Optimal. Leaf size=23 \[ -3+x+\frac {12 e^{-2 e^x+2 x} x^2}{\log (4)} \]
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Rubi [F]
time = 0.61, 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^{-2 e^x+2 x} \left (24 x+24 x^2-24 e^x x^2+e^{2 e^x-2 x} \log (4)\right )}{\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 e^{-2 e^x+2 x} \left (24 x+24 x^2-24 e^x x^2+e^{2 e^x-2 x} \log (4)\right ) \, dx}{\log (4)}\\ &=\frac {\int e^{-2 \left (e^x-x\right )} \left (24 x+24 x^2-24 e^x x^2+e^{2 e^x-2 x} \log (4)\right ) \, dx}{\log (4)}\\ &=\frac {\int \left (24 e^{-2 \left (e^x-x\right )} x+24 e^{-2 \left (e^x-x\right )} x^2-24 e^{-2 \left (e^x-x\right )+x} x^2+\log (4)\right ) \, dx}{\log (4)}\\ &=x+\frac {24 \int e^{-2 \left (e^x-x\right )} x \, dx}{\log (4)}+\frac {24 \int e^{-2 \left (e^x-x\right )} x^2 \, dx}{\log (4)}-\frac {24 \int e^{-2 \left (e^x-x\right )+x} x^2 \, dx}{\log (4)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 23, normalized size = 1.00 \begin {gather*} \frac {x \left (12 e^{-2 e^x+2 x} x+\log (4)\right )}{\log (4)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.31, size = 21, normalized size = 0.91
method | result | size |
risch | \(x +\frac {6 x^{2} {\mathrm e}^{-2 \,{\mathrm e}^{x}+2 x}}{\ln \left (2\right )}\) | \(21\) |
norman | \(\left ({\mathrm e}^{2 \,{\mathrm e}^{x}-2 x} x +\frac {6 x^{2}}{\ln \left (2\right )}\right ) {\mathrm e}^{-2 \,{\mathrm e}^{x}+2 x}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.41, size = 24, normalized size = 1.04 \begin {gather*} \frac {6 \, x^{2} e^{\left (2 \, x - 2 \, e^{x}\right )} + x \log \left (2\right )}{\log \left (2\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 = 1.43 \begin {gather*} \frac {{\left (x e^{\left (-2 \, x + 2 \, e^{x}\right )} \log \left (2\right ) + 6 \, x^{2}\right )} e^{\left (2 \, x - 2 \, e^{x}\right )}}{\log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 19, normalized size = 0.83 \begin {gather*} \frac {6 x^{2} e^{2 x - 2 e^{x}}}{\log {\left (2 \right )}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 24, normalized size = 1.04 \begin {gather*} \frac {6 \, x^{2} e^{\left (2 \, x - 2 \, e^{x}\right )} + x \log \left (2\right )}{\log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.12, size = 20, normalized size = 0.87 \begin {gather*} x+\frac {6\,x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{-2\,{\mathrm {e}}^x}}{\ln \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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