Optimal. Leaf size=23 \[ -4+10 x-\left (-1-e^x+x\right )^2-2 \log (2)+\log (3) \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.17, number of steps used = 4, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2194, 2176} \begin {gather*} -x^2+2 e^x x+12 x-2 e^x-e^{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=12 x-x^2-2 \int e^{2 x} \, dx+2 \int e^x x \, dx\\ &=-e^{2 x}+12 x+2 e^x x-x^2-2 \int e^x \, dx\\ &=-2 e^x-e^{2 x}+12 x+2 e^x x-x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 30, normalized size = 1.30 \begin {gather*} -2 \left (\frac {e^{2 x}}{2}-e^x (-1+x)-6 x+\frac {x^2}{2}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 22, normalized size = 0.96 \begin {gather*} -x^{2} + 2 \, {\left (x - 1\right )} e^{x} + 12 \, x - e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 22, normalized size = 0.96 \begin {gather*} -x^{2} + 2 \, {\left (x - 1\right )} e^{x} + 12 \, x - e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 23, normalized size = 1.00
method | result | size |
risch | \(-{\mathrm e}^{2 x}+2 \left (x -1\right ) {\mathrm e}^{x}-x^{2}+12 x\) | \(23\) |
default | \(-x^{2}+12 x -{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x} x -2 \,{\mathrm e}^{x}\) | \(25\) |
norman | \(-x^{2}+12 x -{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x} x -2 \,{\mathrm e}^{x}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 22, normalized size = 0.96 \begin {gather*} -x^{2} + 2 \, {\left (x - 1\right )} e^{x} + 12 \, x - e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.02, size = 24, normalized size = 1.04 \begin {gather*} 12\,x-{\mathrm {e}}^{2\,x}-2\,{\mathrm {e}}^x+2\,x\,{\mathrm {e}}^x-x^2 \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*} - x^{2} + 12 x + \left (2 x - 2\right ) e^{x} - e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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