Optimal. Leaf size=32 \[ 2 x^2-x^2 (-3-\log (2))-\log (x)-\log \left (\log \left ((3-x)^2\right )\right ) \]
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Rubi [A] time = 0.30, antiderivative size = 25, normalized size of antiderivative = 0.78, number of steps used = 6, number of rules used = 5, integrand size = 64, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.078, Rules used = {1593, 6688, 2390, 2302, 29} \begin {gather*} \frac {1}{2} x^2 (10+\log (4))-\log (x)-\log \left (\log \left ((x-3)^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 1593
Rule 2302
Rule 2390
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2 x+\left (3-x-30 x^2+10 x^3+\left (-6 x^2+2 x^3\right ) \log (2)\right ) \log \left (9-6 x+x^2\right )}{(-3+x) x \log \left (9-6 x+x^2\right )} \, dx\\ &=\int \left (-\frac {1}{x}+x (10+\log (4))-\frac {2}{(-3+x) \log \left ((-3+x)^2\right )}\right ) \, dx\\ &=\frac {1}{2} x^2 (10+\log (4))-\log (x)-2 \int \frac {1}{(-3+x) \log \left ((-3+x)^2\right )} \, dx\\ &=\frac {1}{2} x^2 (10+\log (4))-\log (x)-2 \operatorname {Subst}\left (\int \frac {1}{x \log \left (x^2\right )} \, dx,x,-3+x\right )\\ &=\frac {1}{2} x^2 (10+\log (4))-\log (x)-\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log \left ((-3+x)^2\right )\right )\\ &=\frac {1}{2} x^2 (10+\log (4))-\log (x)-\log \left (\log \left ((-3+x)^2\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 28, normalized size = 0.88 \begin {gather*} 5 x^2+\frac {1}{2} x^2 \log (4)-\log (x)-\log \left (\log \left ((-3+x)^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 28, normalized size = 0.88 \begin {gather*} x^{2} \log \relax (2) + 5 \, x^{2} - \log \relax (x) - \log \left (\log \left (x^{2} - 6 \, x + 9\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 25, normalized size = 0.78 \begin {gather*} x^{2} {\left (\log \relax (2) + 5\right )} - \log \relax (x) - \log \left (\log \left (x^{2} - 6 \, x + 9\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.26, size = 26, normalized size = 0.81
method | result | size |
norman | \(\left (\ln \relax (2)+5\right ) x^{2}-\ln \relax (x )-\ln \left (\ln \left (x^{2}-6 x +9\right )\right )\) | \(26\) |
default | \(5 x^{2}-\ln \relax (x )+x^{2} \ln \relax (2)-\ln \left (\ln \left (x^{2}-6 x +9\right )\right )\) | \(29\) |
risch | \(5 x^{2}-\ln \relax (x )+x^{2} \ln \relax (2)-\ln \left (\ln \left (x^{2}-6 x +9\right )\right )\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.48, size = 71, normalized size = 2.22 \begin {gather*} 5 \, x^{2} + {\left (x^{2} + 6 \, x + 18 \, \log \left (x - 3\right )\right )} \log \relax (2) - 6 \, {\left (x + 3 \, \log \left (x - 3\right )\right )} \log \relax (2) - \frac {1}{2} \, \log \left (x^{2} - 6 \, x + 9\right ) \log \left (\log \left (x - 3\right )\right ) + \log \left (x - 3\right ) \log \left (\log \left (x - 3\right )\right ) - \log \relax (x) - \log \left (\log \left (x - 3\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.33, size = 54, normalized size = 1.69 \begin {gather*} \frac {\left (\ln \relax (2)+5\right )\,x^4+\left (-\ln \left (64\right )-30\right )\,x^3+\left (\ln \left (512\right )+45\right )\,x^2}{x^2-6\,x+9}-\ln \left (\ln \left (x^2-6\,x+9\right )\right )-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 22, normalized size = 0.69 \begin {gather*} x^{2} \left (\log {\relax (2 )} + 5\right ) - \log {\relax (x )} - \log {\left (\log {\left (x^{2} - 6 x + 9 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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