Optimal. Leaf size=29 \[ \frac {5+e^{x-\left (e^{4+x+\frac {1}{\log (x)}}-\frac {3}{x}\right ) x}}{\log (5)} \]
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Rubi [F]
time = 0.98, 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 {e^{3+x-e^{\frac {1+(4+x) \log (x)}{\log (x)}} x} \left (\log ^2(x)+e^{\frac {1+(4+x) \log (x)}{\log (x)}} \left (1+(-1-x) \log ^2(x)\right )\right )}{\log (5) \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} &=\frac {\int \frac {e^{3+x-e^{\frac {1+(4+x) \log (x)}{\log (x)}} x} \left (\log ^2(x)+e^{\frac {1+(4+x) \log (x)}{\log (x)}} \left (1+(-1-x) \log ^2(x)\right )\right )}{\log ^2(x)} \, dx}{\log (5)}\\ &=\frac {\int \left (e^{3+x-e^{\frac {1+(4+x) \log (x)}{\log (x)}} x}-\frac {\exp \left (7+2 x-e^{\frac {1+(4+x) \log (x)}{\log (x)}} x+\frac {1}{\log (x)}\right ) \left (-1+\log ^2(x)+x \log ^2(x)\right )}{\log ^2(x)}\right ) \, dx}{\log (5)}\\ &=\frac {\int e^{3+x-e^{\frac {1+(4+x) \log (x)}{\log (x)}} x} \, dx}{\log (5)}-\frac {\int \frac {\exp \left (7+2 x-e^{\frac {1+(4+x) \log (x)}{\log (x)}} x+\frac {1}{\log (x)}\right ) \left (-1+\log ^2(x)+x \log ^2(x)\right )}{\log ^2(x)} \, dx}{\log (5)}\\ &=\frac {\int e^{3+x-e^{4+x+\frac {1}{\log (x)}} x} \, dx}{\log (5)}-\frac {\int \left (\exp \left (7+2 x-e^{\frac {1+(4+x) \log (x)}{\log (x)}} x+\frac {1}{\log (x)}\right )+\exp \left (7+2 x-e^{\frac {1+(4+x) \log (x)}{\log (x)}} x+\frac {1}{\log (x)}\right ) x-\frac {\exp \left (7+2 x-e^{\frac {1+(4+x) \log (x)}{\log (x)}} x+\frac {1}{\log (x)}\right )}{\log ^2(x)}\right ) \, dx}{\log (5)}\\ &=\frac {\int e^{3+x-e^{4+x+\frac {1}{\log (x)}} x} \, dx}{\log (5)}-\frac {\int \exp \left (7+2 x-e^{\frac {1+(4+x) \log (x)}{\log (x)}} x+\frac {1}{\log (x)}\right ) \, dx}{\log (5)}-\frac {\int \exp \left (7+2 x-e^{\frac {1+(4+x) \log (x)}{\log (x)}} x+\frac {1}{\log (x)}\right ) x \, dx}{\log (5)}+\frac {\int \frac {\exp \left (7+2 x-e^{\frac {1+(4+x) \log (x)}{\log (x)}} x+\frac {1}{\log (x)}\right )}{\log ^2(x)} \, dx}{\log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.23, size = 22, normalized size = 0.76 \begin {gather*} \frac {e^{3+x-e^{4+x+\frac {1}{\log (x)}} x}}{\log (5)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 29, normalized size = 1.00
method | result | size |
risch | \(\frac {{\mathrm e}^{-x \,{\mathrm e}^{\frac {x \ln \left (x \right )+4 \ln \left (x \right )+1}{\ln \left (x \right )}}+3+x}}{\ln \left (5\right )}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 20, normalized size = 0.69 \begin {gather*} \frac {e^{\left (-x e^{\left (x + \frac {1}{\log \left (x\right )} + 4\right )} + x + 3\right )}}{\log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.48, size = 26, normalized size = 0.90 \begin {gather*} \frac {e^{\left (-x e^{\left (\frac {{\left (x + 4\right )} \log \left (x\right ) + 1}{\log \left (x\right )}\right )} + x + 3\right )}}{\log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.52, size = 22, normalized size = 0.76 \begin {gather*} \frac {e^{- x e^{\frac {\left (x + 4\right ) \log {\left (x \right )} + 1}{\log {\left (x \right )}}} + x + 3}}{\log {\left (5 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 20, normalized size = 0.69 \begin {gather*} \frac {e^{\left (-x e^{\left (x + \frac {1}{\log \left (x\right )} + 4\right )} + x + 3\right )}}{\log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.08, size = 22, normalized size = 0.76 \begin {gather*} \frac {{\mathrm {e}}^{-x\,{\mathrm {e}}^4\,{\mathrm {e}}^{\frac {1}{\ln \left (x\right )}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^3\,{\mathrm {e}}^x}{\ln \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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