Optimal. Leaf size=11 \[ \frac{x^2}{2}-x \]
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Rubi [A] time = 0.0074939, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {1586} \[ \frac{x^2}{2}-x \]
Antiderivative was successfully verified.
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Rule 1586
Rubi steps
\begin{align*} \int \frac{-1+x^3}{1+x+x^2} \, dx &=\int (-1+x) \, dx\\ &=-x+\frac{x^2}{2}\\ \end{align*}
Mathematica [A] time = 0.0004252, size = 11, normalized size = 1. \[ \frac{x^2}{2}-x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 10, normalized size = 0.9 \begin{align*} -x+{\frac{{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10546, size = 12, normalized size = 1.09 \begin{align*} \frac{1}{2} \, x^{2} - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.36925, size = 18, normalized size = 1.64 \begin{align*} \frac{1}{2} \, x^{2} - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.054409, size = 5, normalized size = 0.45 \begin{align*} \frac{x^{2}}{2} - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13676, size = 12, normalized size = 1.09 \begin{align*} \frac{1}{2} \, x^{2} - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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