Optimal. Leaf size=26 \[ 9-e^3-x+3 (5+x)-\frac {e}{-x+\log (3)} \]
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Rubi [A]
time = 0.01, antiderivative size = 14, normalized size of antiderivative = 0.54, number of steps
used = 3, number of rules used = 2, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {27, 697}
\begin {gather*} 2 x+\frac {e}{x-\log (3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 697
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e+2 x^2-4 x \log (3)+2 \log ^2(3)}{(x-\log (3))^2} \, dx\\ &=\int \left (2-\frac {e}{(x-\log (3))^2}\right ) \, dx\\ &=2 x+\frac {e}{x-\log (3)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 19, normalized size = 0.73 \begin {gather*} \frac {e}{x-\log (3)}+2 (x-\log (3)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.44, size = 16, normalized size = 0.62
method | result | size |
default | \(2 x +\frac {{\mathrm e}}{-\ln \left (3\right )+x}\) | \(16\) |
risch | \(2 x -\frac {{\mathrm e}}{\ln \left (3\right )-x}\) | \(17\) |
gosper | \(-\frac {2 x^{2}-2 \ln \left (3\right )^{2}+{\mathrm e}}{\ln \left (3\right )-x}\) | \(25\) |
norman | \(\frac {-2 x^{2}+2 \ln \left (3\right )^{2}-{\mathrm e}}{\ln \left (3\right )-x}\) | \(26\) |
meijerg | \(\frac {2 x}{1-\frac {x}{\ln \left (3\right )}}-4 \ln \left (3\right ) \left (\frac {x}{\ln \left (3\right ) \left (1-\frac {x}{\ln \left (3\right )}\right )}+\ln \left (1-\frac {x}{\ln \left (3\right )}\right )\right )-\frac {{\mathrm e} x}{\ln \left (3\right )^{2} \left (1-\frac {x}{\ln \left (3\right )}\right )}-2 \ln \left (3\right ) \left (-\frac {x \left (-\frac {3 x}{\ln \left (3\right )}+6\right )}{3 \ln \left (3\right ) \left (1-\frac {x}{\ln \left (3\right )}\right )}-2 \ln \left (1-\frac {x}{\ln \left (3\right )}\right )\right )\) | \(112\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 15, normalized size = 0.58 \begin {gather*} 2 \, x + \frac {e}{x - \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 22, normalized size = 0.85 \begin {gather*} \frac {2 \, x^{2} - 2 \, x \log \left (3\right ) + e}{x - \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 10, normalized size = 0.38 \begin {gather*} 2 x + \frac {e}{x - \log {\left (3 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 15, normalized size = 0.58 \begin {gather*} 2 \, x + \frac {e}{x - \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 15, normalized size = 0.58 \begin {gather*} 2\,x+\frac {\mathrm {e}}{x-\ln \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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