Optimal. Leaf size=173 \[ \frac {\sqrt [4]{-1-2 x^4+2 x^8} \left (5+2 x^4+9 x^8-4 x^{12}+20 x^{16}\right )}{45 x^9}-\frac {\text {ArcTan}\left (\frac {2^{3/4} x \sqrt [4]{-1-2 x^4+2 x^8}}{\sqrt {2} x^2-\sqrt {-1-2 x^4+2 x^8}}\right )}{2 \sqrt [4]{2}}-\frac {\tanh ^{-1}\left (\frac {2 \sqrt [4]{2} x \sqrt [4]{-1-2 x^4+2 x^8}}{2 x^2+\sqrt {2} \sqrt {-1-2 x^4+2 x^8}}\right )}{2 \sqrt [4]{2}} \]
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Rubi [F]
time = 2.03, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {\left (1+2 x^8\right ) \sqrt [4]{-1-2 x^4+2 x^8} \left (1-3 x^8+4 x^{16}\right )}{x^{10} \left (-1+2 x^8\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (1+2 x^8\right ) \sqrt [4]{-1-2 x^4+2 x^8} \left (1-3 x^8+4 x^{16}\right )}{x^{10} \left (-1+2 x^8\right )} \, dx &=\int \left (-\frac {\sqrt [4]{-1-2 x^4+2 x^8}}{x^{10}}-\frac {\sqrt [4]{-1-2 x^4+2 x^8}}{x^2}+4 x^6 \sqrt [4]{-1-2 x^4+2 x^8}+\frac {4 x^6 \sqrt [4]{-1-2 x^4+2 x^8}}{-1+2 x^8}\right ) \, dx\\ &=4 \int x^6 \sqrt [4]{-1-2 x^4+2 x^8} \, dx+4 \int \frac {x^6 \sqrt [4]{-1-2 x^4+2 x^8}}{-1+2 x^8} \, dx-\int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{x^{10}} \, dx-\int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{x^2} \, dx\\ &=4 \int \left (\frac {x^2 \sqrt [4]{-1-2 x^4+2 x^8}}{2 \left (-\sqrt {2}+2 x^4\right )}+\frac {x^2 \sqrt [4]{-1-2 x^4+2 x^8}}{2 \left (\sqrt {2}+2 x^4\right )}\right ) \, dx-\frac {\sqrt [4]{-1-2 x^4+2 x^8} \int \frac {\sqrt [4]{1+\frac {4 x^4}{-2-2 \sqrt {3}}} \sqrt [4]{1+\frac {4 x^4}{-2+2 \sqrt {3}}}}{x^{10}} \, dx}{\sqrt [4]{1+\frac {4 x^4}{-2-2 \sqrt {3}}} \sqrt [4]{1+\frac {4 x^4}{-2+2 \sqrt {3}}}}-\frac {\sqrt [4]{-1-2 x^4+2 x^8} \int \frac {\sqrt [4]{1+\frac {4 x^4}{-2-2 \sqrt {3}}} \sqrt [4]{1+\frac {4 x^4}{-2+2 \sqrt {3}}}}{x^2} \, dx}{\sqrt [4]{1+\frac {4 x^4}{-2-2 \sqrt {3}}} \sqrt [4]{1+\frac {4 x^4}{-2+2 \sqrt {3}}}}+\frac {\left (4 \sqrt [4]{-1-2 x^4+2 x^8}\right ) \int x^6 \sqrt [4]{1+\frac {4 x^4}{-2-2 \sqrt {3}}} \sqrt [4]{1+\frac {4 x^4}{-2+2 \sqrt {3}}} \, dx}{\sqrt [4]{1+\frac {4 x^4}{-2-2 \sqrt {3}}} \sqrt [4]{1+\frac {4 x^4}{-2+2 \sqrt {3}}}}\\ &=\frac {\sqrt [4]{-1-2 x^4+2 x^8} F_1\left (-\frac {9}{4};-\frac {1}{4},-\frac {1}{4};-\frac {5}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{9 x^9 \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+\frac {\sqrt [4]{-1-2 x^4+2 x^8} F_1\left (-\frac {1}{4};-\frac {1}{4},-\frac {1}{4};\frac {3}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{x \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+\frac {4 x^7 \sqrt [4]{-1-2 x^4+2 x^8} F_1\left (\frac {7}{4};-\frac {1}{4},-\frac {1}{4};\frac {11}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{7 \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+2 \int \frac {x^2 \sqrt [4]{-1-2 x^4+2 x^8}}{-\sqrt {2}+2 x^4} \, dx+2 \int \frac {x^2 \sqrt [4]{-1-2 x^4+2 x^8}}{\sqrt {2}+2 x^4} \, dx\\ &=\frac {\sqrt [4]{-1-2 x^4+2 x^8} F_1\left (-\frac {9}{4};-\frac {1}{4},-\frac {1}{4};-\frac {5}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{9 x^9 \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+\frac {\sqrt [4]{-1-2 x^4+2 x^8} F_1\left (-\frac {1}{4};-\frac {1}{4},-\frac {1}{4};\frac {3}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{x \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+\frac {4 x^7 \sqrt [4]{-1-2 x^4+2 x^8} F_1\left (\frac {7}{4};-\frac {1}{4},-\frac {1}{4};\frac {11}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{7 \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+2 \int \left (-\frac {\sqrt [4]{-1-2 x^4+2 x^8}}{2\ 2^{3/4} \left (i-\sqrt [4]{2} x^2\right )}+\frac {\sqrt [4]{-1-2 x^4+2 x^8}}{2\ 2^{3/4} \left (i+\sqrt [4]{2} x^2\right )}\right ) \, dx+2 \int \left (-\frac {\sqrt [4]{-1-2 x^4+2 x^8}}{2\ 2^{3/4} \left (1-\sqrt [4]{2} x^2\right )}+\frac {\sqrt [4]{-1-2 x^4+2 x^8}}{2\ 2^{3/4} \left (1+\sqrt [4]{2} x^2\right )}\right ) \, dx\\ &=\frac {\sqrt [4]{-1-2 x^4+2 x^8} F_1\left (-\frac {9}{4};-\frac {1}{4},-\frac {1}{4};-\frac {5}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{9 x^9 \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+\frac {\sqrt [4]{-1-2 x^4+2 x^8} F_1\left (-\frac {1}{4};-\frac {1}{4},-\frac {1}{4};\frac {3}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{x \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+\frac {4 x^7 \sqrt [4]{-1-2 x^4+2 x^8} F_1\left (\frac {7}{4};-\frac {1}{4},-\frac {1}{4};\frac {11}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{7 \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}-\frac {\int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{i-\sqrt [4]{2} x^2} \, dx}{2^{3/4}}-\frac {\int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{1-\sqrt [4]{2} x^2} \, dx}{2^{3/4}}+\frac {\int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{i+\sqrt [4]{2} x^2} \, dx}{2^{3/4}}+\frac {\int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{1+\sqrt [4]{2} x^2} \, dx}{2^{3/4}}\\ &=\frac {\sqrt [4]{-1-2 x^4+2 x^8} F_1\left (-\frac {9}{4};-\frac {1}{4},-\frac {1}{4};-\frac {5}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{9 x^9 \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+\frac {\sqrt [4]{-1-2 x^4+2 x^8} F_1\left (-\frac {1}{4};-\frac {1}{4},-\frac {1}{4};\frac {3}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{x \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+\frac {4 x^7 \sqrt [4]{-1-2 x^4+2 x^8} F_1\left (\frac {7}{4};-\frac {1}{4},-\frac {1}{4};\frac {11}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{7 \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+\frac {\int \left (\frac {i \sqrt [4]{-1-2 x^4+2 x^8}}{2 \left (i-\sqrt [8]{2} x\right )}+\frac {i \sqrt [4]{-1-2 x^4+2 x^8}}{2 \left (i+\sqrt [8]{2} x\right )}\right ) \, dx}{2^{3/4}}-\frac {\int \left (\frac {\sqrt [4]{-1-2 x^4+2 x^8}}{2 \left (1-\sqrt [8]{2} x\right )}+\frac {\sqrt [4]{-1-2 x^4+2 x^8}}{2 \left (1+\sqrt [8]{2} x\right )}\right ) \, dx}{2^{3/4}}-\frac {\int \left (-\frac {(-1)^{3/4} \sqrt [4]{-1-2 x^4+2 x^8}}{2 \left (\sqrt [4]{-1}-\sqrt [8]{2} x\right )}-\frac {(-1)^{3/4} \sqrt [4]{-1-2 x^4+2 x^8}}{2 \left (\sqrt [4]{-1}+\sqrt [8]{2} x\right )}\right ) \, dx}{2^{3/4}}+\frac {\int \left (-\frac {\sqrt [4]{-1} \sqrt [4]{-1-2 x^4+2 x^8}}{2 \left (-(-1)^{3/4}-\sqrt [8]{2} x\right )}-\frac {\sqrt [4]{-1} \sqrt [4]{-1-2 x^4+2 x^8}}{2 \left (-(-1)^{3/4}+\sqrt [8]{2} x\right )}\right ) \, dx}{2^{3/4}}\\ &=\frac {\sqrt [4]{-1-2 x^4+2 x^8} F_1\left (-\frac {9}{4};-\frac {1}{4},-\frac {1}{4};-\frac {5}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{9 x^9 \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+\frac {\sqrt [4]{-1-2 x^4+2 x^8} F_1\left (-\frac {1}{4};-\frac {1}{4},-\frac {1}{4};\frac {3}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{x \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+\frac {4 x^7 \sqrt [4]{-1-2 x^4+2 x^8} F_1\left (\frac {7}{4};-\frac {1}{4},-\frac {1}{4};\frac {11}{4};\frac {2 x^4}{1+\sqrt {3}},\frac {2 x^4}{1-\sqrt {3}}\right )}{7 \sqrt [4]{1-\frac {2 x^4}{1-\sqrt {3}}} \sqrt [4]{1-\frac {2 x^4}{1+\sqrt {3}}}}+\frac {i \int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{i-\sqrt [8]{2} x} \, dx}{2\ 2^{3/4}}+\frac {i \int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{i+\sqrt [8]{2} x} \, dx}{2\ 2^{3/4}}-\frac {\int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{1-\sqrt [8]{2} x} \, dx}{2\ 2^{3/4}}-\frac {\int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{1+\sqrt [8]{2} x} \, dx}{2\ 2^{3/4}}-\frac {\sqrt [4]{-1} \int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{-(-1)^{3/4}-\sqrt [8]{2} x} \, dx}{2\ 2^{3/4}}-\frac {\sqrt [4]{-1} \int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{-(-1)^{3/4}+\sqrt [8]{2} x} \, dx}{2\ 2^{3/4}}+-\frac {\left (\frac {1}{4}-\frac {i}{4}\right ) \int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{\sqrt [4]{-1}-\sqrt [8]{2} x} \, dx}{\sqrt [4]{2}}+-\frac {\left (\frac {1}{4}-\frac {i}{4}\right ) \int \frac {\sqrt [4]{-1-2 x^4+2 x^8}}{\sqrt [4]{-1}+\sqrt [8]{2} x} \, dx}{\sqrt [4]{2}}\\ \end {align*}
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Mathematica [A]
time = 1.56, size = 160, normalized size = 0.92 \begin {gather*} \frac {1}{180} \left (\frac {4 \sqrt [4]{-1-2 x^4+2 x^8} \left (5+2 x^4+9 x^8-4 x^{12}+20 x^{16}\right )}{x^9}-45\ 2^{3/4} \text {ArcTan}\left (\frac {2^{3/4} x \sqrt [4]{-1-2 x^4+2 x^8}}{\sqrt {2} x^2-\sqrt {-1-2 x^4+2 x^8}}\right )-45\ 2^{3/4} \tanh ^{-1}\left (\frac {2 x \sqrt [4]{-2-4 x^4+4 x^8}}{2 x^2+\sqrt {-2-4 x^4+4 x^8}}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 131.49, size = 347, normalized size = 2.01
method | result | size |
