Optimal. Leaf size=14 \[ \left (-2+e^3-4 x+\log \left (x^2\right )\right )^2 \]
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Rubi [B] time = 0.05, antiderivative size = 39, normalized size of antiderivative = 2.79, number of steps used = 7, number of rules used = 4, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {14, 2346, 2301, 2295} \begin {gather*} 16 x^2+\log ^2\left (x^2\right )-8 x \log \left (x^2\right )-8 e^3 x+16 x-4 \left (2-e^3\right ) \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2295
Rule 2301
Rule 2346
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {4 \left (-2+e^3-2 e^3 x+8 x^2\right )}{x}-\frac {4 (-1+2 x) \log \left (x^2\right )}{x}\right ) \, dx\\ &=4 \int \frac {-2+e^3-2 e^3 x+8 x^2}{x} \, dx-4 \int \frac {(-1+2 x) \log \left (x^2\right )}{x} \, dx\\ &=4 \int \left (-2 e^3+\frac {-2+e^3}{x}+8 x\right ) \, dx+4 \int \frac {\log \left (x^2\right )}{x} \, dx-8 \int \log \left (x^2\right ) \, dx\\ &=16 x-8 e^3 x+16 x^2-4 \left (2-e^3\right ) \log (x)-8 x \log \left (x^2\right )+\log ^2\left (x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.01, size = 39, normalized size = 2.79 \begin {gather*} 16 x-8 e^3 x+16 x^2-8 \log (x)+4 e^3 \log (x)-8 x \log \left (x^2\right )+\log ^2\left (x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.53, size = 35, normalized size = 2.50 \begin {gather*} 16 \, x^{2} - 8 \, x e^{3} - 2 \, {\left (4 \, x - e^{3} + 2\right )} \log \left (x^{2}\right ) + \log \left (x^{2}\right )^{2} + 16 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.22, size = 37, normalized size = 2.64 \begin {gather*} 16 \, x^{2} - 8 \, x e^{3} - 8 \, x \log \left (x^{2}\right ) + \log \left (x^{2}\right )^{2} + 4 \, e^{3} \log \relax (x) + 16 \, x - 8 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 39, normalized size = 2.79
method | result | size |
norman | \(\ln \left (x^{2}\right )^{2}+\left (16-8 \,{\mathrm e}^{3}\right ) x +\left (2 \,{\mathrm e}^{3}-4\right ) \ln \left (x^{2}\right )+16 x^{2}-8 x \ln \left (x^{2}\right )\) | \(39\) |
default | \(16 x^{2}-8 x \,{\mathrm e}^{3}+4 \ln \relax (x ) {\mathrm e}^{3}-8 \ln \relax (x )-8 x \ln \left (x^{2}\right )+16 x +4 \ln \relax (x ) \ln \left (x^{2}\right )-4 \ln \relax (x )^{2}\) | \(46\) |
risch | \(16 x^{2}-8 x \,{\mathrm e}^{3}+4 \ln \relax (x ) {\mathrm e}^{3}-8 \ln \relax (x )-8 x \ln \left (x^{2}\right )+16 x +4 \ln \relax (x ) \ln \left (x^{2}\right )-4 \ln \relax (x )^{2}\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.36, size = 37, normalized size = 2.64 \begin {gather*} 16 \, x^{2} - 8 \, x e^{3} - 8 \, x \log \left (x^{2}\right ) + \log \left (x^{2}\right )^{2} + 4 \, e^{3} \log \relax (x) + 16 \, x - 8 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.54, size = 26, normalized size = 1.86 \begin {gather*} \left (4\,x-\ln \left (x^2\right )\right )\,\left (4\,x-\ln \left (x^2\right )-2\,{\mathrm {e}}^3+4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.16, size = 37, normalized size = 2.64 \begin {gather*} 16 x^{2} - 8 x \log {\left (x^{2} \right )} + x \left (16 - 8 e^{3}\right ) + 4 \left (-2 + e^{3}\right ) \log {\relax (x )} + \log {\left (x^{2} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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