Optimal. Leaf size=28 \[ x-\frac {10 \left (-3 \log (3)+\frac {\log (\log (x))}{x^2+\log (x)}\right )}{-3+x^2} \]
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Rubi [F] time = 16.09, 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 {30 x^2-10 x^4+\left (30-10 x^2+9 x^5-6 x^7+x^9-60 x^6 \log (3)\right ) \log (x)+\left (18 x^3-12 x^5+2 x^7-120 x^4 \log (3)\right ) \log ^2(x)+\left (9 x-6 x^3+x^5-60 x^2 \log (3)\right ) \log ^3(x)+\left (\left (-30-50 x^2+40 x^4\right ) \log (x)+20 x^2 \log ^2(x)\right ) \log (\log (x))}{\left (9 x^5-6 x^7+x^9\right ) \log (x)+\left (18 x^3-12 x^5+2 x^7\right ) \log ^2(x)+\left (9 x-6 x^3+x^5\right ) \log ^3(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 {30 x^2-10 x^4+\left (30-10 x^2+9 x^5-6 x^7+x^9-60 x^6 \log (3)\right ) \log (x)+\left (18 x^3-12 x^5+2 x^7-120 x^4 \log (3)\right ) \log ^2(x)+\left (9 x-6 x^3+x^5-60 x^2 \log (3)\right ) \log ^3(x)+\left (\left (-30-50 x^2+40 x^4\right ) \log (x)+20 x^2 \log ^2(x)\right ) \log (\log (x))}{x \left (3-x^2\right )^2 \log (x) \left (x^2+\log (x)\right )^2} \, dx\\ &=\int \left (\frac {30-10 x^2+9 x^5-6 x^7+x^9-60 x^6 \log (3)}{x \left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2}+\frac {30 x}{\left (-3+x^2\right )^2 \log (x) \left (x^2+\log (x)\right )^2}-\frac {10 x^3}{\left (-3+x^2\right )^2 \log (x) \left (x^2+\log (x)\right )^2}+\frac {2 x^2 \left (9-6 x^2+x^4-60 x \log (3)\right ) \log (x)}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2}+\frac {\left (9-6 x^2+x^4-60 x \log (3)\right ) \log ^2(x)}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2}+\frac {10 \left (-3-5 x^2+4 x^4+2 x^2 \log (x)\right ) \log (\log (x))}{x \left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2}\right ) \, dx\\ &=2 \int \frac {x^2 \left (9-6 x^2+x^4-60 x \log (3)\right ) \log (x)}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2} \, dx-10 \int \frac {x^3}{\left (-3+x^2\right )^2 \log (x) \left (x^2+\log (x)\right )^2} \, dx+10 \int \frac {\left (-3-5 x^2+4 x^4+2 x^2 \log (x)\right ) \log (\log (x))}{x \left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2} \, dx+30 \int \frac {x}{\left (-3+x^2\right )^2 \log (x) \left (x^2+\log (x)\right )^2} \, dx+\int \frac {30-10 x^2+9 x^5-6 x^7+x^9-60 x^6 \log (3)}{x \left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2} \, dx+\int \frac {\left (9-6 x^2+x^4-60 x \log (3)\right ) \log ^2(x)}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2} \, dx\\ &=2 \int \left (-\frac {x^4 \left (9-6 x^2+x^4-60 x \log (3)\right )}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2}+\frac {x^2 \left (9-6 x^2+x^4-60 x \log (3)\right )}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )}\right ) \, dx-10 \int \left (\frac {1}{x \left (-3+x^2\right )^2 \log (x)}-\frac {x}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2}-\frac {1}{x \left (-3+x^2\right )^2 \left (x^2+\log (x)\right )}\right ) \, dx+10 \int \left (\frac {\left (-3-5 x^2+4 x^4+2 x^2 \log (x)\right ) \log (\log (x))}{9 x \left (x^2+\log (x)\right )^2}+\frac {x \left (-3-5 x^2+4 x^4+2 x^2 \log (x)\right ) \log (\log (x))}{3 \left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2}-\frac {x \left (-3-5 x^2+4 x^4+2 x^2 \log (x)\right ) \log (\log (x))}{9 \left (-3+x^2\right ) \left (x^2+\log (x)\right )^2}\right ) \, dx+30 \int \left (\frac {1}{x^3 \left (-3+x^2\right )^2 \log (x)}-\frac {1}{x \left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2}-\frac {1}{x^3 \left (-3+x^2\right )^2 \left (x^2+\log (x)\right )}\right ) \, dx+\int \left (\frac {10}{3 x \left (x^2+\log (x)\right )^2}+\frac {x^4}{\left (x^2+\log (x)\right )^2}-\frac {60 x \log (3)}{\left (x^2+\log (x)\right )^2}-\frac {540 x \log (3)}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2}+\frac {10 x (1+108 \log (3))}{3 \left (3-x^2\right ) \left (x^2+\log (x)\right )^2}\right ) \, dx+\int \left (\frac {9-6 x^2+x^4-60 x \log (3)}{\left (-3+x^2\right )^2}+\frac {x^4 \left (9-6 x^2+x^4-60 x \log (3)\right )}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2}-\frac {2 x^2 \left (9-6 x^2+x^4-60 x \log (3)\right )}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )}\right ) \, dx\\ &=\frac {10}{9} \int \frac {\left (-3-5 x^2+4 x^4+2 x^2 \log (x)\right ) \log (\log (x))}{x \left (x^2+\log (x)\right )^2} \, dx-\frac {10}{9} \int \frac {x \left (-3-5 x^2+4 x^4+2 x^2 \log (x)\right ) \log (\log (x))}{\left (-3+x^2\right ) \left (x^2+\log (x)\right )^2} \, dx-2 \int \frac {x^4 \left (9-6 x^2+x^4-60 x \log (3)\right )}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2} \, dx+\frac {10}{3} \int \frac {1}{x \left (x^2+\log (x)\right )^2} \, dx+\frac {10}{3} \int \frac {x \left (-3-5 x^2+4 x^4+2 x^2 \log (x)\right ) \log (\log (x))}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2} \, dx-10 \int \frac {1}{x \left (-3+x^2\right )^2 \log (x)} \, dx+10 \int \frac {x}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2} \, dx+10 \int \frac {1}{x \left (-3+x^2\right )^2 \left (x^2+\log (x)\right )} \, dx+30 \int \frac {1}{x^3 \left (-3+x^2\right )^2 \log (x)} \, dx-30 \int \frac {1}{x \left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2} \, dx-30 \int \frac {1}{x^3 \left (-3+x^2\right )^2 \left (x^2+\log (x)\right )} \, dx-(60 \log (3)) \int \frac {x}{\left (x^2+\log (x)\right )^2} \, dx-(540 \log (3)) \int \frac {x}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2} \, dx+\frac {1}{3} (10 (1+108 \log (3))) \int \frac {x}{\left (3-x^2\right ) \left (x^2+\log (x)\right )^2} \, dx+\int \frac {9-6 x^2+x^4-60 x \log (3)}{\left (-3+x^2\right )^2} \, dx+\int \frac {x^4}{\left (x^2+\log (x)\right )^2} \, dx+\int \frac {x^4 \left (9-6 x^2+x^4-60 x \log (3)\right )}{\left (-3+x^2\right )^2 \left (x^2+\log (x)\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 33, normalized size = 1.18 \begin {gather*} x+\frac {30 \log (3)}{-3+x^2}-\frac {10 \log (\log (x))}{\left (-3+x^2\right ) \left (x^2+\log (x)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 55, normalized size = 1.96 \begin {gather*} \frac {x^{5} - 3 \, x^{3} + 30 \, x^{2} \log \relax (3) + {\left (x^{3} - 3 \, x + 30 \, \log \relax (3)\right )} \log \relax (x) - 10 \, \log \left (\log \relax (x)\right )}{x^{4} - 3 \, x^{2} + {\left (x^{2} - 3\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 3.13, size = 39, normalized size = 1.39 \begin {gather*} x + \frac {30 \, \log \relax (3)}{x^{2} - 3} - \frac {10 \, \log \left (\log \relax (x)\right )}{x^{4} + x^{2} \log \relax (x) - 3 \, x^{2} - 3 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 41, normalized size = 1.46
method | result | size |
risch | \(-\frac {10 \ln \left (\ln \relax (x )\right )}{\left (x^{2}-3\right ) \left (\ln \relax (x )+x^{2}\right )}+\frac {x^{3}+30 \ln \relax (3)-3 x}{x^{2}-3}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 55, normalized size = 1.96 \begin {gather*} \frac {x^{5} - 3 \, x^{3} + 30 \, x^{2} \log \relax (3) + {\left (x^{3} - 3 \, x + 30 \, \log \relax (3)\right )} \log \relax (x) - 10 \, \log \left (\log \relax (x)\right )}{x^{4} - 3 \, x^{2} + {\left (x^{2} - 3\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.99, size = 37, normalized size = 1.32 \begin {gather*} x+\frac {30\,x^2\,\ln \relax (3)-10\,\ln \left (\ln \relax (x)\right )+30\,\ln \relax (3)\,\ln \relax (x)}{\left (\ln \relax (x)+x^2\right )\,\left (x^2-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.53, size = 37, normalized size = 1.32 \begin {gather*} x - \frac {10 \log {\left (\log {\relax (x )} \right )}}{x^{4} + x^{2} \log {\relax (x )} - 3 x^{2} - 3 \log {\relax (x )}} + \frac {30 \log {\relax (3 )}}{x^{2} - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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