Optimal. Leaf size=30 \[ \frac {e^{e^{e^x-x^6}}-x+x^2}{x-\log (\log (3))} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 3.74, 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^{x^6} x^2+e^{x^6} (1-2 x) \log (\log (3))+e^{e^{e^x-x^6}} \left (-e^{x^6}+e^{e^x} \left (e^x x-6 x^6+\left (-e^x+6 x^5\right ) \log (\log (3))\right )\right )}{e^{x^6} x^2-2 e^{x^6} x \log (\log (3))+e^{x^6} \log ^2(\log (3))} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-x^6} \left (e^{x^6} x^2+e^{x^6} (1-2 x) \log (\log (3))+e^{e^{e^x-x^6}} \left (-e^{x^6}+e^{e^x} \left (e^x x-6 x^6+\left (-e^x+6 x^5\right ) \log (\log (3))\right )\right )\right )}{(x-\log (\log (3)))^2} \, dx\\ &=\int \left (\frac {e^{e^x+e^{e^x-x^6}-x^6} \left (e^x-6 x^5\right )}{x-\log (\log (3))}+\frac {-e^{e^{e^x-x^6}}+x^2+\log (\log (3))-2 x \log (\log (3))}{(x-\log (\log (3)))^2}\right ) \, dx\\ &=\int \frac {e^{e^x+e^{e^x-x^6}-x^6} \left (e^x-6 x^5\right )}{x-\log (\log (3))} \, dx+\int \frac {-e^{e^{e^x-x^6}}+x^2+\log (\log (3))-2 x \log (\log (3))}{(x-\log (\log (3)))^2} \, dx\\ &=\int \left (\frac {e^{e^x+e^{e^x-x^6}+x-x^6}}{x-\log (\log (3))}-\frac {6 e^{e^x+e^{e^x-x^6}-x^6} x^5}{x-\log (\log (3))}\right ) \, dx+\int \left (-\frac {e^{e^{e^x-x^6}}}{(x-\log (\log (3)))^2}+\frac {x^2+\log (\log (3))-2 x \log (\log (3))}{(x-\log (\log (3)))^2}\right ) \, dx\\ &=-\left (6 \int \frac {e^{e^x+e^{e^x-x^6}-x^6} x^5}{x-\log (\log (3))} \, dx\right )-\int \frac {e^{e^{e^x-x^6}}}{(x-\log (\log (3)))^2} \, dx+\int \frac {e^{e^x+e^{e^x-x^6}+x-x^6}}{x-\log (\log (3))} \, dx+\int \frac {x^2+\log (\log (3))-2 x \log (\log (3))}{(x-\log (\log (3)))^2} \, dx\\ &=-\left (6 \int \left (e^{e^x+e^{e^x-x^6}-x^6} x^4+e^{e^x+e^{e^x-x^6}-x^6} x^3 \log (\log (3))+e^{e^x+e^{e^x-x^6}-x^6} x^2 \log ^2(\log (3))+e^{e^x+e^{e^x-x^6}-x^6} x \log ^3(\log (3))+e^{e^x+e^{e^x-x^6}-x^6} \log ^4(\log (3))+\frac {e^{e^x+e^{e^x-x^6}-x^6} \log ^5(\log (3))}{x-\log (\log (3))}\right ) \, dx\right )-\int \frac {e^{e^{e^x-x^6}}}{(x-\log (\log (3)))^2} \, dx+\int \frac {e^{e^x+e^{e^x-x^6}+x-x^6}}{x-\log (\log (3))} \, dx+\int \left (1-\frac {(-1+\log (\log (3))) \log (\log (3))}{(x-\log (\log (3)))^2}\right ) \, dx\\ &=x-\frac {(1-\log (\log (3))) \log (\log (3))}{x-\log (\log (3))}-6 \int e^{e^x+e^{e^x-x^6}-x^6} x^4 \, dx-(6 \log (\log (3))) \int e^{e^x+e^{e^x-x^6}-x^6} x^3 \, dx-\left (6 \log ^2(\log (3))\right ) \int e^{e^x+e^{e^x-x^6}-x^6} x^2 \, dx-\left (6 \log ^3(\log (3))\right ) \int e^{e^x+e^{e^x-x^6}-x^6} x \, dx-\left (6 \log ^4(\log (3))\right ) \int e^{e^x+e^{e^x-x^6}-x^6} \, dx-\left (6 \log ^5(\log (3))\right ) \int \frac {e^{e^x+e^{e^x-x^6}-x^6}}{x-\log (\log (3))} \, dx-\int \frac {e^{e^{e^x-x^6}}}{(x-\log (\log (3)))^2} \, dx+\int \frac {e^{e^x+e^{e^x-x^6}+x-x^6}}{x-\log (\log (3))} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.09, size = 42, normalized size = 1.40 \begin {gather*} \frac {e^{e^{e^x-x^6}}+x^2-x \log (\log (3))+(-1+\log (\log (3))) \log (\log (3))}{x-\log (\log (3))} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.06, size = 53, normalized size = 1.77
method | result | size |
risch | \(x -\frac {\ln \left (\ln \left (3\right )\right )^{2}}{\ln \left (\ln \left (3\right )\right )-x}+\frac {\ln \left (\ln \left (3\right )\right )}{\ln \left (\ln \left (3\right )\right )-x}-\frac {{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}-x^{6}}}}{\ln \left (\ln \left (3\right )\right )-x}\) | \(53\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 104 vs.
\(2 (27) = 54\).
time = 0.53, size = 104, normalized size = 3.47 \begin {gather*} 2 \, {\left (\frac {\log \left (\log \left (3\right )\right )}{x - \log \left (\log \left (3\right )\right )} - \log \left (x - \log \left (\log \left (3\right )\right )\right )\right )} \log \left (\log \left (3\right )\right ) + 2 \, \log \left (x - \log \left (\log \left (3\right )\right )\right ) \log \left (\log \left (3\right )\right ) + \frac {x^{2} - x \log \left (\log \left (3\right )\right ) - \log \left (\log \left (3\right )\right )^{2}}{x - \log \left (\log \left (3\right )\right )} + \frac {e^{\left (e^{\left (-x^{6} + e^{x}\right )}\right )}}{x - \log \left (\log \left (3\right )\right )} - \frac {\log \left (\log \left (3\right )\right )}{x - \log \left (\log \left (3\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.39, size = 37, normalized size = 1.23 \begin {gather*} \frac {x^{2} - {\left (x + 1\right )} \log \left (\log \left (3\right )\right ) + \log \left (\log \left (3\right )\right )^{2} + e^{\left (e^{\left (-x^{6} + e^{x}\right )}\right )}}{x - \log \left (\log \left (3\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.47, size = 37, normalized size = 1.23 \begin {gather*} x + \frac {e^{e^{- x^{6}} e^{e^{x}}}}{x - \log {\left (\log {\left (3 \right )} \right )}} + \frac {- \log {\left (\log {\left (3 \right )} \right )} + \log {\left (\log {\left (3 \right )} \right )}^{2}}{x - \log {\left (\log {\left (3 \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 6.33, size = 41, normalized size = 1.37 \begin {gather*} \frac {{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{-x^6}}-\ln \left (\ln \left (3\right )\right )+{\ln \left (\ln \left (3\right )\right )}^2-x\,\ln \left (\ln \left (3\right )\right )+x^2}{x-\ln \left (\ln \left (3\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________