Optimal. Leaf size=12 \[ 4 \left (2-e^{2 x}+x\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.92, number of steps
used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2225}
\begin {gather*} 4 x-4 e^{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 x-8 \int e^{2 x} \, dx\\ &=-4 e^{2 x}+4 x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 0.92 \begin {gather*} -4 e^{2 x}+4 x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 11, normalized size = 0.92
method | result | size |
default | \(4 x -4 \,{\mathrm e}^{2 x}\) | \(11\) |
norman | \(4 x -4 \,{\mathrm e}^{2 x}\) | \(11\) |
risch | \(4 x -4 \,{\mathrm e}^{2 x}\) | \(11\) |
derivativedivides | \(-4 \,{\mathrm e}^{2 x}+2 \ln \left ({\mathrm e}^{2 x}\right )\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 10, normalized size = 0.83 \begin {gather*} 4 \, x - 4 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 10, normalized size = 0.83 \begin {gather*} 4 \, x - 4 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 8, normalized size = 0.67 \begin {gather*} 4 x - 4 e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 10, normalized size = 0.83 \begin {gather*} 4 \, x - 4 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 10, normalized size = 0.83 \begin {gather*} 4\,x-4\,{\mathrm {e}}^{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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