Integrand size = 171, antiderivative size = 31 \[ \int \frac {e^{5+e^{2 x}} \left (6+e^{16+x} \left (-9+9 x-18 e^{2 x} x\right )+e^{16+x} \left (3-3 x+6 e^{2 x} x\right ) \log \left (x^2\right )\right )+e^{5+e^{2 x}} \left (9+18 e^{2 x} x+\left (-3-6 e^{2 x} x\right ) \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )}{-3 e^{32+2 x}+e^{32+2 x} \log \left (x^2\right )+\left (6 e^{16+x}-2 e^{16+x} \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )+\left (-3+\log \left (x^2\right )\right ) \log ^2\left (3-\log \left (x^2\right )\right )} \, dx=\frac {3 e^{5+e^{2 x}} x}{e^{16+x}-\log \left (3-\log \left (x^2\right )\right )} \]
[Out]
\[ \int \frac {e^{5+e^{2 x}} \left (6+e^{16+x} \left (-9+9 x-18 e^{2 x} x\right )+e^{16+x} \left (3-3 x+6 e^{2 x} x\right ) \log \left (x^2\right )\right )+e^{5+e^{2 x}} \left (9+18 e^{2 x} x+\left (-3-6 e^{2 x} x\right ) \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )}{-3 e^{32+2 x}+e^{32+2 x} \log \left (x^2\right )+\left (6 e^{16+x}-2 e^{16+x} \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )+\left (-3+\log \left (x^2\right )\right ) \log ^2\left (3-\log \left (x^2\right )\right )} \, dx=\int \frac {e^{5+e^{2 x}} \left (6+e^{16+x} \left (-9+9 x-18 e^{2 x} x\right )+e^{16+x} \left (3-3 x+6 e^{2 x} x\right ) \log \left (x^2\right )\right )+e^{5+e^{2 x}} \left (9+18 e^{2 x} x+\left (-3-6 e^{2 x} x\right ) \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )}{-3 e^{32+2 x}+e^{32+2 x} \log \left (x^2\right )+\left (6 e^{16+x}-2 e^{16+x} \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )+\left (-3+\log \left (x^2\right )\right ) \log ^2\left (3-\log \left (x^2\right )\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {-e^{5+e^{2 x}} \left (6+e^{16+x} \left (-9+9 x-18 e^{2 x} x\right )+e^{16+x} \left (3-3 x+6 e^{2 x} x\right ) \log \left (x^2\right )\right )-e^{5+e^{2 x}} \left (9+18 e^{2 x} x+\left (-3-6 e^{2 x} x\right ) \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )}{\left (3-\log \left (x^2\right )\right ) \left (e^{16+x}-\log \left (3-\log \left (x^2\right )\right )\right )^2} \, dx \\ & = \int \left (6 e^{-11+e^{2 x}+x} x+6 e^{-27+e^{2 x}} x \log \left (3-\log \left (x^2\right )\right )-\frac {3 e^{5+e^{2 x}} \left (-2-3 x \log \left (3-\log \left (x^2\right )\right )+x \log \left (x^2\right ) \log \left (3-\log \left (x^2\right )\right )\right )}{\left (-3+\log \left (x^2\right )\right ) \left (e^{16+x}-\log \left (3-\log \left (x^2\right )\right )\right )^2}-\frac {3 e^{e^{2 x}} \left (-e^{32}+e^{32} x-2 x \log ^2\left (3-\log \left (x^2\right )\right )\right )}{e^{43+x}-e^{27} \log \left (3-\log \left (x^2\right )\right )}\right ) \, dx \\ & = -\left (3 \int \frac {e^{5+e^{2 x}} \left (-2-3 x \log \left (3-\log \left (x^2\right )\right )+x \log \left (x^2\right ) \log \left (3-\log \left (x^2\right )\right )\right )}{\left (-3+\log \left (x^2\right )\right ) \left (e^{16+x}-\log \left (3-\log \left (x^2\right )\right )\right )^2} \, dx\right )-3 \int \frac {e^{e^{2 x}} \left (-e^{32}+e^{32} x-2 x \log ^2\left (3-\log \left (x^2\right )\right )\right )}{e^{43+x}-e^{27} \log \left (3-\log \left (x^2\right )\right )} \, dx+6 \int e^{-11+e^{2 x}+x} x \, dx+6 \int e^{-27+e^{2 x}} x \log \left (3-\log \left (x^2\right )\right ) \, dx \\ & = -\left (3 \int \left (-\frac {2 e^{5+e^{2 x}}}{\left (-3+\log \left (x^2\right )\right ) \left (e^{16+x}-\log \left (3-\log \left (x^2\right )\right )\right )^2}-\frac {3 e^{5+e^{2 x}} x \log \left (3-\log \left (x^2\right )\right )}{\left (-3+\log \left (x^2\right )\right ) \left (e^{16+x}-\log \left (3-\log \left (x^2\right )\right )\right )^2}+\frac {e^{5+e^{2 x}} x \log \left (x^2\right ) \log \left (3-\log \left (x^2\right )\right )}{\left (-3+\log \left (x^2\right )\right ) \left (e^{16+x}-\log \left (3-\log \left (x^2\right )\right )\right )^2}\right ) \, dx\right )-3 \int \left (-\frac {e^{5+e^{2 x}}}{e^{16+x}-\log \left (3-\log \left (x^2\right )\right )}+\frac {e^{5+e^{2 x}} x}{e^{16+x}-\log \left (3-\log \left (x^2\right )\right )}+\frac {2 e^{e^{2 x}} x \log ^2\left (3-\log \left (x^2\right )\right )}{-e^{43+x}+e^{27} \log \left (3-\log \left (x^2\right )\right )}\right ) \, dx+6 \int e^{-11+e^{2 x}+x} x \, dx+6 \int e^{-27+e^{2 x}} x \log \left (3-\log \left (x^2\right )\right ) \, dx \\ & = 3 \int \frac {e^{5+e^{2 x}}}{e^{16+x}-\log \left (3-\log \left (x^2\right )\right )} \, dx-3 \int \frac {e^{5+e^{2 x}} x}{e^{16+x}-\log \left (3-\log \left (x^2\right )\right )} \, dx-3 \int \frac {e^{5+e^{2 x}} x \log \left (x^2\right ) \log \left (3-\log \left (x^2\right )\right )}{\left (-3+\log \left (x^2\right )\right ) \left (e^{16+x}-\log \left (3-\log \left (x^2\right )\right )\right )^2} \, dx+6 \int e^{-11+e^{2 x}+x} x \, dx+6 \int \frac {e^{5+e^{2 x}}}{\left (-3+\log \left (x^2\right )\right ) \left (e^{16+x}-\log \left (3-\log \left (x^2\right )\right )\right )^2} \, dx+6 \int e^{-27+e^{2 x}} x \log \left (3-\log \left (x^2\right )\right ) \, dx-6 \int \frac {e^{e^{2 x}} x \log ^2\left (3-\log \left (x^2\right )\right )}{-e^{43+x}+e^{27} \log \left (3-\log \left (x^2\right )\right )} \, dx+9 \int \frac {e^{5+e^{2 x}} x \log \left (3-\log \left (x^2\right )\right )}{\left (-3+\log \left (x^2\right )\right ) \left (e^{16+x}-\log \left (3-\log \left (x^2\right )\right )\right )^2} \, dx \\ \end{align*}
Time = 0.18 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00 \[ \int \frac {e^{5+e^{2 x}} \left (6+e^{16+x} \left (-9+9 x-18 e^{2 x} x\right )+e^{16+x} \left (3-3 x+6 e^{2 x} x\right ) \log \left (x^2\right )\right )+e^{5+e^{2 x}} \left (9+18 e^{2 x} x+\left (-3-6 e^{2 x} x\right ) \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )}{-3 e^{32+2 x}+e^{32+2 x} \log \left (x^2\right )+\left (6 e^{16+x}-2 e^{16+x} \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )+\left (-3+\log \left (x^2\right )\right ) \log ^2\left (3-\log \left (x^2\right )\right )} \, dx=-\frac {3 e^{5+e^{2 x}} x}{-e^{16+x}+\log \left (3-\log \left (x^2\right )\right )} \]
