Optimal. Leaf size=32 \[ 3-e^{4+x+\frac {x}{4 \left (i \pi -\log \left (\frac {5}{2}\right )\right )-\log (x)}} \]
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Rubi [F] time = 4.66, 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 {\exp \left (\frac {-x+(-16-4 x) \left (i \pi -\log \left (\frac {5}{2}\right )\right )+(4+x) \log (x)}{-4 \left (i \pi -\log \left (\frac {5}{2}\right )\right )+\log (x)}\right ) \left (-1-4 \left (i \pi -\log \left (\frac {5}{2}\right )\right )-16 \left (i \pi -\log \left (\frac {5}{2}\right )\right )^2+\left (1+8 \left (i \pi -\log \left (\frac {5}{2}\right )\right )\right ) \log (x)-\log ^2(x)\right )}{16 \left (i \pi -\log \left (\frac {5}{2}\right )\right )^2-8 \left (i \pi -\log \left (\frac {5}{2}\right )\right ) \log (x)+\log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {-x+(-16-4 x) \left (i \pi -\log \left (\frac {5}{2}\right )\right )+(4+x) \log (x)}{-4 \left (i \pi -\log \left (\frac {5}{2}\right )\right )+\log (x)}\right ) \left (1-4 \left (\pi +i \log \left (\frac {5}{2}\right )\right ) \left (-i+4 \pi +4 i \log \left (\frac {5}{2}\right )\right )-\left (1+8 \left (i \pi -\log \left (\frac {5}{2}\right )\right )\right ) \log (x)+\log ^2(x)\right )}{\left (4 \pi \left (1+\frac {i \log \left (\frac {5}{2}\right )}{\pi }\right )+i \log (x)\right )^2} \, dx\\ &=\int \left (-\exp \left (\frac {-x+(-16-4 x) \left (i \pi -\log \left (\frac {5}{2}\right )\right )+(4+x) \log (x)}{-4 \left (i \pi -\log \left (\frac {5}{2}\right )\right )+\log (x)}\right )+\frac {\exp \left (\frac {-x+(-16-4 x) \left (i \pi -\log \left (\frac {5}{2}\right )\right )+(4+x) \log (x)}{-4 \left (i \pi -\log \left (\frac {5}{2}\right )\right )+\log (x)}\right )}{\left (4 \pi \left (1+\frac {i \log \left (\frac {5}{2}\right )}{\pi }\right )+i \log (x)\right )^2}+\frac {i \exp \left (\frac {-x+(-16-4 x) \left (i \pi -\log \left (\frac {5}{2}\right )\right )+(4+x) \log (x)}{-4 \left (i \pi -\log \left (\frac {5}{2}\right )\right )+\log (x)}\right )}{4 \pi \left (1+\frac {i \log \left (\frac {5}{2}\right )}{\pi }\right )+i \log (x)}\right ) \, dx\\ &=i \int \frac {\exp \left (\frac {-x+(-16-4 x) \left (i \pi -\log \left (\frac {5}{2}\right )\right )+(4+x) \log (x)}{-4 \left (i \pi -\log \left (\frac {5}{2}\right )\right )+\log (x)}\right )}{4 \pi \left (1+\frac {i \log \left (\frac {5}{2}\right )}{\pi }\right )+i \log (x)} \, dx-\int \exp \left (\frac {-x+(-16-4 x) \left (i \pi -\log \left (\frac {5}{2}\right )\right )+(4+x) \log (x)}{-4 \left (i \pi -\log \left (\frac {5}{2}\right )\right )+\log (x)}\right ) \, dx+\int \frac {\exp \left (\frac {-x+(-16-4 x) \left (i \pi -\log \left (\frac {5}{2}\right )\right )+(4+x) \log (x)}{-4 \left (i \pi -\log \left (\frac {5}{2}\right )\right )+\log (x)}\right )}{\left (4 \pi \left (1+\frac {i \log \left (\frac {5}{2}\right )}{\pi }\right )+i \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.36, size = 85, normalized size = 2.66 \begin {gather*} -e^{4+x+\frac {4 \pi (4+x)+i \left (16 \log \left (\frac {5}{2}\right )+x \left (-1+4 \log \left (\frac {5}{2}\right )\right )\right )}{4 \pi +4 i \log \left (\frac {5}{2}\right )+i \log (x)}} x^{(4+x) \left (-\frac {1}{\log (x)}+\frac {1}{-4 i \pi +4 \log \left (\frac {5}{2}\right )+\log (x)}\right )} \end {gather*}
Warning: Unable to verify antiderivative.
