Optimal. Leaf size=25 \[ \frac {2 x \left (x+\frac {x^3}{8}+\frac {x}{\log (7)}\right )}{1-x} \]
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Rubi [B] time = 0.06, antiderivative size = 51, normalized size of antiderivative = 2.04, number of steps used = 5, number of rules used = 3, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {12, 27, 1850} \begin {gather*} -\frac {x^3}{4}-\frac {x^2}{4}-\frac {x (8+9 \log (7))}{4 \log (7)}+\frac {8+9 \log (7)}{4 (1-x) \log (7)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 1850
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {16 x-8 x^2+\left (16 x-8 x^2+4 x^3-3 x^4\right ) \log (7)}{4-8 x+4 x^2} \, dx}{\log (7)}\\ &=\frac {\int \frac {16 x-8 x^2+\left (16 x-8 x^2+4 x^3-3 x^4\right ) \log (7)}{4 (-1+x)^2} \, dx}{\log (7)}\\ &=\frac {\int \frac {16 x-8 x^2+\left (16 x-8 x^2+4 x^3-3 x^4\right ) \log (7)}{(-1+x)^2} \, dx}{4 \log (7)}\\ &=\frac {\int \left (-2 x \log (7)-3 x^2 \log (7)-8 \left (1+\frac {9 \log (7)}{8}\right )+\frac {8+9 \log (7)}{(-1+x)^2}\right ) \, dx}{4 \log (7)}\\ &=-\frac {x^2}{4}-\frac {x^3}{4}+\frac {8+9 \log (7)}{4 (1-x) \log (7)}-\frac {x (8+9 \log (7))}{4 \log (7)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 50, normalized size = 2.00 \begin {gather*} \frac {\frac {-8-9 \log (7)}{-1+x}-4 (-1+x)^2 \log (7)-(-1+x)^3 \log (7)-2 (-1+x) (4+7 \log (7))}{4 \log (7)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 37, normalized size = 1.48 \begin {gather*} -\frac {8 \, x^{2} + {\left (x^{4} + 8 \, x^{2} - 9 \, x + 9\right )} \log \relax (7) - 8 \, x + 8}{4 \, {\left (x - 1\right )} \log \relax (7)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 39, normalized size = 1.56 \begin {gather*} -\frac {x^{3} \log \relax (7) + x^{2} \log \relax (7) + 9 \, x \log \relax (7) + 8 \, x + \frac {9 \, \log \relax (7) + 8}{x - 1}}{4 \, \log \relax (7)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.79, size = 26, normalized size = 1.04
method | result | size |
norman | \(\frac {-\frac {x^{4}}{4}-\frac {2 \left (\ln \relax (7)+1\right ) x^{2}}{\ln \relax (7)}}{x -1}\) | \(26\) |
gosper | \(-\frac {x^{2} \left (x^{2} \ln \relax (7)+8 \ln \relax (7)+8\right )}{4 \ln \relax (7) \left (x -1\right )}\) | \(27\) |
risch | \(-\frac {x^{3}}{4}-\frac {x^{2}}{4}-\frac {9 x}{4}-\frac {2 x}{\ln \relax (7)}-\frac {9}{4 \left (x -1\right )}-\frac {2}{\ln \relax (7) \left (x -1\right )}\) | \(40\) |
default | \(\frac {-\ln \relax (7) x^{3}-x^{2} \ln \relax (7)-9 x \ln \relax (7)-8 x -\frac {9 \ln \relax (7)+8}{x -1}}{4 \ln \relax (7)}\) | \(43\) |
meijerg | \(-\frac {x \left (-5 x^{3}-10 x^{2}-30 x +60\right )}{20 \left (1-x \right )}+\frac {x \left (-2 x^{2}-6 x +12\right )}{-4 x +4}-\frac {\left (-2 \ln \relax (7)-2\right ) \left (-\frac {x \left (-3 x +6\right )}{3 \left (1-x \right )}-2 \ln \left (1-x \right )\right )}{\ln \relax (7)}+\frac {\left (4 \ln \relax (7)+4\right ) \left (\frac {x}{1-x}+\ln \left (1-x \right )\right )}{\ln \relax (7)}\) | \(110\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 39, normalized size = 1.56 \begin {gather*} -\frac {x^{3} \log \relax (7) + x^{2} \log \relax (7) + x {\left (9 \, \log \relax (7) + 8\right )} + \frac {9 \, \log \relax (7) + 8}{x - 1}}{4 \, \log \relax (7)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.04, size = 47, normalized size = 1.88 \begin {gather*} \frac {9\,\ln \relax (7)+8}{4\,\ln \relax (7)-4\,x\,\ln \relax (7)}-x\,\left (\frac {8\,\ln \relax (7)+8}{4\,\ln \relax (7)}+\frac {1}{4}\right )-\frac {x^2}{4}-\frac {x^3}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.23, size = 39, normalized size = 1.56 \begin {gather*} - \frac {x^{3}}{4} - \frac {x^{2}}{4} - x \left (\frac {2}{\log {\relax (7 )}} + \frac {9}{4}\right ) - \frac {8 + 9 \log {\relax (7 )}}{4 x \log {\relax (7 )} - 4 \log {\relax (7 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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