Optimal. Leaf size=17 \[ \log \left (\frac {4}{3} \left (3+\log (4)+\log \left (\left (-\frac {1}{4}+x\right )^2\right )\right )\right ) \]
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Rubi [A] time = 0.07, antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps used = 5, number of rules used = 5, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.132, Rules used = {12, 6688, 2390, 2302, 29} \begin {gather*} \log \left (\log \left (\frac {1}{4} (1-4 x)^2\right )+3\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rule 2302
Rule 2390
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=8 \int \frac {1}{-3+12 x+(-1+4 x) \log (4)+(-1+4 x) \log \left (\frac {1}{16} \left (1-8 x+16 x^2\right )\right )} \, dx\\ &=8 \int \frac {1}{(-1+4 x) \left (3+\log \left (\frac {1}{4} (1-4 x)^2\right )\right )} \, dx\\ &=2 \operatorname {Subst}\left (\int \frac {1}{x \left (3+\log \left (\frac {x^2}{4}\right )\right )} \, dx,x,1-4 x\right )\\ &=\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,3+\log \left (\frac {1}{4} (1-4 x)^2\right )\right )\\ &=\log \left (3+\log \left (\frac {1}{4} (1-4 x)^2\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 15, normalized size = 0.88 \begin {gather*} \log \left (3+\log \left (\frac {1}{4} (1-4 x)^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 16, normalized size = 0.94 \begin {gather*} \log \left (2 \, \log \relax (2) + \log \left (x^{2} - \frac {1}{2} \, x + \frac {1}{16}\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 18, normalized size = 1.06 \begin {gather*} \log \left (-2 \, \log \relax (2) + \log \left (16 \, x^{2} - 8 \, x + 1\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 17, normalized size = 1.00
method | result | size |
norman | \(\ln \left (2 \ln \relax (2)+\ln \left (x^{2}-\frac {1}{2} x +\frac {1}{16}\right )+3\right )\) | \(17\) |
risch | \(\ln \left (2 \ln \relax (2)+\ln \left (x^{2}-\frac {1}{2} x +\frac {1}{16}\right )+3\right )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 13, normalized size = 0.76 \begin {gather*} \log \left (-\log \relax (2) + \log \left (4 \, x - 1\right ) + \frac {3}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {8}{12\,x+2\,\ln \relax (2)\,\left (4\,x-1\right )+\ln \left (x^2-\frac {x}{2}+\frac {1}{16}\right )\,\left (4\,x-1\right )-3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 19, normalized size = 1.12 \begin {gather*} \log {\left (\log {\left (x^{2} - \frac {x}{2} + \frac {1}{16} \right )} + 2 \log {\relax (2 )} + 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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