Optimal. Leaf size=33 \[ -3+\frac {5+x}{3-x-\frac {5+\frac {x^2 \log (x)}{2+x}}{2 x}} \]
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Rubi [F] time = 1.15, 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 {-200-280 x+18 x^2+122 x^3+34 x^4+\left (20 x^2-2 x^4\right ) \log (x)}{100-140 x+9 x^2+68 x^3-24 x^4-8 x^5+4 x^6+\left (20 x^2-14 x^3-4 x^4+4 x^5\right ) \log (x)+x^4 \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 {2 \left (-100-140 x+9 x^2+61 x^3+17 x^4-x^2 \left (-10+x^2\right ) \log (x)\right )}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2} \, dx\\ &=2 \int \frac {-100-140 x+9 x^2+61 x^3+17 x^4-x^2 \left (-10+x^2\right ) \log (x)}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2} \, dx\\ &=2 \int \left (\frac {-200-70 x+39 x^2+34 x^3+15 x^4+2 x^5}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2}+\frac {10-x^2}{10-7 x-2 x^2+2 x^3+x^2 \log (x)}\right ) \, dx\\ &=2 \int \frac {-200-70 x+39 x^2+34 x^3+15 x^4+2 x^5}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2} \, dx+2 \int \frac {10-x^2}{10-7 x-2 x^2+2 x^3+x^2 \log (x)} \, dx\\ &=2 \int \left (-\frac {200}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2}-\frac {70 x}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2}+\frac {39 x^2}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2}+\frac {34 x^3}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2}+\frac {15 x^4}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2}+\frac {2 x^5}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2}\right ) \, dx+2 \int \left (\frac {10}{10-7 x-2 x^2+2 x^3+x^2 \log (x)}-\frac {x^2}{10-7 x-2 x^2+2 x^3+x^2 \log (x)}\right ) \, dx\\ &=-\left (2 \int \frac {x^2}{10-7 x-2 x^2+2 x^3+x^2 \log (x)} \, dx\right )+4 \int \frac {x^5}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2} \, dx+20 \int \frac {1}{10-7 x-2 x^2+2 x^3+x^2 \log (x)} \, dx+30 \int \frac {x^4}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2} \, dx+68 \int \frac {x^3}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2} \, dx+78 \int \frac {x^2}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2} \, dx-140 \int \frac {x}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2} \, dx-400 \int \frac {1}{\left (10-7 x-2 x^2+2 x^3+x^2 \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.55, size = 34, normalized size = 1.03 \begin {gather*} -\frac {2 x \left (10+7 x+x^2\right )}{10-7 x-2 x^2+2 x^3+x^2 \log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 37, normalized size = 1.12 \begin {gather*} -\frac {2 \, {\left (x^{3} + 7 \, x^{2} + 10 \, x\right )}}{2 \, x^{3} + x^{2} \log \relax (x) - 2 \, x^{2} - 7 \, x + 10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 37, normalized size = 1.12 \begin {gather*} -\frac {2 \, {\left (x^{3} + 7 \, x^{2} + 10 \, x\right )}}{2 \, x^{3} + x^{2} \log \relax (x) - 2 \, x^{2} - 7 \, x + 10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 35, normalized size = 1.06
method | result | size |
risch | \(-\frac {2 \left (x^{2}+7 x +10\right ) x}{x^{2} \ln \relax (x )+2 x^{3}-2 x^{2}-7 x +10}\) | \(35\) |
norman | \(\frac {-2 x^{3}-14 x^{2}-20 x}{x^{2} \ln \relax (x )+2 x^{3}-2 x^{2}-7 x +10}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 37, normalized size = 1.12 \begin {gather*} -\frac {2 \, {\left (x^{3} + 7 \, x^{2} + 10 \, x\right )}}{2 \, x^{3} + x^{2} \log \relax (x) - 2 \, x^{2} - 7 \, x + 10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.37, size = 39, normalized size = 1.18 \begin {gather*} -\frac {2\,x^3+14\,x^2+20\,x}{x^2\,\ln \relax (x)-7\,x-2\,x^2+2\,x^3+10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 36, normalized size = 1.09 \begin {gather*} \frac {- 2 x^{3} - 14 x^{2} - 20 x}{2 x^{3} + x^{2} \log {\relax (x )} - 2 x^{2} - 7 x + 10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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