Optimal. Leaf size=30 \[ x \left (-e^{3-x}+x+\left (3+\frac {2}{x}\right ) x (1+x) (5+x)^2\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 46, normalized size of antiderivative = 1.53, number of steps used = 3, number of rules used = 2, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {2176, 2194} \begin {gather*} 3 x^5+35 x^4+127 x^3+146 x^2+50 x-e^{3-x}+e^{3-x} (1-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=50 x+146 x^2+127 x^3+35 x^4+3 x^5+\int e^{3-x} (-1+x) \, dx\\ &=e^{3-x} (1-x)+50 x+146 x^2+127 x^3+35 x^4+3 x^5+\int e^{3-x} \, dx\\ &=-e^{3-x}+e^{3-x} (1-x)+50 x+146 x^2+127 x^3+35 x^4+3 x^5\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 34, normalized size = 1.13 \begin {gather*} 50 x-e^{3-x} x+146 x^2+127 x^3+35 x^4+3 x^5 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 33, normalized size = 1.10 \begin {gather*} 3 \, x^{5} + 35 \, x^{4} + 127 \, x^{3} + 146 \, x^{2} - x e^{\left (-x + 3\right )} + 50 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 33, normalized size = 1.10 \begin {gather*} 3 \, x^{5} + 35 \, x^{4} + 127 \, x^{3} + 146 \, x^{2} - x e^{\left (-x + 3\right )} + 50 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 34, normalized size = 1.13
method | result | size |
norman | \(50 x +146 x^{2}+127 x^{3}+35 x^{4}+3 x^{5}-x \,{\mathrm e}^{3-x}\) | \(34\) |
risch | \(50 x +146 x^{2}+127 x^{3}+35 x^{4}+3 x^{5}-x \,{\mathrm e}^{3-x}\) | \(34\) |
default | \(50 x +{\mathrm e}^{3-x} \left (3-x \right )-3 \,{\mathrm e}^{3-x}+146 x^{2}+127 x^{3}+35 x^{4}+3 x^{5}\) | \(45\) |
derivativedivides | \(146 \left (3-x \right )^{2}-2778+926 x +127 x^{3}+35 x^{4}+3 x^{5}+{\mathrm e}^{3-x} \left (3-x \right )-3 \,{\mathrm e}^{3-x}\) | \(50\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 33, normalized size = 1.10 \begin {gather*} 3 \, x^{5} + 35 \, x^{4} + 127 \, x^{3} + 146 \, x^{2} - x e^{\left (-x + 3\right )} + 50 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 30, normalized size = 1.00 \begin {gather*} x\,\left (146\,x-{\mathrm {e}}^{3-x}+127\,x^2+35\,x^3+3\,x^4+50\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 29, normalized size = 0.97 \begin {gather*} 3 x^{5} + 35 x^{4} + 127 x^{3} + 146 x^{2} - x e^{3 - x} + 50 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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