Optimal. Leaf size=27 \[ e^{4-\frac {\left (-1+\frac {2}{e^3}+\log (5)\right )^2}{x^2}} (4-x) x \]
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Rubi [A] time = 2.57, antiderivative size = 34, normalized size of antiderivative = 1.26, number of steps used = 2, number of rules used = 2, integrand size = 124, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {6741, 2288} \begin {gather*} (4-x) x e^{4-\frac {\left (2-e^3 (1-\log (5))\right )^2}{e^6 x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (-2+\frac {-4+4 e^3-e^6-4 e^3 \log (5)+2 e^6 \log (5)-e^6 \log ^2(5)}{e^6 x^2}\right ) \left (4 e^6 x^2-2 e^6 x^3+8 \left (2-e^3 (1-\log (5))\right )^2-2 x \left (2-e^3 (1-\log (5))\right )^2\right )}{x^2} \, dx\\ &=e^{4-\frac {\left (2-e^3 (1-\log (5))\right )^2}{e^6 x^2}} (4-x) x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 54, normalized size = 2.00 \begin {gather*} -5^{\frac {2 \left (-2+e^3\right )}{e^3 x^2}} e^{\frac {-4+4 e^3+e^6 \left (-1+4 x^2-\log ^2(5)\right )}{e^6 x^2}} (-4+x) x \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.47, size = 53, normalized size = 1.96 \begin {gather*} -{\left (x^{2} - 4 \, x\right )} e^{\left (-\frac {{\left (e^{6} \log \relax (5)^{2} + {\left (2 \, x^{2} + 1\right )} e^{6} - 2 \, {\left (e^{6} - 2 \, e^{3}\right )} \log \relax (5) - 4 \, e^{3} + 4\right )} e^{\left (-6\right )}}{x^{2}} + 6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.60, size = 99, normalized size = 3.67 \begin {gather*} -x^{2} e^{\left (\frac {{\left (x^{2} e^{6} - e^{6} \log \relax (5)^{2} + 2 \, e^{6} \log \relax (5) - 4 \, e^{3} \log \relax (5) - e^{6} + 4 \, e^{3} - 4\right )} e^{\left (-6\right )}}{x^{2}} + 3\right )} + 4 \, x e^{\left (\frac {{\left (x^{2} e^{6} - e^{6} \log \relax (5)^{2} + 2 \, e^{6} \log \relax (5) - 4 \, e^{3} \log \relax (5) - e^{6} + 4 \, e^{3} - 4\right )} e^{\left (-6\right )}}{x^{2}} + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.78, size = 54, normalized size = 2.00
method | result | size |
risch | \(\left (\frac {1}{625}\right )^{\frac {{\mathrm e}^{-3}}{x^{2}}} 25^{\frac {1}{x^{2}}} \left (-x^{2} {\mathrm e}^{6}+4 x \,{\mathrm e}^{6}\right ) {\mathrm e}^{\frac {-\ln \relax (5)^{2}-2 x^{2}-4 \,{\mathrm e}^{-6}+4 \,{\mathrm e}^{-3}-1}{x^{2}}}\) | \(54\) |
gosper | \(-{\mathrm e}^{-\frac {\left ({\mathrm e}^{6} \ln \relax (5)^{2}-4 x^{2} {\mathrm e}^{6}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4\right ) {\mathrm e}^{-6}}{x^{2}}} \left (x -4\right ) x\) | \(59\) |
norman | \(\frac {\left (4 x^{2} {\mathrm e}^{3} {\mathrm e}^{\frac {\left (-{\mathrm e}^{6} \ln \relax (5)^{2}+\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+\left (4 x^{2}-1\right ) {\mathrm e}^{6}+4 \,{\mathrm e}^{3}-4\right ) {\mathrm e}^{-6}}{x^{2}}}-x^{3} {\mathrm e}^{3} {\mathrm e}^{\frac {\left (-{\mathrm e}^{6} \ln \relax (5)^{2}+\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+\left (4 x^{2}-1\right ) {\mathrm e}^{6}+4 \,{\mathrm e}^{3}-4\right ) {\mathrm e}^{-6}}{x^{2}}}\right ) {\mathrm e}^{-3}}{x}\) | \(126\) |