[In]
[Out]
Time = 229.61 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94
method | result | size |
parallelrisch | \(\frac {3 \,{\mathrm e}^{5+{\mathrm e}^{2 x}} x}{{\mathrm e}^{x +16}-\ln \left (3-\ln \left (x^{2}\right )\right )}\) | \(29\) |
risch | \(\frac {3 \,{\mathrm e}^{5+{\mathrm e}^{2 x}} x}{{\mathrm e}^{x +16}-\ln \left (3-2 \ln \left (x \right )+\frac {i \pi \,\operatorname {csgn}\left (i x^{2}\right ) {\left (-\operatorname {csgn}\left (i x^{2}\right )+\operatorname {csgn}\left (i x \right )\right )}^{2}}{2}\right )}\) | \(55\) |
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.16 \[ \int \frac {e^{5+e^{2 x}} \left (6+e^{16+x} \left (-9+9 x-18 e^{2 x} x\right )+e^{16+x} \left (3-3 x+6 e^{2 x} x\right ) \log \left (x^2\right )\right )+e^{5+e^{2 x}} \left (9+18 e^{2 x} x+\left (-3-6 e^{2 x} x\right ) \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )}{-3 e^{32+2 x}+e^{32+2 x} \log \left (x^2\right )+\left (6 e^{16+x}-2 e^{16+x} \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )+\left (-3+\log \left (x^2\right )\right ) \log ^2\left (3-\log \left (x^2\right )\right )} \, dx=\frac {3 \, x e^{\left ({\left (5 \, e^{32} + e^{\left (2 \, x + 32\right )}\right )} e^{\left (-32\right )}\right )}}{e^{\left (x + 16\right )} - \log \left (-\log \left (x^{2}\right ) + 3\right )} \]
[In]
[Out]
Timed out. \[ \int \frac {e^{5+e^{2 x}} \left (6+e^{16+x} \left (-9+9 x-18 e^{2 x} x\right )+e^{16+x} \left (3-3 x+6 e^{2 x} x\right ) \log \left (x^2\right )\right )+e^{5+e^{2 x}} \left (9+18 e^{2 x} x+\left (-3-6 e^{2 x} x\right ) \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )}{-3 e^{32+2 x}+e^{32+2 x} \log \left (x^2\right )+\left (6 e^{16+x}-2 e^{16+x} \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )+\left (-3+\log \left (x^2\right )\right ) \log ^2\left (3-\log \left (x^2\right )\right )} \, dx=\text {Timed out} \]
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.84 \[ \int \frac {e^{5+e^{2 x}} \left (6+e^{16+x} \left (-9+9 x-18 e^{2 x} x\right )+e^{16+x} \left (3-3 x+6 e^{2 x} x\right ) \log \left (x^2\right )\right )+e^{5+e^{2 x}} \left (9+18 e^{2 x} x+\left (-3-6 e^{2 x} x\right ) \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )}{-3 e^{32+2 x}+e^{32+2 x} \log \left (x^2\right )+\left (6 e^{16+x}-2 e^{16+x} \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )+\left (-3+\log \left (x^2\right )\right ) \log ^2\left (3-\log \left (x^2\right )\right )} \, dx=\frac {3 \, x e^{\left (e^{\left (2 \, x\right )} + 5\right )}}{e^{\left (x + 16\right )} - \log \left (-2 \, \log \left (x\right ) + 3\right )} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 127 vs. \(2 (28) = 56\).
