Optimal. Leaf size=22 \[ -5-x+\frac {e^{2 e^{-5 x}}}{x^2 \log (4)} \]
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Rubi [F]
time = 0.30, 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 = 0.19, 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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Maple [A]
time = 0.18, size = 21, normalized size = 0.95
method | result | size |
risch | \(-x +\frac {{\mathrm e}^{2 \,{\mathrm e}^{-5 x}}}{2 x^{2} \ln \left (2\right )}\) | \(21\) |
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*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 26, normalized size = 1.18 \begin {gather*} -\frac {2 \, x^{3} \log \left (2\right ) - e^{\left (2 \, e^{\left (-5 \, x\right )}\right )}}{2 \, x^{2} \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 17, normalized size = 0.77 \begin {gather*} - x + \frac {e^{2 e^{- 5 x}}}{2 x^{2} \log {\left (2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 26, normalized size = 1.18 \begin {gather*} -\frac {2 \, x^{3} \log \left (2\right ) - e^{\left (2 \, e^{\left (-5 \, x\right )}\right )}}{2 \, x^{2} \log \left (2\right )} \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 \left (2\right )}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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