Optimal. Leaf size=15 \[ \frac{1}{1-x}-\frac{2}{(x+1)^2} \]
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Rubi [A] time = 0.0270943, antiderivative size = 15, 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 = {1620} \[ \frac{1}{1-x}-\frac{2}{(x+1)^2} \]
Antiderivative was successfully verified.
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Rule 1620
Rubi steps
\begin{align*} \int \frac{5-5 x+7 x^2+x^3}{(-1+x)^2 (1+x)^3} \, dx &=\int \left (\frac{1}{(-1+x)^2}+\frac{4}{(1+x)^3}\right ) \, dx\\ &=\frac{1}{1-x}-\frac{2}{(1+x)^2}\\ \end{align*}
Mathematica [A] time = 0.011732, size = 15, normalized size = 1. \[ -\frac{2}{(x+1)^2}-\frac{1}{x-1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 16, normalized size = 1.1 \begin{align*} - \left ( x-1 \right ) ^{-1}-2\, \left ( 1+x \right ) ^{-2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.970745, size = 31, normalized size = 2.07 \begin{align*} -\frac{x^{2} + 4 \, x - 1}{x^{3} + x^{2} - x - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47772, size = 51, normalized size = 3.4 \begin{align*} -\frac{x^{2} + 4 \, x - 1}{x^{3} + x^{2} - x - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.110862, size = 19, normalized size = 1.27 \begin{align*} - \frac{x^{2} + 4 x - 1}{x^{3} + x^{2} - x - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.11392, size = 41, normalized size = 2.73 \begin{align*} -\frac{1}{x - 1} + \frac{\frac{4}{x - 1} + 1}{2 \,{\left (\frac{2}{x - 1} + 1\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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