default | \({\mathrm e}^{-6} \left (-\frac {4 \,{\mathrm e}^{9} \ln \relax (5)^{2} \sqrt {\pi }\, {\mathrm e}^{4} \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}-\frac {\left (-16 \,{\mathrm e}^{6}+32 \,{\mathrm e}^{3}\right ) \ln \relax (5) \sqrt {\pi }\, {\mathrm e}^{4} {\mathrm e}^{3} \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}{x}\right )}{2 \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}-\frac {4 \,{\mathrm e}^{9} \sqrt {\pi }\, {\mathrm e}^{4} \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}+\frac {16 \,{\mathrm e}^{6} \sqrt {\pi }\, {\mathrm e}^{4} \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}-\frac {16 \sqrt {\pi }\, {\mathrm e}^{4} {\mathrm e}^{3} \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}+\frac {\left (-2 \,{\mathrm e}^{6} \ln \relax (5)^{2}+\left (4 \,{\mathrm e}^{6}-8 \,{\mathrm e}^{3}\right ) \ln \relax (5)-2 \,{\mathrm e}^{6}+8 \,{\mathrm e}^{3}-8\right ) {\mathrm e}^{4} \expIntegralEi \left (1, \frac {\left ({\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4\right ) {\mathrm e}^{-6}}{x^{2}}\right )}{2}+4 \,{\mathrm e}^{6} x \,{\mathrm e}^{4-\frac {\left ({\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4\right ) {\mathrm e}^{-6}}{x^{2}}}+4 \,{\mathrm e}^{3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}\, \sqrt {\pi }\, {\mathrm e}^{4} \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}{x}\right )-{\mathrm e}^{6} x^{2} {\mathrm e}^{4-\frac {\left ({\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4\right ) {\mathrm e}^{-6}}{x^{2}}}+\left ({\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4\right ) {\mathrm e}^{4} \expIntegralEi \left (1, \frac {\left ({\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4\right ) {\mathrm e}^{-6}}{x^{2}}\right )\right )\) | \(826\) |
derivativedivides | \(-{\mathrm e}^{-6} \left (\frac {4 \,{\mathrm e}^{9} \ln \relax (5)^{2} \sqrt {\pi }\, {\mathrm e}^{4} \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}+\frac {\left (-16 \,{\mathrm e}^{6}+32 \,{\mathrm e}^{3}\right ) \ln \relax (5) \sqrt {\pi }\, {\mathrm e}^{4} {\mathrm e}^{3} \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}{x}\right )}{2 \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}+\frac {4 \,{\mathrm e}^{9} \sqrt {\pi }\, {\mathrm e}^{4} \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}-\frac {16 \,{\mathrm e}^{6} \sqrt {\pi }\, {\mathrm e}^{4} \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}+\frac {16 \sqrt {\pi }\, {\mathrm e}^{4} {\mathrm e}^{3} \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}-\frac {\left (-2 \,{\mathrm e}^{6} \ln \relax (5)^{2}+\left (4 \,{\mathrm e}^{6}-8 \,{\mathrm e}^{3}\right ) \ln \relax (5)-2 \,{\mathrm e}^{6}+8 \,{\mathrm e}^{3}-8\right ) {\mathrm e}^{4} \expIntegralEi \left (1, \frac {\left ({\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4\right ) {\mathrm e}^{-6}}{x^{2}}\right )}{2}-4 \,{\mathrm e}^{6} x \,{\mathrm e}^{4-\frac {\left ({\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4\right ) {\mathrm e}^{-6}}{x^{2}}}-4 \,{\mathrm e}^{3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}\, \sqrt {\pi }\, {\mathrm e}^{4} \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4}}{x}\right )+{\mathrm e}^{6} x^{2} {\mathrm e}^{4-\frac {\left ({\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4\right ) {\mathrm e}^{-6}}{x^{2}}}-\left ({\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4\right ) {\mathrm e}^{4} \expIntegralEi \left (1, \frac {\left ({\mathrm e}^{6} \ln \relax (5)^{2}+4 \,{\mathrm e}^{3} \ln \relax (5)-2 \ln \relax (5) {\mathrm e}^{6}-4 \,{\mathrm e}^{3}+{\mathrm e}^{6}+4\right ) {\mathrm e}^{-6}}{x^{2}}\right )\right )\) | \(827\) |
