Optimal. Leaf size=20 \[ \frac {25 x}{x-x (x+4 (x-\log (16)))} \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.65, number of steps used = 4, number of rules used = 4, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 1981, 27, 32} \begin {gather*} \frac {25}{-5 x+1+4 \log (16)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 32
Rule 1981
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=125 \int \frac {1}{1-10 x+25 x^2+(8-40 x) \log (16)+16 \log ^2(16)} \, dx\\ &=125 \int \frac {1}{25 x^2-10 x (1+4 \log (16))+(1+4 \log (16))^2} \, dx\\ &=125 \int \frac {1}{(-1+5 x-4 \log (16))^2} \, dx\\ &=\frac {25}{1-5 x+4 \log (16)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 0.65 \begin {gather*} \frac {25}{1-5 x+4 \log (16)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 13, normalized size = 0.65 \begin {gather*} -\frac {25}{5 \, x - 16 \, \log \relax (2) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.65 \begin {gather*} -\frac {25}{5 \, x - 16 \, \log \relax (2) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 12, normalized size = 0.60
method | result | size |
risch | \(\frac {25}{16 \left (\ln \relax (2)-\frac {5 x}{16}+\frac {1}{16}\right )}\) | \(12\) |
gosper | \(\frac {25}{16 \ln \relax (2)-5 x +1}\) | \(14\) |
default | \(-\frac {25}{-16 \ln \relax (2)+5 x -1}\) | \(14\) |
norman | \(\frac {25}{16 \ln \relax (2)-5 x +1}\) | \(14\) |
meijerg | \(-\frac {25 x}{\left (-\frac {16 \ln \relax (2)}{5}-\frac {1}{5}\right ) \left (1-\frac {5 x}{16 \ln \relax (2)+1}\right ) \left (16 \ln \relax (2)+1\right )}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 13, normalized size = 0.65 \begin {gather*} -\frac {25}{5 \, x - 16 \, \log \relax (2) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 13, normalized size = 0.65 \begin {gather*} \frac {25}{16\,\ln \relax (2)-5\,x+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 12, normalized size = 0.60 \begin {gather*} - \frac {125}{25 x - 80 \log {\relax (2 )} - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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