Optimal. Leaf size=105 \[ -\frac {2}{3} \log \left (\sqrt [3]{x^6-1}+x\right )-\frac {2 \tan ^{-1}\left (\frac {\sqrt {3} x}{2 \sqrt [3]{x^6-1}-x}\right )}{\sqrt {3}}+\frac {1}{3} \log \left (-\sqrt [3]{x^6-1} x+\left (x^6-1\right )^{2/3}+x^2\right )+\frac {\left (x^6-1\right )^{2/3} \left (x^6-5 x^3-1\right )}{5 x^5} \]
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Rubi [C] time = 1.19, antiderivative size = 380, normalized size of antiderivative = 3.62, number of steps used = 25, number of rules used = 12, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.316, Rules used = {6728, 246, 245, 365, 364, 275, 1438, 430, 429, 465, 511, 510} \begin {gather*} -\frac {2 \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 {2 \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 {\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 )}{\left (3-\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}+\frac {\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 )}{\left (3+\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}+\frac {\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 {\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 {\left (x^6-1\right )^{2/3} \, _2F_1\left (-\frac {2}{3},-\frac {1}{3};\frac {2}{3};x^6\right )}{\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 (-1-x^3+x^6\right )}{x^6 \left (-1+x^3+x^6\right )} \, dx &=\int \left (\left (-1+x^6\right )^{2/3}+\frac {\left (-1+x^6\right )^{2/3}}{x^6}+\frac {2 \left (-1+x^6\right )^{2/3}}{x^3}-\frac {2 \left (1+2 x^3\right ) \left (-1+x^6\right )^{2/3}}{-1+x^3+x^6}\right ) \, dx\\ &=2 \int \frac {\left (-1+x^6\right )^{2/3}}{x^3} \, dx-2 \int \frac {\left (1+2 x^3\right ) \left (-1+x^6\right )^{2/3}}{-1+x^3+x^6} \, dx+\int \left (-1+x^6\right )^{2/3} \, dx+\int \frac {\left (-1+x^6\right )^{2/3}}{x^6} \, dx\\ &=-\left (2 \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\right )+\frac {\left (-1+x^6\right )^{2/3} \int \left (1-x^6\right )^{2/3} \, dx}{\left (1-x^6\right )^{2/3}}+\frac {\left (-1+x^6\right )^{2/3} \int \frac {\left (1-x^6\right )^{2/3}}{x^6} \, dx}{\left (1-x^6\right )^{2/3}}+\operatorname {Subst}\left (\int \frac {\left (-1+x^3\right )^{2/3}}{x^2} \, dx,x,x^2\right )\\ &=-\frac {\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 {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}}-4 \int \frac {\left (-1+x^6\right )^{2/3}}{1-\sqrt {5}+2 x^3} \, dx-4 \int \frac {\left (-1+x^6\right )^{2/3}}{1+\sqrt {5}+2 x^3} \, dx+\frac {\left (-1+x^6\right )^{2/3} \operatorname {Subst}\left (\int \frac {\left (1-x^3\right )^{2/3}}{x^2} \, dx,x,x^2\right )}{\left (1-x^6\right )^{2/3}}\\ &=-\frac {\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 {\left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},-\frac {1}{3};\frac {2}{3};x^6\right )}{x^2 \left (1-x^6\right )^{2/3}}+\frac {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}}-4 \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-4 \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 {\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 {\left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},-\frac {1}{3};\frac {2}{3};x^6\right )}{x^2 \left (1-x^6\right )^{2/3}}+\frac {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}}-4 \int \frac {x^3 \left (-1+x^6\right )^{2/3}}{-3-\sqrt {5}+2 x^6} \, dx-4 \int \frac {x^3 \left (-1+x^6\right )^{2/3}}{-3+\sqrt {5}+2 x^6} \, dx+\left (2 \left (1-\sqrt {5}\right )\right ) \int \frac {\left (-1+x^6\right )^{2/3}}{-3+\sqrt {5}+2 x^6} \, dx-\left (2 \left (1+\sqrt {5}\right )\right ) \int \frac {\left (-1+x^6\right )^{2/3}}{3+\sqrt {5}-2 x^6} \, dx\\ &=-\frac {\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 {\left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},-\frac {1}{3};\frac {2}{3};x^6\right )}{x^2 \left (1-x^6\right )^{2/3}}+\frac {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}}-2 \operatorname {Subst}\left (\int \frac {x \left (-1+x^3\right )^{2/3}}{-3-\sqrt {5}+2 x^3} \, dx,x,x^2\right )-2 \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 (2 \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 (2 \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 {2 \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 {2 \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 {\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 {\left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},-\frac {1}{3};\frac {2}{3};x^6\right )}{x^2 \left (1-x^6\right )^{2/3}}+\frac {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 (2 \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 (2 \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 {2 \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 {2 \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 {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 )}{\left (3-\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}+\frac {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 )}{\left (3+\sqrt {5}\right ) \left (1-x^6\right )^{2/3}}-\frac {\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 {\left (-1+x^6\right )^{2/3} \, _2F_1\left (-\frac {2}{3},-\frac {1}{3};\frac {2}{3};x^6\right )}{x^2 \left (1-x^6\right )^{2/3}}+\frac {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 = 0.93, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (-1+x^6\right )^{2/3} \left (1+x^6\right ) \left (-1-x^3+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 = 2.26, size = 105, normalized size = 1.00 \begin {gather*} \frac {\left (-1+x^6\right )^{2/3} \left (-1-5 x^3+x^6\right )}{5 x^5}-\frac {2 \tan ^{-1}\left (\frac {\sqrt {3} x}{-x+2 \sqrt [3]{-1+x^6}}\right )}{\sqrt {3}}-\frac {2}{3} \log \left (x+\sqrt [3]{-1+x^6}\right )+\frac {1}{3} \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 = 17.40, size = 142, normalized size = 1.35 \begin {gather*} -\frac {10 \, \sqrt {3} x^{5} \arctan \left (\frac {17707979315346691547103487078601066282657059082726673278841963389300888497059669011634 \, \sqrt {3} {\left (x^{6} - 1\right )}^{\frac {1}{3}} x^{2} + 18779074824464902023518972945875034013564452605964125877184864112405550428883609929964 \, \sqrt {3} {\left (x^{6} - 1\right )}^{\frac {2}{3}} x + \sqrt {3} {\left (8791266734992875261237504664599259772605087326251698970792557525513888268399719816592 \, x^{6} + 9326814489551980499445247598236243638058784087870425269964007887066219234311690275757 \, x^{3} - 8791266734992875261237504664599259772605087326251698970792557525513888268399719816592\right )}}{3 \, {\left (9923243904393545413458713816471868889492119646716071835561526356358143878603884871272 \, x^{6} - 8320283165512251371852516195766181258618636197629327742451887394495075584367754599527 \, x^{3} - 9923243904393545413458713816471868889492119646716071835561526356358143878603884871272\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 ) - 3 \, {\left (x^{6} - 5 \, x^{3} - 1\right )} {\left (x^{6} - 1\right )}^{\frac {2}{3}}}{15 \, 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 (x^{6} - x^{3} - 1\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 = 28.88, size = 298, normalized size = 2.84
method | result | size |
risch | \(\frac {x^{12}-5 x^{9}-2 x^{6}+5 x^{3}+1}{5 x^{5} \left (x^{6}-1\right )^{\frac {1}{3}}}-\frac {2 \ln \left (-\frac {3 \RootOf \left (9 \textit {\_Z}^{2}-3 \textit {\_Z} +1\right ) x^{6}+x^{6}+9 \RootOf \left (9 \textit {\_Z}^{2}-3 \textit {\_Z} +1\right )^{2} x^{3}+9 \RootOf \left (9 \textit {\_Z}^{2}-3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x +9 \RootOf \left (9 \textit {\_Z}^{2}-3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}} x^{2}-3 x^{2} \left (x^{6}-1\right )^{\frac {1}{3}}-x^{3}-3 \RootOf \left (9 \textit {\_Z}^{2}-3 \textit {\_Z} +1\right )-1}{x^{6}+x^{3}-1}\right )}{3}+2 \RootOf \left (9 \textit {\_Z}^{2}-3 \textit {\_Z} +1\right ) \ln \left (\frac {3 \RootOf \left (9 \textit {\_Z}^{2}-3 \textit {\_Z} +1\right ) x^{6}+x^{6}-9 \RootOf \left (9 \textit {\_Z}^{2}-3 \textit {\_Z} +1\right )^{2} x^{3}+9 \RootOf \left (9 \textit {\_Z}^{2}-3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x -3 \RootOf \left (9 \textit {\_Z}^{2}-3 \textit {\_Z} +1\right ) x^{3}-3 x \left (x^{6}-1\right )^{\frac {2}{3}}-3 x^{2} \left (x^{6}-1\right )^{\frac {1}{3}}-3 \RootOf \left (9 \textit {\_Z}^{2}-3 \textit {\_Z} +1\right )-1}{x^{6}+x^{3}-1}\right )\) | \(298\) |
