x+6 \sqrt {7} x+7 x^2\right )^2 \left (2 \sqrt {7}+630 x+238 \sqrt {7} x+147 x^2+56 \sqrt {7} x^2\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((-500+192*7^(1/2)+952*x+360*7^(1/2)*x+672*x^2+252*7^(1/2)*x^2+19 6*x^3+84*7^(1/2)*x^3+49*x^4)/(16-6*7^(1/2)+14*x+6*7^(1/2)*x+7*x^2)^2/(2*7^ (1/2)+630*x+238*7^(1/2)*x+147*x^2+56*7^(1/2)*x^2),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%%%{%%{[-168,0]:[1,0,-7]%%},[2]%%%}+%%%{%%{[-336,-1008]:[1,0,- 7]%%},[1]
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(44\)
Exception generated. \[ \int \frac {624 x^3+144 x^7+24 x^{11}}{\left (-460-936 x^4-376 x^8-36 x^{12}-x^{16}\right )^2} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((24*x^11+144*x^7+624*x^3)/(-x^16-36*x^12-376*x^8-936*x^4-460)^2, x, algorithm="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to find common minimal polyn omial Error: Bad Argument ValueUnable to find common minimal polynomial Er ror: Bad
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(46\)
Exception generated. \[ \int \frac {5000 \sqrt {5} \left (1000 \sqrt {3}-750 \sqrt {5}\right ) x+5000 \sqrt {5} \left (-5250 \sqrt {3}-3150 \sqrt {5}\right ) x^3+65625000 \sqrt {15} x^5}{-1937500+500000 \sqrt {15}+\left (3125000-625000 \sqrt {15}\right ) x^2+\left (-88750000-4062500 \sqrt {15}\right ) x^4+\left (164062500+32812500 \sqrt {15}\right ) x^6-172265625 x^8} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((5000*5^(1/2)*(1000*3^(1/2)-750*5^(1/2))*x+5000*5^(1/2)*(-5250*3 ^(1/2)-3150*5^(1/2))*x^3+65625000*15^(1/2)*x^5)/(-1937500+500000*15^(1/2)+ (3125000-625000*15^(1/2))*x^2+(-88750000-4062500*15^(1/2))*x^4+(164062500+ 32812500*15^(1/2))*x^6-172265625*x^8),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.Francis algorithm failure for[-1.0,0.0,infinity,infinity,in finity]pr
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(49\)
Exception generated. \[ \int \frac {3 \sqrt {7}+6 \sqrt {11}+\left (-121 \sqrt {105}-98 \sqrt {165}\right ) x^4}{-12 \sqrt {15}+10200 x^4-118580 \sqrt {15} x^8} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((3*7^(1/2)+6*11^(1/2)+(-121*105^(1/2)-98*165^(1/2))*x^4)/(-12*15 ^(1/2)+10200*x^4-118580*15^(1/2)*x^8),x, 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%%%{%%{[1274,0,-1480290,0,427747950,0,-19021101750,0]:[1,0,-11 40,0,3163
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(50\)
Exception generated. \[ \int \frac {15 x-2 \sqrt {3} x+12 \sqrt {3} x^3+3 \sqrt {3} x^5}{-4-20 x^2+60 \sqrt {3} x^2-100 x^4+10 \sqrt {3} x^4+12 x^6+60 \sqrt {3} x^6-36 x^8} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((15*x-2*3^(1/2)*x+12*3^(1/2)*x^3+3*3^(1/2)*x^5)/(-4-20*x^2+60*3^ (1/2)*x^2-100*x^4+10*3^(1/2)*x^4+12*x^6+60*x^6*3^(1/2)-36*x^8),x, algorith m="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to find common minimal polyn omial Error: Bad Argument ValueUnable to find common minimal polynomial Er ror: Bad
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(53\)
Exception generated. \[ \int \frac {8 \left (15-2 \sqrt {3}\right ) x+96 \sqrt {3} x^3+24 \sqrt {3} x^5}{-4+\left (-20+60 \sqrt {3}\right ) x^2+\left (-100+10 \sqrt {3}\right ) x^4+\left (12+60 \sqrt {3}\right ) x^6-36 x^8} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((8*(15-2*3^(1/2))*x+96*3^(1/2)*x^3+24*3^(1/2)*x^5)/(-4+(-20+60*3 ^(1/2))*x^2+(-100+10*3^(1/2))*x^4+(12+60*3^(1/2))*x^6-36*x^8),x, algorithm ="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to find common minimal polyn omial Error: Bad Argument ValueUnable to find common minimal polynomial Er ror: Bad
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(55\)
Exception generated. \[ \int \frac {-80 \left (-3+2 \sqrt {3}\right ) x-80 \left (3-2 \sqrt {3}\right ) x^3-80 \left (90+30 \sqrt {3}\right ) x^5-960 \sqrt {3} x^7-7440 \sqrt {3} x^9-1440 \sqrt {3} x^{11}}{14-8 \sqrt {3}+\left (-28+20 \sqrt {3}\right ) x^2+\left (-1110-418 \sqrt {3}\right ) x^4+\left (296-268 \sqrt {3}\right ) x^6+\left (434-2401 \sqrt {3}\right ) x^8+\left (204-828 \sqrt {3}\right ) x^{10}+\left (-324-468 \sqrt {3}\right ) x^{12}-432 x^{14}+648 x^{16}} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((-80*(-3+2*3^(1/2))*x-80*(3-2*3^(1/2))*x^3-80*(90+30*3^(1/2))*x^ 5-960*3^(1/2)*x^7-7440*3^(1/2)*x^9-1440*3^(1/2)*x^11)/(14-8*3^(1/2)+(-28+2 0*3^(1/2))*x^2+(-1110-418*3^(1/2))*x^4+(296-268*3^(1/2))*x^6+(434-2401*3^( 1/2))*x^8+(204-828*3^(1/2))*x^10+(-324-468*3^(1/2))*x^12-432*x^14+648*x^16 ),x, algorithm="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Francis algorithm failure for[infin ity,infinity,infinity,infinity,infinity]proot error [undef,undef,undef,und ef,undef]
