Optimal. Leaf size=19 \[ 2+e^{10}+x+\log \left (\frac {2}{3}-\frac {2}{x+\log (49)}\right ) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(47\) vs. \(2(19)=38\).
time = 0.10, antiderivative size = 47, normalized size of antiderivative = 2.47, number of steps
used = 5, number of rules used = 4, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2009, 1671,
632, 212} \begin {gather*} x+\frac {6 \tanh ^{-1}\left (\frac {-2 x+3-\log (2401)}{\sqrt {9+\log ^2(2401)-\log (49) \log (5764801)}}\right )}{\sqrt {9+\log ^2(2401)-\log (49) \log (5764801)}} \end {gather*}
Antiderivative was successfully verified.
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Rule 212
Rule 632
Rule 1671
Rule 2009
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3+x^2-3 \log (49)+\log ^2(49)-x (3-\log (2401))}{x^2-(3-\log (49)) \log (49)+x (-3+\log (2401))} \, dx\\ &=\int \left (1+\frac {3}{x^2-(3-\log (49)) \log (49)+x (-3+\log (2401))}\right ) \, dx\\ &=x+3 \int \frac {1}{x^2-(3-\log (49)) \log (49)+x (-3+\log (2401))} \, dx\\ &=x-6 \text {Subst}\left (\int \frac {1}{9-x^2+\log ^2(2401)-\log (49) \log (5764801)} \, dx,x,-3+2 x+\log (2401)\right )\\ &=x+\frac {6 \tanh ^{-1}\left (\frac {3-2 x-\log (2401)}{\sqrt {9+\log ^2(2401)-\log (49) \log (5764801)}}\right )}{\sqrt {9+\log ^2(2401)-\log (49) \log (5764801)}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} x+\log (3-x-\log (49))-\log (x+\log (49)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 2.11, size = 20, normalized size = 1.05
method | result | size |
default | \(x +\ln \left (2 \ln \left (7\right )+x -3\right )-\ln \left (x +2 \ln \left (7\right )\right )\) | \(20\) |
norman | \(x +\ln \left (2 \ln \left (7\right )+x -3\right )-\ln \left (x +2 \ln \left (7\right )\right )\) | \(20\) |
risch | \(x +\ln \left (2 \ln \left (7\right )+x -3\right )-\ln \left (x +2 \ln \left (7\right )\right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 19, normalized size = 1.00 \begin {gather*} x - \log \left (x + 2 \, \log \left (7\right )\right ) + \log \left (x + 2 \, \log \left (7\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 19, normalized size = 1.00 \begin {gather*} x - \log \left (x + 2 \, \log \left (7\right )\right ) + \log \left (x + 2 \, \log \left (7\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 19, normalized size = 1.00 \begin {gather*} x - \log {\left (x + 2 \log {\left (7 \right )} \right )} + \log {\left (x - 3 + 2 \log {\left (7 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 21, normalized size = 1.11 \begin {gather*} x - \log \left ({\left | x + 2 \, \log \left (7\right ) \right |}\right ) + \log \left ({\left | x + 2 \, \log \left (7\right ) - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 14, normalized size = 0.74 \begin {gather*} x-2\,\mathrm {atanh}\left (\frac {2\,x}{3}+\frac {4\,\ln \left (7\right )}{3}-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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