Integrand size = 167, antiderivative size = 31 \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=2 e^{-x+\frac {x+\log \left (e^x \left (4+\log \left (x^2\right )\right )\right )}{-\frac {4}{x^2}+x}} \]
Leaf count is larger than twice the leaf count of optimal. \(64\) vs. \(2(31)=62\).
Time = 0.35 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.06 \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=2 e^{\frac {x \left (4+x^2-x^3-x \log \left (4+\log \left (x^2\right )\right )+x \log \left (e^x \left (4+\log \left (x^2\right )\right )\right )\right )}{-4+x^3}} \left (4+\log \left (x^2\right )\right )^{\frac {x^2}{-4+x^3}} \]
Integrate[(E^((4*x + x^3 - x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3) )*(-128 - 16*x - 128*x^2 + 64*x^3 + 4*x^4 + 8*x^5 - 8*x^6 + (-32 - 32*x^2 + 16*x^3 + 2*x^5 - 2*x^6)*Log[x^2] + (-64*x - 8*x^4 + (-16*x - 2*x^4)*Log[ x^2])*Log[4*E^x + E^x*Log[x^2]]))/(64 - 32*x^3 + 4*x^6 + (16 - 8*x^3 + x^6 )*Log[x^2]),x]
2*E^((x*(4 + x^2 - x^3 - x*Log[4 + Log[x^2]] + x*Log[E^x*(4 + Log[x^2])])) /(-4 + x^3))*(4 + Log[x^2])^(x^2/(-4 + x^3))
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.
| \(\displaystyle \int \frac {\left (-8 x^6+8 x^5+4 x^4+64 x^3-128 x^2+\left (-8 x^4+\left (-2 x^4-16 x\right ) \log \left (x^2\right )-64 x\right ) \log \left (e^x \log \left (x^2\right )+4 e^x\right )+\left (-2 x^6+2 x^5+16 x^3-32 x^2-32\right ) \log \left (x^2\right )-16 x-128\right ) \exp \left (\frac {-x^4+x^3+x^2 \log \left (e^x \log \left (x^2\right )+4 e^x\right )+4 x}{x^3-4}\right )}{4 x^6-32 x^3+\left (x^6-8 x^3+16\right ) \log \left (x^2\right )+64} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (-8 x^6+8 x^5+4 x^4+64 x^3-128 x^2+\left (-8 x^4+\left (-2 x^4-16 x\right ) \log \left (x^2\right )-64 x\right ) \log \left (e^x \log \left (x^2\right )+4 e^x\right )+\left (-2 x^6+2 x^5+16 x^3-32 x^2-32\right ) \log \left (x^2\right )-16 x-128\right ) \exp \left (\frac {-x^4+x^3+x^2 \log \left (e^x \log \left (x^2\right )+4 e^x\right )+4 x}{x^3-4}\right )}{\left (4-x^3\right )^2 \left (\log \left (x^2\right )+4\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {4 x^4 \exp \left (\frac {-x^4+x^3+x^2 \log \left (e^x \log \left (x^2\right )+4 e^x\right )+4 x}{x^3-4}\right )}{\left (x^3-4\right )^2 \left (\log \left (x^2\right )+4\right )}+\frac {64 x^3 \exp \left (\frac {-x^4+x^3+x^2 \log \left (e^x \log \left (x^2\right )+4 e^x\right )+4 x}{x^3-4}\right )}{\left (x^3-4\right )^2 \left (\log \left (x^2\right )+4\right )}-\frac {128 x^2 \exp \left (\frac {-x^4+x^3+x^2 \log \left (e^x \log \left (x^2\right )+4 e^x\right )+4 x}{x^3-4}\right )}{\left (x^3-4\right )^2 \left (\log \left (x^2\right )+4\right )}-\frac {2 (x+2) \left (x^2-2 x+4\right ) x \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) \exp \left (\frac {-x^4+x^3+x^2 \log \left (e^x \log \left (x^2\right )+4 e^x\right )+4 x}{x^3-4}\right )}{\left (x^3-4\right )^2}-\frac {16 x \exp \left (\frac {-x^4+x^3+x^2 \log \left (e^x \log \left (x^2\right )+4 e^x\right )+4 x}{x^3-4}\right )}{\left (x^3-4\right )^2 \left (\log \left (x^2\right )+4\right )}-\frac {128 \exp \left (\frac {-x^4+x^3+x^2 \log \left (e^x \log \left (x^2\right )+4 e^x\right )+4 x}{x^3-4}\right )}{\left (x^3-4\right )^2 \left (\log \left (x^2\right )+4\right )}-\frac {8 x^6 \exp \left (\frac {-x^4+x^3+x^2 \log \left (e^x \log \left (x^2\right )+4 e^x\right )+4 x}{x^3-4}\right )}{\left (x^3-4\right )^2 \left (\log \left (x^2\right )+4\right )}+\frac {8 x^5 \exp \left (\frac {-x^4+x^3+x^2 \log \left (e^x \log \left (x^2\right )+4 e^x\right )+4 x}{x^3-4}\right )}{\left (x^3-4\right )^2 \left (\log \left (x^2\right )+4\right )}-\frac {2 \left (x^6-x^5-8 x^3+16 x^2+16\right ) \log \left (x^2\right ) \exp \left (\frac {-x^4+x^3+x^2 \log \left (e^x \log \left (x^2\right )+4 e^x\right )+4 x}{x^3-4}\right )}{\left (x^3-4\right )^2 \left (\log \left (x^2\right )+4\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {x^2}{x^3-4}-1} \left (-4 x^6+4 x^5+2 x^4+32 x^3-64 x^2-4 \left (x^3+8\right ) x \log \left (e^x \left (\log \left (x^2\right )+4\right )\right )-\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) x \log \left (e^x \left (\log \left (x^2\right )+4\right )\right )+16\right )-8 x-64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {e^{-\frac {x^3}{4-x^3}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{-\frac {x^2}{4-x^3}-1} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {e^{-\frac {x^3}{4-x^3}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{-\frac {x^2}{4-x^3}-1} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle -2 \int \frac {e^{-\frac {x^3}{4-x^3}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {16 e^{-\frac {x^3}{4-x^3}} \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{-\frac {x^3}{4-x^3}} x^6 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {e^{-\frac {x^3}{4-x^3}} x^5 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {8 e^{-\frac {x^3}{4-x^3}} x^3 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {16 e^{-\frac {x^3}{4-x^3}} x^2 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{-\frac {x^3}{4-x^3}} x \left (x^3+8\right ) \left (\log \left (x^2\right )+4\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{-\frac {x^3}{4-x^3}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {4 e^{-\frac {x^3}{4-x^3}} x^6 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {4 e^{-\frac {x^3}{4-x^3}} x^5 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {2 e^{-\frac {x^3}{4-x^3}} x^4 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {32 e^{-\frac {x^3}{4-x^3}} x^3 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{-\frac {x^3}{4-x^3}} x^2 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {8 e^{-\frac {x^3}{4-x^3}} x \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {16 e^{\frac {x^3}{x^3-4}} \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x^6 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {e^{\frac {x^3}{x^3-4}} x^5 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {8 e^{\frac {x^3}{x^3-4}} x^3 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {16 e^{\frac {x^3}{x^3-4}} x^2 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x \left (x^3+8\right ) \left (\log \left (x^2\right )+4\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {4 e^{\frac {x^3}{x^3-4}} x^6 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {4 e^{\frac {x^3}{x^3-4}} x^5 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {2 e^{\frac {x^3}{x^3-4}} x^4 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {32 e^{\frac {x^3}{x^3-4}} x^3 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} x^2 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {8 e^{\frac {x^3}{x^3-4}} x \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {16 e^{\frac {x^3}{x^3-4}} \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x^6 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {e^{\frac {x^3}{x^3-4}} x^5 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {8 e^{\frac {x^3}{x^3-4}} x^3 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {16 e^{\frac {x^3}{x^3-4}} x^2 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x \left (x^3+8\right ) \left (\log \left (x^2\right )+4\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {4 e^{\frac {x^3}{x^3-4}} x^6 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {4 e^{\frac {x^3}{x^3-4}} x^5 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {2 e^{\frac {x^3}{x^3-4}} x^4 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {32 e^{\frac {x^3}{x^3-4}} x^3 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} x^2 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {8 e^{\frac {x^3}{x^3-4}} x \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {16 e^{\frac {x^3}{x^3-4}} \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x^6 