Optimal. Leaf size=23 \[ 5+\left (420+\frac {9}{x}\right ) \left (3+2 x+\frac {x}{x+\log (x)}\right ) \]
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Rubi [F] time = 0.48, 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 {-9 x-456 x^2+840 x^4+\left (-54 x+420 x^2+1680 x^3\right ) \log (x)+\left (-27+840 x^2\right ) \log ^2(x)}{x^4+2 x^3 \log (x)+x^2 \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 {-9 x-456 x^2+840 x^4+\left (-54 x+420 x^2+1680 x^3\right ) \log (x)+\left (-27+840 x^2\right ) \log ^2(x)}{x^2 (x+\log (x))^2} \, dx\\ &=\int \left (\frac {3 \left (-9+280 x^2\right )}{x^2}-\frac {3 \left (3+143 x+140 x^2\right )}{x (x+\log (x))^2}+\frac {420}{x+\log (x)}\right ) \, dx\\ &=3 \int \frac {-9+280 x^2}{x^2} \, dx-3 \int \frac {3+143 x+140 x^2}{x (x+\log (x))^2} \, dx+420 \int \frac {1}{x+\log (x)} \, dx\\ &=3 \int \left (280-\frac {9}{x^2}\right ) \, dx-3 \int \left (\frac {143}{(x+\log (x))^2}+\frac {3}{x (x+\log (x))^2}+\frac {140 x}{(x+\log (x))^2}\right ) \, dx+420 \int \frac {1}{x+\log (x)} \, dx\\ &=\frac {27}{x}+840 x-9 \int \frac {1}{x (x+\log (x))^2} \, dx-420 \int \frac {x}{(x+\log (x))^2} \, dx+420 \int \frac {1}{x+\log (x)} \, dx-429 \int \frac {1}{(x+\log (x))^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.13, size = 23, normalized size = 1.00 \begin {gather*} 3 \left (\frac {9}{x}+280 x+\frac {3+140 x}{x+\log (x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 36, normalized size = 1.57 \begin {gather*} \frac {3 \, {\left (280 \, x^{3} + 140 \, x^{2} + {\left (280 \, x^{2} + 9\right )} \log \relax (x) + 12 \, x\right )}}{x^{2} + x \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 22, normalized size = 0.96 \begin {gather*} 840 \, x + \frac {3 \, {\left (140 \, x + 3\right )}}{x + \log \relax (x)} + \frac {27}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 27, normalized size = 1.17
method | result | size |
risch | \(\frac {840 x^{2}+27}{x}+\frac {420 x +9}{x +\ln \relax (x )}\) | \(27\) |
norman | \(\frac {-420 x \ln \relax (x )+840 x^{2} \ln \relax (x )+36 x +840 x^{3}+27 \ln \relax (x )}{\left (x +\ln \relax (x )\right ) x}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 36, normalized size = 1.57 \begin {gather*} \frac {3 \, {\left (280 \, x^{3} + 140 \, x^{2} + {\left (280 \, x^{2} + 9\right )} \log \relax (x) + 12 \, x\right )}}{x^{2} + x \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.18, size = 28, normalized size = 1.22 \begin {gather*} 840\,x+\frac {27\,\ln \relax (x)-x\,\left (420\,\ln \relax (x)-36\right )}{x\,\left (x+\ln \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 15, normalized size = 0.65 \begin {gather*} 840 x + \frac {420 x + 9}{x + \log {\relax (x )}} + \frac {27}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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