Integrand size = 95, antiderivative size = 18 \[ \int \frac {e^{\frac {1}{\log ^4\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )}} \left (40 x^4-24 x^5+(8-8 x) \log (36)\right )}{\left (-2 x^5+x^6+\left (-2 x+x^2\right ) \log (36)\right ) \log ^5\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )} \, dx=e^{\frac {1}{\log ^4\left ((2-x) x \left (x^4+\log (36)\right )\right )}} \]
[Out]
\[ \int \frac {e^{\frac {1}{\log ^4\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )}} \left (40 x^4-24 x^5+(8-8 x) \log (36)\right )}{\left (-2 x^5+x^6+\left (-2 x+x^2\right ) \log (36)\right ) \log ^5\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )} \, dx=\int \frac {e^{\frac {1}{\log ^4\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )}} \left (40 x^4-24 x^5+(8-8 x) \log (36)\right )}{\left (-2 x^5+x^6+\left (-2 x+x^2\right ) \log (36)\right ) \log ^5\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {8 e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}} \left (-5 x^4+3 x^5-\log (36)+x \log (36)\right )}{(2-x) x \left (x^4+\log (36)\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx \\ & = 8 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}} \left (-5 x^4+3 x^5-\log (36)+x \log (36)\right )}{(2-x) x \left (x^4+\log (36)\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx \\ & = 8 \int \left (-\frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{2 (-2+x) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}-\frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{2 x \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}-\frac {2 e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}} x^3}{\left (x^4+\log (36)\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}\right ) \, dx \\ & = -\left (4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{(-2+x) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx\right )-4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{x \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx-16 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}} x^3}{\left (x^4+\log (36)\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx \\ & = -\left (4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{(-2+x) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx\right )-4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{x \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx-16 \int \left (\frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}} x}{2 \left (x^2-i \sqrt {\log (36)}\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}+\frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}} x}{2 \left (x^2+i \sqrt {\log (36)}\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}\right ) \, dx \\ & = -\left (4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{(-2+x) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx\right )-4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{x \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx-8 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}} x}{\left (x^2-i \sqrt {\log (36)}\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx-8 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}} x}{\left (x^2+i \sqrt {\log (36)}\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx \\ & = -\left (4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{(-2+x) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx\right )-4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{x \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx-8 \int \left (-\frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{2 \left (-x+\sqrt [4]{-\log (36)}\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}+\frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{2 \left (x+\sqrt [4]{-\log (36)}\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}\right ) \, dx-8 \int \left (-\frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{2 \left (-x-(-1)^{3/4} \sqrt [4]{\log (36)}\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}+\frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{2 \left (x-(-1)^{3/4} \sqrt [4]{\log (36)}\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}\right ) \, dx \\ & = -\left (4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{(-2+x) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx\right )-4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{x \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx+4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{\left (-x+\sqrt [4]{-\log (36)}\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx-4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{\left (x+\sqrt [4]{-\log (36)}\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx+4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{\left (-x-(-1)^{3/4} \sqrt [4]{\log (36)}\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx-4 \int \frac {e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}}}{\left (x-(-1)^{3/4} \sqrt [4]{\log (36)}\right ) \log ^5\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )} \, dx \\ \end{align*}
Time = 0.50 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {e^{\frac {1}{\log ^4\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )}} \left (40 x^4-24 x^5+(8-8 x) \log (36)\right )}{\left (-2 x^5+x^6+\left (-2 x+x^2\right ) \log (36)\right ) \log ^5\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )} \, dx=e^{\frac {1}{\log ^4\left (-\left ((-2+x) x \left (x^4+\log (36)\right )\right )\right )}} \]
[In]
[Out]
Time = 0.49 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.78
\[{\mathrm e}^{\frac {1}{{\ln \left (2 \left (-x^{2}+2 x \right ) \left (\ln \left (2\right )+\ln \left (3\right )\right )-x^{6}+2 x^{5}\right )}^{4}}}\]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.44 \[ \int \frac {e^{\frac {1}{\log ^4\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )}} \left (40 x^4-24 x^5+(8-8 x) \log (36)\right )}{\left (-2 x^5+x^6+\left (-2 x+x^2\right ) \log (36)\right ) \log ^5\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )} \, dx=e^{\left (\frac {1}{\log \left (-x^{6} + 2 \, x^{5} - 2 \, {\left (x^{2} - 2 \, x\right )} \log \left (6\right )\right )^{4}}\right )} \]
[In]
[Out]
Time = 0.23 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.44 \[ \int \frac {e^{\frac {1}{\log ^4\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )}} \left (40 x^4-24 x^5+(8-8 x) \log (36)\right )}{\left (-2 x^5+x^6+\left (-2 x+x^2\right ) \log (36)\right ) \log ^5\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )} \, dx=e^{\frac {1}{\log {\left (- x^{6} + 2 x^{5} + \left (- 2 x^{2} + 4 x\right ) \log {\left (6 \right )} \right )}^{4}}} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 1148 vs. \(2 (18) = 36\).
Time = 0.49 (sec) , antiderivative size = 1148, normalized size of antiderivative = 63.78 \[ \int \frac {e^{\frac {1}{\log ^4\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )}} \left (40 x^4-24 x^5+(8-8 x) \log (36)\right )}{\left (-2 x^5+x^6+\left (-2 x+x^2\right ) \log (36)\right ) \log ^5\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )} \, dx=\text {Too large to display} \]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.50 \[ \int \frac {e^{\frac {1}{\log ^4\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )}} \left (40 x^4-24 x^5+(8-8 x) \log (36)\right )}{\left (-2 x^5+x^6+\left (-2 x+x^2\right ) \log (36)\right ) \log ^5\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )} \, dx=e^{\left (\frac {1}{\log \left (-x^{6} + 2 \, x^{5} - 2 \, x^{2} \log \left (6\right ) + 4 \, x \log \left (6\right )\right )^{4}}\right )} \]
[In]
[Out]
Time = 10.71 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.50 \[ \int \frac {e^{\frac {1}{\log ^4\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )}} \left (40 x^4-24 x^5+(8-8 x) \log (36)\right )}{\left (-2 x^5+x^6+\left (-2 x+x^2\right ) \log (36)\right ) \log ^5\left (2 x^5-x^6+\left (2 x-x^2\right ) \log (36)\right )} \, dx={\mathrm {e}}^{\frac {1}{{\ln \left (-x^6+2\,x^5-2\,\ln \left (6\right )\,x^2+4\,\ln \left (6\right )\,x\right )}^4}} \]
[In]
[Out]