Optimal. Leaf size=29 \[ e^3-e^3 (-4+x)+\frac {e^2}{x}+2 x-\frac {x^2}{3} \]
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Rubi [A] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 0.83, number of steps used = 4, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {6, 12, 14} \begin {gather*} -\frac {x^2}{3}+\left (2-e^3\right ) x+\frac {e^2}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-\frac {3 e^2}{x}+\left (6-3 e^3\right ) x-2 x^2}{3 x} \, dx\\ &=\frac {1}{3} \int \frac {-\frac {3 e^2}{x}+\left (6-3 e^3\right ) x-2 x^2}{x} \, dx\\ &=\frac {1}{3} \int \left (-3 \left (-2+e^3\right )-\frac {3 e^2}{x^2}-2 x\right ) \, dx\\ &=\frac {e^2}{x}+\left (2-e^3\right ) x-\frac {x^2}{3}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 24, normalized size = 0.83 \begin {gather*} \frac {e^2}{x}+2 x-e^3 x-\frac {x^2}{3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 25, normalized size = 0.86 \begin {gather*} -\frac {x^{3} + 3 \, x^{2} e^{3} - 6 \, x^{2} - 3 \, e^{2}}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 20, normalized size = 0.69 \begin {gather*} -\frac {1}{3} \, x^{2} - x e^{3} + 2 \, x + \frac {e^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 21, normalized size = 0.72
method | result | size |
risch | \(-x \,{\mathrm e}^{3}-\frac {x^{2}}{3}+2 x +\frac {{\mathrm e}^{2}}{x}\) | \(21\) |
default | \(-\frac {x^{2}}{3}+2 x +{\mathrm e}^{-\ln \relax (x )+2}-x \,{\mathrm e}^{3}\) | \(22\) |
norman | \(\frac {\left (2-{\mathrm e}^{3}\right ) x^{2}-\frac {x^{3}}{3}+{\mathrm e}^{2}}{x}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 19, normalized size = 0.66 \begin {gather*} -\frac {1}{3} \, x^{2} - x {\left (e^{3} - 2\right )} + \frac {e^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 23, normalized size = 0.79 \begin {gather*} -\frac {\frac {x^3}{3}+\left ({\mathrm {e}}^3-2\right )\,x^2-{\mathrm {e}}^2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 19, normalized size = 0.66 \begin {gather*} - \frac {x^{2}}{3} - \frac {x \left (-6 + 3 e^{3}\right )}{3} + \frac {e^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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