Optimal. Leaf size=43 \[ -\frac {3}{25 (1-4 x)}+\frac {1}{10 (1-4 x)^2}-\frac {9}{125} \log (1-4 x)+\frac {9}{125} \log (2-3 x) \]
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Rubi [A] time = 0.02, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {44} \[ -\frac {3}{25 (1-4 x)}+\frac {1}{10 (1-4 x)^2}-\frac {9}{125} \log (1-4 x)+\frac {9}{125} \log (2-3 x) \]
Antiderivative was successfully verified.
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Rule 44
Rubi steps
\begin {align*} \int \frac {1}{(1-4 x)^3 (2-3 x)} \, dx &=\int \left (\frac {27}{125 (-2+3 x)}-\frac {4}{5 (-1+4 x)^3}-\frac {12}{25 (-1+4 x)^2}-\frac {36}{125 (-1+4 x)}\right ) \, dx\\ &=\frac {1}{10 (1-4 x)^2}-\frac {3}{25 (1-4 x)}-\frac {9}{125} \log (1-4 x)+\frac {9}{125} \log (2-3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 46, normalized size = 1.07 \[ \frac {120 x+18 (1-4 x)^2 \log (8-12 x)-18 (1-4 x)^2 \log (4 x-1)-5}{250 (1-4 x)^2} \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.03, size = 33, normalized size = 0.77 \[ \frac {24 x-1}{50 (4 x-1)^2}-\frac {18}{125} \tanh ^{-1}\left (\frac {x+1}{7 x-3}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.19, size = 55, normalized size = 1.28 \[ -\frac {18 \, {\left (16 \, x^{2} - 8 \, x + 1\right )} \log \left (4 \, x - 1\right ) - 18 \, {\left (16 \, x^{2} - 8 \, x + 1\right )} \log \left (3 \, x - 2\right ) - 120 \, x + 5}{250 \, {\left (16 \, x^{2} - 8 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.77, size = 33, normalized size = 0.77 \[ \frac {24 \, x - 1}{50 \, {\left (4 \, x - 1\right )}^{2}} - \frac {9}{125} \, \log \left ({\left | 4 \, x - 1 \right |}\right ) + \frac {9}{125} \, \log \left ({\left | 3 \, x - 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.32, size = 32, normalized size = 0.74
method | result | size |
risch | \(\frac {\frac {12 x}{25}-\frac {1}{50}}{\left (4 x -1\right )^{2}}+\frac {9 \ln \left (-2+3 x \right )}{125}-\frac {9 \ln \left (4 x -1\right )}{125}\) | \(32\) |
norman | \(\frac {\frac {8}{25} x +\frac {8}{25} x^{2}}{\left (4 x -1\right )^{2}}+\frac {9 \ln \left (-2+3 x \right )}{125}-\frac {9 \ln \left (4 x -1\right )}{125}\) | \(35\) |
default | \(\frac {9 \ln \left (-2+3 x \right )}{125}+\frac {1}{10 \left (4 x -1\right )^{2}}+\frac {3}{25 \left (4 x -1\right )}-\frac {9 \ln \left (4 x -1\right )}{125}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 36, normalized size = 0.84 \[ \frac {24 \, x - 1}{50 \, {\left (16 \, x^{2} - 8 \, x + 1\right )}} - \frac {9}{125} \, \log \left (4 \, x - 1\right ) + \frac {9}{125} \, \log \left (3 \, x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 25, normalized size = 0.58 \[ \frac {\frac {3\,x}{100}-\frac {1}{800}}{x^2-\frac {x}{2}+\frac {1}{16}}-\frac {18\,\mathrm {atanh}\left (\frac {24\,x}{5}-\frac {11}{5}\right )}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 34, normalized size = 0.79 \[ \frac {24 x - 1}{800 x^{2} - 400 x + 50} + \frac {9 \log {\left (x - \frac {2}{3} \right )}}{125} - \frac {9 \log {\left (x - \frac {1}{4} \right )}}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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