Optimal. Leaf size=16 \[ \frac {19}{3}-\frac {1}{3} x \left (e^2+2 x\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.81, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {9} \begin {gather*} -\frac {1}{24} \left (4 x+e^2\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 9
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{24} \left (e^2+4 x\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} \frac {1}{3} \left (-e^2 x-2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 11, normalized size = 0.69 \begin {gather*} -\frac {2}{3} \, x^{2} - \frac {1}{3} \, x e^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 11, normalized size = 0.69 \begin {gather*} -\frac {2}{3} \, x^{2} - \frac {1}{3} \, x e^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 10, normalized size = 0.62
method | result | size |
gosper | \(-\frac {\left ({\mathrm e}^{2}+2 x \right ) x}{3}\) | \(10\) |
default | \(-\frac {{\mathrm e}^{2} x}{3}-\frac {2 x^{2}}{3}\) | \(12\) |
norman | \(-\frac {{\mathrm e}^{2} x}{3}-\frac {2 x^{2}}{3}\) | \(12\) |
risch | \(-\frac {{\mathrm e}^{2} x}{3}-\frac {2 x^{2}}{3}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 11, normalized size = 0.69 \begin {gather*} -\frac {2}{3} \, x^{2} - \frac {1}{3} \, x e^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 9, normalized size = 0.56 \begin {gather*} -\frac {x\,\left (2\,x+{\mathrm {e}}^2\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 14, normalized size = 0.88 \begin {gather*} - \frac {2 x^{2}}{3} - \frac {x e^{2}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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