Integrand size = 866, antiderivative size = 31 \[ \int e^{-5+x^4+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (-4 e^{3 x} x-12 e^{2 x} x^2-12 e^x x^3-4 x^4\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (-4 e^x x^3-4 x^4\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (e^{4 x}+4 e^{3 x} x+6 e^{2 x} x^2+4 e^x x^3+x^4\right )+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (6 e^{2 x} x^2+12 e^x x^3+6 x^4\right )} x^{-2-x} \left (4 x^{5+x}+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x^x \left (24 x^5+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (36 x^4+12 x^5\right )\right )+e^{3 x^{-x}} \left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5+x^x \left (-12 e^{2 x} x^2-24 e^x x^3-12 x^4\right )+\left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5\right ) \log (x)\right )\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x^x \left (4 e^{4 x} x^2+4 x^5+e^{3 x} \left (4 x^2+12 x^3\right )+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (12 x^4+4 x^5\right )\right )+e^{3 x^{-x}} \left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5+x^x \left (-4 e^{4 x}-16 e^{3 x} x-24 e^{2 x} x^2-16 e^x x^3-4 x^4\right )+\left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5\right ) \log (x)\right )\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^x \left (-12 x^4-4 x^5\right )\right )+e^{3 x^{-x}} \left (12 e^x x^4+12 x^5+x^x \left (4 e^x x^3+4 x^4\right )+\left (12 e^x x^4+12 x^5\right ) \log (x)\right )\right )+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^{3 x} \left (-4 x^2-12 x^3\right )+e^{2 x} \left (-24 x^3-24 x^4\right )+e^x \left (-36 x^4-12 x^5\right )\right )+e^{3 x^{-x}} \left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5+x^x \left (12 e^{3 x} x+36 e^{2 x} x^2+36 e^x x^3+12 x^4\right )+\left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5\right ) \log (x)\right )\right )\right ) \, dx=e^{-5+\left (-x+e^{\frac {e^{3 x^{-x}}}{x}} \left (e^x+x\right )\right )^4} \]
Leaf count is larger than twice the leaf count of optimal. \(110\) vs. \(2(31)=62\).
Time = 1.07 (sec) , antiderivative size = 110, normalized size of antiderivative = 3.55 \[ \int e^{-5+x^4+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (-4 e^{3 x} x-12 e^{2 x} x^2-12 e^x x^3-4 x^4\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (-4 e^x x^3-4 x^4\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (e^{4 x}+4 e^{3 x} x+6 e^{2 x} x^2+4 e^x x^3+x^4\right )+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (6 e^{2 x} x^2+12 e^x x^3+6 x^4\right )} x^{-2-x} \left (4 x^{5+x}+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x^x \left (24 x^5+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (36 x^4+12 x^5\right )\right )+e^{3 x^{-x}} \left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5+x^x \left (-12 e^{2 x} x^2-24 e^x x^3-12 x^4\right )+\left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5\right ) \log (x)\right )\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x^x \left (4 e^{4 x} x^2+4 x^5+e^{3 x} \left (4 x^2+12 x^3\right )+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (12 x^4+4 x^5\right )\right )+e^{3 x^{-x}} \left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5+x^x \left (-4 e^{4 x}-16 e^{3 x} x-24 e^{2 x} x^2-16 e^x x^3-4 x^4\right )+\left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5\right ) \log (x)\right )\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^x \left (-12 x^4-4 x^5\right )\right )+e^{3 x^{-x}} \left (12 e^x x^4+12 x^5+x^x \left (4 e^x x^3+4 x^4\right )+\left (12 e^x x^4+12 x^5\right ) \log (x)\right )\right )+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^{3 x} \left (-4 x^2-12 x^3\right )+e^{2 x} \left (-24 x^3-24 x^4\right )+e^x \left (-36 x^4-12 x^5\right )\right )+e^{3 x^{-x}} \left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5+x^x \left (12 e^{3 x} x+36 e^{2 x} x^2+36 e^x x^3+12 x^4\right )+\left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5\right ) \log (x)\right )\right )\right ) \, dx=e^{-5+x^4-4 e^{\frac {e^{3 x^{-x}}}{x}} x^3 \left (e^x+x\right )+6 e^{\frac {2 e^{3 x^{-x}}}{x}} x^2 \left (e^x+x\right )^2-4 e^{\frac {3 e^{3 x^{-x}}}{x}} x \left (e^x+x\right )^3+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (e^x+x\right )^4} \]
Integrate[E^(-5 + x^4 + E^((3*E^(3/x^x))/x)*(-4*E^(3*x)*x - 12*E^(2*x)*x^2 - 12*E^x*x^3 - 4*x^4) + E^(E^(3/x^x)/x)*(-4*E^x*x^3 - 4*x^4) + E^((4*E^(3 /x^x))/x)*(E^(4*x) + 4*E^(3*x)*x + 6*E^(2*x)*x^2 + 4*E^x*x^3 + x^4) + E^(( 2*E^(3/x^x))/x)*(6*E^(2*x)*x^2 + 12*E^x*x^3 + 6*x^4))*x^(-2 - x)*(4*x^(5 + x) + E^((2*E^(3/x^x))/x)*(x^x*(24*x^5 + E^(2*x)*(12*x^3 + 12*x^4) + E^x*( 36*x^4 + 12*x^5)) + E^(3/x^x)*(-36*E^(2*x)*x^3 - 72*E^x*x^4 - 36*x^5 + x^x *(-12*E^(2*x)*x^2 - 24*E^x*x^3 - 12*x^4) + (-36*E^(2*x)*x^3 - 72*E^x*x^4 - 36*x^5)*Log[x])) + E^((4*E^(3/x^x))/x)*(x^x*(4*E^(4*x)*x^2 + 4*x^5 + E^(3 *x)*(4*x^2 + 12*x^3) + E^(2*x)*(12*x^3 + 12*x^4) + E^x*(12*x^4 + 4*x^5)) + E^(3/x^x)*(-12*E^(4*x)*x - 48*E^(3*x)*x^2 - 72*E^(2*x)*x^3 - 48*E^x*x^4 - 12*x^5 + x^x*(-4*E^(4*x) - 16*E^(3*x)*x - 24*E^(2*x)*x^2 - 16*E^x*x^3 - 4 *x^4) + (-12*E^(4*x)*x - 48*E^(3*x)*x^2 - 72*E^(2*x)*x^3 - 48*E^x*x^4 - 12 *x^5)*Log[x])) + E^(E^(3/x^x)/x)*(x^x*(-16*x^5 + E^x*(-12*x^4 - 4*x^5)) + E^(3/x^x)*(12*E^x*x^4 + 12*x^5 + x^x*(4*E^x*x^3 + 4*x^4) + (12*E^x*x^4 + 1 2*x^5)*Log[x])) + E^((3*E^(3/x^x))/x)*(x^x*(-16*x^5 + E^(3*x)*(-4*x^2 - 12 *x^3) + E^(2*x)*(-24*x^3 - 24*x^4) + E^x*(-36*x^4 - 12*x^5)) + E^(3/x^x)*( 36*E^(3*x)*x^2 + 108*E^(2*x)*x^3 + 108*E^x*x^4 + 36*x^5 + x^x*(12*E^(3*x)* x + 36*E^(2*x)*x^2 + 36*E^x*x^3 + 12*x^4) + (36*E^(3*x)*x^2 + 108*E^(2*x)* x^3 + 108*E^x*x^4 + 36*x^5)*Log[x]))),x]
E^(-5 + x^4 - 4*E^(E^(3/x^x)/x)*x^3*(E^x + x) + 6*E^((2*E^(3/x^x))/x)*x^2* (E^x + x)^2 - 4*E^((3*E^(3/x^x))/x)*x*(E^x + x)^3 + E^((4*E^(3/x^x))/x)*(E ^x + x)^4)
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.
| \(\displaystyle \int e^{x^4+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (-4 x^4-12 e^x x^3-12 e^{2 x} x^2-4 e^{3 x} x\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (-4 x^4-4 e^x x^3\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x^4+4 e^x x^3+6 e^{2 x} x^2+4 e^{3 x} x+e^{4 x}\right )+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (6 x^4+12 e^x x^3+6 e^{2 x} x^2\right )-5} x^{-x-2} \left (4 x^{x+5}+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (\left (24 x^5+e^{2 x} \left (12 x^4+12 x^3\right )+e^x \left (12 x^5+36 x^4\right )\right ) x^x+e^{3 x^{-x}} \left (\left (-12 x^4-24 e^x x^3-12 e^{2 x} x^2\right ) x^x-36 x^5-72 e^x x^4-36 e^{2 x} x^3+\left (-36 x^5-72 e^x x^4-36 e^{2 x} x^3\right ) \log (x)\right )\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (\left (4 x^5+4 e^{4 x} x^2+e^{3 x} \left (12 x^3+4 x^2\right )+e^{2 x} \left (12 x^4+12 x^3\right )+e^x \left (4 x^5+12 x^4\right )\right ) x^x+e^{3 x^{-x}} \left (\left (-4 x^4-16 e^x x^3-24 e^{2 x} x^2-16 e^{3 x} x-4 e^{4 x}\right ) x^x-12 x^5-48 e^x x^4-72 e^{2 x} x^3-48 e^{3 x} x^2-12 e^{4 x} x+\left (-12 x^5-48 e^x x^4-72 e^{2 x} x^3-48 e^{3 x} x^2-12 e^{4 x} x\right ) \log (x)\right )\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (\left (e^x \left (-4 x^5-12 x^4\right )-16 x^5\right ) x^x+e^{3 x^{-x}} \left (\left (4 x^4+4 e^x x^3\right ) x^x+12 x^5+12 e^x x^4+\left (12 x^5+12 e^x x^4\right ) \log (x)\right )\right )+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (\left (-16 x^5+e^{3 x} \left (-12 x^3-4 x^2\right )+e^{2 x} \left (-24 x^4-24 x^3\right )+e^x \left (-12 x^5-36 x^4\right )\right ) x^x+e^{3 x^{-x}} \left (\left (12 x^4+36 e^x x^3+36 e^{2 x} x^2+12 e^{3 x} x\right ) x^x+36 x^5+108 e^x x^4+108 e^{2 x} x^3+36 e^{3 x} x^2+\left (36 x^5+108 e^x x^4+108 e^{2 x} x^3+36 e^{3 x} x^2\right ) \log (x)\right )\right )\right ) \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int 4 x^{-x-2} \left (e^{\frac {e^{3 x^{-x}}}{x}} x+e^{\frac {e^{3 x^{-x}}}{x}+x}-x\right )^3 \exp \left (-4 e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^3 x+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^4+x^4-4 e^{\frac {e^{3 x^{-x}}}{x}} \left (x+e^x\right ) x^3+6 e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^2 x^2-5\right ) \left (e^{\frac {e^{3 x^{-x}}}{x}} x^{x+2}+e^{\frac {e^{3 x^{-x}}}{x}+x} x^{x+2}-x^{x+2}-3 e^{3 x^{-x}+\frac {e^{3 x^{-x}}}{x}} \left (x+e^x\right ) x \log (x)-e^{3 x^{-x}+\frac {e^{3 x^{-x}}}{x}} \left (x^x+3 x\right ) x-e^{3 x^{-x}+\frac {e^{3 x^{-x}}}{x}+x} \left (x^x+3 x\right )\right )dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int -\exp \left (x^4-4 e^{\frac {e^{3 x^{-x}}}{x}} \left (x+e^x\right ) x^3+6 e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^2 x^2-4 e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^3 x+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^4-5\right ) x^{-x-2} \left (e^{\frac {e^{3 x^{-x}}}{x}} x-x+e^{x+\frac {e^{3 x^{-x}}}{x}}\right )^3 \left (-e^{\frac {e^{3 x^{-x}}}{x}} x^{x+2}-e^{x+\frac {e^{3 x^{-x}}}{x}} x^{x+2}+x^{x+2}+e^{3 x^{-x}+\frac {e^{3 x^{-x}}}{x}} \left (x^x+3 x\right ) x+3 e^{3 x^{-x}+\frac {e^{3 x^{-x}}}{x}} \left (x+e^x\right ) \log (x) x+e^{3 x^{-x}+x+\frac {e^{3 x^{-x}}}{x}} \left (x^x+3 x\right )\right )dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -4 \int \exp \left (x^4-4 e^{\frac {e^{3 x^{-x}}}{x}} \left (x+e^x\right ) x^3+6 e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^2 x^2-4 e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^3 x+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^4-5\right ) x^{-x-2} \left (e^{\frac {e^{3 x^{-x}}}{x}} x-x+e^{x+\frac {e^{3 x^{-x}}}{x}}\right )^3 \left (-e^{\frac {e^{3 x^{-x}}}{x}} x^{x+2}-e^{x+\frac {e^{3 x^{-x}}}{x}} x^{x+2}+x^{x+2}+e^{3 x^{-x}+\frac {e^{3 x^{-x}}}{x}} \left (x^x+3 x\right ) x+3 e^{3 x^{-x}+\frac {e^{3 x^{-x}}}{x}} \left (x+e^x\right ) \log (x) x+e^{3 x^{-x}+x+\frac {e^{3 x^{-x}}}{x}} \left (x^x+3 x\right )\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (3 \exp \left (3 x^{-x}+x^4-4 e^{\frac {e^{3 x^{-x}}}{x}} \left (x+e^x\right ) x^3+6 