Optimal. Leaf size=32 \[ x \left (1-2 x+\frac {\left (-(7-x)^2+x\right )^2}{(5+\log (3))^2}-\log (\log (x))\right ) \]
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Rubi [B] time = 0.36, antiderivative size = 78, normalized size of antiderivative = 2.44, number of steps used = 9, number of rules used = 6, integrand size = 88, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.068, Rules used = {12, 6741, 6742, 6688, 2298, 2520} \begin {gather*} \frac {x^5}{(5+\log (3))^2}-\frac {30 x^4}{(5+\log (3))^2}+\frac {323 x^3}{(5+\log (3))^2}-\frac {2 x^2 \left (760+\log ^2(3)+10 \log (3)\right )}{(5+\log (3))^2}+\frac {x \left (2426+\log ^2(3)+10 \log (3)\right )}{(5+\log (3))^2}-x \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2298
Rule 2520
Rule 6688
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-25-10 \log (3)-\log ^2(3)+\left (2426-3040 x+969 x^2-120 x^3+5 x^4+(10-40 x) \log (3)+(1-4 x) \log ^2(3)\right ) \log (x)+\left (-25-10 \log (3)-\log ^2(3)\right ) \log (x) \log (\log (x))}{\log (x)} \, dx}{(5+\log (3))^2}\\ &=\frac {\int \frac {-25 \left (1+\frac {1}{25} \log (3) (10+\log (3))\right )+\left (2426-3040 x+969 x^2-120 x^3+5 x^4+(10-40 x) \log (3)+(1-4 x) \log ^2(3)\right ) \log (x)+\left (-25-10 \log (3)-\log ^2(3)\right ) \log (x) \log (\log (x))}{\log (x)} \, dx}{(5+\log (3))^2}\\ &=\frac {\int \left (\frac {-25 \left (1+\frac {1}{25} \log (3) (10+\log (3))\right )+969 x^2 \log (x)-120 x^3 \log (x)+5 x^4 \log (x)+2426 \left (1+\frac {\log (3) (10+\log (3))}{2426}\right ) \log (x)-3040 x \left (1+\frac {1}{760} \log (3) (10+\log (3))\right ) \log (x)}{\log (x)}-(5+\log (3))^2 \log (\log (x))\right ) \, dx}{(5+\log (3))^2}\\ &=\frac {\int \frac {-25 \left (1+\frac {1}{25} \log (3) (10+\log (3))\right )+969 x^2 \log (x)-120 x^3 \log (x)+5 x^4 \log (x)+2426 \left (1+\frac {\log (3) (10+\log (3))}{2426}\right ) \log (x)-3040 x \left (1+\frac {1}{760} \log (3) (10+\log (3))\right ) \log (x)}{\log (x)} \, dx}{(5+\log (3))^2}-\int \log (\log (x)) \, dx\\ &=-x \log (\log (x))+\frac {\int \left (2426+969 x^2-120 x^3+5 x^4+10 \log (3)+\log ^2(3)-4 x \left (760+10 \log (3)+\log ^2(3)\right )-\frac {(5+\log (3))^2}{\log (x)}\right ) \, dx}{(5+\log (3))^2}+\int \frac {1}{\log (x)} \, dx\\ &=\frac {323 x^3}{(5+\log (3))^2}-\frac {30 x^4}{(5+\log (3))^2}+\frac {x^5}{(5+\log (3))^2}-\frac {2 x^2 \left (760+10 \log (3)+\log ^2(3)\right )}{(5+\log (3))^2}+\frac {x \left (2426+10 \log (3)+\log ^2(3)\right )}{(5+\log (3))^2}-x \log (\log (x))+\text {li}(x)-\int \frac {1}{\log (x)} \, dx\\ &=\frac {323 x^3}{(5+\log (3))^2}-\frac {30 x^4}{(5+\log (3))^2}+\frac {x^5}{(5+\log (3))^2}-\frac {2 x^2 \left (760+10 \log (3)+\log ^2(3)\right )}{(5+\log (3))^2}+\frac {x \left (2426+10 \log (3)+\log ^2(3)\right )}{(5+\log (3))^2}-x \log (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 55, normalized size = 1.72 \begin {gather*} \frac {x \left (2426+323 x^2-30 x^3+x^4+10 \log (3)+\log ^2(3)-2 x \left (760+10 \log (3)+\log ^2(3)\right )-(5+\log (3))^2 \log (\log (x))\right )}{(5+\log (3))^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.51, size = 83, normalized size = 2.59 \begin {gather*} \frac {x^{5} - 30 \, x^{4} + 323 \, x^{3} - {\left (2 \, x^{2} - x\right )} \log \relax (3)^{2} - 1520 \, x^{2} - 10 \, {\left (2 \, x^{2} - x\right )} \log \relax (3) - {\left (x \log \relax (3)^{2} + 10 \, x \log \relax (3) + 25 \, x\right )} \log \left (\log \relax (x)\right ) + 2426 \, x}{\log \relax (3)^{2} + 10 \, \log \relax (3) + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.33, size = 86, normalized size = 2.69 \begin {gather*} \frac {x^{5} - 30 \, x^{4} - 2 \, x^{2} \log \relax (3)^{2} - x \log \relax (3)^{2} \log \left (\log \relax (x)\right ) + 323 \, x^{3} - 20 \, x^{2} \log \relax (3) + x \log \relax (3)^{2} - 10 \, x \log \relax (3) \log \left (\log \relax (x)\right ) - 1520 \, x^{2} + 10 \, x \log \relax (3) - 25 \, x \log \left (\log \relax (x)\right ) + 2426 \, x}{\log \relax (3)^{2} + 10 \, \log \relax (3) + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 87, normalized size = 2.72
