Optimal. Leaf size=18 \[ \log \left (x+\log \left (1+\log \left (\frac {5}{3+x-\log (48)}\right )\right )\right ) \]
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Rubi [A] time = 0.27, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 112, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {6, 6688, 6684} \begin {gather*} \log \left (x+\log \left (\log \left (\frac {5}{x+3-\log (48)}\right )+1\right )\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 {-2-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )}{-x^2+x (-3+\log (48))+\left (-3 x-x^2+x \log (48)\right ) \log \left (-\frac {5}{-3-x+\log (48)}\right )+\left (-3-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )\right ) \log \left (1+\log \left (-\frac {5}{-3-x+\log (48)}\right )\right )} \, dx\\ &=\int \frac {x+2 \left (1-\frac {\log (48)}{2}\right )+(3+x-\log (48)) \log \left (\frac {5}{3+x-\log (48)}\right )}{(3+x-\log (48)) \left (1+\log \left (\frac {5}{3+x-\log (48)}\right )\right ) \left (x+\log \left (1+\log \left (\frac {5}{3+x-\log (48)}\right )\right )\right )} \, dx\\ &=\log \left (x+\log \left (1+\log \left (\frac {5}{3+x-\log (48)}\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.72, size = 22, normalized size = 1.22 \begin {gather*} \log \left (-x-\log \left (1+\log \left (\frac {5}{3+x-\log (48)}\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 18, normalized size = 1.00 \begin {gather*} \log \left (x + \log \left (\log \left (\frac {5}{x - \log \left (48\right ) + 3}\right ) + 1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [C] time = 0.24, size = 21, normalized size = 1.17 \begin {gather*} \log \left (x + \log \left (2 i \, \pi + \log \relax (5) - \log \left (x - \log \left (48\right ) + 3\right ) + 1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.51, size = 19, normalized size = 1.06
method | result | size |
norman | \(\ln \left (\ln \left (\ln \left (-\frac {5}{\ln \left (48\right )-3-x}\right )+1\right )+x \right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 22, normalized size = 1.22 \begin {gather*} \log \left (x + \log \left (\log \relax (5) - \log \left (x - \log \relax (3) - 4 \, \log \relax (2) + 3\right ) + 1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F(-1)] time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \text {Hanged} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.91, size = 17, normalized size = 0.94 \begin {gather*} \log {\left (x + \log {\left (\log {\left (- \frac {5}{- x - 3 + \log {\left (48 \right )}} \right )} + 1 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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