Optimal. Leaf size=24 \[ -1+e^{e^x}-\frac {11 x}{5}-\frac {e^{4 x} x}{\log (x)} \]
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Rubi [A] time = 0.19, antiderivative size = 23, normalized size of antiderivative = 0.96, number of steps used = 6, number of rules used = 5, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.104, Rules used = {12, 6742, 2282, 2194, 2288} \begin {gather*} -\frac {11 x}{5}+e^{e^x}-\frac {e^{4 x} x}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rule 2282
Rule 2288
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {5 e^{4 x}+e^{4 x} (-5-20 x) \log (x)-11 \log ^2(x)+5 e^{e^x+x} \log ^2(x)}{\log ^2(x)} \, dx\\ &=\frac {1}{5} \int \left (-11+5 e^{e^x+x}-\frac {5 e^{4 x} (-1+\log (x)+4 x \log (x))}{\log ^2(x)}\right ) \, dx\\ &=-\frac {11 x}{5}+\int e^{e^x+x} \, dx-\int \frac {e^{4 x} (-1+\log (x)+4 x \log (x))}{\log ^2(x)} \, dx\\ &=-\frac {11 x}{5}-\frac {e^{4 x} x}{\log (x)}+\operatorname {Subst}\left (\int e^x \, dx,x,e^x\right )\\ &=e^{e^x}-\frac {11 x}{5}-\frac {e^{4 x} x}{\log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 23, normalized size = 0.96 \begin {gather*} e^{e^x}-\frac {11 x}{5}-\frac {e^{4 x} x}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 34, normalized size = 1.42 \begin {gather*} -\frac {{\left (11 \, x e^{x} \log \relax (x) + 5 \, x e^{\left (5 \, x\right )} - 5 \, e^{\left (x + e^{x}\right )} \log \relax (x)\right )} e^{\left (-x\right )}}{5 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 34, normalized size = 1.42 \begin {gather*} -\frac {{\left (11 \, x e^{x} \log \relax (x) + 5 \, x e^{\left (5 \, x\right )} - 5 \, e^{\left (x + e^{x}\right )} \log \relax (x)\right )} e^{\left (-x\right )}}{5 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 19, normalized size = 0.79
method | result | size |
default | \(-\frac {11 x}{5}-\frac {{\mathrm e}^{4 x} x}{\ln \relax (x )}+{\mathrm e}^{{\mathrm e}^{x}}\) | \(19\) |
risch | \(-\frac {11 x}{5}-\frac {{\mathrm e}^{4 x} x}{\ln \relax (x )}+{\mathrm e}^{{\mathrm e}^{x}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 18, normalized size = 0.75 \begin {gather*} -\frac {11}{5} \, x - \frac {x e^{\left (4 \, x\right )}}{\log \relax (x)} + e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.32, size = 18, normalized size = 0.75 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^x}-\frac {11\,x}{5}-\frac {x\,{\mathrm {e}}^{4\,x}}{\ln \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.38, size = 19, normalized size = 0.79 \begin {gather*} - \frac {x e^{4 x}}{\log {\relax (x )}} - \frac {11 x}{5} + e^{e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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