Optimal. Leaf size=23 \[ 3-e^{2 e^2}+3 x^2-\frac {x^3}{16} \]
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Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.57, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12}
\begin {gather*} 3 x^2-\frac {x^3}{16} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{16} \int \left (96 x-3 x^2\right ) \, dx\\ &=3 x^2-\frac {x^3}{16}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 0.74 \begin {gather*} -\frac {3}{16} \left (-16 x^2+\frac {x^3}{3}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 12, normalized size = 0.52
method | result | size |
gosper | \(-\frac {x^{2} \left (x -48\right )}{16}\) | \(9\) |
default | \(-\frac {1}{16} x^{3}+3 x^{2}\) | \(12\) |
norman | \(-\frac {1}{16} x^{3}+3 x^{2}\) | \(12\) |
risch | \(-\frac {1}{16} x^{3}+3 x^{2}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 11, normalized size = 0.48 \begin {gather*} -\frac {1}{16} \, x^{3} + 3 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 11, normalized size = 0.48 \begin {gather*} -\frac {1}{16} \, x^{3} + 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 = 8, normalized size = 0.35 \begin {gather*} - \frac {x^{3}}{16} + 3 x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 11, normalized size = 0.48 \begin {gather*} -\frac {1}{16} \, x^{3} + 3 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 8, normalized size = 0.35 \begin {gather*} -\frac {x^2\,\left (x-48\right )}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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