Optimal. Leaf size=28 \[ e^3-e^{4 \left (\log ^2(2)+\log \left (4 x^2 \left (-5+x^2\right )^2\right )\right )} \]
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Rubi [A] time = 0.06, antiderivative size = 21, normalized size of antiderivative = 0.75, number of steps used = 3, number of rules used = 3, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.070, Rules used = {12, 1586, 1588} \begin {gather*} -256 \left (5 x-x^3\right )^8 e^{4 \log ^2(2)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1586
Rule 1588
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{4 \log ^2(2)} \int \frac {\left (40-24 x^2\right ) \left (100 x^2-40 x^4+4 x^6\right )^4}{-5 x+x^3} \, dx\\ &=e^{4 \log ^2(2)} \int \left (40-24 x^2\right ) \left (-5 x+x^3\right )^3 \left (-20 x+4 x^3\right )^4 \, dx\\ &=-256 e^{4 \log ^2(2)} \left (5 x-x^3\right )^8\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.01, size = 66, normalized size = 2.36 \begin {gather*} -2048 e^{4 \log ^2(2)} \left (\frac {390625 x^8}{8}-78125 x^{10}+\frac {109375 x^{12}}{2}-21875 x^{14}+\frac {21875 x^{16}}{4}-875 x^{18}+\frac {175 x^{20}}{2}-5 x^{22}+\frac {x^{24}}{8}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 53, normalized size = 1.89 \begin {gather*} -256 \, {\left (x^{24} - 40 \, x^{22} + 700 \, x^{20} - 7000 \, x^{18} + 43750 \, x^{16} - 175000 \, x^{14} + 437500 \, x^{12} - 625000 \, x^{10} + 390625 \, x^{8}\right )} e^{\left (4 \, \log \relax (2)^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.13, size = 109, normalized size = 3.89 \begin {gather*} -256 \, x^{24} e^{\left (4 \, \log \relax (2)^{2}\right )} + 10240 \, x^{22} e^{\left (4 \, \log \relax (2)^{2}\right )} - 179200 \, x^{20} e^{\left (4 \, \log \relax (2)^{2}\right )} + 1792000 \, x^{18} e^{\left (4 \, \log \relax (2)^{2}\right )} - 11200000 \, x^{16} e^{\left (4 \, \log \relax (2)^{2}\right )} + 44800000 \, x^{14} e^{\left (4 \, \log \relax (2)^{2}\right )} - 112000000 \, x^{12} e^{\left (4 \, \log \relax (2)^{2}\right )} + 160000000 \, x^{10} e^{\left (4 \, \log \relax (2)^{2}\right )} - 100000000 \, x^{8} e^{\left (4 \, \log \relax (2)^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.38, size = 30, normalized size = 1.07
method | result | size |
gosper | \(-{\mathrm e}^{4 \ln \left (4 x^{6}-40 x^{4}+100 x^{2}\right )+4 \ln \relax (2)^{2}}\) | \(30\) |
default | \(2048 \,{\mathrm e}^{4 \ln \relax (2)^{2}} \left (-\frac {1}{8} x^{24}+5 x^{22}-\frac {175}{2} x^{20}+875 x^{18}-\frac {21875}{4} x^{16}+21875 x^{14}-\frac {109375}{2} x^{12}+78125 x^{10}-\frac {390625}{8} x^{8}\right )\) | \(56\) |
norman | \(-100000000 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{8}+160000000 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{10}-112000000 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{12}+44800000 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{14}-11200000 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{16}+1792000 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{18}-179200 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{20}+10240 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{22}-256 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{24}\) | \(110\) |
risch | \(-100000000 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{8}+160000000 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{10}-112000000 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{12}+44800000 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{14}-11200000 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{16}+1792000 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{18}-179200 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{20}+10240 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{22}-256 \,{\mathrm e}^{4 \ln \relax (2)^{2}} x^{24}\) | \(110\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 53, normalized size = 1.89 \begin {gather*} -256 \, {\left (x^{24} - 40 \, x^{22} + 700 \, x^{20} - 7000 \, x^{18} + 43750 \, x^{16} - 175000 \, x^{14} + 437500 \, x^{12} - 625000 \, x^{10} + 390625 \, x^{8}\right )} e^{\left (4 \, \log \relax (2)^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 19, normalized size = 0.68 \begin {gather*} -256\,x^8\,{\mathrm {e}}^{4\,{\ln \relax (2)}^2}\,{\left (x^2-5\right )}^8 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.12, size = 121, normalized size = 4.32 \begin {gather*} - 256 x^{24} e^{4 \log {\relax (2 )}^{2}} + 10240 x^{22} e^{4 \log {\relax (2 )}^{2}} - 179200 x^{20} e^{4 \log {\relax (2 )}^{2}} + 1792000 x^{18} e^{4 \log {\relax (2 )}^{2}} - 11200000 x^{16} e^{4 \log {\relax (2 )}^{2}} + 44800000 x^{14} e^{4 \log {\relax (2 )}^{2}} - 112000000 x^{12} e^{4 \log {\relax (2 )}^{2}} + 160000000 x^{10} e^{4 \log {\relax (2 )}^{2}} - 100000000 x^{8} e^{4 \log {\relax (2 )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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