Optimal. Leaf size=10 \[ \left (7+e+2 x^2\right )^2 \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.40, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {6} \begin {gather*} 4 x^4+4 (7+e) x^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left ((56+8 e) x+16 x^3\right ) \, dx\\ &=4 (7+e) x^2+4 x^4\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.70 \begin {gather*} 28 x^2+4 e x^2+4 x^4 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 18, normalized size = 1.80 \begin {gather*} 4 \, x^{4} + 4 \, x^{2} e + 28 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 18, normalized size = 1.80 \begin {gather*} 4 \, x^{4} + 4 \, x^{2} e + 28 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 13, normalized size = 1.30
method | result | size |
gosper | \(4 x^{2} \left (x^{2}+{\mathrm e}+7\right )\) | \(13\) |
norman | \(\left (4 \,{\mathrm e}+28\right ) x^{2}+4 x^{4}\) | \(17\) |
default | \(4 x^{2} {\mathrm e}+4 x^{4}+28 x^{2}\) | \(19\) |
risch | \(4 x^{2} {\mathrm e}+4 x^{4}+28 x^{2}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 18, normalized size = 1.80 \begin {gather*} 4 \, x^{4} + 4 \, x^{2} e + 28 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.62, size = 16, normalized size = 1.60 \begin {gather*} 4\,x^4+\left (4\,\mathrm {e}+28\right )\,x^2 \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 = 1.40 \begin {gather*} 4 x^{4} + x^{2} \left (4 e + 28\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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