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {e^{\frac {x^3}{x^3-4}} x^5 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {8 e^{\frac {x^3}{x^3-4}} x^3 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {16 e^{\frac {x^3}{x^3-4}} x^2 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x \left (x^3+8\right ) \left (\log \left (x^2\right )+4\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {4 e^{\frac {x^3}{x^3-4}} x^6 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {4 e^{\frac {x^3}{x^3-4}} x^5 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {2 e^{\frac {x^3}{x^3-4}} x^4 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {32 e^{\frac {x^3}{x^3-4}} x^3 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} x^2 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {8 e^{\frac {x^3}{x^3-4}} x \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {16 e^{\frac {x^3}{x^3-4}} \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x^6 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {e^{\frac {x^3}{x^3-4}} x^5 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {8 e^{\frac {x^3}{x^3-4}} x^3 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {16 e^{\frac {x^3}{x^3-4}} x^2 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x \left (x^3+8\right ) \left (\log \left (x^2\right )+4\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {4 e^{\frac {x^3}{x^3-4}} x^6 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {4 e^{\frac {x^3}{x^3-4}} x^5 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {2 e^{\frac {x^3}{x^3-4}} x^4 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {32 e^{\frac {x^3}{x^3-4}} x^3 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} x^2 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {8 e^{\frac {x^3}{x^3-4}} x \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {16 e^{\frac {x^3}{x^3-4}} \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x^6 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {e^{\frac {x^3}{x^3-4}} x^5 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {8 e^{\frac {x^3}{x^3-4}} x^3 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {16 e^{\frac {x^3}{x^3-4}} x^2 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x \left (x^3+8\right ) \left (\log \left (x^2\right )+4\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {4 e^{\frac {x^3}{x^3-4}} x^6 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {4 e^{\frac {x^3}{x^3-4}} x^5 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {2 e^{\frac {x^3}{x^3-4}} x^4 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {32 e^{\frac {x^3}{x^3-4}} x^3 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} x^2 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {8 e^{\frac {x^3}{x^3-4}} x \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {16 e^{\frac {x^3}{x^3-4}} \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x^6 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {e^{\frac {x^3}{x^3-4}} x^5 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {8 e^{\frac {x^3}{x^3-4}} x^3 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {16 e^{\frac {x^3}{x^3-4}} x^2 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x \left (x^3+8\right ) \left (\log \left (x^2\right )+4\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {4 e^{\frac {x^3}{x^3-4}} x^6 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {4 e^{\frac {x^3}{x^3-4}} x^5 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {2 e^{\frac {x^3}{x^3-4}} x^4 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {32 e^{\frac {x^3}{x^3-4}} x^3 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} x^2 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {8 e^{\frac {x^3}{x^3-4}} x \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {16 e^{\frac {x^3}{x^3-4}} \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x^6 