Integrand size = 398, antiderivative size = 30 \[ \int \frac {-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-2 x)-4 x\right )+e^x (-2+4 x)+\left (-2+e^{4 x}+e^{e^x} \left (-2 e^x+e^{5 x}\right )\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-x)\right )+e^x (-2+2 x)\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+e^{e^x} \left (-8 e^{3 x}+4 e^{7 x}+\left (-8 e^{3 x}+4 e^{7 x}\right ) \log (x)+\left (-2 e^{3 x}+e^{7 x}\right ) \log ^2(x)\right )+\log \left (2-e^{4 x}\right ) \left (-2-8 e^x+e^{4 x} \left (1+4 e^x\right )+\left (-4 e^x+2 e^{5 x}\right ) \log (x)+e^{e^x} \left (-8 e^{2 x}+4 e^{6 x}+\left (-4 e^{2 x}+2 e^{6 x}\right ) \log (x)\right )\right )}{-8 e^{2 x}+4 e^{6 x}+\left (-2+e^{4 x}\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+4 e^{6 x}\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+\log \left (2-e^{4 x}\right ) \left (-8 e^x+4 e^{5 x}+\left (-4 e^x+2 e^{5 x}\right ) \log (x)\right )} \, dx=e^{e^x}+x+\frac {x}{\log \left (2-e^{4 x}\right )+e^x (2+\log (x))} \]
[Out]
Timed out. \[ \int \frac {-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-2 x)-4 x\right )+e^x (-2+4 x)+\left (-2+e^{4 x}+e^{e^x} \left (-2 e^x+e^{5 x}\right )\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-x)\right )+e^x (-2+2 x)\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+e^{e^x} \left (-8 e^{3 x}+4 e^{7 x}+\left (-8 e^{3 x}+4 e^{7 x}\right ) \log (x)+\left (-2 e^{3 x}+e^{7 x}\right ) \log ^2(x)\right )+\log \left (2-e^{4 x}\right ) \left (-2-8 e^x+e^{4 x} \left (1+4 e^x\right )+\left (-4 e^x+2 e^{5 x}\right ) \log (x)+e^{e^x} \left (-8 e^{2 x}+4 e^{6 x}+\left (-4 e^{2 x}+2 e^{6 x}\right ) \log (x)\right )\right )}{-8 e^{2 x}+4 e^{6 x}+\left (-2+e^{4 x}\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+4 e^{6 x}\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+\log \left (2-e^{4 x}\right ) \left (-8 e^x+4 e^{5 x}+\left (-4 e^x+2 e^{5 x}\right ) \log (x)\right )} \, dx=\text {\$Aborted} \]
[In]
[Out]
Rubi steps Aborted
Time = 0.39 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-2 x)-4 x\right )+e^x (-2+4 x)+\left (-2+e^{4 x}+e^{e^x} \left (-2 e^x+e^{5 x}\right )\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-x)\right )+e^x (-2+2 x)\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+e^{e^x} \left (-8 e^{3 x}+4 e^{7 x}+\left (-8 e^{3 x}+4 e^{7 x}\right ) \log (x)+\left (-2 e^{3 x}+e^{7 x}\right ) \log ^2(x)\right )+\log \left (2-e^{4 x}\right ) \left (-2-8 e^x+e^{4 x} \left (1+4 e^x\right )+\left (-4 e^x+2 e^{5 x}\right ) \log (x)+e^{e^x} \left (-8 e^{2 x}+4 e^{6 x}+\left (-4 e^{2 x}+2 e^{6 x}\right ) \log (x)\right )\right )}{-8 e^{2 x}+4 e^{6 x}+\left (-2+e^{4 x}\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+4 e^{6 x}\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+\log \left (2-e^{4 x}\right ) \left (-8 e^x+4 e^{5 x}+\left (-4 e^x+2 e^{5 x}\right ) \log (x)\right )} \, dx=e^{e^x}+x+\frac {x}{\log \left (2-e^{4 x}\right )+e^x (2+\log (x))} \]
[In]
[Out]
Time = 0.09 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.97
\[x +{\mathrm e}^{{\mathrm e}^{x}}+\frac {x}{{\mathrm e}^{x} \ln \left (x \right )+2 \,{\mathrm e}^{x}+\ln \left (-{\mathrm e}^{4 x}+2\right )}\]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (26) = 52\).
