Optimal. Leaf size=26 \[ \frac {e^{\frac {1}{x}}}{\log \left (\left (\frac {26}{x^2}-x\right ) (2-x+\log (3))\right )} \]
________________________________________________________________________________________
Rubi [A] time = 0.74, 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 = {6688, 2288} \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.
[In]
[Out]
Rule 2288
Rule 6688
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*}
________________________________________________________________________________________
Mathematica [A] time = 0.09, 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.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.17, 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 \relax (3) - 26 \, x + 52}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.54, size = 39, normalized size = 1.50 \begin {gather*} \frac {e^{\frac {1}{x}}}{\log \left (x^{4} - x^{3} \log \relax (3) - 2 \, x^{3} - 26 \, x + 26 \, \log \relax (3) + 52\right ) - \log \left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [C] time = 0.17, size = 364, normalized size = 14.00
method | result | size |
risch | \(-\frac {2 i {\mathrm e}^{\frac {1}{x}}}{\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}-2 \pi \mathrm {csgn}\left (\frac {i \left (x^{3}-26\right ) \left (\ln \relax (3)-x +2\right )}{x^{2}}\right )^{2}-\pi \,\mathrm {csgn}\left (\frac {i}{x^{2}}\right ) \mathrm {csgn}\left (i \left (\ln \relax (3)-x +2\right ) \left (x^{3}-26\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}-26\right ) \left (\ln \relax (3)-x +2\right )}{x^{2}}\right )+\pi \,\mathrm {csgn}\left (\frac {i}{x^{2}}\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}-26\right ) \left (\ln \relax (3)-x +2\right )}{x^{2}}\right )^{2}-\pi \,\mathrm {csgn}\left (i \left (\ln \relax (3)-x +2\right )\right ) \mathrm {csgn}\left (i \left (x^{3}-26\right )\right ) \mathrm {csgn}\left (i \left (\ln \relax (3)-x +2\right ) \left (x^{3}-26\right )\right )+\pi \,\mathrm {csgn}\left (i \left (\ln \relax (3)-x +2\right )\right ) \mathrm {csgn}\left (i \left (\ln \relax (3)-x +2\right ) \left (x^{3}-26\right )\right )^{2}+\pi \,\mathrm {csgn}\left (i \left (x^{3}-26\right )\right ) \mathrm {csgn}\left (i \left (\ln \relax (3)-x +2\right ) \left (x^{3}-26\right )\right )^{2}-\pi \mathrm {csgn}\left (i \left (\ln \relax (3)-x +2\right ) \left (x^{3}-26\right )\right )^{3}+\pi \,\mathrm {csgn}\left (i \left (\ln \relax (3)-x +2\right ) \left (x^{3}-26\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}-26\right ) \left (\ln \relax (3)-x +2\right )}{x^{2}}\right )^{2}+\pi \mathrm {csgn}\left (\frac {i \left (x^{3}-26\right ) \left (\ln \relax (3)-x +2\right )}{x^{2}}\right )^{3}+2 \pi -2 i \ln \left (x^{3}-26\right )-2 i \ln \left (\ln \relax (3)-x +2\right )+4 i \ln \relax (x )}\) | \(364\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.59, size = 26, normalized size = 1.00 \begin {gather*} \frac {e^{\frac {1}{x}}}{\log \left (x^{3} - 26\right ) + \log \left (x - \log \relax (3) - 2\right ) - 2 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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 \relax (3)\,\left (x^4+52\,x\right )\right )+\ln \left (-\frac {26\,x+\ln \relax (3)\,\left (x^3-26\right )+2\,x^3-x^4-52}{x^2}\right )\,{\mathrm {e}}^{1/x}\,\left (26\,x+\ln \relax (3)\,\left (x^3-26\right )+2\,x^3-x^4-52\right )}{{\ln \left (-\frac {26\,x+\ln \relax (3)\,\left (x^3-26\right )+2\,x^3-x^4-52}{x^2}\right )}^2\,\left (\ln \relax (3)\,\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.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.75, 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 {\relax (3 )} + 52}{x^{2}} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________