Optimal. Leaf size=32 \[ -\frac {9}{32 (1-2 x)}+\frac {41}{128} \log (1-2 x)-\frac {25}{128} \log (3+2 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {907}
\begin {gather*} -\frac {9}{32 (1-2 x)}+\frac {41}{128} \log (1-2 x)-\frac {25}{128} \log (2 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 907
Rubi steps
\begin {align*} \int \frac {-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx &=\int \left (-\frac {9}{16 (-1+2 x)^2}+\frac {41}{64 (-1+2 x)}-\frac {25}{64 (3+2 x)}\right ) \, dx\\ &=-\frac {9}{32 (1-2 x)}+\frac {41}{128} \log (1-2 x)-\frac {25}{128} \log (3+2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 32, normalized size = 1.00 \begin {gather*} \frac {9}{32 (-1+2 x)}+\frac {41}{128} \log (1-2 x)-\frac {25}{128} \log (3+2 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 27, normalized size = 0.84
method | result | size |
risch | \(\frac {9}{64 \left (x -\frac {1}{2}\right )}-\frac {25 \ln \left (3+2 x \right )}{128}+\frac {41 \ln \left (2 x -1\right )}{128}\) | \(25\) |
default | \(\frac {9}{32 \left (2 x -1\right )}+\frac {41 \ln \left (2 x -1\right )}{128}-\frac {25 \ln \left (3+2 x \right )}{128}\) | \(27\) |
norman | \(\frac {9 x}{16 \left (2 x -1\right )}-\frac {25 \ln \left (3+2 x \right )}{128}+\frac {41 \ln \left (2 x -1\right )}{128}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.16, size = 26, normalized size = 0.81 \begin {gather*} \frac {9}{32 \, {\left (2 \, x - 1\right )}} - \frac {25}{128} \, \log \left (2 \, x + 3\right ) + \frac {41}{128} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.43, size = 37, normalized size = 1.16 \begin {gather*} -\frac {25 \, {\left (2 \, x - 1\right )} \log \left (2 \, x + 3\right ) - 41 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 36}{128 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 26, normalized size = 0.81 \begin {gather*} \frac {41 \log {\left (x - \frac {1}{2} \right )}}{128} - \frac {25 \log {\left (x + \frac {3}{2} \right )}}{128} + \frac {9}{64 x - 32} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.61, size = 43, normalized size = 1.34 \begin {gather*} \frac {9}{32 \, {\left (2 \, x - 1\right )}} - \frac {1}{8} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) - \frac {25}{128} \, \log \left ({\left | -\frac {4}{2 \, x - 1} - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.10, size = 22, normalized size = 0.69 \begin {gather*} \frac {41\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {25\,\ln \left (x+\frac {3}{2}\right )}{128}+\frac {9}{64\,\left (x-\frac {1}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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