Optimal. Leaf size=26 \[ \frac {e^{e^{-4+4 x^2}}}{x}+\frac {\log (3)}{4-2 x} \]
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Rubi [A] time = 0.82, antiderivative size = 29, normalized size of antiderivative = 1.12, number of steps used = 6, number of rules used = 5, integrand size = 74, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.068, Rules used = {1594, 27, 12, 6688, 2288} \begin {gather*} \frac {e^{e^{4 x^2-4}}}{x}+\frac {\log (3)}{2 (2-x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 1594
Rule 2288
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{e^{-4+4 x^2}} \left (-8+8 x-2 x^2+e^{-4+4 x^2} \left (64 x^2-64 x^3+16 x^4\right )\right )+x^2 \log (3)}{x^2 \left (8-8 x+2 x^2\right )} \, dx\\ &=\int \frac {e^{e^{-4+4 x^2}} \left (-8+8 x-2 x^2+e^{-4+4 x^2} \left (64 x^2-64 x^3+16 x^4\right )\right )+x^2 \log (3)}{2 (-2+x)^2 x^2} \, dx\\ &=\frac {1}{2} \int \frac {e^{e^{-4+4 x^2}} \left (-8+8 x-2 x^2+e^{-4+4 x^2} \left (64 x^2-64 x^3+16 x^4\right )\right )+x^2 \log (3)}{(-2+x)^2 x^2} \, dx\\ &=\frac {1}{2} \int \left (-\frac {2 e^{-4+e^{-4+4 x^2}} \left (e^4-8 e^{4 x^2} x^2\right )}{x^2}+\frac {\log (3)}{(-2+x)^2}\right ) \, dx\\ &=\frac {\log (3)}{2 (2-x)}-\int \frac {e^{-4+e^{-4+4 x^2}} \left (e^4-8 e^{4 x^2} x^2\right )}{x^2} \, dx\\ &=\frac {e^{e^{-4+4 x^2}}}{x}+\frac {\log (3)}{2 (2-x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 39, normalized size = 1.50 \begin {gather*} \frac {\frac {2 e^{4+e^{-4+4 x^2}}}{x}+\frac {e^4 \log (3)}{2-x}}{2 e^4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 31, normalized size = 1.19 \begin {gather*} \frac {2 \, {\left (x - 2\right )} e^{\left (e^{\left (4 \, x^{2} - 4\right )}\right )} - x \log \relax (3)}{2 \, {\left (x^{2} - 2 \, 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 {x^{2} \log \relax (3) - 2 \, {\left (x^{2} - 8 \, {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2}\right )} e^{\left (4 \, x^{2} - 4\right )} - 4 \, x + 4\right )} e^{\left (e^{\left (4 \, x^{2} - 4\right )}\right )}}{2 \, {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2}\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 25, normalized size = 0.96
method | result | size |
risch | \(-\frac {\ln \relax (3)}{2 \left (x -2\right )}+\frac {{\mathrm e}^{{\mathrm e}^{4 \left (x -1\right ) \left (x +1\right )}}}{x}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.87, size = 23, normalized size = 0.88 \begin {gather*} \frac {e^{\left (e^{\left (4 \, x^{2} - 4\right )}\right )}}{x} - \frac {\log \relax (3)}{2 \, {\left (x - 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.19, size = 26, normalized size = 1.00 \begin {gather*} \frac {{\mathrm {e}}^{{\mathrm {e}}^{-4}\,{\mathrm {e}}^{4\,x^2}}}{x}-\frac {\ln \relax (3)}{2\,x-4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 19, normalized size = 0.73 \begin {gather*} - \frac {\log {\relax (3 )}}{2 x - 4} + \frac {e^{e^{4 x^{2} - 4}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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