Optimal. Leaf size=16 \[ \frac {x^3}{3}+\frac {x^2}{2}+x \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {x^3}{3}+\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} \, dx &=\int \left (1+x+x^2\right ) \, dx\\ &=x+\frac {x^2}{2}+\frac {x^3}{3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} \frac {x^3}{3}+\frac {x^2}{2}+x \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 21, normalized size = 1.31 \begin {gather*} \frac {1}{6} \left (2 (x-1)^2+9 (x-1)+18\right ) (x-1) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.24, size = 12, normalized size = 0.75 \begin {gather*} \frac {1}{3} \, x^{3} + \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 = 0.35, size = 12, normalized size = 0.75 \begin {gather*} \frac {1}{3} \, x^{3} + \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 = 13, normalized size = 0.81 \begin {gather*} \frac {1}{3} x^{3}+\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 = 0.89, size = 12, normalized size = 0.75 \begin {gather*} \frac {1}{3} \, x^{3} + \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 = 13, normalized size = 0.81 \begin {gather*} \frac {x\,\left (2\,x^2+3\,x+6\right )}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 10, normalized size = 0.62 \begin {gather*} \frac {x^{3}}{3} + \frac {x^{2}}{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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