Optimal. Leaf size=23 \[ x \left (-3+4 (-2+x)+x^2-\frac {3}{-3+x-\log (x)}\right ) \]
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Rubi [F] time = 0.28, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-93+138 x-32 x^2-10 x^3+3 x^4+\left (-63+70 x+2 x^2-6 x^3\right ) \log (x)+\left (-11+8 x+3 x^2\right ) \log ^2(x)}{9-6 x+x^2+(6-2 x) \log (x)+\log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-93+138 x-32 x^2-10 x^3+3 x^4+\left (-63+70 x+2 x^2-6 x^3\right ) \log (x)+\left (-11+8 x+3 x^2\right ) \log ^2(x)}{(3-x+\log (x))^2} \, dx\\ &=\int \left (-11+8 x+3 x^2+\frac {3 (-1+x)}{(-3+x-\log (x))^2}-\frac {3}{-3+x-\log (x)}\right ) \, dx\\ &=-11 x+4 x^2+x^3+3 \int \frac {-1+x}{(-3+x-\log (x))^2} \, dx-3 \int \frac {1}{-3+x-\log (x)} \, dx\\ &=-11 x+4 x^2+x^3+3 \int \left (-\frac {1}{(-3+x-\log (x))^2}+\frac {x}{(-3+x-\log (x))^2}\right ) \, dx-3 \int \frac {1}{-3+x-\log (x)} \, dx\\ &=-11 x+4 x^2+x^3-3 \int \frac {1}{(-3+x-\log (x))^2} \, dx+3 \int \frac {x}{(-3+x-\log (x))^2} \, dx-3 \int \frac {1}{-3+x-\log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 21, normalized size = 0.91 \begin {gather*} x \left (-11+4 x+x^2+\frac {3}{3-x+\log (x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 41, normalized size = 1.78 \begin {gather*} \frac {x^{4} + x^{3} - 23 \, x^{2} - {\left (x^{3} + 4 \, x^{2} - 11 \, x\right )} \log \relax (x) + 30 \, x}{x - \log \relax (x) - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 24, normalized size = 1.04 \begin {gather*} x^{3} + 4 \, x^{2} - 11 \, x - \frac {3 \, x}{x - \log \relax (x) - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 25, normalized size = 1.09
method | result | size |
risch | \(x^{3}+4 x^{2}-11 x -\frac {3 x}{x -\ln \relax (x )-3}\) | \(25\) |
norman | \(\frac {x^{3}+x^{4}+30 \ln \relax (x )-23 x^{2}+11 x \ln \relax (x )-4 x^{2} \ln \relax (x )-x^{3} \ln \relax (x )+90}{x -\ln \relax (x )-3}\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 41, normalized size = 1.78 \begin {gather*} \frac {x^{4} + x^{3} - 23 \, x^{2} - {\left (x^{3} + 4 \, x^{2} - 11 \, x\right )} \log \relax (x) + 30 \, x}{x - \log \relax (x) - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.16, size = 28, normalized size = 1.22 \begin {gather*} \frac {3\,\ln \relax (x)+9}{\ln \relax (x)-x+3}-11\,x+4\,x^2+x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 20, normalized size = 0.87 \begin {gather*} x^{3} + 4 x^{2} - 11 x + \frac {3 x}{- x + \log {\relax (x )} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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