Optimal. Leaf size=28 \[ \left (x+(1-x) \left (x+\frac {1}{4} x (1+3 (12-x)+x)\right )\right ) \log (3) \]
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Rubi [A] time = 0.00, antiderivative size = 26, normalized size of antiderivative = 0.93, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {12} \begin {gather*} \frac {1}{2} x^3 \log (3)-\frac {43}{4} x^2 \log (3)+\frac {45}{4} x \log (3) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \log (3) \int \left (45-86 x+6 x^2\right ) \, dx\\ &=\frac {45}{4} x \log (3)-\frac {43}{4} x^2 \log (3)+\frac {1}{2} x^3 \log (3)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 0.71 \begin {gather*} \frac {1}{4} \left (45 x-43 x^2+2 x^3\right ) \log (3) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 18, normalized size = 0.64 \begin {gather*} \frac {1}{4} \, {\left (2 \, x^{3} - 43 \, x^{2} + 45 \, x\right )} \log \relax (3) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.93, size = 18, normalized size = 0.64 \begin {gather*} \frac {1}{4} \, {\left (2 \, x^{3} - 43 \, x^{2} + 45 \, x\right )} \log \relax (3) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 16, normalized size = 0.57
method | result | size |
gosper | \(\frac {x \left (2 x^{2}-43 x +45\right ) \ln \relax (3)}{4}\) | \(16\) |
default | \(\frac {\left (2 x^{3}-43 x^{2}+45 x \right ) \ln \relax (3)}{4}\) | \(19\) |
norman | \(\frac {45 x \ln \relax (3)}{4}-\frac {43 x^{2} \ln \relax (3)}{4}+\frac {x^{3} \ln \relax (3)}{2}\) | \(21\) |
risch | \(\frac {45 x \ln \relax (3)}{4}-\frac {43 x^{2} \ln \relax (3)}{4}+\frac {x^{3} \ln \relax (3)}{2}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 18, normalized size = 0.64 \begin {gather*} \frac {1}{4} \, {\left (2 \, x^{3} - 43 \, x^{2} + 45 \, x\right )} \log \relax (3) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 15, normalized size = 0.54 \begin {gather*} \frac {x\,\ln \relax (3)\,\left (2\,x^2-43\,x+45\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 26, normalized size = 0.93 \begin {gather*} \frac {x^{3} \log {\relax (3 )}}{2} - \frac {43 x^{2} \log {\relax (3 )}}{4} + \frac {45 x \log {\relax (3 )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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