Optimal. Leaf size=32 \[ -1+e^{-4/x} \left (-2+e^{\frac {4}{-4+(25+x)^2}}+\frac {3}{x}\right )^2 \]
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Rubi [A] time = 8.45, antiderivative size = 34, normalized size of antiderivative = 1.06, number of steps used = 1, number of rules used = 1, integrand size = 174, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.006, Rules used = {6706} \begin {gather*} \frac {e^{-4/x} \left (e^{\frac {4}{x^2+50 x+621}} x-2 x+3\right )^2}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{-4/x} \left (3-2 x+e^{\frac {4}{621+50 x+x^2}} x\right )^2}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.13, size = 33, normalized size = 1.03 \begin {gather*} \frac {e^{-4/x} \left (3+\left (-2+e^{\frac {4}{621+50 x+x^2}}\right ) x\right )^2}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 35, normalized size = 1.09 \begin {gather*} e^{\left (\frac {2 \, {\left (x \log \left (\frac {x e^{\left (\frac {4}{x^{2} + 50 \, x + 621}\right )} - 2 \, x + 3}{x}\right ) - 2\right )}}{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 {2 \, {\left (7 \, x^{5} + 694 \, x^{4} + 25594 \, x^{3} + 412248 \, x^{2} - 2 \, {\left (x^{5} + 96 \, x^{4} + 3642 \, x^{3} + 62100 \, x^{2} + 385641 \, x\right )} e^{\left (\frac {4}{x^{2} + 50 \, x + 621}\right )} + 2326887 \, x - 2313846\right )} e^{\left (\frac {2 \, {\left (x \log \left (\frac {x e^{\left (\frac {4}{x^{2} + 50 \, x + 621}\right )} - 2 \, x + 3}{x}\right ) - 2\right )}}{x}\right )}}{2 \, x^{7} + 197 \, x^{6} + 7184 \, x^{5} + 112974 \, x^{4} + 584982 \, x^{3} - 1156923 \, x^{2} - {\left (x^{7} + 100 \, x^{6} + 3742 \, x^{5} + 62100 \, x^{4} + 385641 \, x^{3}\right )} e^{\left (\frac {4}{x^{2} + 50 \, x + 621}\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.15, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (4 x^{5}+384 x^{4}+14568 x^{3}+248400 x^{2}+1542564 x \right ) {\mathrm e}^{\frac {4}{x^{2}+50 x +621}}-14 x^{5}-1388 x^{4}-51188 x^{3}-824496 x^{2}-4653774 x +4627692\right ) {\mathrm e}^{\frac {2 x \ln \left (\frac {x \,{\mathrm e}^{\frac {4}{x^{2}+50 x +621}}+3-2 x}{x}\right )-4}{x}}}{\left (x^{7}+100 x^{6}+3742 x^{5}+62100 x^{4}+385641 x^{3}\right ) {\mathrm e}^{\frac {4}{x^{2}+50 x +621}}-2 x^{7}-197 x^{6}-7184 x^{5}-112974 x^{4}-584982 x^{3}+1156923 x^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {{\left (2 \, {\left (2 \, x - 3\right )} e^{\left (-\frac {1}{x + 27} + \frac {1}{x + 23}\right )} - x e^{\left (-\frac {2}{x + 27} + \frac {2}{x + 23}\right )}\right )} e^{\left (-\frac {4}{x}\right )}}{x} + 2 \, \int \frac {{\left (14 \, x^{2} - 33 \, x + 18\right )} e^{\left (-\frac {4}{x}\right )}}{x^{4}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.95, size = 95, normalized size = 2.97 \begin {gather*} 4\,{\mathrm {e}}^{-\frac {4}{x}}-4\,{\mathrm {e}}^{\frac {4}{x^2+50\,x+621}-\frac {4}{x}}+{\mathrm {e}}^{\frac {8}{x^2+50\,x+621}-\frac {4}{x}}-\frac {12\,{\mathrm {e}}^{-\frac {4}{x}}}{x}+\frac {9\,{\mathrm {e}}^{-\frac {4}{x}}}{x^2}+\frac {6\,{\mathrm {e}}^{\frac {4}{x^2+50\,x+621}-\frac {4}{x}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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