Optimal. Leaf size=19 \[ 2+4 e^{-x}+x+x^2+4 (1+\log (5)) \]
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Rubi [A]
time = 0.02, antiderivative size = 12, normalized size of antiderivative = 0.63, number of steps
used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {6820, 2225}
\begin {gather*} x^2+x+4 e^{-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-4 e^{-x}+2 x\right ) \, dx\\ &=x+x^2-4 \int e^{-x} \, dx\\ &=4 e^{-x}+x+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 12, normalized size = 0.63 \begin {gather*} 4 e^{-x}+x+x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 12, normalized size = 0.63
method | result | size |
default | \(x^{2}+x +4 \,{\mathrm e}^{-x}\) | \(12\) |
risch | \(x^{2}+x +4 \,{\mathrm e}^{-x}\) | \(12\) |
norman | \(\left (4+{\mathrm e}^{x} x +{\mathrm e}^{x} x^{2}\right ) {\mathrm e}^{-x}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 11, normalized size = 0.58 \begin {gather*} x^{2} + x + 4 \, e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 15, normalized size = 0.79 \begin {gather*} {\left ({\left (x^{2} + x\right )} e^{x} + 4\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.42 \begin {gather*} x^{2} + x + 4 e^{- x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 11, normalized size = 0.58 \begin {gather*} x^{2} + x + 4 \, e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 11, normalized size = 0.58 \begin {gather*} x+4\,{\mathrm {e}}^{-x}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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