trager | \(\frac {\left (x^{6}-1\right )^{\frac {2}{3}} \left (x^{6}-5 x^{3}-1\right )}{5 x^{5}}+\frac {2 \ln \left (\frac {241382040842688197903703905476608 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right )^{2} x^{6}+14360235166545558502709989692576 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right ) x^{6}-209561394779200926893843501540 x^{6}-1900883571636169558491668255628288 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right )^{2} x^{3}-11116972693065830085107918919360 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x +11116972693065830085107918919360 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}} x^{2}+25558529270134496713387197451392 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right ) x^{3}+411530433155258870911591637547 x \left (x^{6}-1\right )^{\frac {2}{3}}-411530433155258870911591637547 x^{2} \left (x^{6}-1\right )^{\frac {1}{3}}-30481657422429225730013600224 x^{3}-241382040842688197903703905476608 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right )^{2}-14360235166545558502709989692576 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right )+209561394779200926893843501540}{x^{6}+x^{3}-1}\right )}{3}-64 \ln \left (\frac {241382040842688197903703905476608 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right )^{2} x^{6}+14360235166545558502709989692576 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right ) x^{6}-209561394779200926893843501540 x^{6}-1900883571636169558491668255628288 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right )^{2} x^{3}-11116972693065830085107918919360 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x +11116972693065830085107918919360 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}} x^{2}+25558529270134496713387197451392 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right ) x^{3}+411530433155258870911591637547 x \left (x^{6}-1\right )^{\frac {2}{3}}-411530433155258870911591637547 x^{2} \left (x^{6}-1\right )^{\frac {1}{3}}-30481657422429225730013600224 x^{3}-241382040842688197903703905476608 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right )^{2}-14360235166545558502709989692576 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right )+209561394779200926893843501540}{x^{6}+x^{3}-1}\right ) \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right )+64 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right ) \ln \left (\frac {241382040842688197903703905476608 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right )^{2} x^{6}-19389027684101562625703821056672 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right ) x^{6}-33783984098747171016688237221 x^{6}-1900883571636169558491668255628288 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right )^{2} x^{3}+11116972693065830085107918919360 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x -11116972693065830085107918919360 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}} x^{2}+14043211805619035755189224540864 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right ) x^{3}+295728634269156474191717482137 x \left (x^{6}-1\right )^{\frac {2}{3}}-295728634269156474191717482137 x^{2} \left (x^{6}-1\right )^{\frac {1}{3}}+29493954371922133427267508685 x^{3}-241382040842688197903703905476608 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right )^{2}+19389027684101562625703821056672 \RootOf \left (9216 \textit {\_Z}^{2}-96 \textit {\_Z} +1\right )+33783984098747171016688237221}{x^{6}+x^{3}-1}\right )\) | \(610\) |
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 (x^{6} - x^{3} - 1\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 (-x^6+x^3+1\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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