Optimal. Leaf size=19 \[ \frac {144}{x \left (1+3 \left (x+\frac {\log (x)}{x}\right )\right )} \]
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Rubi [A] time = 0.16, antiderivative size = 15, normalized size of antiderivative = 0.79, number of steps used = 3, number of rules used = 3, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {6688, 12, 6686} \begin {gather*} \frac {144}{3 x^2+x+3 \log (x)} \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 {144 \left (-3-x-6 x^2\right )}{x \left (x+3 x^2+3 \log (x)\right )^2} \, dx\\ &=144 \int \frac {-3-x-6 x^2}{x \left (x+3 x^2+3 \log (x)\right )^2} \, dx\\ &=\frac {144}{x+3 x^2+3 \log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 0.79 \begin {gather*} \frac {144}{x+3 x^2+3 \log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 15, normalized size = 0.79 \begin {gather*} \frac {144}{3 \, x^{2} + x + 3 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 15, normalized size = 0.79 \begin {gather*} \frac {144}{3 \, x^{2} + x + 3 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 16, normalized size = 0.84
method | result | size |
norman | \(\frac {144}{3 x^{2}+3 \ln \relax (x )+x}\) | \(16\) |
risch | \(\frac {144}{3 x^{2}+3 \ln \relax (x )+x}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 15, normalized size = 0.79 \begin {gather*} \frac {144}{3 \, x^{2} + x + 3 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.81, size = 15, normalized size = 0.79 \begin {gather*} \frac {144}{x+3\,\ln \relax (x)+3\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 12, normalized size = 0.63 \begin {gather*} \frac {144}{3 x^{2} + x + 3 \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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