Optimal. Leaf size=79 \[ \frac {1}{3} \log \left (\sqrt [3]{x^6-1}+x\right )-\frac {\tan ^{-1}\left (\frac {\sqrt {3} x}{2 \sqrt [3]{x^6-1}-x}\right )}{\sqrt {3}}-\frac {1}{6} \log \left (-\sqrt [3]{x^6-1} x+\left (x^6-1\right )^{2/3}+x^2\right ) \]
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Rubi [C] time = 1.74, antiderivative size = 601, normalized size of antiderivative = 7.61, number of steps used = 40, number of rules used = 11, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.440, Rules used = {1593, 6728, 275, 246, 245, 1562, 465, 430, 429, 511, 510} \begin {gather*} \frac {\left (5-\sqrt {5}\right ) \left (1-x^6\right )^{2/3} x^5 F_1\left (\frac {5}{6};\frac {2}{3},1;\frac {11}{6};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{25 \left (3-\sqrt {5}\right ) \left (x^6-1\right )^{2/3}}-\frac {4 \left (1-x^6\right )^{2/3} x^5 F_1\left (\frac {5}{6};\frac {2}{3},1;\frac {11}{6};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{5 \sqrt {5} \left (3-\sqrt {5}\right ) \left (x^6-1\right )^{2/3}}+\frac {\left (5+\sqrt {5}\right ) \left (1-x^6\right )^{2/3} x^5 F_1\left (\frac {5}{6};\frac {2}{3},1;\frac {11}{6};x^6,\frac {2 x^6}{3+\sqrt {5}}\right )}{25 \left (3+\sqrt {5}\right ) \left (x^6-1\right )^{2/3}}+\frac {4 \left (1-x^6\right )^{2/3} x^5 F_1\left (\frac {5}{6};\frac {2}{3},1;\frac {11}{6};x^6,\frac {2 x^6}{3+\sqrt {5}}\right )}{5 \sqrt {5} \left (3+\sqrt {5}\right ) \left (x^6-1\right )^{2/3}}-\frac {\left (5-\sqrt {5}\right ) \left (1-x^6\right )^{2/3} x^2 F_1\left (\frac {1}{3};\frac {2}{3},1;\frac {4}{3};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{5 \left (3-\sqrt {5}\right ) \left (x^6-1\right )^{2/3}}+\frac {\left (1-x^6\right )^{2/3} x^2 F_1\left (\frac {1}{3};\frac {2}{3},1;\frac {4}{3};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{2 \sqrt {5} \left (x^6-1\right )^{2/3}}-\frac {\left (5+\sqrt {5}\right ) \left (1-x^6\right )^{2/3} x^2 F_1\left (\frac {1}{3};1,\frac {2}{3};\frac {4}{3};\frac {2 x^6}{3+\sqrt {5}},x^6\right )}{5 \left (3+\sqrt {5}\right ) \left (x^6-1\right )^{2/3}}-\frac {\left (1-x^6\right )^{2/3} x^2 F_1\left (\frac {1}{3};1,\frac {2}{3};\frac {4}{3};\frac {2 x^6}{3+\sqrt {5}},x^6\right )}{2 \sqrt {5} \left (x^6-1\right )^{2/3}}+\frac {\left (1-x^6\right )^{2/3} x^2 \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};x^6\right )}{2 \left (x^6-1\right )^{2/3}} \end {gather*}
Warning: Unable to verify antiderivative.
