Optimal. Leaf size=102 \[ \log \left (\sqrt [3]{x^6-1}-x\right )-\sqrt {3} \tan ^{-1}\left (\frac {\sqrt {3} x}{2 \sqrt [3]{x^6-1}+x}\right )-\frac {1}{2} \log \left (\sqrt [3]{x^6-1} x+\left (x^6-1\right )^{2/3}+x^2\right )+\frac {\left (x^6-1\right )^{2/3} \left (4 x^6+15 x^3-4\right )}{10 x^5} \]
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Rubi [C] time = 1.29, antiderivative size = 389, normalized size of antiderivative = 3.81, number of steps used = 25, number of rules used = 12, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.300, Rules used = {6728, 246, 245, 365, 364, 275, 1438, 430, 429, 465, 511, 510} \begin {gather*} -\frac {3 \left (1-\sqrt {5}\right ) \left (x^6-1\right )^{2/3} x F_1\left (\frac {1}{6};-\frac {2}{3},1;\frac {7}{6};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{\left (3-\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}-\frac {3 \left (1+\sqrt {5}\right ) \left (x^6-1\right )^{2/3} x F_1\left (\frac {1}{6};1,-\frac {2}{3};\frac {7}{6};\frac {2 x^6}{3+\sqrt {5}},x^6\right )}{\left (3+\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}-\frac {3 \left (x^6-1\right )^{2/3} x^4 F_1\left (\frac {2}{3};-\frac {2}{3},1;\frac {5}{3};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{2 \left (3-\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}-\frac {3 \left (x^6-1\right )^{2/3} x^4 F_1\left (\frac {2}{3};-\frac {2}{3},1;\frac {5}{3};x^6,\frac {2 x^6}{3+\sqrt {5}}\right )}{2 \left (3+\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}+\frac {2 \left (x^6-1\right )^{2/3} x \, _2F_1\left (-\frac {2}{3},\frac {1}{6};\frac {7}{6};x^6\right )}{\left (1-x^6\right )^{2/3}}-\frac {2 \left (x^6-1\right )^{2/3} \, _2F_1\left (-\frac {5}{6},-\frac {2}{3};\frac {1}{6};x^6\right )}{5 \left (1-x^6\right )^{2/3} x^5}+\frac {3 \left (x^6-1\right )^{2/3} \, _2F_1\left (-\frac {2}{3},-\frac {1}{3};\frac {2}{3};x^6\right )}{2 \left (1-x^6\right )^{2/3} x^2} \end {gather*}
Warning: Unable to verify antiderivative.
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Rule 245
Rule 246
Rule 275
Rule 364
Rule 365
Rule 429
Rule 430
Rule 465
Rule 510
Rule 511
Rule 1438
Rule 6728
Rubi steps
\begin {align*} \int \frac {\left (-1+x^6\right )^{2/3} \left (1+x^6\right ) \left (-2+x^3+2 x^6\right )}{x^6 \left (-1-x^3+x^6\right )} \, dx &=\int \left (2 \left (-1+x^6\right )^{2/3}+\frac {2 \left (-1+x^6\right )^{2/3}}{x^6}-\frac {3 \left (-1+x^6\right )^{2/3}}{x^3}+\frac {3 \left (-1+2 x^3\right ) \left (-1+x^6\right )^{2/3}}{-1-x^3+x^6}\right ) \, dx\\ &=2 \int \left (-1+x^6\right )^{2/3} \, dx+2 \int \frac {\left (-1+x^6\right )^{2/3}}{x^6} \, dx-3 \int \frac {\left (-1+x^6\right )^{2/3}}{x^3} \, dx+3 \int \frac {\left (-1+2 x^3\right ) \left (-1+x^6\right )^{2/3}}{-1-x^3+x^6} \, dx\\ &=-\left (\frac {3}{2} \operatorname {Subst}\left (\int \frac {\left (-1+x^3\right )^{2/3}}{x^2} \, dx,x,x^2\right )\right )+3 \int \left (\frac {2 \left (-1+x^6\right )^{2/3}}{-1-\sqrt {5}+2 x^3}+\frac {2 \left (-1+x^6\right )^{2/3}}{-1+\sqrt {5}+2 x^3}\right ) \, dx+\frac {\left (2 \left (-1+x^6\right )^{2/3}\right ) \int \left (1-x^6\right )^{2/3} \, dx}{\left (1-x^6\right )^{2/3}}+\frac {\left (2 \left (-1+x^6\right )^{2/3}\right ) \int \frac {\left (1-x^6\right )^{2/3}}{x^6} \, dx}{\left (1-x^6\right )^{2/3}}\\ &=-\frac {2 \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {5}{6},-\frac {2}{3};\frac {1}{6};x^6\right )}{5 x^5 \left (1-x^6\right )^{2/3}}+\frac {2 x \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},\frac {1}{6};\frac {7}{6};x^6\right )}{\left (1-x^6\right )^{2/3}}+6 \int \frac {\left (-1+x^6\right )^{2/3}}{-1-\sqrt {5}+2 x^3} \, dx+6 \int \frac {\left (-1+x^6\right )^{2/3}}{-1+\sqrt {5}+2 x^3} \, dx-\frac {\left (3 \left (-1+x^6\right )^{2/3}\right ) \operatorname {Subst}\left (\int \frac {\left (1-x^3\right )^{2/3}}{x^2} \, dx,x,x^2\right )}{2 \left (1-x^6\right )^{2/3}}\\ &=-\frac {2 \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {5}{6},-\frac {2}{3};\frac {1}{6};x^6\right )}{5 x^5 \left (1-x^6\right )^{2/3}}+\frac {3 \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},-\frac {1}{3};\frac {2}{3};x^6\right )}{2 x^2 \left (1-x^6\right )^{2/3}}+\frac {2 x \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},\frac {1}{6};\frac {7}{6};x^6\right )}{\left (1-x^6\right )^{2/3}}+6 \int \left (\frac {\left (-1-\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}}{2 \left (3+\sqrt {5}-2 x^6\right )}+\frac {x^3 \left (-1+x^6\right )^{2/3}}{-3-\sqrt {5}+2 x^6}\right ) \, dx+6 \int \left (\frac {\left (1-\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}}{2 \left (-3+\sqrt {5}+2 x^6\right )}+\frac {x^3 \left (-1+x^6\right )^{2/3}}{-3+\sqrt {5}+2 x^6}\right ) \, dx\\ &=-\frac {2 \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {5}{6},-\frac {2}{3};\frac {1}{6};x^6\right )}{5 x^5 \left (1-x^6\right )^{2/3}}+\frac {3 \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},-\frac {1}{3};\frac {2}{3};x^6\right )}{2 x^2 \left (1-x^6\right )^{2/3}}+\frac {2 x \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},\frac {1}{6};\frac {7}{6};x^6\right )}{\left (1-x^6\right )^{2/3}}+6 \int \frac {x^3 \left (-1+x^6\right )^{2/3}}{-3-\sqrt {5}+2 x^6} \, dx+6 \int \frac {x^3 \left (-1+x^6\right )^{2/3}}{-3+\sqrt {5}+2 x^6} \, dx+\left (3 \left (1-\sqrt {5}\right )\right ) \int \frac {\left (-1+x^6\right )^{2/3}}{-3+\sqrt {5}+2 x^6} \, dx-\left (3 \left (1+\sqrt {5}\right )\right ) \int \frac {\left (-1+x^6\right )^{2/3}}{3+\sqrt {5}-2 x^6} \, dx\\ &=-\frac {2 \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {5}{6},-\frac {2}{3};\frac {1}{6};x^6\right )}{5 x^5 \left (1-x^6\right )^{2/3}}+\frac {3 \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},-\frac {1}{3};\frac {2}{3};x^6\right )}{2 x^2 \left (1-x^6\right )^{2/3}}+\frac {2 x \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},\frac {1}{6};\frac {7}{6};x^6\right )}{\left (1-x^6\right )^{2/3}}+3 \operatorname {Subst}\left (\int \frac {x \left (-1+x^3\right )^{2/3}}{-3-\sqrt {5}+2 x^3} \, dx,x,x^2\right )+3 \operatorname {Subst}\left (\int \frac {x \left (-1+x^3\right )^{2/3}}{-3+\sqrt {5}+2 x^3} \, dx,x,x^2\right )+\frac {\left (3 \left (1-\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}\right ) \int \frac {\left (1-x^6\right )^{2/3}}{-3+\sqrt {5}+2 x^6} \, dx}{\left (1-x^6\right )^{2/3}}-\frac {\left (3 \left (1+\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}\right ) \int \frac {\left (1-x^6\right )^{2/3}}{3+\sqrt {5}-2 x^6} \, dx}{\left (1-x^6\right )^{2/3}}\\ &=-\frac {3 \left (1-\sqrt {5}\right ) x \left (-1+x^6\right )^{2/3} F_1\left (\frac {1}{6};-\frac {2}{3},1;\frac {7}{6};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{\left (3-\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}-\frac {3 \left (1+\sqrt {5}\right ) x \left (-1+x^6\right )^{2/3} F_1\left (\frac {1}{6};1,-\frac {2}{3};\frac {7}{6};\frac {2 x^6}{3+\sqrt {5}},x^6\right )}{\left (3+\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}-\frac {2 \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {5}{6},-\frac {2}{3};\frac {1}{6};x^6\right )}{5 x^5 \left (1-x^6\right )^{2/3}}+\frac {3 \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},-\frac {1}{3};\frac {2}{3};x^6\right )}{2 x^2 \left (1-x^6\right )^{2/3}}+\frac {2 x \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},\frac {1}{6};\frac {7}{6};x^6\right )}{\left (1-x^6\right )^{2/3}}+\frac {\left (3 \left (-1+x^6\right )^{2/3}\right ) \operatorname {Subst}\left (\int \frac {x \left (1-x^3\right )^{2/3}}{-3-\sqrt {5}+2 x^3} \, dx,x,x^2\right )}{\left (1-x^6\right )^{2/3}}+\frac {\left (3 \left (-1+x^6\right )^{2/3}\right ) \operatorname {Subst}\left (\int \frac {x \left (1-x^3\right )^{2/3}}{-3+\sqrt {5}+2 x^3} \, dx,x,x^2\right )}{\left (1-x^6\right )^{2/3}}\\ &=-\frac {3 \left (1-\sqrt {5}\right ) x \left (-1+x^6\right )^{2/3} F_1\left (\frac {1}{6};-\frac {2}{3},1;\frac {7}{6};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{\left (3-\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}-\frac {3 \left (1+\sqrt {5}\right ) x \left (-1+x^6\right )^{2/3} F_1\left (\frac {1}{6};1,-\frac {2}{3};\frac {7}{6};\frac {2 x^6}{3+\sqrt {5}},x^6\right )}{\left (3+\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}-\frac {3 x^4 \left (-1+x^6\right )^{2/3} F_1\left (\frac {2}{3};-\frac {2}{3},1;\frac {5}{3};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{2 \left (3-\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}-\frac {3 x^4 \left (-1+x^6\right )^{2/3} F_1\left (\frac {2}{3};-\frac {2}{3},1;\frac {5}{3};x^6,\frac {2 x^6}{3+\sqrt {5}}\right )}{2 \left (3+\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}-\frac {2 \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {5}{6},-\frac {2}{3};\frac {1}{6};x^6\right )}{5 x^5 \left (1-x^6\right )^{2/3}}+\frac {3 \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},-\frac {1}{3};\frac {2}{3};x^6\right )}{2 x^2 \left (1-x^6\right )^{2/3}}+\frac {2 x \left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},\frac {1}{6};\frac {7}{6};x^6\right )}{\left (1-x^6\right )^{2/3}}\\ \end {align*}
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Mathematica [F] time = 0.91, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (-1+x^6\right )^{2/3} \left (1+x^6\right ) \left (-2+x^3+2 x^6\right )}{x^6 \left (-1-x^3+x^6\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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IntegrateAlgebraic [A] time = 2.27, size = 102, normalized size = 1.00 \begin {gather*} \frac {\left (-1+x^6\right )^{2/3} \left (-4+15 x^3+4 x^6\right )}{10 x^5}-\sqrt {3} \tan ^{-1}\left (\frac {\sqrt {3} x}{x+2 \sqrt [3]{-1+x^6}}\right )+\log \left (-x+\sqrt [3]{-1+x^6}\right )-\frac {1}{2} \log \left (x^2+x \sqrt [3]{-1+x^6}+\left (-1+x^6\right )^{2/3}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 13.27, size = 148, normalized size = 1.45 \begin {gather*} -\frac {10 \, \sqrt {3} x^{5} \arctan \left (\frac {473996388635948633452428917614298985996886224511260115036680453514888144148250 \, \sqrt {3} {\left (x^{6} - 1\right )}^{\frac {1}{3}} x^{2} + 19325031480489228255674265966448835967818926087643600184123099965366515892788 \, \sqrt {3} {\left (x^{6} - 1\right )}^{\frac {2}{3}} x + \sqrt {3} {\left (771225779807741020855977802972631216428368740202755221603971931588718036144 \, x^{6} + 245889484278411189833195613987401279765924206559249102388797804808538611984375 \, x^{3} - 771225779807741020855977802972631216428368740202755221603971931588718036144\right )}}{3 \, {\left (15407513785538665202033017569552164636906896740149986002803824712402669144 \, x^{6} - 227351086091515241263579358841494627179170556108548407412281480599473216796875 \, x^{3} - 15407513785538665202033017569552164636906896740149986002803824712402669144\right )}}\right ) - 5 \, x^{5} \log \left (\frac {x^{6} - x^{3} + 3 \, {\left (x^{6} - 1\right )}^{\frac {1}{3}} x^{2} - 3 \, {\left (x^{6} - 1\right )}^{\frac {2}{3}} x - 1}{x^{6} - x^{3} - 1}\right ) - {\left (4 \, x^{6} + 15 \, x^{3} - 4\right )} {\left (x^{6} - 1\right )}^{\frac {2}{3}}}{10 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (2 \, x^{6} + x^{3} - 2\right )} {\left (x^{6} + 1\right )} {\left (x^{6} - 1\right )}^{\frac {2}{3}}}{{\left (x^{6} - x^{3} - 1\right )} x^{6}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 21.09, size = 490, normalized size = 4.80
method | result | size |
risch | \(\frac {4 x^{12}+15 x^{9}-8 x^{6}-15 x^{3}+4}{10 x^{5} \left (x^{6}-1\right )^{\frac {1}{3}}}-3 \ln \left (\frac {6 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) x^{6}+x^{6}-18 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )^{2} x^{3}+9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x +9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}} x^{2}-3 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) x^{3}+3 x \left (x^{6}-1\right )^{\frac {2}{3}}+3 x^{2} \left (x^{6}-1\right )^{\frac {1}{3}}-6 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )-1}{x^{6}-x^{3}-1}\right ) \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )+3 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \ln \left (-\frac {6 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) x^{6}+x^{6}+18 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )^{2} x^{3}+9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x +9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}} x^{2}+9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) x^{3}+x^{3}-6 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )-1}{x^{6}-x^{3}-1}\right )-\ln \left (\frac {6 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) x^{6}+x^{6}-18 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )^{2} x^{3}+9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x +9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}} x^{2}-3 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) x^{3}+3 x \left (x^{6}-1\right )^{\frac {2}{3}}+3 x^{2} \left (x^{6}-1\right )^{\frac {1}{3}}-6 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )-1}{x^{6}-x^{3}-1}\right )\) | \(490\) |