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {e^{\frac {x^3}{x^3-4}} x^5 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {8 e^{\frac {x^3}{x^3-4}} x^3 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {16 e^{\frac {x^3}{x^3-4}} x^2 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x \left (x^3+8\right ) \left (\log \left (x^2\right )+4\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {4 e^{\frac {x^3}{x^3-4}} x^6 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {4 e^{\frac {x^3}{x^3-4}} x^5 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {2 e^{\frac {x^3}{x^3-4}} x^4 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {32 e^{\frac {x^3}{x^3-4}} x^3 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} x^2 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {8 e^{\frac {x^3}{x^3-4}} x \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {16 e^{\frac {x^3}{x^3-4}} \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x^6 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {e^{\frac {x^3}{x^3-4}} x^5 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {8 e^{\frac {x^3}{x^3-4}} x^3 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {16 e^{\frac {x^3}{x^3-4}} x^2 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x \left (x^3+8\right ) \left (\log \left (x^2\right )+4\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {4 e^{\frac {x^3}{x^3-4}} x^6 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {4 e^{\frac {x^3}{x^3-4}} x^5 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {2 e^{\frac {x^3}{x^3-4}} x^4 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {32 e^{\frac {x^3}{x^3-4}} x^3 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} x^2 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {8 e^{\frac {x^3}{x^3-4}} x \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {16 e^{\frac {x^3}{x^3-4}} \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x^6 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {e^{\frac {x^3}{x^3-4}} x^5 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {8 e^{\frac {x^3}{x^3-4}} x^3 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {16 e^{\frac {x^3}{x^3-4}} x^2 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x \left (x^3+8\right ) \left (\log \left (x^2\right )+4\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {4 e^{\frac {x^3}{x^3-4}} x^6 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {4 e^{\frac {x^3}{x^3-4}} x^5 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {2 e^{\frac {x^3}{x^3-4}} x^4 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {32 e^{\frac {x^3}{x^3-4}} x^3 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} x^2 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {8 e^{\frac {x^3}{x^3-4}} x \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {16 e^{\frac {x^3}{x^3-4}} \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x^6 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {e^{\frac {x^3}{x^3-4}} x^5 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {8 e^{\frac {x^3}{x^3-4}} x^3 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {16 e^{\frac {x^3}{x^3-4}} x^2 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x \left (x^3+8\right ) \left (\log \left (x^2\right )+4\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {4 e^{\frac {x^3}{x^3-4}} x^6 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {4 e^{\frac {x^3}{x^3-4}} x^5 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {2 e^{\frac {x^3}{x^3-4}} x^4 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {32 e^{\frac {x^3}{x^3-4}} x^3 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} x^2 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {8 e^{\frac {x^3}{x^3-4}} x \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {16 e^{\frac {x^3}{x^3-4}} \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x^6 