Optimal. Leaf size=30 \[ e^{\frac {5+2 \log (\log (4))}{4+e^{e^5-x} \log (5)}}+5 x \]
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Rubi [F] time = 1.66, 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 {80 e^{-2 e^5+2 x}+40 e^{-e^5+x} \log (5)+5 \log ^2(5)+\exp \left (\frac {5 e^{-e^5+x}+2 e^{-e^5+x} \log (\log (4))}{4 e^{-e^5+x}+\log (5)}\right ) \left (5 e^{-e^5+x} \log (5)+2 e^{-e^5+x} \log (5) \log (\log (4))\right )}{16 e^{-2 e^5+2 x}+8 e^{-e^5+x} \log (5)+\log ^2(5)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int \frac {80 x^2+5 \log ^2(5)+x \log (5) \left (40+e^{\frac {5 x}{4 x+\log (5)}} \log ^{\frac {2 x}{4 x+\log (5)}}(4) (5+2 \log (\log (4)))\right )}{x (4 x+\log (5))^2} \, dx,x,e^{\frac {1}{2} \left (-2 e^5+2 x\right )}\right )\\ &=\operatorname {Subst}\left (\int \left (\frac {5}{x}+\frac {e^{\frac {5 x}{4 x+\log (5)}} \log ^{\frac {2 x}{4 x+\log (5)}}(4) \log (5) (5+2 \log (\log (4)))}{(4 x+\log (5))^2}\right ) \, dx,x,e^{\frac {1}{2} \left (-2 e^5+2 x\right )}\right )\\ &=5 x+(\log (5) (5+2 \log (\log (4)))) \operatorname {Subst}\left (\int \frac {e^{\frac {5 x}{4 x+\log (5)}} \log ^{\frac {2 x}{4 x+\log (5)}}(4)}{(4 x+\log (5))^2} \, dx,x,e^{\frac {1}{2} \left (-2 e^5+2 x\right )}\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.72, size = 61, normalized size = 2.03 \begin {gather*} 5 x+5^{-\frac {5 e^{e^5}}{4 \left (4 e^x+e^{e^5} \log (5)\right )}} e^{5/4} \log ^{\frac {2 e^x}{4 e^x+e^{e^5} \log (5)}}(4) \end {gather*}
Warning: Unable to verify antiderivative.
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fricas [A] time = 0.62, size = 45, normalized size = 1.50 \begin {gather*} 5 \, x + e^{\left (\frac {e^{\left (x - e^{5}\right )} \log \left (4 \, \log \relax (2)^{2}\right ) + 5 \, e^{\left (x - e^{5}\right )}}{4 \, e^{\left (x - e^{5}\right )} + \log \relax (5)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.48, size = 110, normalized size = 3.67 \begin {gather*} {\left (5 \, x e^{x} + 5 \, e^{x} \log \left (4 \, e^{\left (x - e^{5}\right )} + \log \relax (5)\right ) - 5 \, e^{x} \log \left (-4 \, e^{\left (x - e^{5}\right )} - \log \relax (5)\right ) + e^{\left (\frac {4 \, x e^{\left (x - e^{5}\right )} + x \log \relax (5) + 2 \, e^{\left (x - e^{5}\right )} \log \relax (2) + 2 \, e^{\left (x - e^{5}\right )} \log \left (\log \relax (2)\right ) + 5 \, e^{\left (x - e^{5}\right )}}{4 \, e^{\left (x - e^{5}\right )} + \log \relax (5)}\right )}\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.55, size = 39, normalized size = 1.30
method | result | size |
risch | \(5 x +{\mathrm e}^{\frac {{\mathrm e}^{-{\mathrm e}^{5}+x} \left (5+2 \ln \relax (2)+2 \ln \left (\ln \relax (2)\right )\right )}{4 \,{\mathrm e}^{-{\mathrm e}^{5}+x}+\ln \relax (5)}}\) | \(39\) |
