Optimal. Leaf size=21 \[ (2-x) (3+4 x (256+2 x (4+x))+\log (x)) \]
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Rubi [A] time = 0.05, antiderivative size = 28, normalized size of antiderivative = 1.33, number of steps used = 5, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {14, 2295} \begin {gather*} -8 x^4-16 x^3-960 x^2+2045 x-x \log (x)+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2295
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2 \left (-1-1022 x+960 x^2+24 x^3+16 x^4\right )}{x}-\log (x)\right ) \, dx\\ &=-\left (2 \int \frac {-1-1022 x+960 x^2+24 x^3+16 x^4}{x} \, dx\right )-\int \log (x) \, dx\\ &=x-x \log (x)-2 \int \left (-1022-\frac {1}{x}+960 x+24 x^2+16 x^3\right ) \, dx\\ &=2045 x-960 x^2-16 x^3-8 x^4+2 \log (x)-x \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 1.33 \begin {gather*} 2045 x-960 x^2-16 x^3-8 x^4+2 \log (x)-x \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 26, normalized size = 1.24 \begin {gather*} -8 \, x^{4} - 16 \, x^{3} - 960 \, x^{2} - {\left (x - 2\right )} \log \relax (x) + 2045 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 28, normalized size = 1.33 \begin {gather*} -8 \, x^{4} - 16 \, x^{3} - 960 \, x^{2} - x \log \relax (x) + 2045 \, x + 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 29, normalized size = 1.38
method | result | size |
default | \(-8 x^{4}-16 x^{3}+2045 x -x \ln \relax (x )-960 x^{2}+2 \ln \relax (x )\) | \(29\) |
norman | \(-8 x^{4}-16 x^{3}+2045 x -x \ln \relax (x )-960 x^{2}+2 \ln \relax (x )\) | \(29\) |
risch | \(-8 x^{4}-16 x^{3}+2045 x -x \ln \relax (x )-960 x^{2}+2 \ln \relax (x )\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 28, normalized size = 1.33 \begin {gather*} -8 \, x^{4} - 16 \, x^{3} - 960 \, x^{2} - x \log \relax (x) + 2045 \, x + 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.71, size = 28, normalized size = 1.33 \begin {gather*} 2045\,x+2\,\ln \relax (x)-x\,\ln \relax (x)-960\,x^2-16\,x^3-8\,x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 27, normalized size = 1.29 \begin {gather*} - 8 x^{4} - 16 x^{3} - 960 x^{2} - x \log {\relax (x )} + 2045 x + 2 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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