Optimal. Leaf size=26 \[ -e^4+\frac {4 e^4 \left (1+\frac {e^{2 x}}{x}\right )}{\log (3)} \]
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Rubi [A] time = 0.03, antiderivative size = 16, normalized size of antiderivative = 0.62, number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 2197} \begin {gather*} \frac {4 e^{2 x+4}}{x \log (3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{4+2 x} (-4+8 x)}{x^2} \, dx}{\log (3)}\\ &=\frac {4 e^{4+2 x}}{x \log (3)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.62 \begin {gather*} \frac {4 e^{4+2 x}}{x \log (3)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.92, size = 15, normalized size = 0.58 \begin {gather*} \frac {4 \, e^{\left (2 \, x + 4\right )}}{x \log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 15, normalized size = 0.58 \begin {gather*} \frac {4 \, e^{\left (2 \, x + 4\right )}}{x \log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 16, normalized size = 0.62
method | result | size |
gosper | \(\frac {4 \,{\mathrm e}^{4} {\mathrm e}^{2 x}}{\ln \relax (3) x}\) | \(16\) |
default | \(\frac {4 \,{\mathrm e}^{4} {\mathrm e}^{2 x}}{\ln \relax (3) x}\) | \(16\) |
norman | \(\frac {4 \,{\mathrm e}^{4} {\mathrm e}^{2 x}}{\ln \relax (3) x}\) | \(16\) |
risch | \(\frac {4 \,{\mathrm e}^{2 x +4}}{x \ln \relax (3)}\) | \(16\) |
meijerg | \(\frac {8 \,{\mathrm e}^{4} \left (\ln \relax (x )+\ln \relax (2)+i \pi -\ln \left (-2 x \right )-\expIntegralEi \left (1, -2 x \right )\right )}{\ln \relax (3)}+\frac {8 \,{\mathrm e}^{4} \left (\frac {1}{2 x}+1-\ln \relax (x )-\ln \relax (2)-i \pi -\frac {4 x +2}{4 x}+\frac {{\mathrm e}^{2 x}}{2 x}+\ln \left (-2 x \right )+\expIntegralEi \left (1, -2 x \right )\right )}{\ln \relax (3)}\) | \(87\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.42, size = 23, normalized size = 0.88 \begin {gather*} \frac {8 \, {\left ({\rm Ei}\left (2 \, x\right ) e^{4} - e^{4} \Gamma \left (-1, -2 \, x\right )\right )}}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.13, size = 15, normalized size = 0.58 \begin {gather*} \frac {4\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^4}{x\,\ln \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.54 \begin {gather*} \frac {4 e^{4} e^{2 x}}{x \log {\relax (3 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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