Optimal. Leaf size=23 \[ -(-2+e)^2+x+\frac {1}{64} \left (-\frac {9}{2}+x\right )^2 x^2 \]
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Rubi [A] time = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {12} \begin {gather*} \frac {x^4}{64}-\frac {9 x^3}{64}+\frac {81 x^2}{256}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{128} \int \left (128+81 x-54 x^2+8 x^3\right ) \, dx\\ &=x+\frac {81 x^2}{256}-\frac {9 x^3}{64}+\frac {x^4}{64}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 25, normalized size = 1.09 \begin {gather*} \frac {1}{128} \left (128 x+\frac {81 x^2}{2}-18 x^3+2 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 17, normalized size = 0.74 \begin {gather*} \frac {1}{64} \, x^{4} - \frac {9}{64} \, x^{3} + \frac {81}{256} \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 17, normalized size = 0.74 \begin {gather*} \frac {1}{64} \, x^{4} - \frac {9}{64} \, x^{3} + \frac {81}{256} \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 18, normalized size = 0.78
method | result | size |
default | \(\frac {1}{64} x^{4}-\frac {9}{64} x^{3}+\frac {81}{256} x^{2}+x\) | \(18\) |
norman | \(\frac {1}{64} x^{4}-\frac {9}{64} x^{3}+\frac {81}{256} x^{2}+x\) | \(18\) |
risch | \(\frac {1}{64} x^{4}-\frac {9}{64} x^{3}+\frac {81}{256} x^{2}+x\) | \(18\) |
gosper | \(\frac {x \left (4 x^{3}-36 x^{2}+81 x +256\right )}{256}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 17, normalized size = 0.74 \begin {gather*} \frac {1}{64} \, x^{4} - \frac {9}{64} \, x^{3} + \frac {81}{256} \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 17, normalized size = 0.74 \begin {gather*} \frac {x^4}{64}-\frac {9\,x^3}{64}+\frac {81\,x^2}{256}+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 19, normalized size = 0.83 \begin {gather*} \frac {x^{4}}{64} - \frac {9 x^{3}}{64} + \frac {81 x^{2}}{256} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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