Optimal. Leaf size=28 \[ x+\log \left (\frac {9 x}{20}-x \left (1-(5+\log (x)) \left (x+(x+\log (x))^2\right )\right )\right ) \]
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Rubi [A] time = 0.49, antiderivative size = 46, normalized size of antiderivative = 1.64, number of steps used = 5, number of rules used = 3, integrand size = 110, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {6742, 43, 6684} \begin {gather*} \log \left (-100 x^2-20 x^2 \log (x)-100 x-20 \log ^3(x)-40 x \log ^2(x)-100 \log ^2(x)-220 x \log (x)+11\right )+x+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 6684
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1+x}{x}+\frac {20 \left (16 x+11 x^2+10 \log (x)+15 x \log (x)+2 x^2 \log (x)+3 \log ^2(x)+2 x \log ^2(x)\right )}{x \left (-11+100 x+100 x^2+220 x \log (x)+20 x^2 \log (x)+100 \log ^2(x)+40 x \log ^2(x)+20 \log ^3(x)\right )}\right ) \, dx\\ &=20 \int \frac {16 x+11 x^2+10 \log (x)+15 x \log (x)+2 x^2 \log (x)+3 \log ^2(x)+2 x \log ^2(x)}{x \left (-11+100 x+100 x^2+220 x \log (x)+20 x^2 \log (x)+100 \log ^2(x)+40 x \log ^2(x)+20 \log ^3(x)\right )} \, dx+\int \frac {1+x}{x} \, dx\\ &=\log \left (11-100 x-100 x^2-220 x \log (x)-20 x^2 \log (x)-100 \log ^2(x)-40 x \log ^2(x)-20 \log ^3(x)\right )+\int \left (1+\frac {1}{x}\right ) \, dx\\ &=x+\log (x)+\log \left (11-100 x-100 x^2-220 x \log (x)-20 x^2 \log (x)-100 \log ^2(x)-40 x \log ^2(x)-20 \log ^3(x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 46, normalized size = 1.64 \begin {gather*} x+\log (x)+\log \left (11-100 x-100 x^2-220 x \log (x)-20 x^2 \log (x)-100 \log ^2(x)-40 x \log ^2(x)-20 \log ^3(x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 43, normalized size = 1.54 \begin {gather*} x + \log \left (20 \, {\left (2 \, x + 5\right )} \log \relax (x)^{2} + 20 \, \log \relax (x)^{3} + 100 \, x^{2} + 20 \, {\left (x^{2} + 11 \, x\right )} \log \relax (x) + 100 \, x - 11\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 46, normalized size = 1.64 \begin {gather*} x + \log \left (20 \, x^{2} \log \relax (x) + 40 \, x \log \relax (x)^{2} + 20 \, \log \relax (x)^{3} + 100 \, x^{2} + 220 \, x \log \relax (x) + 100 \, \log \relax (x)^{2} + 100 \, x - 11\right ) + \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 = 40, normalized size = 1.43
method | result | size |
risch | \(x +\ln \relax (x )+\ln \left (\ln \relax (x )^{3}+\left (5+2 x \right ) \ln \relax (x )^{2}+\left (x^{2}+11 x \right ) \ln \relax (x )+5 x^{2}+5 x -\frac {11}{20}\right )\) | \(40\) |
norman | \(x +\ln \relax (x )+\ln \left (20 \ln \relax (x )^{3}+40 x \ln \relax (x )^{2}+20 x^{2} \ln \relax (x )+100 \ln \relax (x )^{2}+220 x \ln \relax (x )+100 x^{2}+100 x -11\right )\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 39, normalized size = 1.39 \begin {gather*} x + \log \left ({\left (2 \, x + 5\right )} \log \relax (x)^{2} + \log \relax (x)^{3} + 5 \, x^{2} + {\left (x^{2} + 11 \, x\right )} \log \relax (x) + 5 \, x - \frac {11}{20}\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.76, size = 57, normalized size = 2.04 \begin {gather*} \ln \left (20\,x^2\,\ln \relax (x)+100\,x^2+40\,x\,{\ln \relax (x)}^2+220\,x\,\ln \relax (x)+100\,x+20\,{\ln \relax (x)}^3+100\,{\ln \relax (x)}^2-11\right )+\frac {x^2\,\ln \relax (x)+x^3}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 42, normalized size = 1.50 \begin {gather*} x + \log {\relax (x )} + \log {\left (5 x^{2} + 5 x + \left (2 x + 5\right ) \log {\relax (x )}^{2} + \left (x^{2} + 11 x\right ) \log {\relax (x )} + \log {\relax (x )}^{3} - \frac {11}{20} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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