Optimal. Leaf size=19 \[ 25+4 x \log \left (-5+\frac {1}{25 x^2}+x+\log (\log (x))\right ) \]
________________________________________________________________________________________
Rubi [F] time = 1.08, 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 {100 x^2+\left (-8+100 x^3\right ) \log (x)+\left (\left (4-500 x^2+100 x^3\right ) \log (x)+100 x^2 \log (x) \log (\log (x))\right ) \log \left (\frac {1-125 x^2+25 x^3+25 x^2 \log (\log (x))}{25 x^2}\right )}{\left (1-125 x^2+25 x^3\right ) \log (x)+25 x^2 \log (x) \log (\log (x))} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {100 x^2+\left (-8+100 x^3\right ) \log (x)+\left (\left (4-500 x^2+100 x^3\right ) \log (x)+100 x^2 \log (x) \log (\log (x))\right ) \log \left (\frac {1-125 x^2+25 x^3+25 x^2 \log (\log (x))}{25 x^2}\right )}{\log (x) \left (1-125 x^2+25 x^3+25 x^2 \log (\log (x))\right )} \, dx\\ &=\int \frac {4 \left (25 x^2+\log (x) \left (-2+25 x^3+\left (1-125 x^2+25 x^3+25 x^2 \log (\log (x))\right ) \log \left (-5+\frac {1}{25 x^2}+x+\log (\log (x))\right )\right )\right )}{\log (x) \left (1-125 x^2+25 x^3+25 x^2 \log (\log (x))\right )} \, dx\\ &=4 \int \frac {25 x^2+\log (x) \left (-2+25 x^3+\left (1-125 x^2+25 x^3+25 x^2 \log (\log (x))\right ) \log \left (-5+\frac {1}{25 x^2}+x+\log (\log (x))\right )\right )}{\log (x) \left (1-125 x^2+25 x^3+25 x^2 \log (\log (x))\right )} \, dx\\ &=4 \int \left (\frac {25 x^2-2 \log (x)+25 x^3 \log (x)}{\log (x) \left (1-125 x^2+25 x^3+25 x^2 \log (\log (x))\right )}+\log \left (-5+\frac {1}{25 x^2}+x+\log (\log (x))\right )\right ) \, dx\\ &=4 \int \frac {25 x^2-2 \log (x)+25 x^3 \log (x)}{\log (x) \left (1-125 x^2+25 x^3+25 x^2 \log (\log (x))\right )} \, dx+4 \int \log \left (-5+\frac {1}{25 x^2}+x+\log (\log (x))\right ) \, dx\\ &=4 \int \left (-\frac {2}{1-125 x^2+25 x^3+25 x^2 \log (\log (x))}+\frac {25 x^3}{1-125 x^2+25 x^3+25 x^2 \log (\log (x))}+\frac {25 x^2}{\log (x) \left (1-125 x^2+25 x^3+25 x^2 \log (\log (x))\right )}\right ) \, dx+4 \int \log \left (-5+\frac {1}{25 x^2}+x+\log (\log (x))\right ) \, dx\\ &=4 \int \log \left (-5+\frac {1}{25 x^2}+x+\log (\log (x))\right ) \, dx-8 \int \frac {1}{1-125 x^2+25 x^3+25 x^2 \log (\log (x))} \, dx+100 \int \frac {x^3}{1-125 x^2+25 x^3+25 x^2 \log (\log (x))} \, dx+100 \int \frac {x^2}{\log (x) \left (1-125 x^2+25 x^3+25 x^2 \log (\log (x))\right )} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.27, size = 17, normalized size = 0.89 \begin {gather*} 4 x \log \left (-5+\frac {1}{25 x^2}+x+\log (\log (x))\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.71, size = 29, normalized size = 1.53 \begin {gather*} 4 \, x \log \left (\frac {25 \, x^{3} + 25 \, x^{2} \log \left (\log \relax (x)\right ) - 125 \, x^{2} + 1}{25 \, x^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.37, size = 35, normalized size = 1.84 \begin {gather*} -8 \, x \log \relax (5) + 4 \, x \log \left (25 \, x^{3} + 25 \, x^{2} \log \left (\log \relax (x)\right ) - 125 \, x^{2} + 1\right ) - 8 \, x \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [C] time = 0.12, size = 237, normalized size = 12.47
method | result | size |
risch | \(4 x \ln \left (\frac {1}{25}+x^{3}+\left (\ln \left (\ln \relax (x )\right )-5\right ) x^{2}\right )+2 i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-4 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-2 i \pi x \,\mathrm {csgn}\left (\frac {i}{x^{2}}\right ) \mathrm {csgn}\left (i \left (\frac {1}{25}+x^{3}+\left (\ln \left (\ln \relax (x )\right )-5\right ) x^{2}\right )\right ) \mathrm {csgn}\left (\frac {i \left (\frac {1}{25}+x^{3}+\left (\ln \left (\ln \relax (x )\right )-5\right ) x^{2}\right )}{x^{2}}\right )+2 i \pi x \,\mathrm {csgn}\left (\frac {i}{x^{2}}\right ) \mathrm {csgn}\left (\frac {i \left (\frac {1}{25}+x^{3}+\left (\ln \left (\ln \relax (x )\right )-5\right ) x^{2}\right )}{x^{2}}\right )^{2}+2 i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}+2 i \pi x \,\mathrm {csgn}\left (i \left (\frac {1}{25}+x^{3}+\left (\ln \left (\ln \relax (x )\right )-5\right ) x^{2}\right )\right ) \mathrm {csgn}\left (\frac {i \left (\frac {1}{25}+x^{3}+\left (\ln \left (\ln \relax (x )\right )-5\right ) x^{2}\right )}{x^{2}}\right )^{2}-2 i \pi x \mathrm {csgn}\left (\frac {i \left (\frac {1}{25}+x^{3}+\left (\ln \left (\ln \relax (x )\right )-5\right ) x^{2}\right )}{x^{2}}\right )^{3}-8 x \ln \relax (x )\) | \(237\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.90, size = 35, normalized size = 1.84 \begin {gather*} -8 \, x \log \relax (5) + 4 \, x \log \left (25 \, x^{3} + 25 \, x^{2} \log \left (\log \relax (x)\right ) - 125 \, x^{2} + 1\right ) - 8 \, x \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.70, size = 25, normalized size = 1.32 \begin {gather*} 4\,x\,\ln \left (\frac {x^2\,\ln \left (\ln \relax (x)\right )-5\,x^2+x^3+\frac {1}{25}}{x^2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 2.20, size = 27, normalized size = 1.42 \begin {gather*} 4 x \log {\left (\frac {x^{3} + x^{2} \log {\left (\log {\relax (x )} \right )} - 5 x^{2} + \frac {1}{25}}{x^{2}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________