Integrand size = 180, antiderivative size = 30 \[ \int \frac {-8 e^{e^5}+8 x+24 x^2+\sqrt [4]{x^2} \left (2 e^{e^5}-2 x-6 x^2\right )+\left (8 e^{e^5}+8 x+8 x^2+\sqrt [4]{x^2} \left (-3 e^{e^5}-3 x-3 x^2\right )\right ) \log \left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )}{\left (2 e^{e^5}+2 x+2 x^2\right ) \log ^2\left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )} \, dx=\frac {x \left (4-\sqrt [4]{x^2}\right )}{\log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \]
Time = 0.14 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.97 \[ \int \frac {-8 e^{e^5}+8 x+24 x^2+\sqrt [4]{x^2} \left (2 e^{e^5}-2 x-6 x^2\right )+\left (8 e^{e^5}+8 x+8 x^2+\sqrt [4]{x^2} \left (-3 e^{e^5}-3 x-3 x^2\right )\right ) \log \left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )}{\left (2 e^{e^5}+2 x+2 x^2\right ) \log ^2\left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )} \, dx=-\frac {x \left (-4+\sqrt [4]{x^2}\right )}{\log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \]
Integrate[(-8*E^E^5 + 8*x + 24*x^2 + (x^2)^(1/4)*(2*E^E^5 - 2*x - 6*x^2) + (8*E^E^5 + 8*x + 8*x^2 + (x^2)^(1/4)*(-3*E^E^5 - 3*x - 3*x^2))*Log[x/(E^( 2*E^5) + x^2 + 2*x^3 + x^4 + E^E^5*(2*x + 2*x^2))])/((2*E^E^5 + 2*x + 2*x^ 2)*Log[x/(E^(2*E^5) + x^2 + 2*x^3 + x^4 + E^E^5*(2*x + 2*x^2))]^2),x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {24 x^2+\sqrt [4]{x^2} \left (-6 x^2-2 x+2 e^{e^5}\right )+\left (8 x^2+\sqrt [4]{x^2} \left (-3 x^2-3 x-3 e^{e^5}\right )+8 x+8 e^{e^5}\right ) \log \left (\frac {x}{x^4+2 x^3+x^2+e^{e^5} \left (2 x^2+2 x\right )+e^{2 e^5}}\right )+8 x-8 e^{e^5}}{\left (2 x^2+2 x+2 e^{e^5}\right ) \log ^2\left (\frac {x}{x^4+2 x^3+x^2+e^{e^5} \left (2 x^2+2 x\right )+e^{2 e^5}}\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\frac {2 \left (3 x^2+x-e^{e^5}\right ) \left (\sqrt [4]{x^2}-4\right )}{x^2+x+e^{e^5}}-\left (3 \sqrt [4]{x^2}-8\right ) \log \left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}{2 \log ^2\left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{2} \int -\frac {\frac {2 \left (-3 x^2-x+e^{e^5}\right ) \left (4-\sqrt [4]{x^2}\right )}{x^2+x+e^{e^5}}-\left (8-3 \sqrt [4]{x^2}\right ) \log \left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}{\log ^2\left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{2} \int \frac {\frac {2 \left (-3 x^2-x+e^{e^5}\right ) \left (4-\sqrt [4]{x^2}\right )}{x^2+x+e^{e^5}}-\left (8-3 \sqrt [4]{x^2}\right ) \log \left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}{\log ^2\left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{2} \int \left (\frac {6 \left (x^2\right )^{5/4}}{\left (x^2+x+e^{e^5}\right ) \log ^2\left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}+\frac {3 \sqrt [4]{x^2}}{\log \left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}+\frac {2 x \sqrt [4]{x^2}}{\left (x^2+x+e^{e^5}\right ) \log ^2\left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}-\frac {2 e^{e^5} \sqrt [4]{x^2}}{\left (x^2+x+e^{e^5}\right ) \log ^2\left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}-\frac {8}{\log \left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}+\frac {8 \left (-3 x^2-x+e^{e^5}\right )}{\left (x^2+x+e^{e^5}\right ) \log ^2\left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{2} \left (\frac {8 \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {x}}-\frac {12 \sqrt [4]{x^2} \text {Subst}\left (\int \frac {x^2}{\log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {x}}+\frac {8 i e^{e^5} \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {-1-i \sqrt {-1+4 e^{e^5}}}-\sqrt {2} x\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {\left (1-4 e^{e^5}\right ) \left (1+i \sqrt {-1+4 e^{e^5}}\right )} \sqrt {x}}+\frac {6 \left (1-e^{e^5}\right ) \left (1-\frac {i}{\sqrt {-1+4 e^{e^5}}}\right ) \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {-1-i \sqrt {-1+4 e^{e^5}}}-\sqrt {2} x\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {-1-i \sqrt {-1+4 e^{e^5}}} \sqrt {x}}-\frac {2 e^{e^5} \left (1-\frac {i}{\sqrt {-1+4 e^{e^5}}}\right ) \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {-1-i \sqrt {-1+4 e^{e^5}}}-\sqrt {2} x\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {-1-i \sqrt {-1+4 e^{e^5}}} \sqrt {x}}-\frac {2 \left (1-\frac {i}{\sqrt {-1+4 e^{e^5}}}\right ) \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {-1-i \sqrt {-1+4 e^{e^5}}}-\sqrt {2} x\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {-1-i \sqrt {-1+4 e^{e^5}}} \sqrt {x}}-\frac {8 i e^{e^5} \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {-1+i \sqrt {-1+4 e^{e^5}}}-\sqrt {2} x\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {-i \left (1-4 e^{e^5}\right ) \left (i+\sqrt {-1+4 e^{e^5}}\right )} \sqrt {x}}-\frac {6 i \left (1-e^{e^5}\right ) \sqrt {\frac {1-i \sqrt {-1+4 e^{e^5}}}{1-4 e^{e^5}}} \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {-1+i \sqrt {-1+4 e^{e^5}}}-\sqrt {2} x\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {x}}+\frac {2 i e^{e^5} \sqrt {\frac {1-i \sqrt {-1+4 e^{e^5}}}{1-4 e^{e^5}}} \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {-1+i \sqrt {-1+4 e^{e^5}}}-\sqrt {2} x\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {x}}+\frac {2 i \sqrt {\frac {1-i \sqrt {-1+4 e^{e^5}}}{1-4 e^{e^5}}} \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {-1+i \sqrt {-1+4 e^{e^5}}}-\sqrt {2} x\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {x}}+\frac {8 i e^{e^5} \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {2} x+\sqrt {-1-i \sqrt {-1+4 e^{e^5}}}\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {\left (1-4 e^{e^5}\right ) \left (1+i \sqrt {-1+4 e^{e^5}}\right )} \sqrt {x}}+\frac {6 \left (1-e^{e^5}\right ) \left (1-\frac {i}{\sqrt {-1+4 e^{e^5}}}\right ) \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {2} x+\sqrt {-1-i \sqrt {-1+4 e^{e^5}}}\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {-1-i \sqrt {-1+4 e^{e^5}}} \sqrt {x}}-\frac {2 e^{e^5} \left (1-\frac {i}{\sqrt {-1+4 e^{e^5}}}\right ) \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {2} x+\sqrt {-1-i \sqrt {-1+4 e^{e^5}}}\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {-1-i \sqrt {-1+4 e^{e^5}}} \sqrt {x}}-\frac {2 \left (1-\frac {i}{\sqrt {-1+4 e^{e^5}}}\right ) \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {2} x+\sqrt {-1-i \sqrt {-1+4 e^{e^5}}}\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {-1-i \sqrt {-1+4 e^{e^5}}} \sqrt {x}}-\frac {8 i e^{e^5} \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {2} x+\sqrt {-1+i \sqrt {-1+4 e^{e^5}}}\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {-i \left (1-4 e^{e^5}\right ) \left (i+\sqrt {-1+4 e^{e^5}}\right )} \sqrt {x}}-\frac {6 i \left (1-e^{e^5}\right ) \sqrt {\frac {1-i \sqrt {-1+4 e^{e^5}}}{1-4 e^{e^5}}} \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {2} x+\sqrt {-1+i \sqrt {-1+4 e^{e^5}}}\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {x}}+\frac {2 i e^{e^5} \sqrt {\frac {1-i \sqrt {-1+4 e^{e^5}}}{1-4 e^{e^5}}} \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {2} x+\sqrt {-1+i \sqrt {-1+4 e^{e^5}}}\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {x}}+\frac {2 i \sqrt {\frac {1-i \sqrt {-1+4 e^{e^5}}}{1-4 e^{e^5}}} \sqrt [4]{x^2} \text {Subst}\left (\int \frac {1}{\left (\sqrt {2} x+\sqrt {-1+i \sqrt {-1+4 e^{e^5}}}\right ) \log ^2\left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {x}}-\frac {6 \sqrt [4]{x^2} \text {Subst}\left (\int \frac {x^2}{\log \left (\frac {x^2}{\left (x^4+x^2+e^{e^5}\right )^2}\right )}dx,x,\sqrt {x}\right )}{\sqrt {x}}+24 \int \frac {1}{\log ^2\left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}dx-\frac {64 i e^{e^5} \int \frac {1}{\left (-2 x+i \sqrt {-1+4 e^{e^5}}-1\right ) \log ^2\left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}dx}{\sqrt {-1+4 e^{e^5}}}-16 \left (1+\frac {i}{\sqrt {-1+4 e^{e^5}}}\right ) \int \frac {1}{\left (2 x-i \sqrt {-1+4 e^{e^5}}+1\right ) \log ^2\left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}dx-16 \left (1-\frac {i}{\sqrt {-1+4 e^{e^5}}}\right ) \int \frac {1}{\left (2 x+i \sqrt {-1+4 e^{e^5}}+1\right ) \log ^2\left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}dx-\frac {64 i e^{e^5} \int \frac {1}{\left (2 x+i \sqrt {-1+4 e^{e^5}}+1\right ) \log ^2\left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}dx}{\sqrt {-1+4 e^{e^5}}}+8 \int \frac {1}{\log \left (\frac {x}{\left (x^2+x+e^{e^5}\right )^2}\right )}dx\right )\) |
Int[(-8*E^E^5 + 8*x + 24*x^2 + (x^2)^(1/4)*(2*E^E^5 - 2*x - 6*x^2) + (8*E^ E^5 + 8*x + 8*x^2 + (x^2)^(1/4)*(-3*E^E^5 - 3*x - 3*x^2))*Log[x/(E^(2*E^5) + x^2 + 2*x^3 + x^4 + E^E^5*(2*x + 2*x^2))])/((2*E^E^5 + 2*x + 2*x^2)*Log [x/(E^(2*E^5) + x^2 + 2*x^3 + x^4 + E^E^5*(2*x + 2*x^2))]^2),x]
3.17.81.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
\[\int \frac {\left (\left (-3 \,{\mathrm e}^{{\mathrm e}^{5}}-3 x^{2}-3 x \right ) \left (x^{2}\right )^{\frac {1}{4}}+8 \,{\mathrm e}^{{\mathrm e}^{5}}+8 x^{2}+8 x \right ) \ln \left (\frac {x}{{\mathrm e}^{2 \,{\mathrm e}^{5}}+\left (2 x^{2}+2 x \right ) {\mathrm e}^{{\mathrm e}^{5}}+x^{4}+2 x^{3}+x^{2}}\right )+\left (2 \,{\mathrm e}^{{\mathrm e}^{5}}-6 x^{2}-2 x \right ) \left (x^{2}\right )^{\frac {1}{4}}-8 \,{\mathrm e}^{{\mathrm e}^{5}}+24 x^{2}+8 x}{\left (2 \,{\mathrm e}^{{\mathrm e}^{5}}+2 x^{2}+2 x \right ) \ln \left (\frac {x}{{\mathrm e}^{2 \,{\mathrm e}^{5}}+\left (2 x^{2}+2 x \right ) {\mathrm e}^{{\mathrm e}^{5}}+x^{4}+2 x^{3}+x^{2}}\right )^{2}}d x\]
int((((-3*exp(exp(5))-3*x^2-3*x)*(x^2)^(1/4)+8*exp(exp(5))+8*x^2+8*x)*ln(x /(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))+(2*exp(exp(5))-6*x ^2-2*x)*(x^2)^(1/4)-8*exp(exp(5))+24*x^2+8*x)/(2*exp(exp(5))+2*x^2+2*x)/ln (x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))^2,x)
int((((-3*exp(exp(5))-3*x^2-3*x)*(x^2)^(1/4)+8*exp(exp(5))+8*x^2+8*x)*ln(x /(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))+(2*exp(exp(5))-6*x ^2-2*x)*(x^2)^(1/4)-8*exp(exp(5))+24*x^2+8*x)/(2*exp(exp(5))+2*x^2+2*x)/ln (x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))^2,x)
Time = 0.41 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.57 \[ \int \frac {-8 e^{e^5}+8 x+24 x^2+\sqrt [4]{x^2} \left (2 e^{e^5}-2 x-6 x^2\right )+\left (8 e^{e^5}+8 x+8 x^2+\sqrt [4]{x^2} \left (-3 e^{e^5}-3 x-3 x^2\right )\right ) \log \left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )}{\left (2 e^{e^5}+2 x+2 x^2\right ) \log ^2\left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )} \, dx=-\frac {{\left (x^{2}\right )}^{\frac {1}{4}} x - 4 \, x}{\log \left (\frac {x}{x^{4} + 2 \, x^{3} + x^{2} + 2 \, {\left (x^{2} + x\right )} e^{\left (e^{5}\right )} + e^{\left (2 \, e^{5}\right )}}\right )} \]
integrate((((-3*exp(exp(5))-3*x^2-3*x)*(x^2)^(1/4)+8*exp(exp(5))+8*x^2+8*x )*log(x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))+(2*exp(exp( 5))-6*x^2-2*x)*(x^2)^(1/4)-8*exp(exp(5))+24*x^2+8*x)/(2*exp(exp(5))+2*x^2+ 2*x)/log(x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))^2,x, alg orithm=\
Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (24) = 48\).
