Optimal. Leaf size=26 \[ \frac {e^{\frac {1}{x}}}{\log \left (\left (\frac {26}{x^2}-x\right ) (2-x+\log (3))\right )} \]
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Rubi [A]
time = 0.78, antiderivative size = 27, normalized size of antiderivative = 1.04, number of steps
used = 2, number of rules used = 2, integrand size = 161, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {6820, 2326}
\begin {gather*} \frac {e^{\frac {1}{x}}}{\log \left (\frac {\left (26-x^3\right ) (-x+2+\log (3))}{x^2}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {1}{x}} \left (\frac {x \left (-26 x-2 x^4+52 (2+\log (3))+x^3 (2+\log (3))\right )}{\left (-26+x^3\right ) (-2+x-\log (3))}-\log \left (\frac {\left (-26+x^3\right ) (-2+x-\log (3))}{x^2}\right )\right )}{x^2 \log ^2\left (\frac {\left (-26+x^3\right ) (-2+x-\log (3))}{x^2}\right )} \, dx\\ &=\frac {e^{\frac {1}{x}}}{\log \left (\frac {\left (26-x^3\right ) (2-x+\log (3))}{x^2}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 25, normalized size = 0.96 \begin {gather*} \frac {e^{\frac {1}{x}}}{\log \left (\frac {\left (-26+x^3\right ) (-2+x-\log (3))}{x^2}\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 1.00, size = 364, normalized size = 14.00
method | result | size |
risch | \(-\frac {2 i {\mathrm e}^{\frac {1}{x}}}{\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}-\pi \,\mathrm {csgn}\left (i \left (\ln \left (3\right )-x +2\right )\right ) \mathrm {csgn}\left (i \left (x^{3}-26\right )\right ) \mathrm {csgn}\left (i \left (\ln \left (3\right )-x +2\right ) \left (x^{3}-26\right )\right )+\pi \,\mathrm {csgn}\left (i \left (\ln \left (3\right )-x +2\right )\right ) \mathrm {csgn}\left (i \left (\ln \left (3\right )-x +2\right ) \left (x^{3}-26\right )\right )^{2}+\pi \,\mathrm {csgn}\left (i \left (x^{3}-26\right )\right ) \mathrm {csgn}\left (i \left (\ln \left (3\right )-x +2\right ) \left (x^{3}-26\right )\right )^{2}-\pi \mathrm {csgn}\left (i \left (\ln \left (3\right )-x +2\right ) \left (x^{3}-26\right )\right )^{3}+\pi \,\mathrm {csgn}\left (i \left (\ln \left (3\right )-x +2\right ) \left (x^{3}-26\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}-26\right ) \left (\ln \left (3\right )-x +2\right )}{x^{2}}\right )^{2}-\pi \,\mathrm {csgn}\left (i \left (\ln \left (3\right )-x +2\right ) \left (x^{3}-26\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}-26\right ) \left (\ln \left (3\right )-x +2\right )}{x^{2}}\right ) \mathrm {csgn}\left (\frac {i}{x^{2}}\right )+\pi \mathrm {csgn}\left (\frac {i \left (x^{3}-26\right ) \left (\ln \left (3\right )-x +2\right )}{x^{2}}\right )^{3}-2 \pi \mathrm {csgn}\left (\frac {i \left (x^{3}-26\right ) \left (\ln \left (3\right )-x +2\right )}{x^{2}}\right )^{2}+\pi \mathrm {csgn}\left (\frac {i \left (x^{3}-26\right ) \left (\ln \left (3\right )-x +2\right )}{x^{2}}\right )^{2} \mathrm {csgn}\left (\frac {i}{x^{2}}\right )+2 \pi -2 i \ln \left (\ln \left (3\right )-x +2\right )+4 i \ln \left (x \right )-2 i \ln \left (x^{3}-26\right )}\) | \(364\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.53, size = 26, normalized size = 1.00 \begin {gather*} \frac {e^{\frac {1}{x}}}{\log \left (x^{3} - 26\right ) + \log \left (x - \log \left (3\right ) - 2\right ) - 2 \, \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 34, normalized size = 1.31 \begin {gather*} \frac {e^{\frac {1}{x}}}{\log \left (\frac {x^{4} - 2 \, x^{3} - {\left (x^{3} - 26\right )} \log \left (3\right ) - 26 \, x + 52}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.24, size = 31, normalized size = 1.19 \begin {gather*} \frac {e^{\frac {1}{x}}}{\log {\left (\frac {x^{4} - 2 x^{3} - 26 x + \left (26 - x^{3}\right ) \log {\left (3 \right )} + 52}{x^{2}} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.59, size = 39, normalized size = 1.50 \begin {gather*} \frac {e^{\frac {1}{x}}}{\log \left (x^{4} - x^{3} \log \left (3\right ) - 2 \, x^{3} - 26 \, x + 26 \, \log \left (3\right ) + 52\right ) - \log \left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{1/x}\,\left (104\,x-26\,x^2+2\,x^4-2\,x^5+\ln \left (3\right )\,\left (x^4+52\,x\right )\right )+\ln \left (-\frac {26\,x+\ln \left (3\right )\,\left (x^3-26\right )+2\,x^3-x^4-52}{x^2}\right )\,{\mathrm {e}}^{1/x}\,\left (26\,x+\ln \left (3\right )\,\left (x^3-26\right )+2\,x^3-x^4-52\right )}{{\ln \left (-\frac {26\,x+\ln \left (3\right )\,\left (x^3-26\right )+2\,x^3-x^4-52}{x^2}\right )}^2\,\left (\ln \left (3\right )\,\left (26\,x^2-x^5\right )+52\,x^2-26\,x^3-2\,x^5+x^6\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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