Optimal. Leaf size=33 \[ x+e^{-e^4+\frac {-x+\log ^2(4)}{x}} \left (x-e^{-x} x\right ) \]
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Rubi [A] time = 1.01, antiderivative size = 66, normalized size of antiderivative = 2.00, number of steps used = 6, number of rules used = 3, integrand size = 77, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.039, Rules used = {14, 6742, 2288} \begin {gather*} -\frac {e^{-x+\frac {\log ^2(4)}{x}-e^4-1} \left (x^2+\log ^2(4)\right )}{x \left (\frac {\log ^2(4)}{x^2}+1\right )}+x+x e^{\frac {\log ^2(4)}{x}-e^4-1} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2288
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {e^{-1-e^4-x+\frac {\log ^2(4)}{x}} \left (-x+e^x x+x^2+\log ^2(4)-e^x \log ^2(4)\right )}{x}\right ) \, dx\\ &=x+\int \frac {e^{-1-e^4-x+\frac {\log ^2(4)}{x}} \left (-x+e^x x+x^2+\log ^2(4)-e^x \log ^2(4)\right )}{x} \, dx\\ &=x+\int \left (\frac {e^{-1-e^4+\frac {\log ^2(4)}{x}} \left (x-\log ^2(4)\right )}{x}+\frac {e^{-1-e^4-x+\frac {\log ^2(4)}{x}} \left (-x+x^2+\log ^2(4)\right )}{x}\right ) \, dx\\ &=x+\int \frac {e^{-1-e^4+\frac {\log ^2(4)}{x}} \left (x-\log ^2(4)\right )}{x} \, dx+\int \frac {e^{-1-e^4-x+\frac {\log ^2(4)}{x}} \left (-x+x^2+\log ^2(4)\right )}{x} \, dx\\ &=x+e^{-1-e^4+\frac {\log ^2(4)}{x}} x-\frac {e^{-1-e^4-x+\frac {\log ^2(4)}{x}} \left (x^2+\log ^2(4)\right )}{x \left (1+\frac {\log ^2(4)}{x^2}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.13, size = 43, normalized size = 1.30 \begin {gather*} \left (1+e^{-1-e^4+\frac {\log ^2(4)}{x}}-e^{-1-e^4-x+\frac {\log ^2(4)}{x}}\right ) x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 50, normalized size = 1.52 \begin {gather*} x e^{\left (-\frac {x e^{4} - 4 \, \log \relax (2)^{2} + x}{x}\right )} + x - e^{\left (-\frac {x^{2} + x e^{4} - 4 \, \log \relax (2)^{2} - x \log \relax (x) + x}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 46, normalized size = 1.39 \begin {gather*} -x e^{\left (-\frac {x^{2} + x e^{4} - 4 \, \log \relax (2)^{2} + x}{x}\right )} + x e^{\left (-\frac {x e^{4} - 4 \, \log \relax (2)^{2} + x}{x}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.19, size = 47, normalized size = 1.42
method | result | size |
risch | \(x \,{\mathrm e}^{-\frac {-4 \ln \relax (2)^{2}+x \,{\mathrm e}^{4}+x}{x}}-x \,{\mathrm e}^{-\frac {-4 \ln \relax (2)^{2}+x \,{\mathrm e}^{4}+x^{2}+x}{x}}+x\) | \(47\) |
default | \(x +\frac {{\mathrm e}^{\frac {4 \ln \relax (2)^{2}-x \,{\mathrm e}^{4}-x}{x}} x^{2}-{\mathrm e}^{\frac {4 \ln \relax (2)^{2}-x \,{\mathrm e}^{4}-x}{x}} {\mathrm e}^{\ln \relax (x )-x} x}{x}\) | \(62\) |
norman | \(\frac {x^{2}+{\mathrm e}^{\frac {4 \ln \relax (2)^{2}-x \,{\mathrm e}^{4}-x}{x}} x^{2}-{\mathrm e}^{\frac {4 \ln \relax (2)^{2}-x \,{\mathrm e}^{4}-x}{x}} {\mathrm e}^{\ln \relax (x )-x} x}{x}\) | \(63\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.54, size = 71, normalized size = 2.15 \begin {gather*} 4 \, {\rm Ei}\left (\frac {4 \, \log \relax (2)^{2}}{x}\right ) e^{\left (-e^{4} - 1\right )} \log \relax (2)^{2} - 4 \, e^{\left (-e^{4} - 1\right )} \Gamma \left (-1, -\frac {4 \, \log \relax (2)^{2}}{x}\right ) \log \relax (2)^{2} - x e^{\left (-x + \frac {4 \, \log \relax (2)^{2}}{x} - e^{4} - 1\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.56, size = 45, normalized size = 1.36 \begin {gather*} x+x\,{\mathrm {e}}^{-{\mathrm {e}}^4}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{\frac {4\,{\ln \relax (2)}^2}{x}}-x\,{\mathrm {e}}^{-{\mathrm {e}}^4}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{\frac {4\,{\ln \relax (2)}^2}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 14.62, size = 24, normalized size = 0.73 \begin {gather*} x + \left (x - x e^{- x}\right ) e^{\frac {- x e^{4} - x + 4 \log {\relax (2 )}^{2}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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