Optimal. Leaf size=16 \[ 2 \log (1-x)-\frac{3}{x+1} \]
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Rubi [A] time = 0.0249667, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042, Rules used = {2074} \[ 2 \log (1-x)-\frac{3}{x+1} \]
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin{align*} \int \frac{-1+7 x+2 x^2}{-1-x+x^2+x^3} \, dx &=\int \left (\frac{2}{-1+x}+\frac{3}{(1+x)^2}\right ) \, dx\\ &=-\frac{3}{1+x}+2 \log (1-x)\\ \end{align*}
Mathematica [A] time = 0.0081222, size = 14, normalized size = 0.88 \[ 2 \log (x-1)-\frac{3}{x+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 15, normalized size = 0.9 \begin{align*} 2\,\ln \left ( x-1 \right ) -3\, \left ( 1+x \right ) ^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.969146, size = 19, normalized size = 1.19 \begin{align*} -\frac{3}{x + 1} + 2 \, \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.54451, size = 49, normalized size = 3.06 \begin{align*} \frac{2 \,{\left (x + 1\right )} \log \left (x - 1\right ) - 3}{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.08878, size = 10, normalized size = 0.62 \begin{align*} 2 \log{\left (x - 1 \right )} - \frac{3}{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12265, size = 20, normalized size = 1.25 \begin{align*} -\frac{3}{x + 1} + 2 \, \log \left ({\left | x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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