Optimal. Leaf size=19 \[ 5+e^{-8-\frac {2 \left (7-e^{10}\right )}{x}}+x \]
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Rubi [A] time = 0.06, antiderivative size = 18, normalized size of antiderivative = 0.95, 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 = {14, 2209} \begin {gather*} x+e^{-\frac {2 \left (7-e^{10}\right )}{x}-8} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {2 e^{-8+\frac {-14+2 e^{10}}{x}} \left (7-e^{10}\right )}{x^2}\right ) \, dx\\ &=x+\left (2 \left (7-e^{10}\right )\right ) \int \frac {e^{-8+\frac {-14+2 e^{10}}{x}}}{x^2} \, dx\\ &=e^{-8-\frac {2 \left (7-e^{10}\right )}{x}}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 17, normalized size = 0.89 \begin {gather*} e^{\frac {2 \left (-7+e^{10}-4 x\right )}{x}}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 17, normalized size = 0.89 \begin {gather*} x + e^{\left (-\frac {2 \, {\left (4 \, x - e^{10} + 7\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.38, size = 129, normalized size = 6.79 \begin {gather*} \frac {\frac {{\left (4 \, x - e^{10} + 7\right )} e^{\left (-\frac {2 \, {\left (4 \, x - e^{10} + 7\right )}}{x} + 10\right )}}{x} - \frac {7 \, {\left (4 \, x - e^{10} + 7\right )} e^{\left (-\frac {2 \, {\left (4 \, x - e^{10} + 7\right )}}{x}\right )}}{x} - e^{20} + 14 \, e^{10} - 4 \, e^{\left (-\frac {2 \, {\left (4 \, x - e^{10} + 7\right )}}{x} + 10\right )} + 28 \, e^{\left (-\frac {2 \, {\left (4 \, x - e^{10} + 7\right )}}{x}\right )} - 49}{{\left (\frac {4 \, x - e^{10} + 7}{x} - 4\right )} {\left (e^{10} - 7\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 16, normalized size = 0.84
method | result | size |
risch | \({\mathrm e}^{\frac {2 \,{\mathrm e}^{10}-8 x -14}{x}}+x\) | \(16\) |
norman | \(\frac {x^{2}+x \,{\mathrm e}^{\frac {2 \,{\mathrm e}^{10}-8 x -14}{x}}}{x}\) | \(27\) |
derivativedivides | \(x +{\mathrm e}^{\frac {2 \,{\mathrm e}^{10}}{x}-8-\frac {14}{x}}\) | \(39\) |
default | \(x +{\mathrm e}^{\frac {2 \,{\mathrm e}^{10}}{x}-8-\frac {14}{x}}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.64, size = 47, normalized size = 2.47 \begin {gather*} x + \frac {e^{\left (\frac {2 \, e^{10}}{x} - \frac {14}{x} + 2\right )}}{e^{10} - 7} - \frac {7 \, e^{\left (\frac {2 \, e^{10}}{x} - \frac {14}{x} - 8\right )}}{e^{10} - 7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.36, size = 19, normalized size = 1.00 \begin {gather*} x+{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^{10}}{x}}\,{\mathrm {e}}^{-8}\,{\mathrm {e}}^{-\frac {14}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 14, normalized size = 0.74 \begin {gather*} x + e^{\frac {2 \left (- 4 x - 7 + e^{10}\right )}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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