Time = 0.27 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.13 \[ \int \frac {-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-2 x)-4 x\right )+e^x (-2+4 x)+\left (-2+e^{4 x}+e^{e^x} \left (-2 e^x+e^{5 x}\right )\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-x)\right )+e^x (-2+2 x)\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+e^{e^x} \left (-8 e^{3 x}+4 e^{7 x}+\left (-8 e^{3 x}+4 e^{7 x}\right ) \log (x)+\left (-2 e^{3 x}+e^{7 x}\right ) \log ^2(x)\right )+\log \left (2-e^{4 x}\right ) \left (-2-8 e^x+e^{4 x} \left (1+4 e^x\right )+\left (-4 e^x+2 e^{5 x}\right ) \log (x)+e^{e^x} \left (-8 e^{2 x}+4 e^{6 x}+\left (-4 e^{2 x}+2 e^{6 x}\right ) \log (x)\right )\right )}{-8 e^{2 x}+4 e^{6 x}+\left (-2+e^{4 x}\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+4 e^{6 x}\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+\log \left (2-e^{4 x}\right ) \left (-8 e^x+4 e^{5 x}+\left (-4 e^x+2 e^{5 x}\right ) \log (x)\right )} \, dx=\frac {x e^{x} \log \left (x\right ) + 2 \, x e^{x} + {\left (e^{x} \log \left (x\right ) + 2 \, e^{x}\right )} e^{\left (e^{x}\right )} + {\left (x + e^{\left (e^{x}\right )}\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + x}{e^{x} \log \left (x\right ) + 2 \, e^{x} + \log \left (-e^{\left (4 \, x\right )} + 2\right )} \]
[In]
[Out]
Time = 0.38 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.90 \[ \int \frac {-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-2 x)-4 x\right )+e^x (-2+4 x)+\left (-2+e^{4 x}+e^{e^x} \left (-2 e^x+e^{5 x}\right )\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-x)\right )+e^x (-2+2 x)\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+e^{e^x} \left (-8 e^{3 x}+4 e^{7 x}+\left (-8 e^{3 x}+4 e^{7 x}\right ) \log (x)+\left (-2 e^{3 x}+e^{7 x}\right ) \log ^2(x)\right )+\log \left (2-e^{4 x}\right ) \left (-2-8 e^x+e^{4 x} \left (1+4 e^x\right )+\left (-4 e^x+2 e^{5 x}\right ) \log (x)+e^{e^x} \left (-8 e^{2 x}+4 e^{6 x}+\left (-4 e^{2 x}+2 e^{6 x}\right ) \log (x)\right )\right )}{-8 e^{2 x}+4 e^{6 x}+\left (-2+e^{4 x}\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+4 e^{6 x}\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+\log \left (2-e^{4 x}\right ) \left (-8 e^x+4 e^{5 x}+\left (-4 e^x+2 e^{5 x}\right ) \log (x)\right )} \, dx=x + \frac {x}{e^{x} \log {\left (x \right )} + 2 e^{x} + \log {\left (2 - e^{4 x} \right )}} + e^{e^{x}} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (26) = 52\).
Time = 0.52 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.93 \[ \int \frac {-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-2 x)-4 x\right )+e^x (-2+4 x)+\left (-2+e^{4 x}+e^{e^x} \left (-2 e^x+e^{5 x}\right )\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-x)\right )+e^x (-2+2 x)\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+e^{e^x} \left (-8 e^{3 x}+4 e^{7 x}+\left (-8 e^{3 x}+4 e^{7 x}\right ) \log (x)+\left (-2 e^{3 x}+e^{7 x}\right ) \log ^2(x)\right )+\log \left (2-e^{4 x}\right ) \left (-2-8 e^x+e^{4 x} \left (1+4 e^x\right )+\left (-4 e^x+2 e^{5 x}\right ) \log (x)+e^{e^x} \left (-8 e^{2 x}+4 e^{6 x}+\left (-4 e^{2 x}+2 e^{6 x}\right ) \log (x)\right )\right )}{-8 e^{2 x}+4 e^{6 x}+\left (-2+e^{4 x}\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+4 e^{6 x}\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+\log \left (2-e^{4 x}\right ) \left (-8 e^x+4 e^{5 x}+\left (-4 e^x+2 e^{5 x}\right ) \log (x)\right )} \, dx=\frac {{\left (\log \left (x\right ) + 2\right )} e^{\left (x + e^{x}\right )} + {\left (x \log \left (x\right ) + 2 \, x\right )} e^{x} + {\left (x + e^{\left (e^{x}\right )}\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + x}{{\left (\log \left (x\right ) + 2\right )} e^{x} + \log \left (-e^{\left (4 \, x\right )} + 2\right )} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 736 vs. \(2 (26) = 52\).
