Optimal. Leaf size=25 \[ \log \left (e^x (x-16 (4+\log (-5-x+\log (4 (1-x)))))\right ) \]
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Rubi [A] time = 0.86, antiderivative size = 22, normalized size of antiderivative = 0.88, number of steps used = 4, number of rules used = 3, integrand size = 133, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6741, 6742, 6684} \begin {gather*} x+\log (-x+16 \log (-x+\log (4-4 x)-5)+64) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {347-273 x-59 x^2+x^3+\left (-63+64 x-x^2\right ) \log (4-4 x)+\left (80-64 x-16 x^2+(-16+16 x) \log (4-4 x)\right ) \log (-5-x+\log (4-4 x))}{(1-x) (5+x-\log (4-4 x)) (64-x+16 \log (-5-x+\log (4-4 x)))} \, dx\\ &=\int \left (1+\frac {27-12 x+x^2+\log (4-4 x)-x \log (4-4 x)}{(-1+x) (5+x-\log (4-4 x)) (-64+x-16 \log (-5-x+\log (4-4 x)))}\right ) \, dx\\ &=x+\int \frac {27-12 x+x^2+\log (4-4 x)-x \log (4-4 x)}{(-1+x) (5+x-\log (4-4 x)) (-64+x-16 \log (-5-x+\log (4-4 x)))} \, dx\\ &=x+\log (64-x+16 \log (-5-x+\log (4-4 x)))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 22, normalized size = 0.88 \begin {gather*} x+\log (64-x+16 \log (-5-x+\log (4-4 x))) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 22, normalized size = 0.88 \begin {gather*} x + \log \left (-x + 16 \, \log \left (-x + \log \left (-4 \, x + 4\right ) - 5\right ) + 64\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.51, size = 20, normalized size = 0.80 \begin {gather*} x + \log \left (x - 16 \, \log \left (-x + \log \left (-4 \, x + 4\right ) - 5\right ) - 64\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 21, normalized size = 0.84
method | result | size |
risch | \(x +\ln \left (\ln \left (\ln \left (-4 x +4\right )-x -5\right )-\frac {x}{16}+4\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.61, size = 25, normalized size = 1.00 \begin {gather*} x + \log \left (-\frac {1}{16} \, x + \log \left (i \, \pi - x + 2 \, \log \relax (2) + \log \left (x - 1\right ) - 5\right ) + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.22, size = 20, normalized size = 0.80 \begin {gather*} x+\ln \left (\ln \left (\ln \left (4-4\,x\right )-x-5\right )-\frac {x}{16}+4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.72, size = 19, normalized size = 0.76 \begin {gather*} x + \log {\left (- \frac {x}{16} + \log {\left (- x + \log {\left (4 - 4 x \right )} - 5 \right )} + 4 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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