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {e^{\frac {x^3}{x^3-4}} x^5 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {8 e^{\frac {x^3}{x^3-4}} x^3 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {16 e^{\frac {x^3}{x^3-4}} x^2 \log \left (x^2\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {e^{\frac {x^3}{x^3-4}} x \left (x^3+8\right ) \left (\log \left (x^2\right )+4\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {4 e^{\frac {x^3}{x^3-4}} x^6 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {4 e^{\frac {x^3}{x^3-4}} x^5 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {2 e^{\frac {x^3}{x^3-4}} x^4 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}-\frac {32 e^{\frac {x^3}{x^3-4}} x^3 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {64 e^{\frac {x^3}{x^3-4}} x^2 \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}+\frac {8 e^{\frac {x^3}{x^3-4}} x \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}}}{\left (x^3-4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{\frac {x^3}{x^3-4}} \left (e^x \left (\log \left (x^2\right )+4\right )\right )^{\frac {-x^3+x^2+4}{x^3-4}} \left (4 x^6-4 x^5-2 x^4-32 x^3+64 x^2+4 \left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+8 x+\log \left (x^2\right ) \left (x^6-x^5-8 x^3+16 x^2+\left (x^3+8\right ) \log \left (e^x \left (\log \left (x^2\right )+4\right )\right ) x+16\right )+64\right )}{\left (4-x^3\right )^2}dx\) |
Int[(E^((4*x + x^3 - x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))*(-12 8 - 16*x - 128*x^2 + 64*x^3 + 4*x^4 + 8*x^5 - 8*x^6 + (-32 - 32*x^2 + 16*x ^3 + 2*x^5 - 2*x^6)*Log[x^2] + (-64*x - 8*x^4 + (-16*x - 2*x^4)*Log[x^2])* Log[4*E^x + E^x*Log[x^2]]))/(64 - 32*x^3 + 4*x^6 + (16 - 8*x^3 + x^6)*Log[ x^2]),x]
3.26.77.3.1 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]]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.20 (sec) , antiderivative size = 569, normalized size of antiderivative = 18.35
\[2 \left (\frac {1}{2}\right )^{\frac {x^{2}}{x^{3}-4}} \left ({\mathrm e}^{x}\right )^{\frac {x^{2}}{x^{3}-4}} \left (8 i+4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )^{\frac {x^{2}}{x^{3}-4}} {\mathrm e}^{-\frac {x \left (i x \pi \,\operatorname {csgn}\left (-i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x \right )^{2}+2 i \pi \operatorname {csgn}\left (i x^{2}\right )^{2} \operatorname {csgn}\left (i x \right )-i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}+4 \ln \left (x \right )+8\right ) \operatorname {csgn}\left (i {\mathrm e}^{x} \left (8 i+4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )\right )^{2}-i x \pi \,\operatorname {csgn}\left (-i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x \right )^{2}+2 i \pi \operatorname {csgn}\left (i x^{2}\right )^{2} \operatorname {csgn}\left (i x \right )-i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}+4 \ln \left (x \right )+8\right ) \operatorname {csgn}\left (i {\mathrm e}^{x} \left (8 i+4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )\right ) \operatorname {csgn}\left (i {\mathrm e}^{x}\right )-i x \pi \operatorname {csgn}\left (i {\mathrm e}^{x} \left (8 i+4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )\right )^{3}-i x \pi \operatorname {csgn}\left (i {\mathrm e}^{x} \left (8 i+4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )\right )^{2} \operatorname {csgn}\left (i {\mathrm e}^{x}\right )+2 i x \pi \operatorname {csgn}\left (i {\mathrm e}^{x} \left (8 i+4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )\right )^{2}-2 i \pi x +2 x^{3}-2 x^{2}-8\right )}{2 \left (x^{3}-4\right )}}\]
int((((-2*x^4-16*x)*ln(x^2)-8*x^4-64*x)*ln(exp(x)*ln(x^2)+4*exp(x))+(-2*x^ 6+2*x^5+16*x^3-32*x^2-32)*ln(x^2)-8*x^6+8*x^5+4*x^4+64*x^3-128*x^2-16*x-12 8)*exp((x^2*ln(exp(x)*ln(x^2)+4*exp(x))-x^4+x^3+4*x)/(x^3-4))/((x^6-8*x^3+ 16)*ln(x^2)+4*x^6-32*x^3+64),x)
