Optimal. Leaf size=20 \[ -x+12 \left (e^{2 x}+e^x (-5+x)+x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 26, normalized size of antiderivative = 1.30, 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*} -12 e^x (4-x)-12 e^x+12 e^{2 x}+11 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=11 x+24 \int e^{2 x} \, dx+\int e^x (-48+12 x) \, dx\\ &=12 e^{2 x}-12 e^x (4-x)+11 x-12 \int e^x \, dx\\ &=-12 e^x+12 e^{2 x}-12 e^x (4-x)+11 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 0.95 \begin {gather*} 12 e^{2 x}+12 e^x (-5+x)+11 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 17, normalized size = 0.85 \begin {gather*} 12 \, {\left (x - 5\right )} e^{x} + 11 \, x + 12 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 17, normalized size = 0.85 \begin {gather*} 12 \, {\left (x - 5\right )} e^{x} + 11 \, x + 12 \, 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 = 19, normalized size = 0.95
method | result | size |
risch | \(12 \,{\mathrm e}^{2 x}+\left (12 x -60\right ) {\mathrm e}^{x}+11 x\) | \(19\) |
default | \(11 x +12 \,{\mathrm e}^{x} x -60 \,{\mathrm e}^{x}+12 \,{\mathrm e}^{2 x}\) | \(20\) |
norman | \(11 x +12 \,{\mathrm e}^{x} x -60 \,{\mathrm e}^{x}+12 \,{\mathrm e}^{2 x}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 21, normalized size = 1.05 \begin {gather*} 12 \, {\left (x - 1\right )} e^{x} + 11 \, x + 12 \, e^{\left (2 \, x\right )} - 48 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.44, size = 19, normalized size = 0.95 \begin {gather*} 11\,x+12\,{\mathrm {e}}^{2\,x}-60\,{\mathrm {e}}^x+12\,x\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 17, normalized size = 0.85 \begin {gather*} 11 x + \left (12 x - 60\right ) e^{x} + 12 e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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