Optimal. Leaf size=43 \[ \frac {1}{10 (1-4 x)^2}-\frac {3}{25 (1-4 x)}-\frac {9}{125} \log (1-4 x)+\frac {9}{125} \log (2-3 x) \]
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Rubi [A]
time = 0.01, 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 = {46}
\begin {gather*} -\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) \end {gather*}
Antiderivative was successfully verified.
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Rule 46
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 = 0.01, size = 46, normalized size = 1.07 \begin {gather*} \frac {-5+120 x+18 (1-4 x)^2 \log (8-12 x)-18 (1-4 x)^2 \log (-1+4 x)}{250 (1-4 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 4.28, size = 42, normalized size = 0.98 \begin {gather*} \frac {-5+120 x+18 \left (1-8 x+16 x^2\right ) \left (\text {Log}\left [-\frac {2}{3}+x\right ]-\text {Log}\left [-\frac {1}{4}+x\right ]\right )}{250-2000 x+4000 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 36, normalized size = 0.84
method | result | size |
risch | \(\frac {\frac {12 x}{25}-\frac {1}{50}}{\left (-1+4 x \right )^{2}}+\frac {9 \ln \left (-2+3 x \right )}{125}-\frac {9 \ln \left (-1+4 x \right )}{125}\) | \(32\) |
norman | \(\frac {\frac {8}{25} x +\frac {8}{25} x^{2}}{\left (-1+4 x \right )^{2}}+\frac {9 \ln \left (-2+3 x \right )}{125}-\frac {9 \ln \left (-1+4 x \right )}{125}\) | \(35\) |
default | \(\frac {1}{10 \left (-1+4 x \right )^{2}}+\frac {3}{25 \left (-1+4 x \right )}-\frac {9 \ln \left (-1+4 x \right )}{125}+\frac {9 \ln \left (-2+3 x \right )}{125}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 36, normalized size = 0.84 \begin {gather*} \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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 55, normalized size = 1.28 \begin {gather*} -\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 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 34, normalized size = 0.79 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 43, normalized size = 1.00 \begin {gather*} \frac {9}{125} \ln \left |3 x-2\right |-\frac {9}{125} \ln \left |4 x-1\right |+\frac {\frac {1}{125} \left (60 x-\frac {5}{2}\right )}{\left (4 x-1\right )^{2}} \end {gather*}
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 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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