Optimal. Leaf size=166 \[ \frac {4}{5} \text {RootSum}\left [\text {$\#$1}^4-2 \text {$\#$1}^3-4 \text {$\#$1}+4\& ,\frac {\text {$\#$1}^2 \log \left (-\text {$\#$1} x+\sqrt {x^4+1}+x^2+1\right )+\text {$\#$1}^2 (-\log (x))-\text {$\#$1} \log \left (-\text {$\#$1} x+\sqrt {x^4+1}+x^2+1\right )+2 \log \left (-\text {$\#$1} x+\sqrt {x^4+1}+x^2+1\right )+\text {$\#$1} \log (x)-2 \log (x)}{2 \text {$\#$1}^3-3 \text {$\#$1}^2-2}\& \right ]-\frac {1}{5} \sqrt {2} \tanh ^{-1}\left (\frac {\sqrt {2} x}{\sqrt {x^4+1}+x^2+2 x+1}\right ) \]
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Rubi [F] time = 0.90, 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 {-1+x^5}{\sqrt {1+x^4} \left (1+x^5\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {align*} \int \frac {-1+x^5}{\sqrt {1+x^4} \left (1+x^5\right )} \, dx &=\int \left (\frac {1}{\sqrt {1+x^4}}-\frac {2}{\sqrt {1+x^4} \left (1+x^5\right )}\right ) \, dx\\ &=-\left (2 \int \frac {1}{\sqrt {1+x^4} \left (1+x^5\right )} \, dx\right )+\int \frac {1}{\sqrt {1+x^4}} \, dx\\ &=\frac {\left (1+x^2\right ) \sqrt {\frac {1+x^4}{\left (1+x^2\right )^2}} F\left (2 \tan ^{-1}(x)|\frac {1}{2}\right )}{2 \sqrt {1+x^4}}-2 \int \left (\frac {1}{5 (1+x) \sqrt {1+x^4}}+\frac {4-3 x+2 x^2-x^3}{5 \sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )}\right ) \, dx\\ &=\frac {\left (1+x^2\right ) \sqrt {\frac {1+x^4}{\left (1+x^2\right )^2}} F\left (2 \tan ^{-1}(x)|\frac {1}{2}\right )}{2 \sqrt {1+x^4}}-\frac {2}{5} \int \frac {1}{(1+x) \sqrt {1+x^4}} \, dx-\frac {2}{5} \int \frac {4-3 x+2 x^2-x^3}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )} \, dx\\ &=\frac {\left (1+x^2\right ) \sqrt {\frac {1+x^4}{\left (1+x^2\right )^2}} F\left (2 \tan ^{-1}(x)|\frac {1}{2}\right )}{2 \sqrt {1+x^4}}-\frac {2}{5} \int \frac {1}{\left (1-x^2\right ) \sqrt {1+x^4}} \, dx+\frac {2}{5} \int \frac {x}{\left (1-x^2\right ) \sqrt {1+x^4}} \, dx-\frac {2}{5} \int \left (\frac {4}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )}-\frac {3 x}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )}+\frac {2 x^2}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )}-\frac {x^3}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )}\right ) \, dx\\ &=\frac {\left (1+x^2\right ) \sqrt {\frac {1+x^4}{\left (1+x^2\right )^2}} F\left (2 \tan ^{-1}(x)|\frac {1}{2}\right )}{2 \sqrt {1+x^4}}-\frac {1}{5} \int \frac {1}{\sqrt {1+x^4}} \, dx-\frac {1}{5} \int \frac {1+x^2}{\left (1-x^2\right ) \sqrt {1+x^4}} \, dx+\frac {1}{5} \operatorname {Subst}\left (\int \frac {1}{(1-x) \sqrt {1+x^2}} \, dx,x,x^2\right )+\frac {2}{5} \int \frac {x^3}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )} \, dx-\frac {4}{5} \int \frac {x^2}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )} \, dx+\frac {6}{5} \int \frac {x}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )} \, dx-\frac {8}{5} \int \frac {1}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )} \, dx\\ &=\frac {2 \left (1+x^2\right ) \sqrt {\frac {1+x^4}{\left (1+x^2\right )^2}} F\left (2 \tan ^{-1}(x)|\frac {1}{2}\right )}{5 \sqrt {1+x^4}}-\frac {1}{5} \operatorname {Subst}\left (\int \frac {1}{1-2 x^2} \, dx,x,\frac {x}{\sqrt {1+x^4}}\right )-\frac {1}{5} \operatorname {Subst}\left (\int \frac {1}{2-x^2} \, dx,x,\frac {-1-x^2}{\sqrt {1+x^4}}\right )+\frac {2}{5} \int \frac {x^3}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )} \, dx-\frac {4}{5} \int \frac {x^2}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )} \, dx+\frac {6}{5} \int \frac {x}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )} \, dx-\frac {8}{5} \int \frac {1}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )} \, dx\\ &=-\frac {\tanh ^{-1}\left (\frac {\sqrt {2} x}{\sqrt {1+x^4}}\right )}{5 \sqrt {2}}+\frac {\tanh ^{-1}\left (\frac {1+x^2}{\sqrt {2} \sqrt {1+x^4}}\right )}{5 \sqrt {2}}+\frac {2 \left (1+x^2\right ) \sqrt {\frac {1+x^4}{\left (1+x^2\right )^2}} F\left (2 \tan ^{-1}(x)|\frac {1}{2}\right )}{5 \sqrt {1+x^4}}+\frac {2}{5} \int \frac {x^3}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )} \, dx-\frac {4}{5} \int \frac {x^2}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )} \, dx+\frac {6}{5} \int \frac {x}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )} \, dx-\frac {8}{5} \int \frac {1}{\sqrt {1+x^4} \left (1-x+x^2-x^3+x^4\right )} \, dx\\ \end {align*}
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Mathematica [C] time = 8.04, size = 841, normalized size = 5.07 \begin {gather*} \frac {\left (3 \left (1-\sqrt [5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right ) x^8-12 \left (1-\sqrt [5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right ) x^6+\left (16-17 \sqrt [5]{-1}+18 (-1)^{2/5}-19 (-1)^{3/5}+20 (-1)^{4/5}\right ) x^4-12 \left (1-\sqrt [5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right ) x^2+3 \left (1-\sqrt [5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right )\right ) \left (\frac {\sqrt {2} \tanh ^{-1}\left (\frac {x^2+1}{\sqrt {2} \sqrt {x^4+1}}\right )}{-4-\sqrt [5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}+2 \left (\frac {(-1)^{4/5} \tanh ^{-1}\left (\frac {1-\sqrt [5]{-1} x^2}{\sqrt {1+(-1)^{2/5}} \sqrt {x^4+1}}\right )}{\sqrt {1+(-1)^{2/5}} \left (1+4 \sqrt [5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right )}-\frac {(-1)^{2/5} \tanh ^{-1}\left (\frac {(-1)^{2/5} x^2+1}{\sqrt {1+(-1)^{4/5}} \sqrt {x^4+1}}\right )}{\left (1+\sqrt [5]{-1}\right )^4 \left (1+(-1)^{4/5}\right )^{5/2}}+\frac {\tanh ^{-1}\left (\frac {1-(-1)^{3/5} x^2}{\sqrt {1-\sqrt [5]{-1}} \sqrt {x^4+1}}\right )}{\left (1-\sqrt [5]{-1}\right )^{3/2} \left (1+\sqrt [5]{-1}\right )^4 \left (1-\sqrt [5]{-1}+(-1)^{2/5}\right )}+\frac {(-1)^{2/5} \tanh ^{-1}\left (\frac {(-1)^{4/5} x^2+1}{\sqrt {1-(-1)^{3/5}} \sqrt {x^4+1}}\right )}{\sqrt {1-(-1)^{3/5}} \left (-4-\sqrt [5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right )}\right )\right )}{2 \left (-1+\sqrt [5]{-1}\right )^2 \left (1+\sqrt [5]{-1}\right )^3 \left (1+(-1)^{2/5}\right ) \left (1-\sqrt [5]{-1}+(-1)^{2/5}\right ) x^4}-\sqrt [4]{-1} F\left (\left .i \sinh ^{-1}\left (\sqrt [4]{-1} x\right )\right |-1\right )+\frac {2 \sqrt [4]{-1} \Pi \left (i;\left .