norman | \(\frac {\ln \relax (5) {\mathrm e}^{\frac {{\mathrm e}^{-{\mathrm e}^{5}+x} \ln \left (4 \ln \relax (2)^{2}\right )+5 \,{\mathrm e}^{-{\mathrm e}^{5}+x}}{4 \,{\mathrm e}^{-{\mathrm e}^{5}+x}+\ln \relax (5)}}+20 x \,{\mathrm e}^{-{\mathrm e}^{5}+x}+5 x \ln \relax (5)+4 \,{\mathrm e}^{-{\mathrm e}^{5}+x} {\mathrm e}^{\frac {{\mathrm e}^{-{\mathrm e}^{5}+x} \ln \left (4 \ln \relax (2)^{2}\right )+5 \,{\mathrm e}^{-{\mathrm e}^{5}+x}}{4 \,{\mathrm e}^{-{\mathrm e}^{5}+x}+\ln \relax (5)}}}{4 \,{\mathrm e}^{-{\mathrm e}^{5}+x}+\ln \relax (5)}\) | \(126\) |
derivativedivides | \(\text {Expression too large to display}\) | \(2274\) |
default | \(\text {Expression too large to display}\) | \(2274\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.49, size = 279, normalized size = 9.30 \begin {gather*} 5 \, {\left (\frac {1}{4 \, e^{\left (x - e^{5}\right )} \log \relax (5) + \log \relax (5)^{2}} + \frac {x - e^{5}}{\log \relax (5)^{2}} - \frac {\log \left (4 \, e^{\left (x - e^{5}\right )} + \log \relax (5)\right )}{\log \relax (5)^{2}}\right )} \log \relax (5)^{2} + \frac {\sqrt {2} e^{\left (-\frac {\log \relax (5) \log \relax (2)}{2 \, {\left (4 \, e^{\left (x - e^{5}\right )} + \log \relax (5)\right )}} - \frac {\log \relax (5) \log \left (\log \relax (2)\right )}{2 \, {\left (4 \, e^{\left (x - e^{5}\right )} + \log \relax (5)\right )}} - \frac {5 \, \log \relax (5)}{4 \, {\left (4 \, e^{\left (x - e^{5}\right )} + \log \relax (5)\right )}} + \frac {5}{4}\right )} \log \relax (5) \sqrt {\log \relax (2)} \log \left (4 \, \log \relax (2)^{2}\right )}{{\left (2 \, \log \left (\log \relax (2)\right ) + 5\right )} \log \relax (5) + 2 \, \log \relax (5) \log \relax (2)} + \frac {5 \, \sqrt {2} e^{\left (-\frac {\log \relax (5) \log \relax (2)}{2 \, {\left (4 \, e^{\left (x - e^{5}\right )} + \log \relax (5)\right )}} - \frac {\log \relax (5) \log \left (\log \relax (2)\right )}{2 \, {\left (4 \, e^{\left (x - e^{5}\right )} + \log \relax (5)\right )}} - \frac {5 \, \log \relax (5)}{4 \, {\left (4 \, e^{\left (x - e^{5}\right )} + \log \relax (5)\right )}} + \frac {5}{4}\right )} \log \relax (5) \sqrt {\log \relax (2)}}{{\left (2 \, \log \left (\log \relax (2)\right ) + 5\right )} \log \relax (5) + 2 \, \log \relax (5) \log \relax (2)} - \frac {5 \, \log \relax (5)}{4 \, e^{\left (x - e^{5}\right )} + \log \relax (5)} + 5 \, \log \left (4 \, e^{\left (x - e^{5}\right )} + \log \relax (5)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.07, size = 80, normalized size = 2.67 \begin {gather*} 5\,x+2^{\frac {2\,{\mathrm {e}}^{x-{\mathrm {e}}^5}}{4\,{\mathrm {e}}^{x-{\mathrm {e}}^5}+\ln \relax (5)}}\,{\mathrm {e}}^{\frac {5\,{\mathrm {e}}^{-{\mathrm {e}}^5}\,{\mathrm {e}}^x}{\ln \relax (5)+4\,{\mathrm {e}}^{-{\mathrm {e}}^5}\,{\mathrm {e}}^x}}\,{\ln \relax (2)}^{\frac {2\,{\mathrm {e}}^{x-{\mathrm {e}}^5}}{4\,{\mathrm {e}}^{x-{\mathrm {e}}^5}+\ln \relax (5)}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.44, size = 39, normalized size = 1.30 \begin {gather*} 5 x + e^{\frac {e^{x - e^{5}} \log {\left (4 \log {\relax (2 )}^{2} \right )} + 5 e^{x - e^{5}}}{4 e^{x - e^{5}} + \log {\relax (5 )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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