Optimal. Leaf size=18 \[ x+\log \left (4 x^2\right )+\log ^2\left (\frac {x^3}{e^2}\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 16, normalized size of antiderivative = 0.89, number of steps used = 5, number of rules used = 3, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {14, 43, 2301} \begin {gather*} \left (2-\log \left (x^3\right )\right )^2+x+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 43
Rule 2301
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2+x}{x}+\frac {6 \left (-2+\log \left (x^3\right )\right )}{x}\right ) \, dx\\ &=6 \int \frac {-2+\log \left (x^3\right )}{x} \, dx+\int \frac {2+x}{x} \, dx\\ &=\left (2-\log \left (x^3\right )\right )^2+\int \left (1+\frac {2}{x}\right ) \, dx\\ &=x+2 \log (x)+\left (2-\log \left (x^3\right )\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 0.67 \begin {gather*} x-10 \log (x)+\log ^2\left (x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 20, normalized size = 1.11 \begin {gather*} \log \left (x^{3} e^{\left (-2\right )}\right )^{2} + x + \frac {2}{3} \, \log \left (x^{3} e^{\left (-2\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 12, normalized size = 0.67 \begin {gather*} \log \left (x^{3}\right )^{2} + x - 10 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 13, normalized size = 0.72
method | result | size |
default | \(x -10 \ln \relax (x )+\ln \left (x^{3}\right )^{2}\) | \(13\) |
risch | \(x +\ln \left (x^{3} {\mathrm e}^{-2}\right )^{2}+2 \ln \relax (x )\) | \(16\) |
norman | \(x +\ln \left (x^{3} {\mathrm e}^{-2}\right )^{2}+2 \ln \relax (x )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 15, normalized size = 0.83 \begin {gather*} \log \left (x^{3} e^{\left (-2\right )}\right )^{2} + x + 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.09, size = 14, normalized size = 0.78 \begin {gather*} {\ln \left (x^3\right )}^2-\frac {10\,\ln \left (x^3\right )}{3}+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 15, normalized size = 0.83 \begin {gather*} x + 2 \log {\relax (x )} + \log {\left (\frac {x^{3}}{e^{2}} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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