Optimal. Leaf size=20 \[ 10 \log (-1+\log (x (2+2 x (4+3 x)) \log (5))) \]
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Rubi [A] time = 0.20, antiderivative size = 23, normalized size of antiderivative = 1.15, number of steps used = 2, number of rules used = 2, integrand size = 58, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {6741, 6684} \begin {gather*} 10 \log \left (1-\log \left (2 x \left (3 x^2+4 x+1\right ) \log (5)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-10-80 x-90 x^2}{x \left (1+4 x+3 x^2\right ) \left (1-\log \left (2 x \left (1+4 x+3 x^2\right ) \log (5)\right )\right )} \, dx\\ &=10 \log \left (1-\log \left (2 x \left (1+4 x+3 x^2\right ) \log (5)\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 21, normalized size = 1.05 \begin {gather*} 10 \log \left (-1+\log \left (2 x \left (1+4 x+3 x^2\right ) \log (5)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 22, normalized size = 1.10 \begin {gather*} 10 \, \log \left (\log \left (2 \, {\left (3 \, x^{3} + 4 \, x^{2} + x\right )} \log \relax (5)\right ) - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 26, normalized size = 1.30 \begin {gather*} 10 \, \log \left (\log \left (6 \, x^{3} \log \relax (5) + 8 \, x^{2} \log \relax (5) + 2 \, x \log \relax (5)\right ) - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 24, normalized size = 1.20
method | result | size |
norman | \(10 \ln \left (\ln \left (\left (6 x^{3}+8 x^{2}+2 x \right ) \ln \relax (5)\right )-1\right )\) | \(24\) |
risch | \(10 \ln \left (\ln \left (\left (6 x^{3}+8 x^{2}+2 x \right ) \ln \relax (5)\right )-1\right )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 22, normalized size = 1.10 \begin {gather*} 10 \, \log \left (\log \relax (2) + \log \left (3 \, x + 1\right ) + \log \left (x + 1\right ) + \log \relax (x) + \log \left (\log \relax (5)\right ) - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.28, size = 23, normalized size = 1.15 \begin {gather*} 10\,\ln \left (\ln \left (\ln \relax (5)\,\left (6\,x^3+8\,x^2+2\,x\right )\right )-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 22, normalized size = 1.10 \begin {gather*} 10 \log {\left (\log {\left (\left (6 x^{3} + 8 x^{2} + 2 x\right ) \log {\relax (5 )} \right )} - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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