Optimal. Leaf size=16 \[ 2 \log (1-x)-\frac {3}{x+1} \]
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Rubi [A] time = 0.02, antiderivative size = 16, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 0.88 \[ 2 \log (x-1)-\frac {3}{x+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 17, normalized size = 1.06 \[ \frac {2 \, {\left (x + 1\right )} \log \left (x - 1\right ) - 3}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.40, size = 15, normalized size = 0.94 \[ -\frac {3}{x + 1} + 2 \, \log \left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.94 \[ 2 \ln \left (x -1\right )-\frac {3}{x +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.09, size = 14, normalized size = 0.88 \[ -\frac {3}{x + 1} + 2 \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 14, normalized size = 0.88 \[ 2\,\ln \left (x-1\right )-\frac {3}{x+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 0.62 \[ 2 \log {\left (x - 1 \right )} - \frac {3}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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