Optimal. Leaf size=20 \[ -x^2+\frac {x^3}{3}+\frac {x^4}{4} \]
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Rubi [A]
time = 0.00, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 0, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \frac {x^4}{4}+\frac {x^3}{3}-x^2 \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (-2 x+x^2+x^3\right ) \, dx &=-x^2+\frac {x^3}{3}+\frac {x^4}{4}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 20, normalized size = 1.00 \begin {gather*} -x^2+\frac {x^3}{3}+\frac {x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.00, size = 17, normalized size = 0.85
method | result | size |
gosper | \(\frac {x^{2} \left (3 x^{2}+4 x -12\right )}{12}\) | \(16\) |
default | \(-x^{2}+\frac {1}{3} x^{3}+\frac {1}{4} x^{4}\) | \(17\) |
norman | \(-x^{2}+\frac {1}{3} x^{3}+\frac {1}{4} x^{4}\) | \(17\) |
risch | \(-x^{2}+\frac {1}{3} x^{3}+\frac {1}{4} x^{4}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.47, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{4} \, x^{4} + \frac {1}{3} \, x^{3} - x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.39, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{4} \, x^{4} + \frac {1}{3} \, x^{3} - x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 12, normalized size = 0.60 \begin {gather*} \frac {x^{4}}{4} + \frac {x^{3}}{3} - x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.02, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{4} \, x^{4} + \frac {1}{3} \, x^{3} - x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 15, normalized size = 0.75 \begin {gather*} \frac {x^2\,\left (3\,x^2+4\,x-12\right )}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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