method | result | size |
default | \(\frac {2426 x -10 \ln \left (\ln \relax (x )\right ) \ln \relax (3) x -20 x^{2} \ln \relax (3)+10 x \ln \relax (3)-x \ln \relax (3)^{2} \ln \left (\ln \relax (x )\right )-2 x^{2} \ln \relax (3)^{2}+x \ln \relax (3)^{2}-1520 x^{2}+323 x^{3}-30 x^{4}+x^{5}-25 x \ln \left (\ln \relax (x )\right )}{\ln \relax (3)^{2}+10 \ln \relax (3)+25}\) | \(87\) |
risch | \(-x \ln \left (\ln \relax (x )\right )+\frac {x^{5}}{\ln \relax (3)^{2}+10 \ln \relax (3)+25}-\frac {2 x^{2} \ln \relax (3)^{2}}{\ln \relax (3)^{2}+10 \ln \relax (3)+25}-\frac {30 x^{4}}{\ln \relax (3)^{2}+10 \ln \relax (3)+25}+\frac {x \ln \relax (3)^{2}}{\ln \relax (3)^{2}+10 \ln \relax (3)+25}-\frac {20 x^{2} \ln \relax (3)}{\ln \relax (3)^{2}+10 \ln \relax (3)+25}+\frac {323 x^{3}}{\ln \relax (3)^{2}+10 \ln \relax (3)+25}+\frac {10 x \ln \relax (3)}{\ln \relax (3)^{2}+10 \ln \relax (3)+25}-\frac {1520 x^{2}}{\ln \relax (3)^{2}+10 \ln \relax (3)+25}+\frac {2426 x}{\ln \relax (3)^{2}+10 \ln \relax (3)+25}\) | \(165\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.57, size = 116, normalized size = 3.62 \begin {gather*} \frac {x^{5} - 30 \, x^{4} - 2 \, x^{2} \log \relax (3)^{2} + 323 \, x^{3} - 20 \, x^{2} \log \relax (3) - {\left (x \log \left (\log \relax (x)\right ) - {\rm Ei}\left (\log \relax (x)\right )\right )} \log \relax (3)^{2} + x \log \relax (3)^{2} - {\rm Ei}\left (\log \relax (x)\right ) \log \relax (3)^{2} - 1520 \, x^{2} - 10 \, {\left (x \log \left (\log \relax (x)\right ) - {\rm Ei}\left (\log \relax (x)\right )\right )} \log \relax (3) + 10 \, x \log \relax (3) - 10 \, {\rm Ei}\left (\log \relax (x)\right ) \log \relax (3) - 25 \, x \log \left (\log \relax (x)\right ) + 2426 \, x}{\log \relax (3)^{2} + 10 \, \log \relax (3) + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.80, size = 112, normalized size = 3.50 \begin {gather*} \frac {323\,x^3}{10\,\ln \relax (3)+{\ln \relax (3)}^2+25}-x\,\ln \left (\ln \relax (x)\right )-\frac {30\,x^4}{10\,\ln \relax (3)+{\ln \relax (3)}^2+25}+\frac {x^5}{10\,\ln \relax (3)+{\ln \relax (3)}^2+25}+\frac {x\,\left (10\,\ln \relax (3)+{\ln \relax (3)}^2+2426\right )}{10\,\ln \relax (3)+{\ln \relax (3)}^2+25}-\frac {x^2\,\left (40\,\ln \relax (3)+4\,{\ln \relax (3)}^2+3040\right )}{2\,\left (10\,\ln \relax (3)+{\ln \relax (3)}^2+25\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.39, size = 110, normalized size = 3.44 \begin {gather*} \frac {x^{5}}{\log {\relax (3 )}^{2} + 10 \log {\relax (3 )} + 25} - \frac {30 x^{4}}{\log {\relax (3 )}^{2} + 10 \log {\relax (3 )} + 25} + \frac {323 x^{3}}{\log {\relax (3 )}^{2} + 10 \log {\relax (3 )} + 25} + \frac {x^{2} \left (-1520 - 20 \log {\relax (3 )} - 2 \log {\relax (3 )}^{2}\right )}{\log {\relax (3 )}^{2} + 10 \log {\relax (3 )} + 25} - x \log {\left (\log {\relax (x )} \right )} + \frac {x \left (\log {\relax (3 )}^{2} + 10 \log {\relax (3 )} + 2426\right )}{\log {\relax (3 )}^{2} + 10 \log {\relax (3 )} + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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