Optimal. Leaf size=16 \[ x-\frac {x^2}{2}+\frac {x^3}{3} \]
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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 = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {1600}
\begin {gather*} \frac {x^3}{3}-\frac {x^2}{2}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 1600
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\int \left (1-x+x^2\right ) \, dx\\ &=x-\frac {x^2}{2}+\frac {x^3}{3}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} x-\frac {x^2}{2}+\frac {x^3}{3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 13, normalized size = 0.81
method | result | size |
default | \(x -\frac {1}{2} x^{2}+\frac {1}{3} x^{3}\) | \(13\) |
norman | \(x -\frac {1}{2} x^{2}+\frac {1}{3} x^{3}\) | \(13\) |
risch | \(x -\frac {1}{2} x^{2}+\frac {1}{3} x^{3}\) | \(13\) |
parallelrisch | \(x -\frac {1}{2} x^{2}+\frac {1}{3} x^{3}\) | \(13\) |
parts | \(x -\frac {1}{2} x^{2}+\frac {1}{3} x^{3}\) | \(13\) |
gosper | \(\frac {x \left (2 x^{2}-3 x +6\right )}{6}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, 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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Fricas [A]
time = 0.56, 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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Sympy [A]
time = 0.02, 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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Giac [A]
time = 0.46, 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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Chatgpt [F] Failed to verify
time = 1.00, size = 11, normalized size = 0.69 \begin {gather*} \frac {1}{3} x^{3}+\frac {1}{2} x^{2} \end {gather*}
Warning: Unable to verify antiderivative.
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