Optimal. Leaf size=22 \[ -5-x+\frac {e^{2 e^{-5 x}}}{x^2 \log (4)} \]
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Rubi [F] time = 0.46, 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^{-5 x} \left (e^{2 e^{-5 x}} \left (-2 e^{5 x}-10 x\right )-e^{5 x} x^3 \log (4)\right )}{x^3 \log (4)} \, 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^{-5 x} \left (e^{2 e^{-5 x}} \left (-2 e^{5 x}-10 x\right )-e^{5 x} x^3 \log (4)\right )}{x^3} \, dx}{\log (4)}\\ &=\frac {\int \left (-\frac {10 e^{2 e^{-5 x}-5 x}}{x^2}-\frac {2 e^{2 e^{-5 x}}+x^3 \log (4)}{x^3}\right ) \, dx}{\log (4)}\\ &=-\frac {\int \frac {2 e^{2 e^{-5 x}}+x^3 \log (4)}{x^3} \, dx}{\log (4)}-\frac {10 \int \frac {e^{2 e^{-5 x}-5 x}}{x^2} \, dx}{\log (4)}\\ &=-\frac {\int \left (\frac {2 e^{2 e^{-5 x}}}{x^3}+\log (4)\right ) \, dx}{\log (4)}-\frac {10 \int \frac {e^{2 e^{-5 x}-5 x}}{x^2} \, dx}{\log (4)}\\ &=-x-\frac {2 \int \frac {e^{2 e^{-5 x}}}{x^3} \, dx}{\log (4)}-\frac {10 \int \frac {e^{2 e^{-5 x}-5 x}}{x^2} \, dx}{\log (4)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.29, size = 25, normalized size = 1.14 \begin {gather*} -\frac {-\frac {e^{2 e^{-5 x}}}{x^2}+x \log (4)}{\log (4)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 26, normalized size = 1.18 \begin {gather*} -\frac {2 \, x^{3} \log \relax (2) - e^{\left (2 \, e^{\left (-5 \, x\right )}\right )}}{2 \, x^{2} \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (x^{3} e^{\left (5 \, x\right )} \log \relax (2) + {\left (5 \, x + e^{\left (5 \, x\right )}\right )} e^{\left (2 \, e^{\left (-5 \, x\right )}\right )}\right )} e^{\left (-5 \, x\right )}}{x^{3} \log \relax (2)}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 21, normalized size = 0.95
method | result | size |
risch | \(-x +\frac {{\mathrm e}^{2 \,{\mathrm e}^{-5 x}}}{2 x^{2} \ln \relax (2)}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {x \log \relax (2) - \frac {e^{\left (2 \, e^{\left (-5 \, x\right )}\right )}}{2 \, x^{2}}}{\log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.49, size = 20, normalized size = 0.91 \begin {gather*} \frac {{\mathrm {e}}^{2\,{\mathrm {e}}^{-5\,x}}}{2\,x^2\,\ln \relax (2)}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 17, normalized size = 0.77 \begin {gather*} - x + \frac {e^{2 e^{- 5 x}}}{2 x^{2} \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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