trager | \(\frac {\left (2 x^{8}-2 x^{4}-1\right )^{\frac {1}{4}} \left (20 x^{16}-4 x^{12}+9 x^{8}+2 x^{4}+5\right )}{45 x^{9}}+\frac {\RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}+2\right )^{2}\right ) \ln \left (-\frac {-2 \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}+2\right )^{2}\right ) \RootOf \left (\textit {\_Z}^{4}+2\right )^{2} x^{8}+4 \RootOf \left (\textit {\_Z}^{4}+2\right )^{2} \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}+2\right )^{2}\right ) x^{4}-4 \left (2 x^{8}-2 x^{4}-1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{4}+2\right )^{2} x^{3}-4 \sqrt {2 x^{8}-2 x^{4}-1}\, \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}+2\right )^{2}\right ) x^{2}+4 \left (2 x^{8}-2 x^{4}-1\right )^{\frac {3}{4}} x +\RootOf \left (\textit {\_Z}^{4}+2\right )^{2} \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}+2\right )^{2}\right )}{2 x^{8}-1}\right )}{4}+\frac {\RootOf \left (\textit {\_Z}^{4}+2\right ) \ln \left (-\frac {2 \RootOf \left (\textit {\_Z}^{4}+2\right )^{3} x^{8}-4 \RootOf \left (\textit {\_Z}^{4}+2\right )^{3} x^{4}+4 \left (2 x^{8}-2 x^{4}-1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{4}+2\right )^{2} x^{3}-4 \sqrt {2 x^{8}-2 x^{4}-1}\, \RootOf \left (\textit {\_Z}^{4}+2\right ) x^{2}+4 \left (2 x^{8}-2 x^{4}-1\right )^{\frac {3}{4}} x -\RootOf \left (\textit {\_Z}^{4}+2\right )^{3}}{2 x^{8}-1}\right )}{4}\) | \(347\) |
risch | \(\text {Expression too large to display}\) | \(1127\) |
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*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 982 vs.
\(2 (145) = 290\).
time = 88.62, size = 982, normalized size = 5.68 \begin {gather*} -\frac {180 \cdot 8^{\frac {3}{4}} \sqrt {2} x^{9} \arctan \left (-\frac {32 \, x^{16} - 32 \, x^{8} + 4 \cdot 8^{\frac {3}{4}} \sqrt {2} {\left (2 \, x^{9} - 8 \, x^{5} - x\right )} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {3}{4}} + 16 \cdot 8^{\frac {1}{4}} \sqrt {2} {\left (6 \, x^{11} - 8 \, x^{7} - 3 \, x^{3}\right )} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {1}{4}} + 32 \, \sqrt {2} {\left (2 \, x^{10} - x^{2}\right )} \sqrt {2 \, x^{8} - 2 \, x^{4} - 1} - \sqrt {2} {\left (128 \, \sqrt {2} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {3}{4}} x^{5} + 8^{\frac {3}{4}} \sqrt {2} {\left (4 \, x^{16} - 40 \, x^{12} + 28 \, x^{8} + 20 \, x^{4} + 1\right )} + 8 \cdot 8^{\frac {1}{4}} \sqrt {2} {\left (2 \, x^{10} - 8 \, x^{6} - x^{2}\right )} \sqrt {2 \, x^{8} - 2 \, x^{4} - 1} + 32 \, {\left (2 \, x^{11} - x^{3}\right )} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {1}{4}}\right )} \sqrt {\frac {8^{\frac {3}{4}} \sqrt {2} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {1}{4}} x^{3} + 2 \cdot 8^{\frac {1}{4}} \sqrt {2} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {3}{4}} x + 8 \, \sqrt {2 \, x^{8} - 2 \, x^{4} - 1} x^{2} + \sqrt {2} {\left (2 \, x^{8} - 1\right )}}{2 \, x^{8} - 1}} + 8}{8 \, {\left (4 \, x^{16} - 64 \, x^{12} + 60 \, x^{8} + 32 \, x^{4} + 1\right )}}\right ) - 180 \cdot 8^{\frac {3}{4}} \sqrt {2} x^{9} \arctan \left (-\frac {32 \, x^{16} - 32 \, x^{8} - 4 \cdot 8^{\frac {3}{4}} \sqrt {2} {\left (2 \, x^{9} - 8 \, x^{5} - x\right )} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {3}{4}} - 16 \cdot 8^{\frac {1}{4}} \sqrt {2} {\left (6 \, x^{11} - 8 \, x^{7} - 3 \, x^{3}\right )} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {1}{4}} + 32 \, \sqrt {2} {\left (2 \, x^{10} - x^{2}\right )} \sqrt {2 \, x^{8} - 2 \, x^{4} - 1} - \sqrt {2} {\left (128 \, \sqrt {2} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {3}{4}} x^{5} - 8^{\frac {3}{4}} \sqrt {2} {\left (4 \, x^{16} - 40 \, x^{12} + 28 \, x^{8} + 20 \, x^{4} + 1\right )} - 8 \cdot 8^{\frac {1}{4}} \sqrt {2} {\left (2 \, x^{10} - 8 \, x^{6} - x^{2}\right )} \sqrt {2 \, x^{8} - 2 \, x^{4} - 1} + 32 \, {\left (2 \, x^{11} - x^{3}\right )} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {1}{4}}\right )} \sqrt {-\frac {8^{\frac {3}{4}} \sqrt {2} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {1}{4}} x^{3} + 2 \cdot 8^{\frac {1}{4}} \sqrt {2} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {3}{4}} x - 8 \, \sqrt {2 \, x^{8} - 2 \, x^{4} - 1} x^{2} - \sqrt {2} {\left (2 \, x^{8} - 1\right )}}{2 \, x^{8} - 1}} + 8}{8 \, {\left (4 \, x^{16} - 64 \, x^{12} + 60 \, x^{8} + 32 \, x^{4} + 1\right )}}\right ) + 45 \cdot 8^{\frac {3}{4}} \sqrt {2} x^{9} \log \left (\frac {8 \, {\left (8^{\frac {3}{4}} \sqrt {2} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {1}{4}} x^{3} + 2 \cdot 8^{\frac {1}{4}} \sqrt {2} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {3}{4}} x + 8 \, \sqrt {2 \, x^{8} - 2 \, x^{4} - 1} x^{2} + \sqrt {2} {\left (2 \, x^{8} - 1\right )}\right )}}{2 \, x^{8} - 1}\right ) - 45 \cdot 8^{\frac {3}{4}} \sqrt {2} x^{9} \log \left (-\frac {8 \, {\left (8^{\frac {3}{4}} \sqrt {2} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {1}{4}} x^{3} + 2 \cdot 8^{\frac {1}{4}} \sqrt {2} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {3}{4}} x - 8 \, \sqrt {2 \, x^{8} - 2 \, x^{4} - 1} x^{2} - \sqrt {2} {\left (2 \, x^{8} - 1\right )}\right )}}{2 \, x^{8} - 1}\right ) - 64 \, {\left (20 \, x^{16} - 4 \, x^{12} + 9 \, x^{8} + 2 \, x^{4} + 5\right )} {\left (2 \, x^{8} - 2 \, x^{4} - 1\right )}^{\frac {1}{4}}}{2880 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
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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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \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 (2\,x^8+1\right )\,{\left (2\,x^8-2\,x^4-1\right )}^{1/4}\,\left (4\,x^{16}-3\,x^8+1\right )}{x^{10}\,\left (2\,x^8-1\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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