Optimal. Leaf size=16 \[ -2+5 e^x+x-(-3+x) x^2 \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.06, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2194} \begin {gather*} -x^3+3 x^2+x+5 e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+3 x^2-x^3+5 \int e^x \, dx\\ &=5 e^x+x+3 x^2-x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.06 \begin {gather*} 5 e^x+x+3 x^2-x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 16, normalized size = 1.00 \begin {gather*} -x^{3} + 3 \, x^{2} + x + 5 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 16, normalized size = 1.00 \begin {gather*} -x^{3} + 3 \, x^{2} + x + 5 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 1.06
method | result | size |
default | \(-x^{3}+3 x^{2}+x +5 \,{\mathrm e}^{x}\) | \(17\) |
norman | \(-x^{3}+3 x^{2}+x +5 \,{\mathrm e}^{x}\) | \(17\) |
risch | \(-x^{3}+3 x^{2}+x +5 \,{\mathrm e}^{x}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 16, normalized size = 1.00 \begin {gather*} -x^{3} + 3 \, x^{2} + x + 5 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.22, size = 16, normalized size = 1.00 \begin {gather*} x+5\,{\mathrm {e}}^x+3\,x^2-x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 14, normalized size = 0.88 \begin {gather*} - x^{3} + 3 x^{2} + x + 5 e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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