Optimal. Leaf size=19 \[ e^{\left (-e^x+x\right ) \left (-3-\frac {1}{x}+\log (2)\right )} \]
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Rubi [F]
time = 2.60, 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 {\exp \left (\frac {-x-3 x^2+x^2 \log (2)+e^x (1+3 x-x \log (2))}{x}\right ) \left (-3 x^2+x^2 \log (2)+e^x \left (-1+x+3 x^2-x^2 \log (2)\right )\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {-x-3 x^2+x^2 \log (2)+e^x (1+3 x-x \log (2))}{x}\right ) \left (x^2 (-3+\log (2))+e^x \left (-1+x+3 x^2-x^2 \log (2)\right )\right )}{x^2} \, dx\\ &=\int \frac {e^{\frac {\left (-e^x+x\right ) (-1-x (3-\log (2)))}{x}} \left (x^2 (-3+\log (2))+e^x \left (-1+x+3 x^2-x^2 \log (2)\right )\right )}{x^2} \, dx\\ &=\int \left (\frac {\exp \left (x+\frac {\left (-e^x+x\right ) (-1-x (3-\log (2)))}{x}\right ) \left (-1+x+x^2 (3-\log (2))\right )}{x^2}-3 e^{\frac {\left (-e^x+x\right ) (-1-x (3-\log (2)))}{x}} \left (1-\frac {\log (2)}{3}\right )\right ) \, dx\\ &=-\left ((3-\log (2)) \int e^{\frac {\left (-e^x+x\right ) (-1-x (3-\log (2)))}{x}} \, dx\right )+\int \frac {\exp \left (x+\frac {\left (-e^x+x\right ) (-1-x (3-\log (2)))}{x}\right ) \left (-1+x+x^2 (3-\log (2))\right )}{x^2} \, dx\\ &=-\left ((3-\log (2)) \int e^{\frac {\left (-e^x+x\right ) (-1-x (3-\log (2)))}{x}} \, dx\right )+\int \left (-\frac {\exp \left (x+\frac {\left (-e^x+x\right ) (-1-x (3-\log (2)))}{x}\right )}{x^2}+\frac {\exp \left (x+\frac {\left (-e^x+x\right ) (-1-x (3-\log (2)))}{x}\right )}{x}+3 \exp \left (x+\frac {\left (-e^x+x\right ) (-1-x (3-\log (2)))}{x}\right ) \left (1-\frac {\log (2)}{3}\right )\right ) \, dx\\ &=(3-\log (2)) \int \exp \left (x+\frac {\left (-e^x+x\right ) (-1-x (3-\log (2)))}{x}\right ) \, dx-(3-\log (2)) \int e^{\frac {\left (-e^x+x\right ) (-1-x (3-\log (2)))}{x}} \, dx-\int \frac {\exp \left (x+\frac {\left (-e^x+x\right ) (-1-x (3-\log (2)))}{x}\right )}{x^2} \, dx+\int \frac {\exp \left (x+\frac {\left (-e^x+x\right ) (-1-x (3-\log (2)))}{x}\right )}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.28, size = 24, normalized size = 1.26 \begin {gather*} 2^x e^{-1-3 x+e^x \left (3+\frac {1}{x}-\log (2)\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 22, normalized size = 1.16
method | result | size |
risch | \({\mathrm e}^{-\frac {\left ({\mathrm e}^{x}-x \right ) \left (x \ln \left (2\right )-3 x -1\right )}{x}}\) | \(22\) |
norman | \({\mathrm e}^{\frac {\left (-x \ln \left (2\right )+3 x +1\right ) {\mathrm e}^{x}+x^{2} \ln \left (2\right )-3 x^{2}-x}{x}}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.55, size = 26, normalized size = 1.37 \begin {gather*} e^{\left (x \log \left (2\right ) - e^{x} \log \left (2\right ) - 3 \, x + \frac {e^{x}}{x} + 3 \, e^{x} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 33, normalized size = 1.74 \begin {gather*} e^{\left (\frac {x^{2} \log \left (2\right ) - 3 \, x^{2} - {\left (x \log \left (2\right ) - 3 \, x - 1\right )} e^{x} - x}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 29 vs.
\(2 (14) = 28\).
time = 0.14, size = 29, normalized size = 1.53 \begin {gather*} e^{\frac {- 3 x^{2} + x^{2} \log {\left (2 \right )} - x + \left (- x \log {\left (2 \right )} + 3 x + 1\right ) e^{x}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 26, normalized size = 1.37 \begin {gather*} e^{\left (x \log \left (2\right ) - e^{x} \log \left (2\right ) - 3 \, x + \frac {e^{x}}{x} + 3 \, e^{x} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.94, size = 27, normalized size = 1.42 \begin {gather*} 2^{x-{\mathrm {e}}^x}\,{\mathrm {e}}^{-3\,x}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{x}}\,{\mathrm {e}}^{3\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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