Optimal. Leaf size=29 \[ \frac {16}{3} \log (1-2 x)-\frac {5}{2} \log (1-x)-\frac {17}{6} \log (x+1) \]
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Rubi [A] time = 0.02, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {801} \begin {gather*} \frac {16}{3} \log (1-2 x)-\frac {5}{2} \log (1-x)-\frac {17}{6} \log (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 801
Rubi steps
\begin {align*} \int \frac {-11+6 x}{(-1+2 x) \left (-1+x^2\right )} \, dx &=\int \left (-\frac {5}{2 (-1+x)}-\frac {17}{6 (1+x)}+\frac {32}{3 (-1+2 x)}\right ) \, dx\\ &=\frac {16}{3} \log (1-2 x)-\frac {5}{2} \log (1-x)-\frac {17}{6} \log (1+x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 31, normalized size = 1.07 \begin {gather*} -\frac {5}{2} \log (2-2 x)+\frac {16}{3} \log (2 x-1)-\frac {17}{6} \log (2 x+2) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-11+6 x}{(-1+2 x) \left (-1+x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.42, size = 21, normalized size = 0.72 \begin {gather*} \frac {16}{3} \, \log \left (2 \, x - 1\right ) - \frac {17}{6} \, \log \left (x + 1\right ) - \frac {5}{2} \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 24, normalized size = 0.83 \begin {gather*} \frac {16}{3} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) - \frac {17}{6} \, \log \left ({\left | x + 1 \right |}\right ) - \frac {5}{2} \, \log \left ({\left | x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 22, normalized size = 0.76 \begin {gather*} -\frac {5 \ln \left (x -1\right )}{2}-\frac {17 \ln \left (x +1\right )}{6}+\frac {16 \ln \left (2 x -1\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 21, normalized size = 0.72 \begin {gather*} \frac {16}{3} \, \log \left (2 \, x - 1\right ) - \frac {17}{6} \, \log \left (x + 1\right ) - \frac {5}{2} \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 19, normalized size = 0.66 \begin {gather*} \frac {16\,\ln \left (x-\frac {1}{2}\right )}{3}-\frac {17\,\ln \left (x+1\right )}{6}-\frac {5\,\ln \left (x-1\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 26, normalized size = 0.90 \begin {gather*} - \frac {5 \log {\left (x - 1 \right )}}{2} + \frac {16 \log {\left (x - \frac {1}{2} \right )}}{3} - \frac {17 \log {\left (x + 1 \right )}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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