Optimal. Leaf size=24 \[ \log \left (-6+x+\log ^2\left (e^3+x+\frac {1}{3} \left (2-e^x+x\right )\right )\right ) \]
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Rubi [A] time = 0.40, antiderivative size = 30, normalized size of antiderivative = 1.25, number of steps used = 2, number of rules used = 2, integrand size = 106, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6741, 6684} \begin {gather*} \log \left (-x-\log ^2\left (\frac {1}{3} \left (4 x-e^x+3 e^3+2\right )\right )+6\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e^x+2 \left (1+\frac {3 e^3}{2}\right )+4 x-\left (-8+2 e^x\right ) \log \left (\frac {1}{3} \left (2+3 e^3-e^x+4 x\right )\right )}{\left (e^x-2 \left (1+\frac {3 e^3}{2}\right )-4 x\right ) \left (6-x-\log ^2\left (\frac {1}{3} \left (2+3 e^3-e^x+4 x\right )\right )\right )} \, dx\\ &=\log \left (6-x-\log ^2\left (\frac {1}{3} \left (2+3 e^3-e^x+4 x\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 30, normalized size = 1.25 \begin {gather*} \log \left (6-x-\log ^2\left (\frac {1}{3} \left (2+3 e^3-e^x+4 x\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 18, normalized size = 0.75 \begin {gather*} \log \left (\log \left (\frac {4}{3} \, x + e^{3} - \frac {1}{3} \, e^{x} + \frac {2}{3}\right )^{2} + x - 6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.64, size = 18, normalized size = 0.75 \begin {gather*} \log \left (\log \left (\frac {4}{3} \, x + e^{3} - \frac {1}{3} \, e^{x} + \frac {2}{3}\right )^{2} + x - 6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.35, size = 19, normalized size = 0.79
method | result | size |
norman | \(\ln \left (\ln \left (-\frac {{\mathrm e}^{x}}{3}+{\mathrm e}^{3}+\frac {4 x}{3}+\frac {2}{3}\right )^{2}-6+x \right )\) | \(19\) |
risch | \(\ln \left (\ln \left (-\frac {{\mathrm e}^{x}}{3}+{\mathrm e}^{3}+\frac {4 x}{3}+\frac {2}{3}\right )^{2}-6+x \right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.72, size = 42, normalized size = 1.75 \begin {gather*} \log \left (\log \relax (3)^{2} - 2 \, \log \relax (3) \log \left (4 \, x + 3 \, e^{3} - e^{x} + 2\right ) + \log \left (4 \, x + 3 \, e^{3} - e^{x} + 2\right )^{2} + x - 6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.32, size = 18, normalized size = 0.75 \begin {gather*} \ln \left ({\ln \left (\frac {4\,x}{3}+{\mathrm {e}}^3-\frac {{\mathrm {e}}^x}{3}+\frac {2}{3}\right )}^2+x-6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.85, size = 24, normalized size = 1.00 \begin {gather*} \log {\left (x + \log {\left (\frac {4 x}{3} - \frac {e^{x}}{3} + \frac {2}{3} + e^{3} \right )}^{2} - 6 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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