Time = 0.57 (sec) , antiderivative size = 736, normalized size of antiderivative = 24.53 \[ \int \frac {-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-2 x)-4 x\right )+e^x (-2+4 x)+\left (-2+e^{4 x}+e^{e^x} \left (-2 e^x+e^{5 x}\right )\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-x)\right )+e^x (-2+2 x)\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+e^{e^x} \left (-8 e^{3 x}+4 e^{7 x}+\left (-8 e^{3 x}+4 e^{7 x}\right ) \log (x)+\left (-2 e^{3 x}+e^{7 x}\right ) \log ^2(x)\right )+\log \left (2-e^{4 x}\right ) \left (-2-8 e^x+e^{4 x} \left (1+4 e^x\right )+\left (-4 e^x+2 e^{5 x}\right ) \log (x)+e^{e^x} \left (-8 e^{2 x}+4 e^{6 x}+\left (-4 e^{2 x}+2 e^{6 x}\right ) \log (x)\right )\right )}{-8 e^{2 x}+4 e^{6 x}+\left (-2+e^{4 x}\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+4 e^{6 x}\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+\log \left (2-e^{4 x}\right ) \left (-8 e^x+4 e^{5 x}+\left (-4 e^x+2 e^{5 x}\right ) \log (x)\right )} \, dx=\text {Too large to display} \]
[In]
[Out]
Timed out. \[ \int \frac {-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-2 x)-4 x\right )+e^x (-2+4 x)+\left (-2+e^{4 x}+e^{e^x} \left (-2 e^x+e^{5 x}\right )\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+e^{4 x} \left (4 e^{2 x}+e^x (1-x)\right )+e^x (-2+2 x)\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+e^{e^x} \left (-8 e^{3 x}+4 e^{7 x}+\left (-8 e^{3 x}+4 e^{7 x}\right ) \log (x)+\left (-2 e^{3 x}+e^{7 x}\right ) \log ^2(x)\right )+\log \left (2-e^{4 x}\right ) \left (-2-8 e^x+e^{4 x} \left (1+4 e^x\right )+\left (-4 e^x+2 e^{5 x}\right ) \log (x)+e^{e^x} \left (-8 e^{2 x}+4 e^{6 x}+\left (-4 e^{2 x}+2 e^{6 x}\right ) \log (x)\right )\right )}{-8 e^{2 x}+4 e^{6 x}+\left (-2+e^{4 x}\right ) \log ^2\left (2-e^{4 x}\right )+\left (-8 e^{2 x}+4 e^{6 x}\right ) \log (x)+\left (-2 e^{2 x}+e^{6 x}\right ) \log ^2(x)+\log \left (2-e^{4 x}\right ) \left (-8 e^x+4 e^{5 x}+\left (-4 e^x+2 e^{5 x}\right ) \log (x)\right )} \, dx=\int \frac {8\,{\mathrm {e}}^{2\,x}+\ln \left (2-{\mathrm {e}}^{4\,x}\right )\,\left (8\,{\mathrm {e}}^x+{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (8\,{\mathrm {e}}^{2\,x}-4\,{\mathrm {e}}^{6\,x}+\ln \left (x\right )\,\left (4\,{\mathrm {e}}^{2\,x}-2\,{\mathrm {e}}^{6\,x}\right )\right )-{\mathrm {e}}^{4\,x}\,\left (4\,{\mathrm {e}}^x+1\right )-\ln \left (x\right )\,\left (2\,{\mathrm {e}}^{5\,x}-4\,{\mathrm {e}}^x\right )+2\right )+{\ln \left (x\right )}^2\,\left (2\,{\mathrm {e}}^{2\,x}-{\mathrm {e}}^{6\,x}\right )-{\ln \left (2-{\mathrm {e}}^{4\,x}\right )}^2\,\left ({\mathrm {e}}^{4\,x}+{\mathrm {e}}^{{\mathrm {e}}^x}\,\left ({\mathrm {e}}^{5\,x}-2\,{\mathrm {e}}^x\right )-2\right )+{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (\left (2\,{\mathrm {e}}^{3\,x}-{\mathrm {e}}^{7\,x}\right )\,{\ln \left (x\right )}^2+\left (8\,{\mathrm {e}}^{3\,x}-4\,{\mathrm {e}}^{7\,x}\right )\,\ln \left (x\right )+8\,{\mathrm {e}}^{3\,x}-4\,{\mathrm {e}}^{7\,x}\right )-\ln \left (x\right )\,\left ({\mathrm {e}}^x\,\left (2\,x-2\right )-8\,{\mathrm {e}}^{2\,x}+{\mathrm {e}}^{4\,x}\,\left (4\,{\mathrm {e}}^{2\,x}-{\mathrm {e}}^x\,\left (x-1\right )\right )\right )-{\mathrm {e}}^x\,\left (4\,x-2\right )+{\mathrm {e}}^{4\,x}\,\left (4\,x-4\,{\mathrm {e}}^{2\,x}+{\mathrm {e}}^x\,\left (2\,x-1\right )\right )}{8\,{\mathrm {e}}^{2\,x}-4\,{\mathrm {e}}^{6\,x}+{\ln \left (x\right )}^2\,\left (2\,{\mathrm {e}}^{2\,x}-{\mathrm {e}}^{6\,x}\right )-\ln \left (2-{\mathrm {e}}^{4\,x}\right )\,\left (4\,{\mathrm {e}}^{5\,x}-8\,{\mathrm {e}}^x+\ln \left (x\right )\,\left (2\,{\mathrm {e}}^{5\,x}-4\,{\mathrm {e}}^x\right )\right )-{\ln \left (2-{\mathrm {e}}^{4\,x}\right )}^2\,\left ({\mathrm {e}}^{4\,x}-2\right )+\ln \left (x\right )\,\left (8\,{\mathrm {e}}^{2\,x}-4\,{\mathrm {e}}^{6\,x}\right )} \,d x \]
[In]
[Out]