Optimal. Leaf size=22 \[ \frac {x^3}{3}+2 e^x+\frac {e^{2 x}}{2} \]
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Rubi [A] time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2194} \[ \frac {x^3}{3}+2 e^x+\frac {e^{2 x}}{2} \]
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin {align*} \int \left (2 e^x+e^{2 x}+x^2\right ) \, dx &=\frac {x^3}{3}+2 \int e^x \, dx+\int e^{2 x} \, dx\\ &=2 e^x+\frac {e^{2 x}}{2}+\frac {x^3}{3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \[ \frac {x^3}{3}+2 e^x+\frac {e^{2 x}}{2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 16, normalized size = 0.73 \[ \frac {1}{3} \, x^{3} + \frac {1}{2} \, e^{\left (2 \, x\right )} + 2 \, e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.08, size = 16, normalized size = 0.73 \[ \frac {1}{3} \, x^{3} + \frac {1}{2} \, e^{\left (2 \, x\right )} + 2 \, e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.77 \[ \frac {x^{3}}{3}+2 \,{\mathrm e}^{x}+\frac {{\mathrm e}^{2 x}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 16, normalized size = 0.73 \[ \frac {1}{3} \, x^{3} + \frac {1}{2} \, e^{\left (2 \, x\right )} + 2 \, e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 16, normalized size = 0.73 \[ \frac {{\mathrm {e}}^{2\,x}}{2}+2\,{\mathrm {e}}^x+\frac {x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.68 \[ \frac {x^{3}}{3} + \frac {e^{2 x}}{2} + 2 e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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