Optimal. Leaf size=113 \[ -\frac {1}{4} \text {RootSum}\left [3-3 \text {$\#$1}^4+\text {$\#$1}^8\& ,\frac {-\log (x)+\log \left (\sqrt [4]{x^2+x^4}-x \text {$\#$1}\right )}{-3 \text {$\#$1}+2 \text {$\#$1}^5}\& \right ]+\frac {1}{4} \text {RootSum}\left [1-\text {$\#$1}^4+\text {$\#$1}^8\& ,\frac {-\log (x)+\log \left (\sqrt [4]{x^2+x^4}-x \text {$\#$1}\right )}{-\text {$\#$1}+2 \text {$\#$1}^5}\& \right ] \]
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Rubi [C] Result contains complex when optimal does not.
time = 1.62, antiderivative size = 1033, normalized size of antiderivative = 9.14, number of steps
used = 33, number of rules used = 12, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.480, Rules used = {2081, 6860,
1284, 1531, 246, 218, 212, 209, 1443, 385, 214, 211} \begin {gather*} -\frac {i \left (-2+\sqrt {-2-2 i \sqrt {3}}\right )^{3/4} \sqrt {x} \sqrt [4]{x^2+1} \text {ArcTan}\left (\frac {\sqrt [4]{-2+\sqrt {-2-2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1-i \sqrt {3}\right )} \sqrt [4]{x^2+1}}\right )}{\sqrt {3} \left (2 \left (-1-i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{x^4+x^2}}-\frac {\left (3-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{x^2+1} \text {ArcTan}\left (\frac {\sqrt [4]{2+\sqrt {-2-2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1-i \sqrt {3}\right )} \sqrt [4]{x^2+1}}\right )}{3 \left (2 \left (-1-i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{2+\sqrt {-2-2 i \sqrt {3}}} \sqrt [4]{x^4+x^2}}+\frac {i \left (-2+\sqrt {-2+2 i \sqrt {3}}\right )^{3/4} \sqrt {x} \sqrt [4]{x^2+1} \text {ArcTan}\left (\frac {\sqrt [4]{-2+\sqrt {-2+2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1+i \sqrt {3}\right )} \sqrt [4]{x^2+1}}\right )}{\sqrt {3} \left (2 \left (-1+i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{x^4+x^2}}-\frac {\left (3+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{x^2+1} \text {ArcTan}\left (\frac {\sqrt [4]{2+\sqrt {-2+2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1+i \sqrt {3}\right )} \sqrt [4]{x^2+1}}\right )}{3 \left (2 \left (-1+i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{2+\sqrt {-2+2 i \sqrt {3}}} \sqrt [4]{x^4+x^2}}-\frac {i \left (-2+\sqrt {-2-2 i \sqrt {3}}\right )^{3/4} \sqrt {x} \sqrt [4]{x^2+1} \tanh ^{-1}\left (\frac {\sqrt [4]{-2+\sqrt {-2-2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1-i \sqrt {3}\right )} \sqrt [4]{x^2+1}}\right )}{\sqrt {3} \left (2 \left (-1-i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{x^4+x^2}}-\frac {\left (3-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{x^2+1} \tanh ^{-1}\left (\frac {\sqrt [4]{2+\sqrt {-2-2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1-i \sqrt {3}\right )} \sqrt [4]{x^2+1}}\right )}{3 \left (2 \left (-1-i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{2+\sqrt {-2-2 i \sqrt {3}}} \sqrt [4]{x^4+x^2}}+\frac {i \left (-2+\sqrt {-2+2 i \sqrt {3}}\right )^{3/4} \sqrt {x} \sqrt [4]{x^2+1} \tanh ^{-1}\left (\frac {\sqrt [4]{-2+\sqrt {-2+2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1+i \sqrt {3}\right )} \sqrt [4]{x^2+1}}\right )}{\sqrt {3} \left (2 \left (-1+i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{x^4+x^2}}-\frac {\left (3+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{x^2+1} \tanh ^{-1}\left (\frac {\sqrt [4]{2+\sqrt {-2+2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1+i \sqrt {3}\right )} \sqrt [4]{x^2+1}}\right )}{3 \left (2 \left (-1+i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{2+\sqrt {-2+2 i \sqrt {3}}} \sqrt [4]{x^4+x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 209
