Optimal. Leaf size=25 \[ \log \left (\frac {5}{4} e^{-\frac {-8 x^2+\log (3)}{4-x}} x\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 20, normalized size of antiderivative = 0.80, number of steps used = 5, number of rules used = 4, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.114, Rules used = {6, 1594, 27, 1620} \begin {gather*} -8 x+\log (x)+\frac {128-\log (3)}{4-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 27
Rule 1594
Rule 1620
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {16+65 x^2-8 x^3+x (-8-\log (3))}{16 x-8 x^2+x^3} \, dx\\ &=\int \frac {16+65 x^2-8 x^3+x (-8-\log (3))}{x \left (16-8 x+x^2\right )} \, dx\\ &=\int \frac {16+65 x^2-8 x^3+x (-8-\log (3))}{(-4+x)^2 x} \, dx\\ &=\int \left (-8+\frac {1}{x}+\frac {128-\log (3)}{(-4+x)^2}\right ) \, dx\\ &=-8 x+\frac {128-\log (3)}{4-x}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.64 \begin {gather*} -8 x+\frac {-128+\log (3)}{-4+x}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 28, normalized size = 1.12 \begin {gather*} -\frac {8 \, x^{2} - {\left (x - 4\right )} \log \relax (x) - 32 \, x - \log \relax (3) + 128}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 17, normalized size = 0.68 \begin {gather*} -8 \, x + \frac {\log \relax (3) - 128}{x - 4} + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 18, normalized size = 0.72
method | result | size |
norman | \(\frac {\ln \relax (3)-8 x^{2}}{x -4}+\ln \relax (x )\) | \(18\) |
default | \(-8 x +\ln \relax (x )-\frac {-\ln \relax (3)+128}{x -4}\) | \(20\) |
risch | \(-8 x +\frac {\ln \relax (3)}{x -4}-\frac {128}{x -4}+\ln \relax (x )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 16, normalized size = 0.64 \begin {gather*} -8 \, x + \frac {\log \relax (3) - 128}{x - 4} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 16, normalized size = 0.64 \begin {gather*} \ln \relax (x)-8\,x+\frac {\ln \relax (3)-128}{x-4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 14, normalized size = 0.56 \begin {gather*} - 8 x + \log {\relax (x )} - \frac {128 - \log {\relax (3 )}}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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