Time = 7.96 (sec) , antiderivative size = 92, normalized size of antiderivative = 3.07 \[ \int \frac {-8 e^{e^5}+8 x+24 x^2+\sqrt [4]{x^2} \left (2 e^{e^5}-2 x-6 x^2\right )+\left (8 e^{e^5}+8 x+8 x^2+\sqrt [4]{x^2} \left (-3 e^{e^5}-3 x-3 x^2\right )\right ) \log \left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )}{\left (2 e^{e^5}+2 x+2 x^2\right ) \log ^2\left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )} \, dx=- \frac {x \sqrt [4]{x^{2}}}{\log {\left (\frac {x}{x^{4} + 2 x^{3} + x^{2} + 2 x^{2} e^{e^{5}} + 2 x e^{e^{5}} + e^{2 e^{5}}} \right )}} + \frac {4 x}{\log {\left (\frac {x}{x^{4} + 2 x^{3} + x^{2} + 2 x^{2} e^{e^{5}} + 2 x e^{e^{5}} + e^{2 e^{5}}} \right )}} \]
integrate((((-3*exp(exp(5))-3*x**2-3*x)*(x**2)**(1/4)+8*exp(exp(5))+8*x**2 +8*x)*ln(x/(exp(exp(5))**2+(2*x**2+2*x)*exp(exp(5))+x**4+2*x**3+x**2))+(2* exp(exp(5))-6*x**2-2*x)*(x**2)**(1/4)-8*exp(exp(5))+24*x**2+8*x)/(2*exp(ex p(5))+2*x**2+2*x)/ln(x/(exp(exp(5))**2+(2*x**2+2*x)*exp(exp(5))+x**4+2*x** 3+x**2))**2,x)
-x*(x**2)**(1/4)/log(x/(x**4 + 2*x**3 + x**2 + 2*x**2*exp(exp(5)) + 2*x*ex p(exp(5)) + exp(2*exp(5)))) + 4*x/log(x/(x**4 + 2*x**3 + x**2 + 2*x**2*exp (exp(5)) + 2*x*exp(exp(5)) + exp(2*exp(5))))
\[ \int \frac {-8 e^{e^5}+8 x+24 x^2+\sqrt [4]{x^2} \left (2 e^{e^5}-2 x-6 x^2\right )+\left (8 e^{e^5}+8 x+8 x^2+\sqrt [4]{x^2} \left (-3 e^{e^5}-3 x-3 x^2\right )\right ) \log \left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )}{\left (2 e^{e^5}+2 x+2 x^2\right ) \log ^2\left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )} \, dx=\int { \frac {24 \, x^{2} + {\left (8 \, x^{2} - 3 \, {\left (x^{2} + x + e^{\left (e^{5}\right )}\right )} {\left (x^{2}\right )}^{\frac {1}{4}} + 8 \, x + 8 \, e^{\left (e^{5}\right )}\right )} \log \left (\frac {x}{x^{4} + 2 \, x^{3} + x^{2} + 2 \, {\left (x^{2} + x\right )} e^{\left (e^{5}\right )} + e^{\left (2 \, e^{5}\right )}}\right ) - 2 \, {\left (3 \, x^{2} + x - e^{\left (e^{5}\right )}\right )} {\left (x^{2}\right )}^{\frac {1}{4}} + 8 \, x - 8 \, e^{\left (e^{5}\right )}}{2 \, {\left (x^{2} + x + e^{\left (e^{5}\right )}\right )} \log \left (\frac {x}{x^{4} + 2 \, x^{3} + x^{2} + 2 \, {\left (x^{2} + x\right )} e^{\left (e^{5}\right )} + e^{\left (2 \, e^{5}\right )}}\right )^{2}} \,d x } \]