trager | \(\frac {\left (x^{6}-1\right )^{\frac {2}{3}} \left (4 x^{6}+15 x^{3}-4\right )}{10 x^{5}}-96 \ln \left (-\frac {6570485565136040671726226079744 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right )^{2} x^{6}-489182598517982885200727925888 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right ) x^{6}-4085365060307585836672246881 x^{6}-51742573825446320289844030377984 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right )^{2} x^{3}+363650051031240685770824996928 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x +654612709216604620411401672864 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}} x^{2}-999622747774761167003559205344 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right ) x^{3}-6818882387672964795952100759 x \left (x^{6}-1\right )^{\frac {2}{3}}+10606903752581721939398194477 x^{2} \left (x^{6}-1\right )^{\frac {1}{3}}-4604141575902199911170309977 x^{3}-6570485565136040671726226079744 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right )^{2}+489182598517982885200727925888 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right )+4085365060307585836672246881}{x^{6}-x^{3}-1}\right ) \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right )+\ln \left (\frac {1789441197416077361152076587008 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right )^{2} x^{6}+115627565201538784058859689760 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right ) x^{6}-4604141575902199911170309977 x^{6}-14091849429651609219072603122688 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right )^{2} x^{3}+363650051031240685770824996928 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x -1018262760247845306182226669792 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}} x^{2}+410835058262612379499203165024 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right ) x^{3}+10606903752581721939398194477 x \left (x^{6}-1\right )^{\frac {2}{3}}-6818882387672964795952100759 x^{2} \left (x^{6}-1\right )^{\frac {1}{3}}-518776515594614074498063096 x^{3}-1789441197416077361152076587008 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right )^{2}-115627565201538784058859689760 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right )+4604141575902199911170309977}{x^{6}-x^{3}-1}\right )-\ln \left (-\frac {6570485565136040671726226079744 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right )^{2} x^{6}-489182598517982885200727925888 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right ) x^{6}-4085365060307585836672246881 x^{6}-51742573825446320289844030377984 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right )^{2} x^{3}+363650051031240685770824996928 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x +654612709216604620411401672864 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}} x^{2}-999622747774761167003559205344 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right ) x^{3}-6818882387672964795952100759 x \left (x^{6}-1\right )^{\frac {2}{3}}+10606903752581721939398194477 x^{2} \left (x^{6}-1\right )^{\frac {1}{3}}-4604141575902199911170309977 x^{3}-6570485565136040671726226079744 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right )^{2}+489182598517982885200727925888 \RootOf \left (9216 \textit {\_Z}^{2}+96 \textit {\_Z} +1\right )+4085365060307585836672246881}{x^{6}-x^{3}-1}\right )\) | \(607\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (2 \, x^{6} + x^{3} - 2\right )} {\left (x^{6} + 1\right )} {\left (x^{6} - 1\right )}^{\frac {2}{3}}}{{\left (x^{6} - x^{3} - 1\right )} x^{6}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int -\frac {{\left (x^6-1\right )}^{2/3}\,\left (x^6+1\right )\,\left (2\,x^6+x^3-2\right )}{x^6\,\left (-x^6+x^3+1\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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