Optimal. Leaf size=16 \[ -5+x^2+x \left (-\frac {8}{3}+2 x\right )+\log (3) \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.69, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {9} \begin {gather*} \frac {1}{27} (4-9 x)^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 9
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{27} (4-9 x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 0.69 \begin {gather*} -\frac {8 x}{3}+3 x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 9, normalized size = 0.56 \begin {gather*} 3 \, x^{2} - \frac {8}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 9, normalized size = 0.56 \begin {gather*} 3 \, x^{2} - \frac {8}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 9, normalized size = 0.56
method | result | size |
gosper | \(\frac {x \left (9 x -8\right )}{3}\) | \(9\) |
default | \(3 x^{2}-\frac {8}{3} x\) | \(10\) |
norman | \(3 x^{2}-\frac {8}{3} x\) | \(10\) |
risch | \(3 x^{2}-\frac {8}{3} x\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 9, normalized size = 0.56 \begin {gather*} 3 \, x^{2} - \frac {8}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 8, normalized size = 0.50 \begin {gather*} \frac {x\,\left (9\,x-8\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.04, size = 8, normalized size = 0.50 \begin {gather*} 3 x^{2} - \frac {8 x}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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