Optimal. Leaf size=25 \[ \frac {1}{5} \left (4+\frac {-2-4 e^e-e^x-x}{x}\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {12, 14, 2197} \begin {gather*} -\frac {e^x}{5 x}-\frac {2 \left (1+2 e^e\right )}{5 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {2+4 e^e+e^x (1-x)}{x^2} \, dx\\ &=\frac {1}{5} \int \left (\frac {2 \left (1+2 e^e\right )}{x^2}-\frac {e^x (-1+x)}{x^2}\right ) \, dx\\ &=-\frac {2 \left (1+2 e^e\right )}{5 x}-\frac {1}{5} \int \frac {e^x (-1+x)}{x^2} \, dx\\ &=-\frac {e^x}{5 x}-\frac {2 \left (1+2 e^e\right )}{5 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 17, normalized size = 0.68 \begin {gather*} -\frac {2+4 e^e+e^x}{5 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.16, size = 14, normalized size = 0.56 \begin {gather*} -\frac {e^{x} + 4 \, e^{e} + 2}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 14, normalized size = 0.56 \begin {gather*} -\frac {e^{x} + 4 \, e^{e} + 2}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 16, normalized size = 0.64
method | result | size |
norman | \(\frac {-\frac {{\mathrm e}^{x}}{5}-\frac {4 \,{\mathrm e}^{{\mathrm e}}}{5}-\frac {2}{5}}{x}\) | \(16\) |
default | \(-\frac {{\mathrm e}^{x}}{5 x}-\frac {2}{5 x}-\frac {4 \,{\mathrm e}^{{\mathrm e}}}{5 x}\) | \(22\) |
risch | \(-\frac {{\mathrm e}^{x}}{5 x}-\frac {2}{5 x}-\frac {4 \,{\mathrm e}^{{\mathrm e}}}{5 x}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.55, size = 25, normalized size = 1.00 \begin {gather*} -\frac {4 \, e^{e}}{5 \, x} - \frac {2}{5 \, x} - \frac {1}{5} \, {\rm Ei}\relax (x) + \frac {1}{5} \, \Gamma \left (-1, -x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 14, normalized size = 0.56 \begin {gather*} -\frac {4\,{\mathrm {e}}^{\mathrm {e}}+{\mathrm {e}}^x+2}{5\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 20, normalized size = 0.80 \begin {gather*} - \frac {e^{x}}{5 x} - \frac {\frac {2}{5} + \frac {4 e^{e}}{5}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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