integrate((((-3*exp(exp(5))-3*x^2-3*x)*(x^2)^(1/4)+8*exp(exp(5))+8*x^2+8*x )*log(x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))+(2*exp(exp( 5))-6*x^2-2*x)*(x^2)^(1/4)-8*exp(exp(5))+24*x^2+8*x)/(2*exp(exp(5))+2*x^2+ 2*x)/log(x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))^2,x, alg orithm=\
-(4*x^3*e^(e^5) + 3*(x^3 + x^2 + x*e^(e^5))*x^(5/2) - 12*(x^3 + x^2 + x*e^ (e^5))*x^2 + 4*x^2*e^(e^5) + (x^3 + x^2 + x*e^(e^5))*x^(3/2) - 4*(x^3 + x^ 2 + x*e^(e^5))*x + 4*x*e^(2*e^5) - (x^3*e^(e^5) + x^2*e^(e^5) + x*e^(2*e^5 ))*sqrt(x))/((3*x^2 + x - e^(e^5))*x^2*log(x) + (3*x^2 + x - e^(e^5))*x*lo g(x) - 2*((3*x^2 + x - e^(e^5))*x^2 + 3*x^2*e^(e^5) + (3*x^2 + x - e^(e^5) )*x + x*e^(e^5) - e^(2*e^5))*log(x^2 + x + e^(e^5)) + (3*x^2*e^(e^5) + x*e ^(e^5) - e^(2*e^5))*log(x)) - 1/2*integrate(-2*(3*(x^3 - x^2*(2*e^(e^5) - 1) - x*e^(e^5) - 2*e^(2*e^5))*x^(9/2) + 8*(x^2*(6*e^(e^5) - 1) + 2*x*e^(e^ 5) + 2*e^(2*e^5))*x^4 + 48*x^4*e^(2*e^5) - (3*x^4 - 6*x^3 - x^2*(2*e^(e^5) + 5) + 2*x*e^(e^5) + 11*e^(2*e^5))*x^(7/2) - 16*(x^3 - x^2*(2*e^(e^5) - 1 ) - x*e^(e^5) - 2*e^(2*e^5))*x^3 + 32*x^3*e^(2*e^5) + (3*x^4*(2*e^(e^5) - 3) + x^3*(22*e^(e^5) - 5) + 12*x^2*(2*e^(2*e^5) + e^(e^5)) + x*(2*e^(2*e^5 ) + e^(e^5)) - 14*e^(3*e^5) - 3*e^(2*e^5))*x^(5/2) - 8*(3*x^4*(2*e^(e^5) - 1) + 2*x^3*(6*e^(e^5) - 1) + 4*x^2*(2*e^(2*e^5) + e^(e^5)) - 6*e^(3*e^5) - e^(2*e^5))*x^2 - 8*x^2*(6*e^(3*e^5) - e^(2*e^5)) - (21*x^4*e^(e^5) + 10* x^3*e^(e^5) - x^2*(22*e^(2*e^5) - e^(e^5)) - 6*x*e^(2*e^5) + 5*e^(3*e^5))* x^(3/2) + 16*(3*x^4*e^(e^5) + x^3*e^(e^5) - 4*x^2*e^(2*e^5) - x*e^(2*e^5) + e^(3*e^5))*x - 16*x*e^(3*e^5) - (18*x^4*e^(2*e^5) + 13*x^3*e^(2*e^5) - x ^2*(14*e^(3*e^5) - 3*e^(2*e^5)) - 5*x*e^(3*e^5))*sqrt(x))/((9*x^4 + 6*x^3 - x^2*(6*e^(e^5) - 1) - 2*x*e^(e^5) + e^(2*e^5))*x^4*log(x) + 2*(9*x^4 ...
