Optimal. Leaf size=29 \[ x \left (4+\left (4-e^{\frac {2-x}{x}}\right )^2-x+(3+x)^2\right ) \]
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Rubi [A] time = 0.11, antiderivative size = 35, normalized size of antiderivative = 1.21, number of steps used = 4, number of rules used = 2, integrand size = 51, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.039, Rules used = {14, 2288} \begin {gather*} x^3+5 x^2-8 e^{\frac {2}{x}-1} x+e^{\frac {4}{x}-2} x+29 x \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (29+\frac {e^{-2+\frac {4}{x}} (-4+x)}{x}-\frac {8 e^{-1+\frac {2}{x}} (-2+x)}{x}+10 x+3 x^2\right ) \, dx\\ &=29 x+5 x^2+x^3-8 \int \frac {e^{-1+\frac {2}{x}} (-2+x)}{x} \, dx+\int \frac {e^{-2+\frac {4}{x}} (-4+x)}{x} \, dx\\ &=29 x-8 e^{-1+\frac {2}{x}} x+e^{-2+\frac {4}{x}} x+5 x^2+x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 35, normalized size = 1.21 \begin {gather*} 29 x-8 e^{-1+\frac {2}{x}} x+e^{-2+\frac {4}{x}} x+5 x^2+x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 35, normalized size = 1.21 \begin {gather*} x^{3} + 5 \, x^{2} - 8 \, x e^{\left (-\frac {x - 2}{x}\right )} + x e^{\left (-\frac {2 \, {\left (x - 2\right )}}{x}\right )} + 29 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 48, normalized size = 1.66 \begin {gather*} x^{3} {\left (\frac {5 \, e^{3}}{x} + \frac {29 \, e^{3}}{x^{2}} + \frac {e^{\left (\frac {4}{x} + 1\right )}}{x^{2}} - \frac {8 \, e^{\left (\frac {2}{x} + 2\right )}}{x^{2}} + e^{3}\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 36, normalized size = 1.24
method | result | size |
derivativedivides | \(x \,{\mathrm e}^{\frac {4}{x}-2}+x^{3}+5 x^{2}+29 x -8 x \,{\mathrm e}^{\frac {2}{x}-1}\) | \(36\) |
default | \(x \,{\mathrm e}^{\frac {4}{x}-2}+x^{3}+5 x^{2}+29 x -8 x \,{\mathrm e}^{\frac {2}{x}-1}\) | \(36\) |
risch | \(x^{3}+x \,{\mathrm e}^{-\frac {2 \left (x -2\right )}{x}}+29 x +5 x^{2}-8 \,{\mathrm e}^{-\frac {x -2}{x}} x\) | \(36\) |
norman | \(x^{3}+x \,{\mathrm e}^{\frac {4-2 x}{x}}+29 x +5 x^{2}-8 x \,{\mathrm e}^{\frac {2-x}{x}}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.42, size = 54, normalized size = 1.86 \begin {gather*} x^{3} + 5 \, x^{2} - 16 \, {\rm Ei}\left (\frac {2}{x}\right ) e^{\left (-1\right )} + 4 \, {\rm Ei}\left (\frac {4}{x}\right ) e^{\left (-2\right )} + 16 \, e^{\left (-1\right )} \Gamma \left (-1, -\frac {2}{x}\right ) - 4 \, e^{\left (-2\right )} \Gamma \left (-1, -\frac {4}{x}\right ) + 29 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.15, size = 33, normalized size = 1.14 \begin {gather*} 29\,x+5\,x^2+x^3-8\,x\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{2/x}+x\,{\mathrm {e}}^{-2}\,{\mathrm {e}}^{4/x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 31, normalized size = 1.07 \begin {gather*} x^{3} + 5 x^{2} + x e^{\frac {2 \left (2 - x\right )}{x}} - 8 x e^{\frac {2 - x}{x}} + 29 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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