Optimal. Leaf size=17 \[ \log (4 x)+\log \left (\frac {x}{3}+6 x^4\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 13, normalized size of antiderivative = 0.76, number of steps used = 4, number of rules used = 3, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {1593, 446, 72} \begin {gather*} \log \left (18 x^3+1\right )+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 72
Rule 446
Rule 1593
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2+90 x^3}{x \left (1+18 x^3\right )} \, dx\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {2+90 x}{x (1+18 x)} \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (\frac {2}{x}+\frac {54}{1+18 x}\right ) \, dx,x,x^3\right )\\ &=2 \log (x)+\log \left (1+18 x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 0.76 \begin {gather*} 2 \log (x)+\log \left (1+18 x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.90, size = 13, normalized size = 0.76 \begin {gather*} \log \left (18 \, x^{3} + 1\right ) + 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 15, normalized size = 0.88 \begin {gather*} \log \left ({\left | 18 \, x^{3} + 1 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.37, size = 14, normalized size = 0.82
method | result | size |
default | \(2 \ln \relax (x )+\ln \left (18 x^{3}+1\right )\) | \(14\) |
norman | \(2 \ln \relax (x )+\ln \left (18 x^{3}+1\right )\) | \(14\) |
risch | \(2 \ln \relax (x )+\ln \left (18 x^{3}+1\right )\) | \(14\) |
meijerg | \(\ln \left (18 x^{3}+1\right )+2 \ln \relax (x )+\frac {2 \ln \relax (2)}{3}+\frac {4 \ln \relax (3)}{3}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 13, normalized size = 0.76 \begin {gather*} \log \left (18 \, x^{3} + 1\right ) + 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.05, size = 11, normalized size = 0.65 \begin {gather*} \ln \left (x^3+\frac {1}{18}\right )+2\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.71 \begin {gather*} 2 \log {\relax (x )} + \log {\left (18 x^{3} + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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