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(56\)
Exception generated. \[ \int \frac {-16 \left (3-2 \sqrt {3}\right ) x-16 \left (15-10 \sqrt {3}\right ) x^3-16 \left (90+30 \sqrt {3}\right ) x^5+960 \sqrt {3} x^7+240 \sqrt {3} x^9-1440 \sqrt {3} x^{11}}{14-8 \sqrt {3}+\left (140-100 \sqrt {3}\right ) x^2+\left (1578+158 \sqrt {3}\right ) x^4+\left (440-820 \sqrt {3}\right ) x^6+\left (1682+1343 \sqrt {3}\right ) x^8+\left (-2580-540 \sqrt {3}\right ) x^{10}+\left (3132-468 \sqrt {3}\right ) x^{12}-2160 x^{14}+648 x^{16}} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((-16*(3-2*3^(1/2))*x-16*(15-10*3^(1/2))*x^3-16*(90+30*3^(1/2))*x ^5+960*3^(1/2)*x^7+240*3^(1/2)*x^9-1440*3^(1/2)*x^11)/(14-8*3^(1/2)+(140-1 00*3^(1/2))*x^2+(1578+158*3^(1/2))*x^4+(440-820*3^(1/2))*x^6+(1682+1343*3^ (1/2))*x^8+(-2580-540*3^(1/2))*x^10+(3132-468*3^(1/2))*x^12-2160*x^14+648* x^16),x, algorithm="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Francis algorithm failure for[infin ity,0.0,infinity,infinity,infinity]proot error [undef,0.0,undef,undef,unde f]proot e
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(57\)
Exception generated. \[ \int \frac {8 \left (3-2 \sqrt {3}\right ) x+24 \sqrt {3} x^5}{-28+16 \sqrt {3}+\left (-20+20 \sqrt {3}\right ) x^2+\left (-148-22 \sqrt {3}\right ) x^4+\left (60+60 \sqrt {3}\right ) x^6-36 x^8} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((8*(3-2*3^(1/2))*x+24*3^(1/2)*x^5)/(-28+16*3^(1/2)+(-20+20*3^(1/ 2))*x^2+(-148-22*3^(1/2))*x^4+(60+60*3^(1/2))*x^6-36*x^8),x, algorithm="gi ac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to find common minimal polyn omial Error: Bad Argument ValueUnable to find common minimal polynomial Er ror: Bad
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(58\)
Exception generated. \[ \int \frac {x \left (-1+2 x^2+x^4\right )}{1+2 x^2+5 x^4+4 x^6+x^8} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(x*(x^4+2*x^2-1)/(x^8+4*x^6+5*x^4+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:Francis algorithm failure for[-1.0, infinity,infinity,infinity,infinity]proot error [1.0,infinity,infinity,inf inity,inf
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(61\)
Exception generated. \[ \int \frac {16 x^3-248 x^{11}+80 x^{15}-392 x^{19}-80 x^{23}+24 x^{27}}{1+10 x^4+26 x^8+40 x^{12}+71 x^{16}+40 x^{20}+26 x^{24}+10 x^{28}+x^{32}} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((24*x^27-80*x^23-392*x^19+80*x^15-248*x^11+16*x^3)/(x^32+10*x^28 +26*x^24+40*x^20+71*x^16+40*x^12+26*x^8+10*x^4+1),x, algorithm="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:int(sage0,sageVARx) Error: Bad Arg ument Type
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(65\)
Exception generated. \[ \int \frac {\left (-\sqrt [4]{2}+\sqrt {3} x+\sqrt [4]{2} x^2\right )^2}{\left (\sqrt {3}+2 \sqrt [4]{2} x\right )^3} \, dx=\text {Exception raised: NotImplementedError} \] Input:
integrate((-2^(1/4)+3^(1/2)*x+x^2*2^(1/4))^2/(3^(1/2)+2*2^(1/4)*x)^3,x, al gorithm="giac")
Output:
Exception raised: NotImplementedError >> unable to parse Giac output: (roo tof([[3107414276067094328724118783432456182672461636123978958372864,0,-362 51401980421570635609481139600442826134612068444647200915456,0,144735628146 4232130181365104903
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(80\)
Exception generated. \[ \int \frac {-36-2 \sqrt {6} x^2}{9 \sqrt {3}+3 \sqrt {2} x^2-x^4} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((-36-2*6^(1/2)*x^2)/(9*3^(1/2)+3*2^(1/2)*x^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 8192000. *** W arning: i
input file name test_cases/extra_tests/367_Blake_2
Test file number \(367\)
Integral number in file \(98\)