Optimal. Leaf size=20 \[ -1+e^{e^{-\frac {e}{5}+2 x} x}+2 x \]
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Rubi [F] time = 0.21, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \left (2+\exp \left (e^{\frac {1}{5} (-e+10 x)} x+\frac {1}{5} (-e+10 x)\right ) (1+2 x)\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 x+\int \exp \left (e^{\frac {1}{5} (-e+10 x)} x+\frac {1}{5} (-e+10 x)\right ) (1+2 x) \, dx\\ &=2 x+\int \left (\exp \left (e^{\frac {1}{5} (-e+10 x)} x+\frac {1}{5} (-e+10 x)\right )+2 \exp \left (e^{\frac {1}{5} (-e+10 x)} x+\frac {1}{5} (-e+10 x)\right ) x\right ) \, dx\\ &=2 x+2 \int \exp \left (e^{\frac {1}{5} (-e+10 x)} x+\frac {1}{5} (-e+10 x)\right ) x \, dx+\int \exp \left (e^{\frac {1}{5} (-e+10 x)} x+\frac {1}{5} (-e+10 x)\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.14, size = 19, normalized size = 0.95 \begin {gather*} e^{e^{-\frac {e}{5}+2 x} x}+2 x \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.55, size = 43, normalized size = 2.15 \begin {gather*} {\left (2 \, x e^{\left (2 \, x - \frac {1}{5} \, e\right )} + e^{\left (x e^{\left (2 \, x - \frac {1}{5} \, e\right )} + 2 \, x - \frac {1}{5} \, e\right )}\right )} e^{\left (-2 \, x + \frac {1}{5} \, e\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 16, normalized size = 0.80 \begin {gather*} 2 \, x + e^{\left (x e^{\left (2 \, x - \frac {1}{5} \, e\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 17, normalized size = 0.85
method | result | size |
default | \(2 x +{\mathrm e}^{x \,{\mathrm e}^{-\frac {{\mathrm e}}{5}+2 x}}\) | \(17\) |
norman | \(2 x +{\mathrm e}^{x \,{\mathrm e}^{-\frac {{\mathrm e}}{5}+2 x}}\) | \(17\) |
risch | \(2 x +{\mathrm e}^{x \,{\mathrm e}^{-\frac {{\mathrm e}}{5}+2 x}}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 16, normalized size = 0.80 \begin {gather*} 2 \, x + e^{\left (x e^{\left (2 \, x - \frac {1}{5} \, e\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.66, size = 16, normalized size = 0.80 \begin {gather*} 2\,x+{\mathrm {e}}^{x\,{\mathrm {e}}^{-\frac {\mathrm {e}}{5}}\,{\mathrm {e}}^{2\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 15, normalized size = 0.75 \begin {gather*} 2 x + e^{x e^{2 x - \frac {e}{5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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