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Rule 245
Rule 246
Rule 275
Rule 429
Rule 430
Rule 465
Rule 510
Rule 511
Rule 1562
Rule 1593
Rule 6728
Rubi steps
\begin {align*} \int \frac {x+x^7}{\left (-1+x^6\right )^{2/3} \left (-1+x^3+x^6\right )} \, dx &=\int \frac {x \left (1+x^6\right )}{\left (-1+x^6\right )^{2/3} \left (-1+x^3+x^6\right )} \, dx\\ &=\int \left (\frac {x}{\left (-1+x^6\right )^{2/3}}+\frac {x \left (2-x^3\right )}{\left (-1+x^6\right )^{2/3} \left (-1+x^3+x^6\right )}\right ) \, dx\\ &=\int \frac {x}{\left (-1+x^6\right )^{2/3}} \, dx+\int \frac {x \left (2-x^3\right )}{\left (-1+x^6\right )^{2/3} \left (-1+x^3+x^6\right )} \, dx\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {1}{\left (-1+x^3\right )^{2/3}} \, dx,x,x^2\right )+\int \left (\frac {2 x}{\left (-1+x^6\right )^{2/3} \left (-1+x^3+x^6\right )}-\frac {x^4}{\left (-1+x^6\right )^{2/3} \left (-1+x^3+x^6\right )}\right ) \, dx\\ &=2 \int \frac {x}{\left (-1+x^6\right )^{2/3} \left (-1+x^3+x^6\right )} \, dx+\frac {\left (1-x^6\right )^{2/3} \operatorname {Subst}\left (\int \frac {1}{\left (1-x^3\right )^{2/3}} \, dx,x,x^2\right )}{2 \left (-1+x^6\right )^{2/3}}-\int \frac {x^4}{\left (-1+x^6\right )^{2/3} \left (-1+x^3+x^6\right )} \, dx\\ &=\frac {x^2 \left (1-x^6\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};x^6\right )}{2 \left (-1+x^6\right )^{2/3}}+2 \int \left (-\frac {2 x}{\sqrt {5} \left (-1+\sqrt {5}-2 x^3\right ) \left (-1+x^6\right )^{2/3}}-\frac {2 x}{\sqrt {5} \left (1+\sqrt {5}+2 x^3\right ) \left (-1+x^6\right )^{2/3}}\right ) \, dx-\int \left (-\frac {\left (-1+\sqrt {5}\right ) x}{\sqrt {5} \left (-1+\sqrt {5}-2 x^3\right ) \left (-1+x^6\right )^{2/3}}+\frac {\left (1+\sqrt {5}\right ) x}{\sqrt {5} \left (1+\sqrt {5}+2 x^3\right ) \left (-1+x^6\right )^{2/3}}\right ) \, dx\\ &=\frac {x^2 \left (1-x^6\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};x^6\right )}{2 \left (-1+x^6\right )^{2/3}}-\frac {4 \int \frac {x}{\left (-1+\sqrt {5}-2 x^3\right ) \left (-1+x^6\right )^{2/3}} \, dx}{\sqrt {5}}-\frac {4 \int \frac {x}{\left (1+\sqrt {5}+2 x^3\right ) \left (-1+x^6\right )^{2/3}} \, dx}{\sqrt {5}}+\frac {1}{5} \left (5-\sqrt {5}\right ) \int \frac {x}{\left (-1+\sqrt {5}-2 x^3\right ) \left (-1+x^6\right )^{2/3}} \, dx-\frac {1}{5} \left (5+\sqrt {5}\right ) \int \frac {x}{\left (1+\sqrt {5}+2 x^3\right ) \left (-1+x^6\right )^{2/3}} \, dx\\ &=\frac {x^2 \left (1-x^6\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};x^6\right )}{2 \left (-1+x^6\right )^{2/3}}-\frac {4 \int \left (\frac {\left (1+\sqrt {5}\right ) x}{2 \left (3+\sqrt {5}-2 x^6\right ) \left (-1+x^6\right )^{2/3}}+\frac {x^4}{\left (-1+x^6\right )^{2/3} \left (-3-\sqrt {5}+2 x^6\right )}\right ) \, dx}{\sqrt {5}}-\frac {4 \int \left (\frac {\left (1-\sqrt {5}\right ) x}{2 \left (-1+x^6\right )^{2/3} \left (-3+\sqrt {5}+2 x^6\right )}-\frac {x^4}{\left (-1+x^6\right )^{2/3} \left (-3+\sqrt {5}+2 x^6\right )}\right ) \, dx}{\sqrt {5}}+\frac {1}{5} \left (5-\sqrt {5}\right ) \int \left (\frac {\left (1-\sqrt {5}\right ) x}{2 \left (-1+x^6\right )^{2/3} \left (-3+\sqrt {5}+2 x^6\right )}-\frac {x^4}{\left (-1+x^6\right )^{2/3} \left (-3+\sqrt {5}+2 x^6\right )}\right ) \, dx-\frac {1}{5} \left (5+\sqrt {5}\right ) \int \left (\frac {\left (1+\sqrt {5}\right ) x}{2 \left (3+\sqrt {5}-2 x^6\right ) \left (-1+x^6\right )^{2/3}}+\frac {x^4}{\left (-1+x^6\right )^{2/3} \left (-3-\sqrt {5}+2 x^6\right )}\right ) \, dx\\ &=\frac {x^2 \left (1-x^6\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};x^6\right )}{2 \left (-1+x^6\right )^{2/3}}-\frac {4 \int \frac {x^4}{\left (-1+x^6\right )^{2/3} \left (-3-\sqrt {5}+2 x^6\right )} \, dx}{\sqrt {5}}+\frac {4 \int \frac {x^4}{\left (-1+x^6\right )^{2/3} \left (-3+\sqrt {5}+2 x^6\right )} \, dx}{\sqrt {5}}+\frac {1}{5} \left (5-3 \sqrt {5}\right ) \int \frac {x}{\left (-1+x^6\right )^{2/3} \left (-3+\sqrt {5}+2 x^6\right )} \, dx+\frac {1}{5} \left (2 \left (5-\sqrt {5}\right )\right ) \int \frac {x}{\left (-1+x^6\right )^{2/3} \left (-3+\sqrt {5}+2 x^6\right )} \, dx+\frac {1}{5} \left (-5+\sqrt {5}\right ) \int \frac {x^4}{\left (-1+x^6\right )^{2/3} \left (-3+\sqrt {5}+2 x^6\right )} \, dx-\frac {1}{5} \left (5+\sqrt {5}\right ) \int \frac {x^4}{\left (-1+x^6\right )^{2/3} \left (-3-\sqrt {5}+2 x^6\right )} \, dx-\frac {1}{5} \left (2 \left (5+\sqrt {5}\right )\right ) \int \frac {x}{\left (3+\sqrt {5}-2 x^6\right ) \left (-1+x^6\right )^{2/3}} \, dx-\frac {1}{5} \left (5+3 \sqrt {5}\right ) \int \frac {x}{\left (3+\sqrt {5}-2 x^6\right ) \left (-1+x^6\right )^{2/3}} \, dx\\ &=\frac {x^2 \left (1-x^6\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};x^6\right )}{2 \left (-1+x^6\right )^{2/3}}+\frac {1}{10} \left (5-3 \sqrt {5}\right ) \operatorname {Subst}\left (\int \frac {1}{\left (-1+x^3\right )^{2/3} \left (-3+\sqrt {5}+2 x^3\right )} \, dx,x,x^2\right )+\frac {1}{5} \left (5-\sqrt {5}\right ) \operatorname {Subst}\left (\int \frac {1}{\left (-1+x^3\right )^{2/3} \left (-3+\sqrt {5}+2 x^3\right )} \, dx,x,x^2\right )-\frac {1}{5} \left (5+\sqrt {5}\right ) \operatorname {Subst}\left (\int \frac {1}{\left (3+\sqrt {5}-2 x^3\right ) \left (-1+x^3\right )^{2/3}} \, dx,x,x^2\right )-\frac {1}{10} \left (5+3 \sqrt {5}\right ) \operatorname {Subst}\left (\int \frac {1}{\left (3+\sqrt {5}-2 x^3\right ) \left (-1+x^3\right )^{2/3}} \, dx,x,x^2\right )-\frac {\left (4 \left (1-x^6\right )^{2/3}\right ) \int \frac {x^4}{\left (1-x^6\right )^{2/3} \left (-3-\sqrt {5}+2 x^6\right )} \, dx}{\sqrt {5} \left (-1+x^6\right )^{2/3}}+\frac {\left (4 \left (1-x^6\right )^{2/3}\right ) \int \frac {x^4}{\left (1-x^6\right )^{2/3} \left (-3+\sqrt {5}+2 x^6\right )} \, dx}{\sqrt {5} \left (-1+x^6\right )^{2/3}}+\frac {\left (\left (-5+\sqrt {5}\right ) \left (1-x^6\right )^{2/3}\right ) \int \frac {x^4}{\left (1-x^6\right )^{2/3} \left (-3+\sqrt {5}+2 x^6\right )} \, dx}{5 \left (-1+x^6\right )^{2/3}}-\frac {\left (\left (5+\sqrt {5}\right ) \left (1-x^6\right )^{2/3}\right ) \int \frac {x^4}{\left (1-x^6\right )^{2/3} \left (-3-\sqrt {5}+2 x^6\right )} \, dx}{5 \left (-1+x^6\right )^{2/3}}\\ &=-\frac {4 x^5 \left (1-x^6\right )^{2/3} F_1\left (\frac {5}{6};\frac {2}{3},1;\frac {11}{6};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{5 \sqrt {5} \left (3-\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}}+\frac {\left (5-\sqrt {5}\right ) x^5 \left (1-x^6\right )^{2/3} F_1\left (\frac {5}{6};\frac {2}{3},1;\frac {11}{6};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{25 \left (3-\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}}+\frac {4 x^5 \left (1-x^6\right )^{2/3} F_1\left (\frac {5}{6};\frac {2}{3},1;\frac {11}{6};x^6,\frac {2 x^6}{3+\sqrt {5}}\right )}{5 \sqrt {5} \left (3+\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}}+\frac {\left (5+\sqrt {5}\right ) x^5 \left (1-x^6\right )^{2/3} F_1\left (\frac {5}{6};\frac {2}{3},1;\frac {11}{6};x^6,\frac {2 x^6}{3+\sqrt {5}}\right )}{25 \left (3+\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}}+\frac {x^2 \left (1-x^6\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};x^6\right )}{2 \left (-1+x^6\right )^{2/3}}+\frac {\left (\left (5-3 \sqrt {5}\right ) \left (1-x^6\right )^{2/3}\right ) \operatorname {Subst}\left (\int \frac {1}{\left (1-x^3\right )^{2/3} \left (-3+\sqrt {5}+2 x^3\right )} \, dx,x,x^2\right )}{10 \left (-1+x^6\right )^{2/3}}+\frac {\left (\left (5-\sqrt {5}\right ) \left (1-x^6\right )^{2/3}\right ) \operatorname {Subst}\left (\int \frac {1}{\left (1-x^3\right )^{2/3} \left (-3+\sqrt {5}+2 x^3\right )} \, dx,x,x^2\right )}{5 \left (-1+x^6\right )^{2/3}}-\frac {\left (\left (5+\sqrt {5}\right ) \left (1-x^6\right )^{2/3}\right ) \operatorname {Subst}\left (\int \frac {1}{\left (3+\sqrt {5}-2 x^3\right ) \left (1-x^3\right )^{2/3}} \, dx,x,x^2\right )}{5 \left (-1+x^6\right )^{2/3}}-\frac {\left (\left (5+3 \sqrt {5}\right ) \left (1-x^6\right )^{2/3}\right ) \operatorname {Subst}\left (\int \frac {1}{\left (3+\sqrt {5}-2 x^3\right ) \left (1-x^3\right )^{2/3}} \, dx,x,x^2\right )}{10 \left (-1+x^6\right )^{2/3}}\\ &=\frac {x^2 \left (1-x^6\right )^{2/3} F_1\left (\frac {1}{3};\frac {2}{3},1;\frac {4}{3};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{2 \sqrt {5} \left (-1+x^6\right )^{2/3}}-\frac {\left (5-\sqrt {5}\right ) x^2 \left (1-x^6\right )^{2/3} F_1\left (\frac {1}{3};\frac {2}{3},1;\frac {4}{3};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{5 \left (3-\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}}-\frac {x^2 \left (1-x^6\right )^{2/3} F_1\left (\frac {1}{3};1,\frac {2}{3};\frac {4}{3};\frac {2 x^6}{3+\sqrt {5}},x^6\right )}{2 \sqrt {5} \left (-1+x^6\right )^{2/3}}-\frac {\left (5+\sqrt {5}\right ) x^2 \left (1-x^6\right )^{2/3} F_1\left (\frac {1}{3};1,\frac {2}{3};\frac {4}{3};\frac {2 x^6}{3+\sqrt {5}},x^6\right )}{5 \left (3+\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}}-\frac {4 x^5 \left (1-x^6\right )^{2/3} F_1\left (\frac {5}{6};\frac {2}{3},1;\frac {11}{6};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{5 \sqrt {5} \left (3-\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}}+\frac {\left (5-\sqrt {5}\right ) x^5 \left (1-x^6\right )^{2/3} F_1\left (\frac {5}{6};\frac {2}{3},1;\frac {11}{6};x^6,\frac {2 x^6}{3-\sqrt {5}}\right )}{25 \left (3-\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}}+\frac {4 x^5 \left (1-x^6\right )^{2/3} F_1\left (\frac {5}{6};\frac {2}{3},1;\frac {11}{6};x^6,\frac {2 x^6}{3+\sqrt {5}}\right )}{5 \sqrt {5} \left (3+\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}}+\frac {\left (5+\sqrt {5}\right ) x^5 \left (1-x^6\right )^{2/3} F_1\left (\frac {5}{6};\frac {2}{3},1;\frac {11}{6};x^6,\frac {2 x^6}{3+\sqrt {5}}\right )}{25 \left (3+\sqrt {5}\right ) \left (-1+x^6\right )^{2/3}}+\frac {x^2 \left (1-x^6\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};x^6\right )}{2 \left (-1+x^6\right )^{2/3}}\\ \end {align*}
