Optimal. Leaf size=23 \[ 4 \left (-25+\frac {e^x}{2}-3 \left (3-x+8 x^2\right )\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.61, number of steps
used = 2, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2225}
\begin {gather*} -96 x^2+12 x+2 e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=12 x-96 x^2+2 \int e^x \, dx\\ &=2 e^x+12 x-96 x^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 0.61 \begin {gather*} 2 \left (e^x+6 x-48 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 14, normalized size = 0.61
method | result | size |
default | \(-96 x^{2}+12 x +2 \,{\mathrm e}^{x}\) | \(14\) |
norman | \(-96 x^{2}+12 x +2 \,{\mathrm e}^{x}\) | \(14\) |
risch | \(-96 x^{2}+12 x +2 \,{\mathrm e}^{x}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 13, normalized size = 0.57 \begin {gather*} -96 \, x^{2} + 12 \, x + 2 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 13, normalized size = 0.57 \begin {gather*} -96 \, x^{2} + 12 \, x + 2 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 12, normalized size = 0.52 \begin {gather*} - 96 x^{2} + 12 x + 2 e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 13, normalized size = 0.57 \begin {gather*} -96 \, x^{2} + 12 \, x + 2 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 13, normalized size = 0.57 \begin {gather*} 12\,x+2\,{\mathrm {e}}^x-96\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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