Optimal. Leaf size=16 \[ \frac {7}{3} \left (2+x-\left (3+x^2\right )^2\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.12, number of steps
used = 2, number of rules used = 1, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.037, Rules used = {1600}
\begin {gather*} -\frac {7 x^4}{3}-14 x^2+\frac {7 x}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 1600
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {7}{3}-28 x-\frac {28 x^3}{3}\right ) \, dx\\ &=\frac {7 x}{3}-14 x^2-\frac {7 x^4}{3}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} -\frac {7}{3} \left (-x+6 x^2+x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.13, size = 15, normalized size = 0.94
method | result | size |
gosper | \(-\frac {7 x \left (x^{3}+6 x -1\right )}{3}\) | \(12\) |
default | \(-\frac {7}{3} x^{4}-14 x^{2}+\frac {7}{3} x\) | \(15\) |
norman | \(-\frac {7}{3} x^{4}-14 x^{2}+\frac {7}{3} x\) | \(15\) |
risch | \(-\frac {7}{3} x^{4}-14 x^{2}+\frac {7}{3} x\) | \(15\) |
meijerg | \(\frac {7 \sqrt {3}\, \arctan \left (\frac {x \sqrt {3}}{3}\right )}{3}+\frac {7 x^{2} \left (-x^{2}+6\right )}{3}-28 x^{2}+\frac {7 \sqrt {3}\, \left (\frac {2 x \sqrt {3}}{3}-2 \arctan \left (\frac {x \sqrt {3}}{3}\right )\right )}{6}\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 14, normalized size = 0.88 \begin {gather*} -\frac {7}{3} \, x^{4} - 14 \, x^{2} + \frac {7}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 14, normalized size = 0.88 \begin {gather*} -\frac {7}{3} \, x^{4} - 14 \, x^{2} + \frac {7}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 15, normalized size = 0.94 \begin {gather*} - \frac {7 x^{4}}{3} - 14 x^{2} + \frac {7 x}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 14, normalized size = 0.88 \begin {gather*} -\frac {7}{3} \, x^{4} - 14 \, x^{2} + \frac {7}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 11, normalized size = 0.69 \begin {gather*} -\frac {7\,x\,\left (x^3+6\,x-1\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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