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fricas [B] time = 0.64, size = 115, normalized size = 3.59 \begin {gather*} -e^{\left (-\frac {4 i \, \pi x}{-4 i \, \pi - 4 \, \log \left (\frac {2}{5}\right ) + \log \relax (x)} - \frac {4 \, x \log \left (\frac {2}{5}\right )}{-4 i \, \pi - 4 \, \log \left (\frac {2}{5}\right ) + \log \relax (x)} + \frac {x \log \relax (x)}{-4 i \, \pi - 4 \, \log \left (\frac {2}{5}\right ) + \log \relax (x)} - \frac {16 i \, \pi }{-4 i \, \pi - 4 \, \log \left (\frac {2}{5}\right ) + \log \relax (x)} - \frac {x}{-4 i \, \pi - 4 \, \log \left (\frac {2}{5}\right ) + \log \relax (x)} - \frac {16 \, \log \left (\frac {2}{5}\right )}{-4 i \, \pi - 4 \, \log \left (\frac {2}{5}\right ) + \log \relax (x)} + \frac {4 \, \log \relax (x)}{-4 i \, \pi - 4 \, \log \left (\frac {2}{5}\right ) + \log \relax (x)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 2.32, size = 117, normalized size = 3.66 \begin {gather*} -e^{\left (\frac {4 \, \pi x}{4 \, \pi + 4 i \, \log \relax (5) - 4 i \, \log \relax (2) + i \, \log \relax (x)} + \frac {4 i \, x \log \relax (5)}{4 \, \pi + 4 i \, \log \relax (5) - 4 i \, \log \relax (2) + i \, \log \relax (x)} - \frac {4 i \, x \log \relax (2)}{4 \, \pi + 4 i \, \log \relax (5) - 4 i \, \log \relax (2) + i \, \log \relax (x)} + \frac {i \, x \log \relax (x)}{4 \, \pi + 4 i \, \log \relax (5) - 4 i \, \log \relax (2) + i \, \log \relax (x)} - \frac {i \, x}{4 \, \pi + 4 i \, \log \relax (5) - 4 i \, \log \relax (2) + i \, \log \relax (x)} + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 2.85, size = 62, normalized size = 1.94
method | result | size |
risch | \(-{\mathrm e}^{\frac {4 i \pi x -x \ln \relax (x )+16 i \pi -4 x \ln \relax (5)+4 x \ln \relax (2)-4 \ln \relax (x )-16 \ln \relax (5)+16 \ln \relax (2)+x}{-4 \ln \relax (5)+4 \ln \relax (2)+4 i \pi -\ln \relax (x )}}\) | \(62\) |
norman | \(\frac {\left (-16 \pi ^{2}-16 \ln \relax (5)^{2}+32 \ln \relax (2) \ln \relax (5)-16 \ln \relax (2)^{2}\right ) {\mathrm e}^{\frac {\left (4+x \right ) \ln \relax (x )+\left (-16-4 x \right ) \left (\ln \left (\frac {2}{5}\right )+i \pi \right )-x}{\ln \relax (x )-4 \ln \left (\frac {2}{5}\right )-4 i \pi }}+\left (-8 \ln \relax (5)+8 \ln \relax (2)\right ) \ln \relax (x ) {\mathrm e}^{\frac {\left (4+x \right ) \ln \relax (x )+\left (-16-4 x \right ) \left (\ln \left (\frac {2}{5}\right )+i \pi \right )-x}{\ln \relax (x )-4 \ln \left (\frac {2}{5}\right )-4 i \pi }}-\ln \relax (x )^{2} {\mathrm e}^{\frac {\left (4+x \right ) \ln \relax (x )+\left (-16-4 x \right ) \left (\ln \left (\frac {2}{5}\right )+i \pi \right )-x}{\ln \relax (x )-4 \ln \left (\frac {2}{5}\right )-4 i \pi }}}{16 \pi ^{2}+16 \ln \relax (5)^{2}-32 \ln \relax (2) \ln \relax (5)+8 \ln \relax (5) \ln \relax (x )+16 \ln \relax (2)^{2}-8 \ln \relax (2) \ln \relax (x )+\ln \relax (x )^{2}}\) | \(202\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 3.33, size = 184, normalized size = 5.75 \begin {gather*} -e^{\left (-\frac {4 i \, \pi x}{-4 i \, \pi + 4 \, \log \relax (5) - 4 \, \log \relax (2) + \log \relax (x)} + \frac {4 \, x \log \relax (5)}{-4 i \, \pi + 4 \, \log \relax (5) - 4 \, \log \relax (2) + \log \relax (x)} - \frac {4 \, x \log \relax (2)}{-4 i \, \pi + 4 \, \log \relax (5) - 4 \, \log \relax (2) + \log \relax (x)} + \frac {x \log \relax (x)}{-4 i \, \pi + 4 \, \log \relax (5) - 4 \, \log \relax (2) + \log \relax (x)} - \frac {16 i \, \pi }{-4 i \, \pi + 4 \, \log \relax (5) - 4 \, \log \relax (2) + \log \relax (x)} - \frac {x}{-4 i \, \pi + 4 \, \log \relax (5) - 4 \, \log \relax (2) + \log \relax (x)} + \frac {16 \, \log \relax (5)}{-4 i \, \pi + 4 \, \log \relax (5) - 4 \, \log \relax (2) + \log \relax (x)} - \frac {16 \, \log \relax (2)}{-4 i \, \pi + 4 \, \log \relax (5) - 4 \, \log \relax (2) + \log \relax (x)} + \frac {4 \, \log \relax (x)}{-4 i \, \pi + 4 \, \log \relax (5) - 4 \, \log \relax (2) + \log \relax (x)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 10.28, size = 82, normalized size = 2.56 \begin {gather*} -{\mathrm {e}}^{\frac {\Pi \,16{}\mathrm {i}}{-\ln \left (\frac {625\,x}{16}\right )+\Pi \,4{}\mathrm {i}}+\frac {x}{-\ln \left (\frac {625\,x}{16}\right )+\Pi \,4{}\mathrm {i}}+\frac {\Pi \,x\,4{}\mathrm {i}}{-\ln \left (\frac {625\,x}{16}\right )+\Pi \,4{}\mathrm {i}}}\,{\left (\frac {625\,x}{16}\right )}^{\frac {x\,1{}\mathrm {i}+4{}\mathrm {i}}{4\,\Pi -\ln \left (\frac {2}{5}\right )\,4{}\mathrm {i}+\ln \relax (x)\,1{}\mathrm {i}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [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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