Optimal. Leaf size=28 \[ e^{\frac {(-4+x) \left (-1+3 \left (-e^5+x\right )-\log (3)\right )}{e^5}}-x \]
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Rubi [A] time = 0.28, antiderivative size = 43, normalized size of antiderivative = 1.54, number of steps used = 4, number of rules used = 3, integrand size = 58, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.052, Rules used = {12, 2244, 2236} \begin {gather*} \exp \left (\frac {3 x^2}{e^5}-\frac {x \left (13+3 e^5+\log (3)\right )}{e^5}+\frac {4+12 e^5+\log (81)}{e^5}\right )-x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2236
Rule 2244
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-e^5+\exp \left (\frac {4+e^5 (12-3 x)-13 x+3 x^2+(4-x) \log (3)}{e^5}\right ) \left (-13-3 e^5+6 x-\log (3)\right )\right ) \, dx}{e^5}\\ &=-x+\frac {\int \exp \left (\frac {4+e^5 (12-3 x)-13 x+3 x^2+(4-x) \log (3)}{e^5}\right ) \left (-13-3 e^5+6 x-\log (3)\right ) \, dx}{e^5}\\ &=-x+\frac {\int \exp \left (\frac {3 x^2}{e^5}+\frac {4 \left (1+3 e^5+\log (3)\right )}{e^5}-\frac {x \left (13+3 e^5+\log (3)\right )}{e^5}\right ) \left (-13-3 e^5+6 x-\log (3)\right ) \, dx}{e^5}\\ &=\exp \left (\frac {3 x^2}{e^5}-\frac {x \left (13+3 e^5+\log (3)\right )}{e^5}+\frac {4+12 e^5+\log (81)}{e^5}\right )-x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.27, size = 44, normalized size = 1.57 \begin {gather*} e^{5+\frac {3 x^2}{e^5}-\frac {x \left (13+3 e^5+\log (3)\right )}{e^5}+\frac {4+7 e^5+\log (81)}{e^5}}-x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 32, normalized size = 1.14 \begin {gather*} -x + e^{\left ({\left (3 \, x^{2} - 3 \, {\left (x - 4\right )} e^{5} - {\left (x - 4\right )} \log \relax (3) - 13 \, x + 4\right )} e^{\left (-5\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.45, size = 46, normalized size = 1.64 \begin {gather*} -{\left (x e^{5} - e^{\left (3 \, x^{2} e^{\left (-5\right )} - x e^{\left (-5\right )} \log \relax (3) - 13 \, x e^{\left (-5\right )} + 4 \, e^{\left (-5\right )} \log \relax (3) - 3 \, x + 4 \, e^{\left (-5\right )} + 17\right )}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 24, normalized size = 0.86
method | result | size |
risch | \(-x +{\mathrm e}^{-\left (x -4\right ) \left (-3 x +\ln \relax (3)+3 \,{\mathrm e}^{5}+1\right ) {\mathrm e}^{-5}}\) | \(24\) |
norman | \(-x +{\mathrm e}^{\left (\left (-x +4\right ) \ln \relax (3)+\left (-3 x +12\right ) {\mathrm e}^{5}+3 x^{2}-13 x +4\right ) {\mathrm e}^{-5}}\) | \(37\) |
default | \({\mathrm e}^{-5} \left ({\mathrm e}^{\left (\left (-x +4\right ) \ln \relax (3)+\left (-3 x +12\right ) {\mathrm e}^{5}+3 x^{2}-13 x +4\right ) {\mathrm e}^{-5}} {\mathrm e}^{5}-x \,{\mathrm e}^{5}\right )\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 41, normalized size = 1.46 \begin {gather*} -{\left (x e^{5} - e^{\left ({\left (3 \, x^{2} - 3 \, {\left (x - 4\right )} e^{5} - {\left (x - 4\right )} \log \relax (3) - 13 \, x + 4\right )} e^{\left (-5\right )} + 5\right )}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.39, size = 44, normalized size = 1.57 \begin {gather*} \frac {3^{4\,{\mathrm {e}}^{-5}}\,{\mathrm {e}}^{3\,x^2\,{\mathrm {e}}^{-5}}\,{\mathrm {e}}^{4\,{\mathrm {e}}^{-5}}\,{\mathrm {e}}^{-3\,x}\,{\mathrm {e}}^{12}\,{\mathrm {e}}^{-13\,x\,{\mathrm {e}}^{-5}}}{3^{x\,{\mathrm {e}}^{-5}}}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 31, normalized size = 1.11 \begin {gather*} - x + e^{\frac {3 x^{2} - 13 x + \left (4 - x\right ) \log {\relax (3 )} + \left (12 - 3 x\right ) e^{5} + 4}{e^{5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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