Timed out. \[ \int \frac {-8 e^{e^5}+8 x+24 x^2+\sqrt [4]{x^2} \left (2 e^{e^5}-2 x-6 x^2\right )+\left (8 e^{e^5}+8 x+8 x^2+\sqrt [4]{x^2} \left (-3 e^{e^5}-3 x-3 x^2\right )\right ) \log \left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )}{\left (2 e^{e^5}+2 x+2 x^2\right ) \log ^2\left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )} \, dx=\text {Timed out} \]
integrate((((-3*exp(exp(5))-3*x^2-3*x)*(x^2)^(1/4)+8*exp(exp(5))+8*x^2+8*x )*log(x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))+(2*exp(exp( 5))-6*x^2-2*x)*(x^2)^(1/4)-8*exp(exp(5))+24*x^2+8*x)/(2*exp(exp(5))+2*x^2+ 2*x)/log(x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))^2,x, alg orithm=\
Time = 14.54 (sec) , antiderivative size = 3644, normalized size of antiderivative = 121.47 \[ \int \frac {-8 e^{e^5}+8 x+24 x^2+\sqrt [4]{x^2} \left (2 e^{e^5}-2 x-6 x^2\right )+\left (8 e^{e^5}+8 x+8 x^2+\sqrt [4]{x^2} \left (-3 e^{e^5}-3 x-3 x^2\right )\right ) \log \left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )}{\left (2 e^{e^5}+2 x+2 x^2\right ) \log ^2\left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )} \, dx=\text {Too large to display} \]
int((8*x - 8*exp(exp(5)) - (x^2)^(1/4)*(2*x - 2*exp(exp(5)) + 6*x^2) + log (x/(exp(2*exp(5)) + exp(exp(5))*(2*x + 2*x^2) + x^2 + 2*x^3 + x^4))*(8*x + 8*exp(exp(5)) - (x^2)^(1/4)*(3*x + 3*exp(exp(5)) + 3*x^2) + 8*x^2) + 24*x ^2)/(log(x/(exp(2*exp(5)) + exp(exp(5))*(2*x + 2*x^2) + x^2 + 2*x^3 + x^4) )^2*(2*x + 2*exp(exp(5)) + 2*x^2)),x)
(x/2 + 1/3)*(x^2)^(1/4) - ((x*((exp(exp(5))*((5832*exp(exp(5)) + 486)/(108 *(12*exp(exp(5)) + 1)^2) - (exp(exp(5))*((exp(-exp(5))*(1944*exp(exp(5)) + 162))/(12*(12*exp(exp(5)) + 1)^2) + (13*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(216*(12*exp(exp(5)) + 1)^2)))/3 + (13*exp(-exp(5))*(1944*exp(exp(5) ) + 162))/(648*(12*exp(exp(5)) + 1)^2) - (13*exp(-exp(5))*(5832*exp(exp(5) ) + 486))/(1944*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(90*exp(exp(5)) - 39)*(1944*exp(exp(5)) + 162))/(972*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5)) *(51*exp(exp(5)) - 9/2)*(5832*exp(exp(5)) + 486))/(972*(12*exp(exp(5)) + 1 )^2) - (exp(-exp(5))*(90*exp(exp(5)) - 39)*(5832*exp(exp(5)) + 486))/(2916 *(12*exp(exp(5)) + 1)^2)))/3 - (exp(exp(5))*((exp(-exp(5))*(1944*exp(exp(5 )) + 162))/(12*(12*exp(exp(5)) + 1)^2) + (13*exp(-exp(5))*(5832*exp(exp(5) ) + 486))/(216*(12*exp(exp(5)) + 1)^2)))/27 + (5832*exp(exp(5)) + 486)/(97 2*(12*exp(exp(5)) + 1)^2) + (exp(exp(5))*((5832*exp(exp(5)) + 486)/(36*(12 *exp(exp(5)) + 1)^2) + (13*exp(-exp(5))*(1944*exp(exp(5)) + 162))/(216*(12 *exp(exp(5)) + 1)^2) - (13*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(648*(12 *exp(exp(5)) + 1)^2) - (exp(-exp(5))*(90*exp(exp(5)) - 39)*(5832*exp(exp(5 )) + 486))/(972*(12*exp(exp(5)) + 1)^2)))/9 - exp(exp(5))*((exp(exp(5))*(( exp(-exp(5))*(1944*exp(exp(5)) + 162))/(12*(12*exp(exp(5)) + 1)^2) + (13*e xp(-exp(5))*(5832*exp(exp(5)) + 486))/(216*(12*exp(exp(5)) + 1)^2)))/9 - ( 5832*exp(exp(5)) + 486)/(324*(12*exp(exp(5)) + 1)^2) - (exp(exp(5))*((5...