Optimal. Leaf size=16 \[ \frac{x^3}{3}+\frac{x^2}{2}+x \]
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Rubi [A] time = 0.0060318, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {1586} \[ \frac{x^3}{3}+\frac{x^2}{2}+x \]
Antiderivative was successfully verified.
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Rule 1586
Rubi steps
\begin{align*} \int \frac{-1+x^3}{-1+x} \, dx &=\int \left (1+x+x^2\right ) \, dx\\ &=x+\frac{x^2}{2}+\frac{x^3}{3}\\ \end{align*}
Mathematica [A] time = 0.0004014, size = 16, normalized size = 1. \[ \frac{x^3}{3}+\frac{x^2}{2}+x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 13, normalized size = 0.8 \begin{align*} x+{\frac{{x}^{2}}{2}}+{\frac{{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.26357, size = 16, normalized size = 1. \begin{align*} \frac{1}{3} \, x^{3} + \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 = 0.944745, size = 31, normalized size = 1.94 \begin{align*} \frac{1}{3} \, x^{3} + \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 = 0.055744, size = 10, normalized size = 0.62 \begin{align*} \frac{x^{3}}{3} + \frac{x^{2}}{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0754, size = 16, normalized size = 1. \begin{align*} \frac{1}{3} \, x^{3} + \frac{1}{2} \, x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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