Optimal. Leaf size=17 \[ \frac {1}{\left (x+x^2 \left (\frac {1}{e}-x^2\right )\right )^4} \]
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Rubi [F] time = 182.56, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Aborted
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Mathematica [A] time = 0.21, size = 18, normalized size = 1.06 \begin {gather*} \frac {e^4}{x^4 \left (e+x-e x^3\right )^4} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.66, size = 86, normalized size = 5.06 \begin {gather*} \frac {e^{4}}{x^{8} + {\left (x^{16} - 4 \, x^{13} + 6 \, x^{10} - 4 \, x^{7} + x^{4}\right )} e^{4} - 4 \, {\left (x^{14} - 3 \, x^{11} + 3 \, x^{8} - x^{5}\right )} e^{3} + 6 \, {\left (x^{12} - 2 \, x^{9} + x^{6}\right )} e^{2} - 4 \, {\left (x^{10} - x^{7}\right )} e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [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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maple [A] time = 1.18, size = 25, normalized size = 1.47
method | result | size |
norman | \(\frac {{\mathrm e}^{4}}{x^{4} \left (x^{3} {\mathrm e}-{\mathrm e}-x \right )^{4}}\) | \(25\) |
risch | \(\frac {{\mathrm e}^{4}}{x^{4} \left ({\mathrm e}^{4} x^{12}-4 x^{9} {\mathrm e}^{4}-4 \,{\mathrm e}^{3} x^{10}+6 x^{6} {\mathrm e}^{4}+12 x^{7} {\mathrm e}^{3}+6 x^{8} {\mathrm e}^{2}-4 x^{3} {\mathrm e}^{4}-12 x^{4} {\mathrm e}^{3}-12 \,{\mathrm e}^{2} x^{5}-4 x^{6} {\mathrm e}+{\mathrm e}^{4}+4 x \,{\mathrm e}^{3}+6 x^{2} {\mathrm e}^{2}+4 x^{3} {\mathrm e}+x^{4}\right )}\) | \(103\) |
gosper | \(\frac {{\mathrm e}^{4}}{x^{4} \left ({\mathrm e}^{4} x^{12}-4 x^{9} {\mathrm e}^{4}-4 \,{\mathrm e}^{3} x^{10}+6 x^{6} {\mathrm e}^{4}+12 x^{7} {\mathrm e}^{3}+6 x^{8} {\mathrm e}^{2}-4 x^{3} {\mathrm e}^{4}-12 x^{4} {\mathrm e}^{3}-12 \,{\mathrm e}^{2} x^{5}-4 x^{6} {\mathrm e}+{\mathrm e}^{4}+4 x \,{\mathrm e}^{3}+6 x^{2} {\mathrm e}^{2}+4 x^{3} {\mathrm e}+x^{4}\right )}\) | \(129\) |
default | \(4 \,{\mathrm e}^{4} \left (\frac {{\mathrm e}^{-25} \left ({\mathrm e}^{21}-5 \,{\mathrm e}^{18}\right )}{x}+\frac {{\mathrm e}^{21} {\mathrm e}^{-25}}{4 x^{4}}+\frac {5 \,{\mathrm e}^{-25} {\mathrm e}^{19}}{2 x^{2}}-\frac {{\mathrm e}^{-25} {\mathrm e}^{20}}{x^{3}}-\frac {{\mathrm e}^{-25} \left (\munderset {\textit {\_R} =\RootOf \left ({\mathrm e}^{5} \textit {\_Z}^{15}-5 \,{\mathrm e}^{4} \textit {\_Z}^{13}-5 \,{\mathrm e}^{5} \textit {\_Z}^{12}+10 \,{\mathrm e}^{3} \textit {\_Z}^{11}+20 \,{\mathrm e}^{4} \textit {\_Z}^{10}+\left (10 \,{\mathrm e}^{5}-10 \,{\mathrm e}^{2}\right ) \textit {\_Z}^{9}-30 \,{\mathrm e}^{3} \textit {\_Z}^{8}+\left (-30 \,{\mathrm e}^{4}+5 \,{\mathrm e}\right ) \textit {\_Z}^{7}+\left (-10 \,{\mathrm e}^{5}+20 \,{\mathrm e}^{2}\right ) \textit {\_Z}^{6}+\left (30 \,{\mathrm e}^{3}-1\right ) \textit {\_Z}^{5}+\left (20 \,{\mathrm e}^{4}-5 \,{\mathrm e}\right ) \textit {\_Z}^{4}+\left (5 \,{\mathrm e}^{5}-10 \,{\mathrm e}^{2}\right ) \textit {\_Z}^{3}-10 \textit {\_Z}^{2} {\mathrm e}^{3}-5 \textit {\_Z} \,{\mathrm e}^{4}-{\mathrm e}^{5}\right )}{\sum }\frac {\left (\left (-{\mathrm e}^{26}+5 \,{\mathrm e}^{23}\right ) \textit {\_R}^{13}-5 \textit {\_R}^{12} {\mathrm e}^{24}+\left (8 \,{\mathrm e}^{25}-25 \,{\mathrm e}^{22}\right ) \textit {\_R}^{11}+4 \textit {\_R}^{10} {\mathrm e}^{26}+50 \textit {\_R}^{9} {\mathrm e}^{21}+10 \left (-3 \,{\mathrm e}^{25}+5 \,{\mathrm e}^{22}\right ) \textit {\_R}^{8}+5 \left (-{\mathrm e}^{26}-2 \,{\mathrm e}^{23}-10 \,{\mathrm e}^{20}\right ) \textit {\_R}^{7}+10 \left (-10 \,{\mathrm e}^{21}+3 \,{\mathrm e}^{24}\right ) \textit {\_R}^{6}+5 \left (8 \,{\mathrm e}^{25}-7 \,{\mathrm e}^{22}+5 \,{\mathrm e}^{19}\right ) \textit {\_R}^{5}+75 \textit {\_R}^{4} {\mathrm e}^{20}+\left (66 \,{\mathrm e}^{21}-40 \,{\mathrm e}^{24}-5 \,{\mathrm e}^{18}\right ) \textit {\_R}^{3}+10 \left (-2 \,{\mathrm e}^{25}+{\mathrm e}^{22}-2 \,{\mathrm e}^{19}\right ) \textit {\_R}^{2}+\left (5 \,{\mathrm e}^{26}+5 \,{\mathrm e}^{23}-28 \,{\mathrm e}^{20}\right ) \textit {\_R} -14 \,{\mathrm e}^{21}+15 \,{\mathrm e}^{24}\right ) \ln \left (x -\textit {\_R} \right )}{3 \textit {\_R}^{14} {\mathrm e}^{5}-12 \,{\mathrm e}^{5} \textit {\_R}^{11}-13 \,{\mathrm e}^{4} \textit {\_R}^{12}+18 \textit {\_R}^{8} {\mathrm e}^{5}+40 \textit {\_R}^{9} {\mathrm e}^{4}+22 \,{\mathrm e}^{3} \textit {\_R}^{10}-12 \textit {\_R}^{5} {\mathrm e}^{5}-42 \textit {\_R}^{6} {\mathrm e}^{4}-48 \textit {\_R}^{7} {\mathrm e}^{3}-18 \textit {\_R}^{8} {\mathrm e}^{2}+3 \textit {\_R}^{2} {\mathrm e}^{5}+16 \textit {\_R}^{3} {\mathrm e}^{4}+30 \textit {\_R}^{4} {\mathrm e}^{3}+24 \,{\mathrm e}^{2} \textit {\_R}^{5}+7 \textit {\_R}^{6} {\mathrm e}-{\mathrm e}^{4}-4 \textit {\_R} \,{\mathrm e}^{3}-6 \textit {\_R}^{2} {\mathrm e}^{2}-4 \textit {\_R}^{3} {\mathrm e}-\textit {\_R}^{4}}\right )}{5}\right )\) | \(507\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.40, size = 104, normalized size = 6.12 \begin {gather*} \frac {e^{4}}{x^{16} e^{4} - 4 \, x^{14} e^{3} - 4 \, x^{13} e^{4} + 6 \, x^{12} e^{2} + 12 \, x^{11} e^{3} + 2 \, x^{10} {\left (3 \, e^{4} - 2 \, e\right )} - 12 \, x^{9} e^{2} - x^{8} {\left (12 \, e^{3} - 1\right )} - 4 \, x^{7} {\left (e^{4} - e\right )} + 6 \, x^{6} e^{2} + 4 \, x^{5} e^{3} + x^{4} e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.27, size = 105, normalized size = 6.18 \begin {gather*} \frac {{\mathrm {e}}^4}{{\mathrm {e}}^4\,x^{16}-4\,{\mathrm {e}}^3\,x^{14}-4\,{\mathrm {e}}^4\,x^{13}+6\,{\mathrm {e}}^2\,x^{12}+12\,{\mathrm {e}}^3\,x^{11}+\left (6\,{\mathrm {e}}^4-4\,\mathrm {e}\right )\,x^{10}-12\,{\mathrm {e}}^2\,x^9+\left (1-12\,{\mathrm {e}}^3\right )\,x^8+\left (4\,\mathrm {e}-4\,{\mathrm {e}}^4\right )\,x^7+6\,{\mathrm {e}}^2\,x^6+4\,{\mathrm {e}}^3\,x^5+{\mathrm {e}}^4\,x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 3.29, size = 112, normalized size = 6.59 \begin {gather*} \frac {e^{4}}{x^{16} e^{4} - 4 x^{14} e^{3} - 4 x^{13} e^{4} + 6 x^{12} e^{2} + 12 x^{11} e^{3} + x^{10} \left (- 4 e + 6 e^{4}\right ) - 12 x^{9} e^{2} + x^{8} \left (1 - 12 e^{3}\right ) + x^{7} \left (- 4 e^{4} + 4 e\right ) + 6 x^{6} e^{2} + 4 x^{5} e^{3} + x^{4} e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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