Optimal. Leaf size=18 \[ \frac {2}{5 (-4+10 (4+x)+\log (1+\log (x)))} \]
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Rubi [A] time = 0.27, antiderivative size = 16, normalized size of antiderivative = 0.89, number of steps used = 3, number of rules used = 3, integrand size = 88, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {6688, 12, 6686} \begin {gather*} \frac {2}{5 (10 x+\log (\log (x)+1)+36)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 (-1-10 x-10 x \log (x))}{5 x (1+\log (x)) (36+10 x+\log (1+\log (x)))^2} \, dx\\ &=\frac {2}{5} \int \frac {-1-10 x-10 x \log (x)}{x (1+\log (x)) (36+10 x+\log (1+\log (x)))^2} \, dx\\ &=\frac {2}{5 (36+10 x+\log (1+\log (x)))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 16, normalized size = 0.89 \begin {gather*} \frac {2}{5 (36+10 x+\log (1+\log (x)))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 14, normalized size = 0.78 \begin {gather*} \frac {2}{5 \, {\left (10 \, x + \log \left (\log \relax (x) + 1\right ) + 36\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.38, size = 14, normalized size = 0.78 \begin {gather*} \frac {2}{5 \, {\left (10 \, x + \log \left (\log \relax (x) + 1\right ) + 36\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 15, normalized size = 0.83
method | result | size |
risch | \(\frac {2}{5 \left (\ln \left (\ln \relax (x )+1\right )+10 x +36\right )}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.79, size = 14, normalized size = 0.78 \begin {gather*} \frac {2}{5 \, {\left (10 \, x + \log \left (\log \relax (x) + 1\right ) + 36\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int -\frac {20\,x+20\,x\,\ln \relax (x)+2}{6480\,x+\ln \left (\ln \relax (x)+1\right )\,\left (360\,x+\ln \relax (x)\,\left (100\,x^2+360\,x\right )+100\,x^2\right )+{\ln \left (\ln \relax (x)+1\right )}^2\,\left (5\,x+5\,x\,\ln \relax (x)\right )+3600\,x^2+500\,x^3+\ln \relax (x)\,\left (500\,x^3+3600\,x^2+6480\,x\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.50, size = 14, normalized size = 0.78 \begin {gather*} \frac {2}{50 x + 5 \log {\left (\log {\relax (x )} + 1 \right )} + 180} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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