Optimal. Leaf size=22 \[ \frac {x}{5 \left (2+x+x^2+x (\log (3)+\log (25))+\log (x)\right )} \]
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Rubi [F] time = 0.52, 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 {1-x^2+\log (x)}{20+20 x+25 x^2+10 x^3+5 x^4+\left (20 x+10 x^2+10 x^3\right ) \log (3)+5 x^2 \log ^2(3)+\left (20 x+10 x^2+10 x^3+10 x^2 \log (3)\right ) \log (25)+5 x^2 \log ^2(25)+\left (20+10 x+10 x^2+10 x \log (3)+10 x \log (25)\right ) \log (x)+5 \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 {1-x^2+\log (x)}{20+20 x+10 x^3+5 x^4+\left (20 x+10 x^2+10 x^3\right ) \log (3)+x^2 \left (25+5 \log ^2(3)\right )+\left (20 x+10 x^2+10 x^3+10 x^2 \log (3)\right ) \log (25)+5 x^2 \log ^2(25)+\left (20+10 x+10 x^2+10 x \log (3)+10 x \log (25)\right ) \log (x)+5 \log ^2(x)} \, dx\\ &=\int \frac {1-x^2+\log (x)}{20+20 x+10 x^3+5 x^4+\left (20 x+10 x^2+10 x^3\right ) \log (3)+\left (20 x+10 x^2+10 x^3+10 x^2 \log (3)\right ) \log (25)+x^2 \left (25+5 \log ^2(3)+5 \log ^2(25)\right )+\left (20+10 x+10 x^2+10 x \log (3)+10 x \log (25)\right ) \log (x)+5 \log ^2(x)} \, dx\\ &=\int \frac {1-x^2+\log (x)}{5 \left (2+x^2+x (1+\log (75))+\log (x)\right )^2} \, dx\\ &=\frac {1}{5} \int \frac {1-x^2+\log (x)}{\left (2+x^2+x (1+\log (75))+\log (x)\right )^2} \, dx\\ &=\frac {1}{5} \int \left (\frac {-1-2 x^2-x (1+\log (75))}{\left (2+x^2+x (1+\log (75))+\log (x)\right )^2}+\frac {1}{2+x^2+x (1+\log (75))+\log (x)}\right ) \, dx\\ &=\frac {1}{5} \int \frac {-1-2 x^2-x (1+\log (75))}{\left (2+x^2+x (1+\log (75))+\log (x)\right )^2} \, dx+\frac {1}{5} \int \frac {1}{2+x^2+x (1+\log (75))+\log (x)} \, dx\\ &=\frac {1}{5} \int \frac {1}{2+x^2+x (1+\log (75))+\log (x)} \, dx+\frac {1}{5} \int \left (-\frac {1}{\left (2+x^2+x (1+\log (75))+\log (x)\right )^2}-\frac {2 x^2}{\left (2+x^2+x (1+\log (75))+\log (x)\right )^2}+\frac {x (-1-\log (75))}{\left (2+x^2+x (1+\log (75))+\log (x)\right )^2}\right ) \, dx\\ &=-\left (\frac {1}{5} \int \frac {1}{\left (2+x^2+x (1+\log (75))+\log (x)\right )^2} \, dx\right )+\frac {1}{5} \int \frac {1}{2+x^2+x (1+\log (75))+\log (x)} \, dx-\frac {2}{5} \int \frac {x^2}{\left (2+x^2+x (1+\log (75))+\log (x)\right )^2} \, dx+\frac {1}{5} (-1-\log (75)) \int \frac {x}{\left (2+x^2+x (1+\log (75))+\log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 19, normalized size = 0.86 \begin {gather*} \frac {x}{5 \left (2+x+x^2+x \log (75)+\log (x)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 22, normalized size = 1.00 \begin {gather*} \frac {x}{5 \, {\left (x^{2} + 2 \, x \log \relax (5) + x \log \relax (3) + x + \log \relax (x) + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.50, size = 22, normalized size = 1.00 \begin {gather*} \frac {x}{5 \, {\left (x^{2} + 2 \, x \log \relax (5) + x \log \relax (3) + x + \log \relax (x) + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.19, size = 23, normalized size = 1.05
method | result | size |
norman | \(\frac {x}{10 x \ln \relax (5)+5 x \ln \relax (3)+5 x^{2}+5 \ln \relax (x )+5 x +10}\) | \(23\) |
risch | \(\frac {x}{10 x \ln \relax (5)+5 x \ln \relax (3)+5 x^{2}+5 \ln \relax (x )+5 x +10}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.08, size = 22, normalized size = 1.00 \begin {gather*} \frac {x}{5 \, {\left (x^{2} + x {\left (2 \, \log \relax (5) + \log \relax (3) + 1\right )} + \log \relax (x) + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.44, size = 22, normalized size = 1.00 \begin {gather*} \frac {x}{5\,\left (\ln \relax (x)+x\,\left (\ln \left (75\right )+1\right )+x^2+2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 29, normalized size = 1.32 \begin {gather*} \frac {x}{5 x^{2} + 5 x + 5 x \log {\relax (3 )} + 10 x \log {\relax (5 )} + 5 \log {\relax (x )} + 10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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