Optimal. Leaf size=32 \[ \frac {1}{2 \left (-e^x+e^{-3+\frac {1}{10} e^{(2-x) x} x}+\log (2)\right )} \]
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Rubi [A]
time = 0.86, antiderivative size = 39, normalized size of antiderivative = 1.22, number of steps
used = 3, number of rules used = 3, integrand size = 126, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6820, 12,
6818} \begin {gather*} \frac {e^3}{2 \left (e^{\frac {1}{10} e^{(2-x) x} x}-e^{x+3}+e^3 \log (2)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {10 e^{6+x}+\exp \left (3+\left (2+\frac {1}{10} e^{-((-2+x) x)}\right ) x-x^2\right ) \left (-1-2 x+2 x^2\right )}{20 \left (e^{\frac {1}{10} e^{-((-2+x) x)} x}-e^{3+x}+e^3 \log (2)\right )^2} \, dx\\ &=\frac {1}{20} \int \frac {10 e^{6+x}+\exp \left (3+\left (2+\frac {1}{10} e^{-((-2+x) x)}\right ) x-x^2\right ) \left (-1-2 x+2 x^2\right )}{\left (e^{\frac {1}{10} e^{-((-2+x) x)} x}-e^{3+x}+e^3 \log (2)\right )^2} \, dx\\ &=\frac {e^3}{2 \left (e^{\frac {1}{10} e^{(2-x) x} x}-e^{3+x}+e^3 \log (2)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.29, size = 38, normalized size = 1.19 \begin {gather*} \frac {e^3}{2 \left (e^{\frac {1}{10} e^{-((-2+x) x)} x}-e^{3+x}+e^3 \log (2)\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.03, size = 25, normalized size = 0.78
method | result | size |
risch | \(\frac {1}{2 \,{\mathrm e}^{\frac {x \,{\mathrm e}^{-\left (x -2\right ) x}}{10}-3}+2 \ln \left (2\right )-2 \,{\mathrm e}^{x}}\) | \(25\) |
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 = 0.35, size = 27, normalized size = 0.84 \begin {gather*} \frac {1}{2 \, {\left (e^{\left (\frac {1}{10} \, x e^{\left (-x^{2} + 2 \, x\right )} - 3\right )} - e^{x} + \log \left (2\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.16, size = 27, normalized size = 0.84 \begin {gather*} \frac {1}{- 2 e^{x} + 2 e^{\frac {x e^{- x^{2} + 2 x}}{10} - 3} + 2 \log {\left (2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {10\,{\mathrm {e}}^x-{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{2\,x-x^2}}{10}-3}\,{\mathrm {e}}^{2\,x-x^2}\,\left (-2\,x^2+2\,x+1\right )}{20\,{\mathrm {e}}^{2\,x}+20\,{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{2\,x-x^2}}{5}-6}+{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{2\,x-x^2}}{10}-3}\,\left (40\,\ln \left (2\right )-40\,{\mathrm {e}}^x\right )-40\,{\mathrm {e}}^x\,\ln \left (2\right )+20\,{\ln \left (2\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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