\sin ^{-1}\left ((-1)^{3/4} x\right )\right |-1\right )}{4+\sqrt [5]{-1}-(-1)^{2/5}+(-1)^{3/5}-(-1)^{4/5}}-\frac {2 (-1)^{17/20} \Pi \left (\sqrt [10]{-1};\left .i \sinh ^{-1}\left (\sqrt [4]{-1} x\right )\right |-1\right )}{\left (-1+\sqrt [5]{-1}\right )^2 \left (1+\sqrt [5]{-1}\right )^4}+\frac {2 (-1)^{9/20} \Pi \left (-(-1)^{3/10};\left .i \sinh ^{-1}\left (\sqrt [4]{-1} x\right )\right |-1\right )}{1+4 \sqrt [5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}+\frac {2 \sqrt [4]{-1} \Pi \left (-(-1)^{7/10};\left .i \sinh ^{-1}\left (\sqrt [4]{-1} x\right )\right |-1\right )}{4+\sqrt [5]{-1}-(-1)^{2/5}+(-1)^{3/5}-(-1)^{4/5}}+\frac {2 (-1)^{9/20} \Pi \left ((-1)^{9/10};\left .i \sinh ^{-1}\left (\sqrt [4]{-1} x\right )\right |-1\right )}{1+4 \sqrt [5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}} \end {gather*}
Warning: Unable to verify antiderivative.
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IntegrateAlgebraic [A] time = 0.00, size = 166, normalized size = 1.00 \begin {gather*} -\frac {1}{5} \sqrt {2} \tanh ^{-1}\left (\frac {\sqrt {2} x}{1+2 x+x^2+\sqrt {1+x^4}}\right )+\frac {4}{5} \text {RootSum}\left [4-4 \text {$\#$1}-2 \text {$\#$1}^3+\text {$\#$1}^4\&,\frac {-2 \log (x)+2 \log \left (1+x^2+\sqrt {1+x^4}-x \text {$\#$1}\right )+\log (x) \text {$\#$1}-\log \left (1+x^2+\sqrt {1+x^4}-x \text {$\#$1}\right ) \text {$\#$1}-\log (x) \text {$\#$1}^2+\log \left (1+x^2+\sqrt {1+x^4}-x \text {$\#$1}\right ) \text {$\#$1}^2}{-2-3 \text {$\#$1}^2+2 \text {$\#$1}^3}\&\right ] \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.79, size = 454, normalized size = 2.73 \begin {gather*} -\frac {2}{5} \, \sqrt {2} \sqrt {\sqrt {5} - 1} \arctan \left (-\frac {\sqrt {2} \sqrt {x^{4} + 1} {\left (3 \, x^{2} + \sqrt {5} {\left (x^{2} - 2 \, x + 1\right )} - 2 \, x + 3\right )} \sqrt {\sqrt {5} - 1} + \sqrt {2} {\left (3 \, x^{4} + 4 \, x^{3} - 8 \, x^{2} - \sqrt {5} {\left (x^{4} + 2 \, x^{3} - 4 \, x^{2} + 2 \, x + 1\right )} + 4 \, x + 3\right )} \sqrt {13 \, \sqrt {5} + 29} \sqrt {\sqrt {5} - 1}}{4 \, {\left (x^{4} + 2 \, x^{3} - 2 \, x^{2} + 2 \, x + 1\right )}}\right ) + \frac {1}{10} \, \sqrt {2} \sqrt {\sqrt {5} + 1} \log \left (-\frac {2 \, {\left (\sqrt {2} {\left (4 \, x^{4} + 7 \, x^{3} - 14 \, x^{2} - \sqrt {5} {\left (2 \, x^{4} + 3 \, x^{3} - 6 \, x^{2} + 3 \, x + 2\right )} + 7 \, x + 4\right )} \sqrt {\sqrt {5} + 1} + 2 \, \sqrt {x^{4} + 1} {\left (7 \, x^{2} - \sqrt {5} {\left (3 \, x^{2} - 5 \, x + 3\right )} - 11 \, x + 7\right )}\right )}}{x^{4} - x^{3} + x^{2} - x + 1}\right ) - \frac {1}{10} \, \sqrt {2} \sqrt {\sqrt {5} + 1} \log \left (\frac {2 \, {\left (\sqrt {2} {\left (4 \, x^{4} + 7 \, x^{3} - 14 \, x^{2} - \sqrt {5} {\left (2 \, x^{4} + 3 \, x^{3} - 6 \, x^{2} + 3 \, x + 2\right )} + 7 \, x + 4\right )} \sqrt {\sqrt {5} + 1} - 2 \, \sqrt {x^{4} + 1} {\left (7 \, x^{2} - \sqrt {5} {\left (3 \, x^{2} - 5 \, x + 3\right )} - 11 \, x + 7\right )}\right )}}{x^{4} - x^{3} + x^{2} - x + 1}\right ) + \frac {1}{20} \, \sqrt {2} \log \left (-\frac {3 \, x^{4} + 4 \, x^{3} + 2 \, \sqrt {2} \sqrt {x^{4} + 1} {\left (x^{2} + x + 1\right )} + 6 \, x^{2} + 4 \, x + 3}{x^{4} + 4 \, x^{3} + 6 \, x^{2} + 4 \, x + 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^{5} - 1}{{\left (x^{5} + 1\right )} \sqrt {x^{4} + 1}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 2.70, size = 206, normalized size = 1.24
method | result | size |
elliptic | \(\frac {\sqrt {2}\, \arctanh \left (\frac {\left (2 x^{2}+2\right ) \sqrt {2}}{4 \sqrt {\left (x^{2}-1\right )^{2}+2 x^{2}}}\right )}{10}+\frac {\left (\munderset {\textit {\_R} =\RootOf \left (\textit {\_Z}^{4}-\textit {\_Z}^{2}-1\right )}{\sum }\textit {\_R} \ln \left (\left (-x^{2}+\sqrt {x^{4}+1}\right )^{2}+\left (\textit {\_R}^{2}-\textit {\_R} -1\right ) \left (-x^{2}+\sqrt {x^{4}+1}\right )+\textit {\_R}^{2}-\textit {\_R} \right )\right )}{5}+\frac {\left (\frac {\ln \left (-1+\frac {\sqrt {2}\, \sqrt {x^{4}+1}}{2 x}\right )}{10}-\frac {\ln \left (1+\frac {\sqrt {2}\, \sqrt {x^{4}+1}}{2 x}\right )}{10}+\frac {4 \arctan \left (\frac {\sqrt {2}\, \sqrt {x^{4}+1}}{x \sqrt {\sqrt {5}+1}}\right )}{5 \sqrt {\sqrt {5}+1}}-\frac {4 \arctanh \left (\frac {\sqrt {2}\, \sqrt {x^{4}+1}}{x \sqrt {\sqrt {5}-1}}\right )}{5 \sqrt {\sqrt {5}-1}}\right ) \sqrt {2}}{2}\) | \(206\) |
default | \(\frac {\sqrt {-i x^{2}+1}\, \sqrt {i x^{2}+1}\, \EllipticF \left (x \left (\frac {\sqrt {2}}{2}+\frac {i \sqrt {2}}{2}\right ), i\right )}{\left (\frac {\sqrt {2}}{2}+\frac {i \sqrt {2}}{2}\right ) \sqrt {x^{4}+1}}+\frac {\sqrt {2}\, \arctanh \left (\frac {\left (2 x^{2}+2\right ) \sqrt {2}}{4 \sqrt {x^{4}+1}}\right )}{10}+\frac {2 \left (-1\right )^{\frac {3}{4}} \sqrt {-i x^{2}+1}\, \sqrt {i x^{2}+1}\, \EllipticPi \left (\left (-1\right )^{\frac {1}{4}} x , -i, -\sqrt {-i}\, \left (-1\right )^{\frac {3}{4}}\right )}{5 \sqrt {x^{4}+1}}+\frac {\left (\munderset {\underline {\hspace {1.25 ex}}\alpha =\RootOf \left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+\textit {\_Z}^{2}-\textit {\_Z} +1\right )}{\sum }\underline {\hspace {1.25 ex}}\alpha \left (-\frac {\arctanh \left (\frac {\underline {\hspace {1.25 ex}}\alpha ^{2} \left (-\underline {\hspace {1.25 ex}}\alpha ^{3}+x^{2}\right )}{\sqrt {\underline {\hspace {1.25 ex}}\alpha ^{3}-\underline {\hspace {1.25 ex}}\alpha ^{2}+\underline {\hspace {1.25 ex}}\alpha }\, \sqrt {x^{4}+1}}\right )}{\sqrt {\underline {\hspace {1.25 ex}}\alpha ^{3}-\underline {\hspace {1.25 ex}}\alpha ^{2}+\underline {\hspace {1.25 ex}}\alpha }}+\frac {2 \left (-1\right )^{\frac {3}{4}} \left (-\underline {\hspace {1.25 ex}}\alpha ^{3}+\underline {\hspace {1.25 ex}}\alpha ^{2}-\underline {\hspace {1.25 ex}}\alpha +1\right ) \sqrt {-i x^{2}+1}\, \sqrt {i x^{2}+1}\, \EllipticPi \left (\left (-1\right )^{\frac {1}{4}} x , i \underline {\hspace {1.25 ex}}\alpha ^{3}, i\right )}{\sqrt {x^{4}+1}}\right )\right )}{5}\) | \(267\) |
