Optimal. Leaf size=25 \[ \frac {3-e^{6+e^{e^{-2 x} \left (3+e^4\right )}}}{x} \]
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Rubi [F] time = 1.36, 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^{-2 x} \left (-3 e^{2 x}+e^{6+e^{e^{-2 x} \left (3+e^4\right )}} \left (e^{2 x}+e^{e^{-2 x} \left (3+e^4\right )} \left (6 x+2 e^4 x\right )\right )\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 \left (\frac {-3+e^{6+e^{e^{4-2 x}+3 e^{-2 x}}}}{x^2}+\frac {2 \exp \left (6+e^{e^{4-2 x}+3 e^{-2 x}}+\left (1+\frac {3}{e^4}\right ) e^{4-2 x}-2 x\right ) \left (3+e^4\right )}{x}\right ) \, dx\\ &=\left (2 \left (3+e^4\right )\right ) \int \frac {\exp \left (6+e^{e^{4-2 x}+3 e^{-2 x}}+\left (1+\frac {3}{e^4}\right ) e^{4-2 x}-2 x\right )}{x} \, dx+\int \frac {-3+e^{6+e^{e^{4-2 x}+3 e^{-2 x}}}}{x^2} \, dx\\ &=\left (2 \left (3+e^4\right )\right ) \int \frac {\exp \left (6+e^{e^{4-2 x}+3 e^{-2 x}}+\left (1+\frac {3}{e^4}\right ) e^{4-2 x}-2 x\right )}{x} \, dx+\int \left (-\frac {3}{x^2}+\frac {e^{6+e^{e^{4-2 x}+3 e^{-2 x}}}}{x^2}\right ) \, dx\\ &=\frac {3}{x}+\left (2 \left (3+e^4\right )\right ) \int \frac {\exp \left (6+e^{e^{4-2 x}+3 e^{-2 x}}+\left (1+\frac {3}{e^4}\right ) e^{4-2 x}-2 x\right )}{x} \, dx+\int \frac {e^{6+e^{e^{4-2 x}+3 e^{-2 x}}}}{x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.66, size = 25, normalized size = 1.00 \begin {gather*} \frac {3-e^{6+e^{e^{-2 x} \left (3+e^4\right )}}}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 20, normalized size = 0.80 \begin {gather*} -\frac {e^{\left (e^{\left ({\left (e^{4} + 3\right )} e^{\left (-2 \, x\right )}\right )} + 6\right )} - 3}{x} \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 {{\left ({\left (2 \, {\left (x e^{4} + 3 \, x\right )} e^{\left ({\left (e^{4} + 3\right )} e^{\left (-2 \, x\right )}\right )} + e^{\left (2 \, x\right )}\right )} e^{\left (e^{\left ({\left (e^{4} + 3\right )} e^{\left (-2 \, x\right )}\right )} + 6\right )} - 3 \, e^{\left (2 \, x\right )}\right )} e^{\left (-2 \, 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 = 0.10, size = 25, normalized size = 1.00
method | result | size |
risch | \(\frac {3}{x}-\frac {{\mathrm e}^{{\mathrm e}^{\left ({\mathrm e}^{4}+3\right ) {\mathrm e}^{-2 x}}+6}}{x}\) | \(25\) |
norman | \(\frac {\left (-{\mathrm e}^{2 x} {\mathrm e}^{{\mathrm e}^{\left ({\mathrm e}^{4}+3\right ) {\mathrm e}^{-2 x}}+6}+3 \,{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x}}{x}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 28, normalized size = 1.12 \begin {gather*} -\frac {e^{\left (e^{\left (3 \, e^{\left (-2 \, x\right )} + e^{\left (-2 \, x + 4\right )}\right )} + 6\right )}}{x} + \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.46, size = 27, normalized size = 1.08 \begin {gather*} -\frac {{\mathrm {e}}^{{\mathrm {e}}^{3\,{\mathrm {e}}^{-2\,x}}\,{\mathrm {e}}^{{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^4}}\,{\mathrm {e}}^6-3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 19, normalized size = 0.76 \begin {gather*} - \frac {e^{e^{\left (3 + e^{4}\right ) e^{- 2 x}} + 6}}{x} + \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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