Optimal. Leaf size=24 \[ \frac {5}{2}-5 \left (5+e^{e^{-x+x^2}}\right ) (-2+x)+\log (3) \]
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Rubi [A] time = 0.04, antiderivative size = 34, normalized size of antiderivative = 1.42, number of steps used = 2, number of rules used = 1, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {2288} \begin {gather*} \frac {5 e^{e^{x^2-x}} \left (2 x^2-5 x+2\right )}{1-2 x}-25 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-25 x+\int e^{e^{-x+x^2}} \left (-5+e^{-x+x^2} \left (-10+25 x-10 x^2\right )\right ) \, dx\\ &=-25 x+\frac {5 e^{e^{-x+x^2}} \left (2-5 x+2 x^2\right )}{1-2 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 19, normalized size = 0.79 \begin {gather*} -5 \left (e^{e^{(-1+x) x}} (-2+x)+5 x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 18, normalized size = 0.75 \begin {gather*} -5 \, {\left (x - 2\right )} e^{\left (e^{\left (x^{2} - x\right )}\right )} - 25 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.20, size = 51, normalized size = 2.12 \begin {gather*} -5 \, {\left (x e^{\left (x^{2} - x + e^{\left (x^{2} - x\right )}\right )} - 2 \, e^{\left (x^{2} - x + e^{\left (x^{2} - x\right )}\right )}\right )} e^{\left (-x^{2} + x\right )} - 25 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 18, normalized size = 0.75
method | result | size |
risch | \(\left (-5 x +10\right ) {\mathrm e}^{{\mathrm e}^{x \left (x -1\right )}}-25 x\) | \(18\) |
default | \(-25 x -5 x \,{\mathrm e}^{{\mathrm e}^{x^{2}-x}}+10 \,{\mathrm e}^{{\mathrm e}^{x^{2}-x}}\) | \(28\) |
norman | \(-25 x -5 x \,{\mathrm e}^{{\mathrm e}^{x^{2}-x}}+10 \,{\mathrm e}^{{\mathrm e}^{x^{2}-x}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 18, normalized size = 0.75 \begin {gather*} -5 \, {\left (x - 2\right )} e^{\left (e^{\left (x^{2} - x\right )}\right )} - 25 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.48, size = 29, normalized size = 1.21 \begin {gather*} 10\,{\mathrm {e}}^{{\mathrm {e}}^{-x}\,{\mathrm {e}}^{x^2}}-25\,x-5\,x\,{\mathrm {e}}^{{\mathrm {e}}^{-x}\,{\mathrm {e}}^{x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 8.38, size = 15, normalized size = 0.62 \begin {gather*} - 25 x + \left (10 - 5 x\right ) e^{e^{x^{2} - x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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