Optimal. Leaf size=21 \[ \log \left (3-\log \left (9+e^4+x\right )+\log \left (\frac {5}{x+\log (3)}\right )\right ) \]
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Rubi [A] time = 0.32, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 108, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {6, 6688, 6684} \begin {gather*} \log \left (-\log \left (x+e^4+9\right )+\log \left (\frac {5}{x+\log (3)}\right )+3\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 6684
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {9+e^4+2 x+\log (3)}{\left (-27-3 e^4\right ) x-3 x^2+\left (-27-3 e^4-3 x\right ) \log (3)+\left (9 x+e^4 x+x^2+\left (9+e^4+x\right ) \log (3)\right ) \log \left (9+e^4+x\right )+\left (-9 x-e^4 x-x^2+\left (-9-e^4-x\right ) \log (3)\right ) \log \left (\frac {5}{x+\log (3)}\right )} \, dx\\ &=\int \frac {-9-e^4-2 x-\log (3)}{\left (9+e^4+x\right ) (x+\log (3)) \left (3-\log \left (9+e^4+x\right )+\log \left (\frac {5}{x+\log (3)}\right )\right )} \, dx\\ &=\log \left (3-\log \left (9+e^4+x\right )+\log \left (\frac {5}{x+\log (3)}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 21, normalized size = 1.00 \begin {gather*} \log \left (-3+\log \left (9+e^4+x\right )-\log \left (\frac {5}{x+\log (3)}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 20, normalized size = 0.95 \begin {gather*} \log \left (\log \left (x + e^{4} + 9\right ) - \log \left (\frac {5}{x + \log \relax (3)}\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 20, normalized size = 0.95 \begin {gather*} \log \left (\log \relax (5) - \log \left (x + e^{4} + 9\right ) - \log \left (x + \log \relax (3)\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.80, size = 21, normalized size = 1.00
method | result | size |
norman | \(\ln \left (\ln \left ({\mathrm e}^{4}+x +9\right )-\ln \left (\frac {5}{\ln \relax (3)+x}\right )-3\right )\) | \(21\) |
risch | \(\ln \left (\ln \left ({\mathrm e}^{4}+x +9\right )+\frac {i \left (2 i \ln \relax (5)-2 i \ln \left (\ln \relax (3)+x \right )+6 i\right )}{2}\right )\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.81, size = 18, normalized size = 0.86 \begin {gather*} \log \left (-\log \relax (5) + \log \left (x + e^{4} + 9\right ) + \log \left (x + \log \relax (3)\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 118.60, size = 20, normalized size = 0.95 \begin {gather*} \ln \left (\ln \left (\frac {5}{x+\ln \relax (3)}\right )-\ln \left (x+{\mathrm {e}}^4+9\right )+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.64, size = 19, normalized size = 0.90 \begin {gather*} \log {\left (\log {\left (\frac {5}{x + \log {\relax (3 )}} \right )} - \log {\left (x + 9 + e^{4} \right )} + 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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