Optimal. Leaf size=11 \[ \frac {x^2}{2}-x \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {x^2}{2}-x \end {gather*}
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*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} \frac {x^2}{2}-x \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{2} (x-1)^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.17, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{2} \, x^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{2} \, x^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.91 \begin {gather*} \frac {1}{2} x^{2}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.84, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{2} \, x^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 6, normalized size = 0.55 \begin {gather*} \frac {x\,\left (x-2\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 5, normalized size = 0.45 \begin {gather*} \frac {x^{2}}{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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