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Mathematica [F] time = 0.16, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x+x^7}{\left (-1+x^6\right )^{2/3} \left (-1+x^3+x^6\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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IntegrateAlgebraic [A] time = 1.74, size = 79, normalized size = 1.00 \begin {gather*} -\frac {\tan ^{-1}\left (\frac {\sqrt {3} x}{-x+2 \sqrt [3]{-1+x^6}}\right )}{\sqrt {3}}+\frac {1}{3} \log \left (x+\sqrt [3]{-1+x^6}\right )-\frac {1}{6} \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 = 2.29, size = 102, normalized size = 1.29 \begin {gather*} -\frac {1}{3} \, \sqrt {3} \arctan \left (\frac {4 \, \sqrt {3} {\left (x^{6} - 1\right )}^{\frac {1}{3}} x^{2} + 2 \, \sqrt {3} {\left (x^{6} - 1\right )}^{\frac {2}{3}} x + \sqrt {3} {\left (x^{6} - 1\right )}}{x^{6} - 8 \, x^{3} - 1}\right ) + \frac {1}{6} \, \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 ) \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 {x^{7} + x}{{\left (x^{6} + x^{3} - 1\right )} {\left (x^{6} - 1\right )}^{\frac {2}{3}}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 1.42, size = 436, normalized size = 5.52
method | result | size |
trager | \(\RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \ln \left (-\frac {-6 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) x^{6}-x^{6}-18 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )^{2} x^{3}+9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x -9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}} x^{2}-3 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) x^{3}+3 x \left (x^{6}-1\right )^{\frac {2}{3}}-3 x^{2} \left (x^{6}-1\right )^{\frac {1}{3}}+6 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )+1}{x^{6}+x^{3}-1}\right )-\frac {\ln \left (\frac {-6 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) x^{6}-x^{6}+18 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )^{2} x^{3}+9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x -9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}} x^{2}+9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) x^{3}+x^{3}+6 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )+1}{x^{6}+x^{3}-1}\right )}{3}-\ln \left (\frac {-6 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) x^{6}-x^{6}+18 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )^{2} x^{3}+9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {2}{3}} x -9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}} x^{2}+9 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right ) x^{3}+x^{3}+6 \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )+1}{x^{6}+x^{3}-1}\right ) \RootOf \left (9 \textit {\_Z}^{2}+3 \textit {\_Z} +1\right )\) | \(436\) |
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 {x^{7} + x}{{\left (x^{6} + x^{3} - 1\right )} {\left (x^{6} - 1\right )}^{\frac {2}{3}}}\,{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 {x^7+x}{{\left (x^6-1\right )}^{2/3}\,\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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