Optimal. Leaf size=30 \[ x+\frac {5}{x \left (-1+\frac {2 \log (x)}{-3+(5+3 (10-x))^2}\right )} \]
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Rubi [F] time = 1.45, 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 {7454200-2564100 x+1823674 x^2-532140 x^3+66501 x^4-3780 x^5+81 x^6+\left (-12220-4798 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)}{1493284 x^2-513240 x^3+66096 x^4-3780 x^5+81 x^6+\left (-4888 x^2+840 x^3-36 x^4\right ) \log (x)+4 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 {7454200-2564100 x+1823674 x^2-532140 x^3+66501 x^4-3780 x^5+81 x^6-2 \left (6110+2399 x^2-420 x^3+18 x^4\right ) \log (x)+4 x^2 \log ^2(x)}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx\\ &=\int \left (1+\frac {10 \left (-1222-128100 x+33039 x^2-2835 x^3+81 x^4\right )}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )^2}-\frac {5 \left (-1222+9 x^2\right )}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )}\right ) \, dx\\ &=x-5 \int \frac {-1222+9 x^2}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )} \, dx+10 \int \frac {-1222-128100 x+33039 x^2-2835 x^3+81 x^4}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx\\ &=x-5 \int \left (\frac {9}{1222-210 x+9 x^2-2 \log (x)}-\frac {1222}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )}\right ) \, dx+10 \int \left (\frac {33039}{\left (1222-210 x+9 x^2-2 \log (x)\right )^2}-\frac {1222}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )^2}-\frac {128100}{x \left (1222-210 x+9 x^2-2 \log (x)\right )^2}-\frac {2835 x}{\left (1222-210 x+9 x^2-2 \log (x)\right )^2}+\frac {81 x^2}{\left (1222-210 x+9 x^2-2 \log (x)\right )^2}\right ) \, dx\\ &=x-45 \int \frac {1}{1222-210 x+9 x^2-2 \log (x)} \, dx+810 \int \frac {x^2}{\left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx+6110 \int \frac {1}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )} \, dx-12220 \int \frac {1}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx-28350 \int \frac {x}{\left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx+330390 \int \frac {1}{\left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx-1281000 \int \frac {1}{x \left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 33, normalized size = 1.10 \begin {gather*} x+\frac {5 \left (1222-210 x+9 x^2\right )}{x \left (-1222+210 x-9 x^2+2 \log (x)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.86, size = 49, normalized size = 1.63 \begin {gather*} \frac {9 \, x^{4} - 210 \, x^{3} - 2 \, x^{2} \log \relax (x) + 1177 \, x^{2} + 1050 \, x - 6110}{9 \, x^{3} - 210 \, x^{2} - 2 \, x \log \relax (x) + 1222 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 2.71, size = 35, normalized size = 1.17 \begin {gather*} x - \frac {5 \, {\left (9 \, x^{2} - 210 \, x + 1222\right )}}{9 \, x^{3} - 210 \, x^{2} - 2 \, x \log \relax (x) + 1222 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 34, normalized size = 1.13
method | result | size |
risch | \(x -\frac {5 \left (9 x^{2}-210 x +1222\right )}{x \left (9 x^{2}-210 x -2 \ln \relax (x )+1222\right )}\) | \(34\) |
norman | \(\frac {-6110-210 x^{3}+1050 x +1177 x^{2}-2 x^{2} \ln \relax (x )+9 x^{4}}{x \left (9 x^{2}-210 x -2 \ln \relax (x )+1222\right )}\) | \(48\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 49, normalized size = 1.63 \begin {gather*} \frac {9 \, x^{4} - 210 \, x^{3} - 2 \, x^{2} \log \relax (x) + 1177 \, x^{2} + 1050 \, x - 6110}{9 \, x^{3} - 210 \, x^{2} - 2 \, x \log \relax (x) + 1222 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.45, size = 32, normalized size = 1.07 \begin {gather*} x+\frac {45\,x^2-1050\,x+6110}{x\,\left (210\,x+2\,\ln \relax (x)-9\,x^2-1222\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 31, normalized size = 1.03 \begin {gather*} x + \frac {45 x^{2} - 1050 x + 6110}{- 9 x^{3} + 210 x^{2} + 2 x \log {\relax (x )} - 1222 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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