2*(1/2)^(1/(x^3-4)*x^2)*exp(x)^(1/(x^3-4)*x^2)*(8*I+4*I*ln(x)+Pi*csgn(I*x) ^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2)^3)^(1/(x^3-4)*x ^2)*exp(-1/2*x*(I*x*Pi*csgn(-I*Pi*csgn(I*x^2)*csgn(I*x)^2+2*I*Pi*csgn(I*x^ 2)^2*csgn(I*x)-I*Pi*csgn(I*x^2)^3+4*ln(x)+8)*csgn(I*exp(x)*(8*I+4*I*ln(x)+ Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2)^3)) ^2-I*x*Pi*csgn(-I*Pi*csgn(I*x^2)*csgn(I*x)^2+2*I*Pi*csgn(I*x^2)^2*csgn(I*x )-I*Pi*csgn(I*x^2)^3+4*ln(x)+8)*csgn(I*exp(x)*(8*I+4*I*ln(x)+Pi*csgn(I*x)^ 2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2)^3))*csgn(I*exp(x ))-I*x*Pi*csgn(I*exp(x)*(8*I+4*I*ln(x)+Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csg n(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2)^3))^3-I*x*Pi*csgn(I*exp(x)*(8*I+4*I*ln (x)+Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2) ^3))^2*csgn(I*exp(x))+2*I*x*Pi*csgn(I*exp(x)*(8*I+4*I*ln(x)+Pi*csgn(I*x)^2 *csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2)^3))^2-2*I*Pi*x+2* x^3-2*x^2-8)/(x^3-4))
Time = 0.27 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.35 \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=2 \, e^{\left (-\frac {x^{4} - x^{3} - x^{2} \log \left (e^{x} \log \left (x^{2}\right ) + 4 \, e^{x}\right ) - 4 \, x}{x^{3} - 4}\right )} \]
integrate((((-2*x^4-16*x)*log(x^2)-8*x^4-64*x)*log(exp(x)*log(x^2)+4*exp(x ))+(-2*x^6+2*x^5+16*x^3-32*x^2-32)*log(x^2)-8*x^6+8*x^5+4*x^4+64*x^3-128*x ^2-16*x-128)*exp((x^2*log(exp(x)*log(x^2)+4*exp(x))-x^4+x^3+4*x)/(x^3-4))/ ((x^6-8*x^3+16)*log(x^2)+4*x^6-32*x^3+64),x, algorithm=\
Timed out. \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=\text {Timed out} \]
integrate((((-2*x**4-16*x)*ln(x**2)-8*x**4-64*x)*ln(exp(x)*ln(x**2)+4*exp( x))+(-2*x**6+2*x**5+16*x**3-32*x**2-32)*ln(x**2)-8*x**6+8*x**5+4*x**4+64*x **3-128*x**2-16*x-128)*exp((x**2*ln(exp(x)*ln(x**2)+4*exp(x))-x**4+x**3+4* x)/(x**3-4))/((x**6-8*x**3+16)*ln(x**2)+4*x**6-32*x**3+64),x)
Time = 0.46 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.48 \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=2 \, e^{\left (\frac {x^{2} \log \left (2\right )}{x^{3} - 4} + \frac {x^{2} \log \left (\log \left (x\right ) + 2\right )}{x^{3} - 4} - x + \frac {8}{x^{3} - 4} + 2\right )} \]
integrate((((-2*x^4-16*x)*log(x^2)-8*x^4-64*x)*log(exp(x)*log(x^2)+4*exp(x ))+(-2*x^6+2*x^5+16*x^3-32*x^2-32)*log(x^2)-8*x^6+8*x^5+4*x^4+64*x^3-128*x ^2-16*x-128)*exp((x^2*log(exp(x)*log(x^2)+4*exp(x))-x^4+x^3+4*x)/(x^3-4))/ ((x^6-8*x^3+16)*log(x^2)+4*x^6-32*x^3+64),x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (29) = 58\).
Time = 0.66 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.97 \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=2 \, e^{\left (-\frac {x^{4}}{x^{3} - 4} + \frac {x^{3}}{x^{3} - 4} + \frac {x^{2} \log \left (e^{x} \log \left (x^{2}\right ) + 4 \, e^{x}\right )}{x^{3} - 4} + \frac {4 \, x}{x^{3} - 4}\right )} \]
integrate((((-2*x^4-16*x)*log(x^2)-8*x^4-64*x)*log(exp(x)*log(x^2)+4*exp(x ))+(-2*x^6+2*x^5+16*x^3-32*x^2-32)*log(x^2)-8*x^6+8*x^5+4*x^4+64*x^3-128*x ^2-16*x-128)*exp((x^2*log(exp(x)*log(x^2)+4*exp(x))-x^4+x^3+4*x)/(x^3-4))/ ((x^6-8*x^3+16)*log(x^2)+4*x^6-32*x^3+64),x, algorithm=\
2*e^(-x^4/(x^3 - 4) + x^3/(x^3 - 4) + x^2*log(e^x*log(x^2) + 4*e^x)/(x^3 - 4) + 4*x/(x^3 - 4))
Time = 14.02 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.00 \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=2\,{\mathrm {e}}^{\frac {x^3}{x^3-4}}\,{\mathrm {e}}^{-\frac {x^4}{x^3-4}}\,{\mathrm {e}}^{\frac {4\,x}{x^3-4}}\,{\left (4\,{\mathrm {e}}^x+\ln \left (x^2\right )\,{\mathrm {e}}^x\right )}^{\frac {x^2}{x^3-4}} \]
int(-(exp((4*x + x^2*log(4*exp(x) + log(x^2)*exp(x)) + x^3 - x^4)/(x^3 - 4 ))*(16*x + log(4*exp(x) + log(x^2)*exp(x))*(64*x + log(x^2)*(16*x + 2*x^4) + 8*x^4) + 128*x^2 - 64*x^3 - 4*x^4 - 8*x^5 + 8*x^6 + log(x^2)*(32*x^2 - 16*x^3 - 2*x^5 + 2*x^6 + 32) + 128))/(log(x^2)*(x^6 - 8*x^3 + 16) - 32*x^3 + 4*x^6 + 64),x)