trager | \(\frac {\RootOf \left (\textit {\_Z}^{2}-2\right ) \ln \left (-\frac {\RootOf \left (\textit {\_Z}^{2}-2\right ) x^{2}+\RootOf \left (\textit {\_Z}^{2}-2\right ) x +\RootOf \left (\textit {\_Z}^{2}-2\right )+\sqrt {x^{4}+1}}{\left (1+x \right )^{2}}\right )}{10}+\frac {\RootOf \left (\textit {\_Z}^{2}+25 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2}-4\right ) \ln \left (-\frac {625 \RootOf \left (\textit {\_Z}^{2}+25 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2}-4\right ) \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{4} x +50 \RootOf \left (\textit {\_Z}^{2}+25 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2}-4\right ) \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2} x^{2}+50 \RootOf \left (\textit {\_Z}^{2}+25 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2}-4\right ) \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2} x +50 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2} \RootOf \left (\textit {\_Z}^{2}+25 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2}-4\right )+4 \RootOf \left (\textit {\_Z}^{2}+25 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2}-4\right ) x^{2}+150 \sqrt {x^{4}+1}\, \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2}+4 \RootOf \left (\textit {\_Z}^{2}+25 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2}-4\right )+16 \sqrt {x^{4}+1}}{4 x^{2}+25 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2} x -4 x +4}\right )}{5}+\RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right ) \ln \left (-\frac {625 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{5} x -50 x^{2} \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{3}-250 x \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{3}-50 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{3}-30 \sqrt {x^{4}+1}\, \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2}+12 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right ) x^{2}+24 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right ) x +12 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )+8 \sqrt {x^{4}+1}}{25 \RootOf \left (625 \textit {\_Z}^{4}-100 \textit {\_Z}^{2}-16\right )^{2} x -4 x^{2}-4}\right )\) | \(560\) |
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^{5} - 1}{{\left (x^{5} + 1\right )} \sqrt {x^{4} + 1}}\,{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^5-1}{\sqrt {x^4+1}\,\left (x^5+1\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (x - 1\right ) \left (x^{4} + x^{3} + x^{2} + x + 1\right )}{\left (x + 1\right ) \sqrt {x^{4} + 1} \left (x^{4} - x^{3} + x^{2} - x + 1\right )}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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