Optimal. Leaf size=19 \[ 2 \left (-1+5 x^3 (-x+\log (4))+\log (-1+x)\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 21, normalized size of antiderivative = 1.11, number of steps used = 2, number of rules used = 1, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {1850} \begin {gather*} -10 x^4+10 x^3 \log (4)+2 \log (1-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1850
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2}{-1+x}-40 x^3+30 x^2 \log (4)\right ) \, dx\\ &=-10 x^4+10 x^3 \log (4)+2 \log (1-x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 23, normalized size = 1.21 \begin {gather*} 10-10 x^4-\log (1048576)+x^3 \log (1048576)+2 \log (-1+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 19, normalized size = 1.00 \begin {gather*} -10 \, x^{4} + 20 \, x^{3} \log \relax (2) + 2 \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 20, normalized size = 1.05 \begin {gather*} -10 \, x^{4} + 20 \, x^{3} \log \relax (2) + 2 \, \log \left ({\left | x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.17, size = 20, normalized size = 1.05
method | result | size |
default | \(-10 x^{4}+20 x^{3} \ln \relax (2)+2 \ln \left (x -1\right )\) | \(20\) |
norman | \(-10 x^{4}+20 x^{3} \ln \relax (2)+2 \ln \left (x -1\right )\) | \(20\) |
risch | \(-10 x^{4}+20 x^{3} \ln \relax (2)+2 \ln \left (x -1\right )\) | \(20\) |
meijerg | \(-38 \ln \left (1-x \right )-\frac {2 x \left (15 x^{3}+20 x^{2}+30 x +60\right )}{3}-\left (60 \ln \relax (2)+40\right ) \left (-\frac {x \left (4 x^{2}+6 x +12\right )}{12}-\ln \left (1-x \right )\right )-60 \ln \relax (2) \left (\frac {x \left (6+3 x \right )}{6}+\ln \left (1-x \right )\right )\) | \(77\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 19, normalized size = 1.00 \begin {gather*} -10 \, x^{4} + 20 \, x^{3} \log \relax (2) + 2 \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 19, normalized size = 1.00 \begin {gather*} 2\,\ln \left (x-1\right )+20\,x^3\,\ln \relax (2)-10\,x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 19, normalized size = 1.00 \begin {gather*} - 10 x^{4} + 20 x^{3} \log {\relax (2 )} + 2 \log {\left (x - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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