Rule 211
Rule 212
Rule 214
Rule 218
Rule 246
Rule 385
Rule 1284
Rule 1443
Rule 1531
Rule 2081
Rule 6860
Rubi steps
\begin {align*} \int \frac {x^4}{\sqrt [4]{x^2+x^4} \left (1+x^4+x^8\right )} \, dx &=\frac {\left (\sqrt {x} \sqrt [4]{1+x^2}\right ) \int \frac {x^{7/2}}{\sqrt [4]{1+x^2} \left (1+x^4+x^8\right )} \, dx}{\sqrt [4]{x^2+x^4}}\\ &=\frac {\left (\sqrt {x} \sqrt [4]{1+x^2}\right ) \int \left (\frac {2 i x^{7/2}}{\sqrt {3} \sqrt [4]{1+x^2} \left (-1+i \sqrt {3}-2 x^4\right )}+\frac {2 i x^{7/2}}{\sqrt {3} \sqrt [4]{1+x^2} \left (1+i \sqrt {3}+2 x^4\right )}\right ) \, dx}{\sqrt [4]{x^2+x^4}}\\ &=\frac {\left (2 i \sqrt {x} \sqrt [4]{1+x^2}\right ) \int \frac {x^{7/2}}{\sqrt [4]{1+x^2} \left (-1+i \sqrt {3}-2 x^4\right )} \, dx}{\sqrt {3} \sqrt [4]{x^2+x^4}}+\frac {\left (2 i \sqrt {x} \sqrt [4]{1+x^2}\right ) \int \frac {x^{7/2}}{\sqrt [4]{1+x^2} \left (1+i \sqrt {3}+2 x^4\right )} \, dx}{\sqrt {3} \sqrt [4]{x^2+x^4}}\\ &=\frac {\left (4 i \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {x^8}{\sqrt [4]{1+x^4} \left (-1+i \sqrt {3}-2 x^8\right )} \, dx,x,\sqrt {x}\right )}{\sqrt {3} \sqrt [4]{x^2+x^4}}+\frac {\left (4 i \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {x^8}{\sqrt [4]{1+x^4} \left (1+i \sqrt {3}+2 x^8\right )} \, dx,x,\sqrt {x}\right )}{\sqrt {3} \sqrt [4]{x^2+x^4}}\\ &=-\frac {\left (2 i \left (1-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt [4]{1+x^4} \left (-1+i \sqrt {3}-2 x^8\right )} \, dx,x,\sqrt {x}\right )}{\sqrt {3} \sqrt [4]{x^2+x^4}}-\frac {\left (2 i \left (1+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt [4]{1+x^4} \left (1+i \sqrt {3}+2 x^8\right )} \, dx,x,\sqrt {x}\right )}{\sqrt {3} \sqrt [4]{x^2+x^4}}\\ &=-\frac {\left (i \sqrt {\frac {2}{3}} \left (1-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\left (\sqrt {2 \left (-1+i \sqrt {3}\right )}-2 x^4\right ) \sqrt [4]{1+x^4}} \, dx,x,\sqrt {x}\right )}{\sqrt {-1+i \sqrt {3}} \sqrt [4]{x^2+x^4}}-\frac {\left (i \sqrt {\frac {2}{3}} \left (1-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt [4]{1+x^4} \left (\sqrt {2 \left (-1+i \sqrt {3}\right )}+2 x^4\right )} \, dx,x,\sqrt {x}\right )}{\sqrt {-1+i \sqrt {3}} \sqrt [4]{x^2+x^4}}+\frac {\left (i \sqrt {\frac {2}{3}} \left (1+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\left (\sqrt {2 \left (-1-i \sqrt {3}\right )}-2 x^4\right ) \sqrt [4]{1+x^4}} \, dx,x,\sqrt {x}\right )}{\sqrt {-1-i \sqrt {3}} \sqrt [4]{x^2+x^4}}+\frac {\left (i \sqrt {\frac {2}{3}} \left (1+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt [4]{1+x^4} \left (\sqrt {2 \left (-1-i \sqrt {3}\right )}+2 x^4\right )} \, dx,x,\sqrt {x}\right )}{\sqrt {-1-i \sqrt {3}} \sqrt [4]{x^2+x^4}}\\ &=-\frac {\left (i \sqrt {\frac {2}{3}} \left (1-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt {2 \left (-1+i \sqrt {3}\right )}-\left (-2+\sqrt {2 \left (-1+i \sqrt {3}\right )}\right ) x^4} \, dx,x,\frac {\sqrt {x}}{\sqrt [4]{1+x^2}}\right )}{\sqrt {-1+i \sqrt {3}} \sqrt [4]{x^2+x^4}}-\frac {\left (i \sqrt {\frac {2}{3}} \left (1-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt {2 \left (-1+i \sqrt {3}\right )}-\left (2+\sqrt {2 \left (-1+i \sqrt {3}\right )}\right ) x^4} \, dx,x,\frac {\sqrt {x}}{\sqrt [4]{1+x^2}}\right )}{\sqrt {-1+i \sqrt {3}} \sqrt [4]{x^2+x^4}}+\frac {\left (i \sqrt {\frac {2}{3}} \left (1+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt {2 \left (-1-i \sqrt {3}\right )}-\left (-2+\sqrt {2 \left (-1-i \sqrt {3}\right )}\right ) x^4} \, dx,x,\frac {\sqrt {x}}{\sqrt [4]{1+x^2}}\right )}{\sqrt {-1-i \sqrt {3}} \sqrt [4]{x^2+x^4}}+\frac {\left (i \sqrt {\frac {2}{3}} \left (1+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt {2 \left (-1-i \sqrt {3}\right )}-\left (2+\sqrt {2 \left (-1-i \sqrt {3}\right )}\right ) x^4} \, dx,x,\frac {\sqrt {x}}{\sqrt [4]{1+x^2}}\right )}{\sqrt {-1-i \sqrt {3}} \sqrt [4]{x^2+x^4}}\\ &=-\frac {\left (i \left (1-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt [4]{2 \left (-1+i \sqrt {3}\right )}-\sqrt {-2+\sqrt {2 \left (-1+i \sqrt {3}\right )}} x^2} \, dx,x,\frac {\sqrt {x}}{\sqrt [4]{1+x^2}}\right )}{\sqrt {3} \left (2 \left (-1+i \sqrt {3}\right )\right )^{3/4} \sqrt [4]{x^2+x^4}}-\frac {\left (i \left (1-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt [4]{2 \left (-1+i \sqrt {3}\right )}+\sqrt {-2+\sqrt {2 \left (-1+i \sqrt {3}\right )}} x^2} \, dx,x,\frac {\sqrt {x}}{\sqrt [4]{1+x^2}}\right )}{\sqrt {3} \left (2 \left (-1+i \sqrt {3}\right )\right )^{3/4} \sqrt [4]{x^2+x^4}}-\frac {\left (i \left (1-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt [4]{2 \left (-1+i \sqrt {3}\right )}-\sqrt {2+\sqrt {2 \left (-1+i \sqrt {3}\right )}} x^2} \, dx,x,\frac {\sqrt {x}}{\sqrt [4]{1+x^2}}\right )}{\sqrt {3} \left (2 \left (-1+i \sqrt {3}\right )\right )^{3/4} \sqrt [4]{x^2+x^4}}-\frac {\left (i \left (1-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt [4]{2 \left (-1+i \sqrt {3}\right )}+\sqrt {2+\sqrt {2 \left (-1+i \sqrt {3}\right )}} x^2} \, dx,x,\frac {\sqrt {x}}{\sqrt [4]{1+x^2}}\right )}{\sqrt {3} \left (2 \left (-1+i \sqrt {3}\right )\right )^{3/4} \sqrt [4]{x^2+x^4}}+\frac {\left (i \left (1+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt [4]{2 \left (-1-i \sqrt {3}\right )}-\sqrt {-2+\sqrt {2 \left (-1-i \sqrt {3}\right )}} x^2} \, dx,x,\frac {\sqrt {x}}{\sqrt [4]{1+x^2}}\right )}{\sqrt {3} \left (2 \left (-1-i \sqrt {3}\right )\right )^{3/4} \sqrt [4]{x^2+x^4}}+\frac {\left (i \left (1+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt [4]{2 \left (-1-i \sqrt {3}\right )}+\sqrt {-2+\sqrt {2 \left (-1-i \sqrt {3}\right )}} x^2} \, dx,x,\frac {\sqrt {x}}{\sqrt [4]{1+x^2}}\right )}{\sqrt {3} \left (2 \left (-1-i \sqrt {3}\right )\right )^{3/4} \sqrt [4]{x^2+x^4}}+\frac {\left (i \left (1+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt [4]{2 \left (-1-i \sqrt {3}\right )}-\sqrt {2+\sqrt {2 \left (-1-i \sqrt {3}\right )}} x^2} \, dx,x,\frac {\sqrt {x}}{\sqrt [4]{1+x^2}}\right )}{\sqrt {3} \left (2 \left (-1-i \sqrt {3}\right )\right )^{3/4} \sqrt [4]{x^2+x^4}}+\frac {\left (i \left (1+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2}\right ) \text {Subst}\left (\int \frac {1}{\sqrt [4]{2 \left (-1-i \sqrt {3}\right )}+\sqrt {2+\sqrt {2 \left (-1-i \sqrt {3}\right )}} x^2} \, dx,x,\frac {\sqrt {x}}{\sqrt [4]{1+x^2}}\right )}{\sqrt {3} \left (2 \left (-1-i \sqrt {3}\right )\right )^{3/4} \sqrt [4]{x^2+x^4}}\\ &=-\frac {\left (3-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2} \tan ^{-1}\left (\frac {\sqrt [4]{-2+\sqrt {-2-2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1-i \sqrt {3}\right )} \sqrt [4]{1+x^2}}\right )}{3 \left (2 \left (-1-i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{-2+\sqrt {-2-2 i \sqrt {3}}} \sqrt [4]{x^2+x^4}}-\frac {\left (3-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2} \tan ^{-1}\left (\frac {\sqrt [4]{2+\sqrt {-2-2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1-i \sqrt {3}\right )} \sqrt [4]{1+x^2}}\right )}{3 \left (2 \left (-1-i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{2+\sqrt {-2-2 i \sqrt {3}}} \sqrt [4]{x^2+x^4}}-\frac {\left (3+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2} \tan ^{-1}\left (\frac {\sqrt [4]{-2+\sqrt {-2+2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1+i \sqrt {3}\right )} \sqrt [4]{1+x^2}}\right )}{3 \left (2 \left (-1+i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{-2+\sqrt {-2+2 i \sqrt {3}}} \sqrt [4]{x^2+x^4}}-\frac {\left (3+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2} \tan ^{-1}\left (\frac {\sqrt [4]{2+\sqrt {-2+2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1+i \sqrt {3}\right )} \sqrt [4]{1+x^2}}\right )}{3 \left (2 \left (-1+i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{2+\sqrt {-2+2 i \sqrt {3}}} \sqrt [4]{x^2+x^4}}-\frac {\left (3-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2} \tanh ^{-1}\left (\frac {\sqrt [4]{-2+\sqrt {-2-2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1-i \sqrt {3}\right )} \sqrt [4]{1+x^2}}\right )}{3 \left (2 \left (-1-i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{-2+\sqrt {-2-2 i \sqrt {3}}} \sqrt [4]{x^2+x^4}}-\frac {\left (3-i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2} \tanh ^{-1}\left (\frac {\sqrt [4]{2+\sqrt {-2-2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1-i \sqrt {3}\right )} \sqrt [4]{1+x^2}}\right )}{3 \left (2 \left (-1-i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{2+\sqrt {-2-2 i \sqrt {3}}} \sqrt [4]{x^2+x^4}}-\frac {\left (3+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2} \tanh ^{-1}\left (\frac {\sqrt [4]{-2+\sqrt {-2+2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1+i \sqrt {3}\right )} \sqrt [4]{1+x^2}}\right )}{3 \left (2 \left (-1+i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{-2+\sqrt {-2+2 i \sqrt {3}}} \sqrt [4]{x^2+x^4}}-\frac {\left (3+i \sqrt {3}\right ) \sqrt {x} \sqrt [4]{1+x^2} \tanh ^{-1}\left (\frac {\sqrt [4]{2+\sqrt {-2+2 i \sqrt {3}}} \sqrt {x}}{\sqrt [8]{2 \left (-1+i \sqrt {3}\right )} \sqrt [4]{1+x^2}}\right )}{3 \left (2 \left (-1+i \sqrt {3}\right )\right )^{7/8} \sqrt [4]{2+\sqrt {-2+2 i \sqrt {3}}} \sqrt [4]{x^2+x^4}}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 148, normalized size = 1.31 \begin {gather*} \frac {\sqrt {x} \sqrt [4]{1+x^2} \left (-\text {RootSum}\left [3-3 \text {$\#$1}^4+\text {$\#$1}^8\&,\frac {-\log \left (\sqrt {x}\right )+\log \left (\sqrt [4]{1+x^2}-\sqrt {x} \text {$\#$1}\right )}{-3 \text {$\#$1}+2 \text {$\#$1}^5}\&\right ]+\text {RootSum}\left [1-\text {$\#$1}^4+\text {$\#$1}^8\&,\frac {-\log \left (\sqrt {x}\right )+\log \left (\sqrt [4]{1+x^2}-\sqrt {x} \text {$\#$1}\right )}{-\text {$\#$1}+2 \text {$\#$1}^5}\&\right ]\right )}{4 \sqrt [4]{x^2+x^4}} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
1.
time = 160.24, size = 11397, normalized size = 100.86
method | result | size |
trager | \(\text {Expression too large to display}\) | \(11397\) |
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 [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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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^{4}}{\sqrt [4]{x^{2} \left (x^{2} + 1\right )} \left (x^{2} - x + 1\right ) \left (x^{2} + x + 1\right ) \left (x^{4} - x^{2} + 1\right )}\, dx \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 {x^4}{{\left (x^4+x^2\right )}^{1/4}\,\left (x^8+x^4+1\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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