Optimal. Leaf size=20 \[ e^{-x+\left (1+\frac {7 e^x}{x}\right ) (2+x)} \]
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Rubi [F] time = 0.78, 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 \frac {e^{-\frac {e^x (-14-7 x)-2 x}{x}+x} \left (-14+14 x+7 x^2\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {(2+x) \left (7 e^x+x\right )}{x}} \left (-14+14 x+7 x^2\right )}{x^2} \, dx\\ &=\int \left (7 e^{\frac {(2+x) \left (7 e^x+x\right )}{x}}-\frac {14 e^{\frac {(2+x) \left (7 e^x+x\right )}{x}}}{x^2}+\frac {14 e^{\frac {(2+x) \left (7 e^x+x\right )}{x}}}{x}\right ) \, dx\\ &=7 \int e^{\frac {(2+x) \left (7 e^x+x\right )}{x}} \, dx-14 \int \frac {e^{\frac {(2+x) \left (7 e^x+x\right )}{x}}}{x^2} \, dx+14 \int \frac {e^{\frac {(2+x) \left (7 e^x+x\right )}{x}}}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.13, size = 15, normalized size = 0.75 \begin {gather*} e^{2+\frac {7 e^x (2+x)}{x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 23, normalized size = 1.15 \begin {gather*} e^{\left (-x + \frac {x^{2} + 7 \, {\left (x + 2\right )} e^{x} + 2 \, x}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {7 \, {\left (x^{2} + 2 \, x - 2\right )} e^{\left (x + \frac {7 \, {\left (x + 2\right )} e^{x} + 2 \, x}{x}\right )}}{x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 19, normalized size = 0.95
method | result | size |
risch | \({\mathrm e}^{\frac {7 \,{\mathrm e}^{x} x +14 \,{\mathrm e}^{x}+2 x}{x}}\) | \(19\) |
norman | \({\mathrm e}^{-\frac {\left (-7 x -14\right ) {\mathrm e}^{x}-2 x}{x}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 14, normalized size = 0.70 \begin {gather*} e^{\left (\frac {14 \, e^{x}}{x} + 7 \, e^{x} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.21, size = 16, normalized size = 0.80 \begin {gather*} {\mathrm {e}}^2\,{\mathrm {e}}^{\frac {14\,{\mathrm {e}}^x}{x}}\,{\mathrm {e}}^{7\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 17, normalized size = 0.85 \begin {gather*} e^{- \frac {- 2 x + \left (- 7 x - 14\right ) e^{x}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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