Time = 0.42 (sec) , antiderivative size = 127, normalized size of antiderivative = 4.10 \[ \int \frac {e^{5+e^{2 x}} \left (6+e^{16+x} \left (-9+9 x-18 e^{2 x} x\right )+e^{16+x} \left (3-3 x+6 e^{2 x} x\right ) \log \left (x^2\right )\right )+e^{5+e^{2 x}} \left (9+18 e^{2 x} x+\left (-3-6 e^{2 x} x\right ) \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )}{-3 e^{32+2 x}+e^{32+2 x} \log \left (x^2\right )+\left (6 e^{16+x}-2 e^{16+x} \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )+\left (-3+\log \left (x^2\right )\right ) \log ^2\left (3-\log \left (x^2\right )\right )} \, dx=-\frac {3 \, {\left (2 \, x^{2} e^{\left (x + e^{\left (2 \, x\right )} + 21\right )} \log \left (x \mathrm {sgn}\left (x\right )\right ) - 3 \, x^{2} e^{\left (x + e^{\left (2 \, x\right )} + 21\right )} - 2 \, x e^{\left (e^{\left (2 \, x\right )} + 5\right )}\right )}}{2 \, x e^{\left (x + 16\right )} \log \left (x \mathrm {sgn}\left (x\right )\right ) \log \left (-2 \, \log \left (x \mathrm {sgn}\left (x\right )\right ) + 3\right ) - 2 \, x e^{\left (2 \, x + 32\right )} \log \left (x \mathrm {sgn}\left (x\right )\right ) - 3 \, x e^{\left (x + 16\right )} \log \left (-2 \, \log \left (x \mathrm {sgn}\left (x\right )\right ) + 3\right ) + 3 \, x e^{\left (2 \, x + 32\right )} + 2 \, e^{\left (x + 16\right )} - 2 \, \log \left (-2 \, \log \left (x \mathrm {sgn}\left (x\right )\right ) + 3\right )} \]
[In]
[Out]
Timed out. \[ \int \frac {e^{5+e^{2 x}} \left (6+e^{16+x} \left (-9+9 x-18 e^{2 x} x\right )+e^{16+x} \left (3-3 x+6 e^{2 x} x\right ) \log \left (x^2\right )\right )+e^{5+e^{2 x}} \left (9+18 e^{2 x} x+\left (-3-6 e^{2 x} x\right ) \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )}{-3 e^{32+2 x}+e^{32+2 x} \log \left (x^2\right )+\left (6 e^{16+x}-2 e^{16+x} \log \left (x^2\right )\right ) \log \left (3-\log \left (x^2\right )\right )+\left (-3+\log \left (x^2\right )\right ) \log ^2\left (3-\log \left (x^2\right )\right )} \, dx=\int \frac {{\mathrm {e}}^{{\mathrm {e}}^{2\,x}+5}\,\left (\ln \left (x^2\right )\,{\mathrm {e}}^{x+16}\,\left (6\,x\,{\mathrm {e}}^{2\,x}-3\,x+3\right )-{\mathrm {e}}^{x+16}\,\left (18\,x\,{\mathrm {e}}^{2\,x}-9\,x+9\right )+6\right )+{\mathrm {e}}^{{\mathrm {e}}^{2\,x}+5}\,\ln \left (3-\ln \left (x^2\right )\right )\,\left (18\,x\,{\mathrm {e}}^{2\,x}-\ln \left (x^2\right )\,\left (6\,x\,{\mathrm {e}}^{2\,x}+3\right )+9\right )}{\left (\ln \left (x^2\right )-3\right )\,{\ln \left (3-\ln \left (x^2\right )\right )}^2+\left (6\,{\mathrm {e}}^{x+16}-2\,\ln \left (x^2\right )\,{\mathrm {e}}^{x+16}\right )\,\ln \left (3-\ln \left (x^2\right )\right )-3\,{\mathrm {e}}^{2\,x+32}+\ln \left (x^2\right )\,{\mathrm {e}}^{2\,x+32}} \,d x \]
[In]
[Out]