Optimal. Leaf size=20 \[ e^x+2 x-e^{5+x} x-x^2 \]
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Rubi [A] time = 0.02, antiderivative size = 27, normalized size of antiderivative = 1.35, number of steps used = 4, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {2194, 2176} \begin {gather*} -x^2+2 x+e^x+e^{x+5}-e^{x+5} (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 x-x^2+\int e^x \, dx+\int e^{5+x} (-1-x) \, dx\\ &=e^x+2 x-x^2-e^{5+x} (1+x)+\int e^{5+x} \, dx\\ &=e^x+e^{5+x}+2 x-x^2-e^{5+x} (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.00 \begin {gather*} e^x+2 x-e^{5+x} x-x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 26, normalized size = 1.30 \begin {gather*} -{\left ({\left (x^{2} - 2 \, x\right )} e^{5} + {\left (x e^{5} - 1\right )} e^{\left (x + 5\right )}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 18, normalized size = 0.90 \begin {gather*} -x^{2} - x e^{\left (x + 5\right )} + 2 \, x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 19, normalized size = 0.95
method | result | size |
norman | \(2 x -x^{2}-x \,{\mathrm e}^{5} {\mathrm e}^{x}+{\mathrm e}^{x}\) | \(19\) |
risch | \(2 x -x^{2}+{\mathrm e}^{x}-x \,{\mathrm e}^{5+x}\) | \(19\) |
default | \(2 x -{\mathrm e}^{5+x} \left (5+x \right )+5 \,{\mathrm e}^{5+x}-x^{2}+{\mathrm e}^{x}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 18, normalized size = 0.90 \begin {gather*} -x^{2} - x e^{\left (x + 5\right )} + 2 \, x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.41, size = 18, normalized size = 0.90 \begin {gather*} 2\,x+{\mathrm {e}}^x-x\,{\mathrm {e}}^{x+5}-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 15, normalized size = 0.75 \begin {gather*} - x^{2} + 2 x + \left (- x e^{5} + 1\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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