Optimal. Leaf size=17 \[ 3 \left (4-e+x^2+\frac {2 \log (x)}{x}\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 13, normalized size of antiderivative = 0.76, number of steps used = 5, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {14, 2304} \begin {gather*} 3 x^2+\frac {6 \log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2304
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {6 \left (1+x^3\right )}{x^2}-\frac {6 \log (x)}{x^2}\right ) \, dx\\ &=6 \int \frac {1+x^3}{x^2} \, dx-6 \int \frac {\log (x)}{x^2} \, dx\\ &=\frac {6}{x}+\frac {6 \log (x)}{x}+6 \int \left (\frac {1}{x^2}+x\right ) \, dx\\ &=3 x^2+\frac {6 \log (x)}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 0.76 \begin {gather*} 3 x^2+\frac {6 \log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 13, normalized size = 0.76 \begin {gather*} \frac {3 \, {\left (x^{3} + 2 \, \log \relax (x)\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 13, normalized size = 0.76 \begin {gather*} 3 \, x^{2} + \frac {6 \, \log \relax (x)}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 14, normalized size = 0.82
method | result | size |
default | \(3 x^{2}+\frac {6 \ln \relax (x )}{x}\) | \(14\) |
risch | \(3 x^{2}+\frac {6 \ln \relax (x )}{x}\) | \(14\) |
norman | \(\frac {3 x^{3}+6 \ln \relax (x )}{x}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 13, normalized size = 0.76 \begin {gather*} 3 \, x^{2} + \frac {6 \, \log \relax (x)}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.20, size = 13, normalized size = 0.76 \begin {gather*} \frac {6\,\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 = 0.09, size = 10, normalized size = 0.59 \begin {gather*} 3 x^{2} + \frac {6 \log {\relax (x )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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