meijerg | \(-\frac {4 \ln \relax (5)^{2} {\mathrm e}^{7} \sqrt {\pi }\, \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}+\frac {8 \ln \relax (5) {\mathrm e}^{7} \sqrt {\pi }\, \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}-\frac {16 \,{\mathrm e}^{4} \ln \relax (5) \sqrt {\pi }\, \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}-\frac {4 \,{\mathrm e}^{7} \sqrt {\pi }\, \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}+\frac {16 \,{\mathrm e}^{4} \sqrt {\pi }\, \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}-\frac {16 \,{\mathrm e} \sqrt {\pi }\, \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}{x}\right )}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}+{\mathrm e}^{-2} \left ({\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4\right ) \left (\frac {x^{2} {\mathrm e}^{6} \left (2-\frac {2 \,{\mathrm e}^{-6} \left ({\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4\right )}{x^{2}}\right )}{2 \,{\mathrm e}^{6} \ln \relax (5)^{2}-2 \left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+2 \,{\mathrm e}^{6}-8 \,{\mathrm e}^{3}+8}-\frac {x^{2} {\mathrm e}^{6-\frac {{\mathrm e}^{-6} \left ({\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4\right )}{x^{2}}}}{{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}+\ln \left (\frac {{\mathrm e}^{-6} \left ({\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4\right )}{x^{2}}\right )+\expIntegralEi \left (1, \frac {{\mathrm e}^{-6} \left ({\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4\right )}{x^{2}}\right )+7+2 \ln \relax (x )-\ln \left ({\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4\right )-\frac {x^{2} {\mathrm e}^{6}}{{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}\right )-2 \,{\mathrm e} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}\, \left (-\frac {2 x \,{\mathrm e}^{3-\frac {{\mathrm e}^{-6} \left ({\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4\right )}{x^{2}}}}{\sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}-2 \sqrt {\pi }\, \erf \left (\frac {{\mathrm e}^{-3} \sqrt {{\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4}}{x}\right )\right )-\frac {{\mathrm e}^{-2} \left (-2 \,{\mathrm e}^{6} \ln \relax (5)^{2}+4 \ln \relax (5) {\mathrm e}^{6}-8 \,{\mathrm e}^{3} \ln \relax (5)-2 \,{\mathrm e}^{6}+8 \,{\mathrm e}^{3}-8\right ) \left (-\ln \left (\frac {{\mathrm e}^{-6} \left ({\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4\right )}{x^{2}}\right )-\expIntegralEi \left (1, \frac {{\mathrm e}^{-6} \left ({\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4\right )}{x^{2}}\right )-2 \ln \relax (x )-6+\ln \left ({\mathrm e}^{6} \ln \relax (5)^{2}-\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \relax (5)+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4\right )\right )}{2}\) | \(1069\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.88, size = 450, normalized size = 16.67 \begin {gather*} 2 \, x \sqrt {\frac {1}{x^{2}}} {\left | e^{3} \log \relax (5) - e^{3} + 2 \right |} e \Gamma \left (-\frac {1}{2}, \frac {{\left (e^{3} \log \relax (5) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) - {\left (e^{3} \log \relax (5) - e^{3} + 2\right )}^{2} e^{\left (-2\right )} \Gamma \left (-1, \frac {{\left (e^{3} \log \relax (5) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) + {\rm Ei}\left (-\frac {{\left (e^{3} \log \relax (5) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) e^{4} \log \relax (5)^{2} - \frac {4 \, \sqrt {\pi } \operatorname {erf}\left (\frac {{\left ({\left (\log \relax (5) - 1\right )} e^{3} + 2\right )} e^{\left (-3\right )}}{x}\right ) e^{7} \log \relax (5)^{2}}{{\left (\log \relax (5) - 1\right )} e^{3} + 2} - 2 \, {\rm Ei}\left (-\frac {{\left (e^{3} \log \relax (5) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) e^{4} \log \relax (5) + 4 \, {\rm Ei}\left (-\frac {{\left (e^{3} \log \relax (5) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) e \log \relax (5) + \frac {8 \, \sqrt {\pi } \operatorname {erf}\left (\frac {{\left ({\left (\log \relax (5) - 1\right )} e^{3} + 2\right )} e^{\left (-3\right )}}{x}\right ) e^{7} \log \relax (5)}{{\left (\log \relax (5) - 1\right )} e^{3} + 2} - \frac {16 \, \sqrt {\pi } \operatorname {erf}\left (\frac {{\left ({\left (\log \relax (5) - 1\right )} e^{3} + 2\right )} e^{\left (-3\right )}}{x}\right ) e^{4} \log \relax (5)}{{\left (\log \relax (5) - 1\right )} e^{3} + 2} + {\rm Ei}\left (-\frac {{\left (e^{3} \log \relax (5) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) e^{4} - 4 \, {\rm Ei}\left (-\frac {{\left (e^{3} \log \relax (5) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) e + 4 \, {\rm Ei}\left (-\frac {{\left (e^{3} \log \relax (5) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) e^{\left (-2\right )} - \frac {4 \, \sqrt {\pi } \operatorname {erf}\left (\frac {{\left ({\left (\log \relax (5) - 1\right )} e^{3} + 2\right )} e^{\left (-3\right )}}{x}\right ) e^{7}}{{\left (\log \relax (5) - 1\right )} e^{3} + 2} + \frac {16 \, \sqrt {\pi } \operatorname {erf}\left (\frac {{\left ({\left (\log \relax (5) - 1\right )} e^{3} + 2\right )} e^{\left (-3\right )}}{x}\right ) e^{4}}{{\left (\log \relax (5) - 1\right )} e^{3} + 2} - \frac {16 \, \sqrt {\pi } \operatorname {erf}\left (\frac {{\left ({\left (\log \relax (5) - 1\right )} e^{3} + 2\right )} e^{\left (-3\right )}}{x}\right ) e}{{\left (\log \relax (5) - 1\right )} e^{3} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.76, size = 56, normalized size = 2.07 \begin {gather*} -\frac {{25}^{\frac {1}{x^2}}\,x\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{-3}}{x^2}}\,{\mathrm {e}}^{-\frac {4\,{\mathrm {e}}^{-6}}{x^2}}\,{\mathrm {e}}^4\,{\mathrm {e}}^{-\frac {{\ln \relax (5)}^2}{x^2}}\,{\mathrm {e}}^{-\frac {1}{x^2}}\,\left (x-4\right )}{{25}^{\frac {2\,{\mathrm {e}}^{-3}}{x^2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.71, size = 53, normalized size = 1.96 \begin {gather*} \left (- x^{2} + 4 x\right ) e^{\frac {\left (4 x^{2} - 1\right ) e^{6} - e^{6} \log {\relax (5 )}^{2} - 4 + 4 e^{3} + \left (- 4 e^{3} + 2 e^{6}\right ) \log {\relax (5 )}}{x^{2} e^{6}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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