e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^2 x^2-4 e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^3 x+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^4-5+\frac {e^{3 x^{-x}}}{x}\right ) x^{-x-1} \left (x+e^x\right ) \left (e^{\frac {e^{3 x^{-x}}}{x}} x-x+e^{x+\frac {e^{3 x^{-x}}}{x}}\right )^3 (\log (x)+1)-\frac {\exp \left (x^4-4 e^{\frac {e^{3 x^{-x}}}{x}} \left (x+e^x\right ) x^3+6 e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^2 x^2-4 e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^3 x+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^4-5\right ) \left (e^{\frac {e^{3 x^{-x}}}{x}} x-x+e^{x+\frac {e^{3 x^{-x}}}{x}}\right )^3 \left (e^{\frac {e^{3 x^{-x}}}{x}} x^2+e^{x+\frac {e^{3 x^{-x}}}{x}} x^2-x^2-e^{3 x^{-x}+\frac {e^{3 x^{-x}}}{x}} x-e^{3 x^{-x}+x+\frac {e^{3 x^{-x}}}{x}}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle -4 \int \left (3 \exp \left (3 x^{-x}+x^4-4 e^{\frac {e^{3 x^{-x}}}{x}} \left (x+e^x\right ) x^3+6 e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^2 x^2-4 e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^3 x+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^4-5+\frac {e^{3 x^{-x}}}{x}\right ) x^{-x-1} \left (x+e^x\right ) \left (e^{\frac {e^{3 x^{-x}}}{x}} x-x+e^{x+\frac {e^{3 x^{-x}}}{x}}\right )^3 (\log (x)+1)-\frac {\exp \left (x^4-4 e^{\frac {e^{3 x^{-x}}}{x}} \left (x+e^x\right ) x^3+6 e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^2 x^2-4 e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^3 x+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x+e^x\right )^4-5\right ) \left (e^{\frac {e^{3 x^{-x}}}{x}} x-x+e^{x+\frac {e^{3 x^{-x}}}{x}}\right )^3 \left (e^{\frac {e^{3 x^{-x}}}{x}} x^2+e^{x+\frac {e^{3 x^{-x}}}{x}} x^2-x^2-e^{3 x^{-x}+\frac {e^{3 x^{-x}}}{x}} x-e^{3 x^{-x}+x+\frac {e^{3 x^{-x}}}{x}}\right )}{x^2}\right )dx\) |
Int[E^(-5 + x^4 + E^((3*E^(3/x^x))/x)*(-4*E^(3*x)*x - 12*E^(2*x)*x^2 - 12* E^x*x^3 - 4*x^4) + E^(E^(3/x^x)/x)*(-4*E^x*x^3 - 4*x^4) + E^((4*E^(3/x^x)) /x)*(E^(4*x) + 4*E^(3*x)*x + 6*E^(2*x)*x^2 + 4*E^x*x^3 + x^4) + E^((2*E^(3 /x^x))/x)*(6*E^(2*x)*x^2 + 12*E^x*x^3 + 6*x^4))*x^(-2 - x)*(4*x^(5 + x) + E^((2*E^(3/x^x))/x)*(x^x*(24*x^5 + E^(2*x)*(12*x^3 + 12*x^4) + E^x*(36*x^4 + 12*x^5)) + E^(3/x^x)*(-36*E^(2*x)*x^3 - 72*E^x*x^4 - 36*x^5 + x^x*(-12* E^(2*x)*x^2 - 24*E^x*x^3 - 12*x^4) + (-36*E^(2*x)*x^3 - 72*E^x*x^4 - 36*x^ 5)*Log[x])) + E^((4*E^(3/x^x))/x)*(x^x*(4*E^(4*x)*x^2 + 4*x^5 + E^(3*x)*(4 *x^2 + 12*x^3) + E^(2*x)*(12*x^3 + 12*x^4) + E^x*(12*x^4 + 4*x^5)) + E^(3/ x^x)*(-12*E^(4*x)*x - 48*E^(3*x)*x^2 - 72*E^(2*x)*x^3 - 48*E^x*x^4 - 12*x^ 5 + x^x*(-4*E^(4*x) - 16*E^(3*x)*x - 24*E^(2*x)*x^2 - 16*E^x*x^3 - 4*x^4) + (-12*E^(4*x)*x - 48*E^(3*x)*x^2 - 72*E^(2*x)*x^3 - 48*E^x*x^4 - 12*x^5)* Log[x])) + E^(E^(3/x^x)/x)*(x^x*(-16*x^5 + E^x*(-12*x^4 - 4*x^5)) + E^(3/x ^x)*(12*E^x*x^4 + 12*x^5 + x^x*(4*E^x*x^3 + 4*x^4) + (12*E^x*x^4 + 12*x^5) *Log[x])) + E^((3*E^(3/x^x))/x)*(x^x*(-16*x^5 + E^(3*x)*(-4*x^2 - 12*x^3) + E^(2*x)*(-24*x^3 - 24*x^4) + E^x*(-36*x^4 - 12*x^5)) + E^(3/x^x)*(36*E^( 3*x)*x^2 + 108*E^(2*x)*x^3 + 108*E^x*x^4 + 36*x^5 + x^x*(12*E^(3*x)*x + 36 *E^(2*x)*x^2 + 36*E^x*x^3 + 12*x^4) + (36*E^(3*x)*x^2 + 108*E^(2*x)*x^3 + 108*E^x*x^4 + 36*x^5)*Log[x]))),x]
3.21.24.3.1 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]]
Leaf count of result is larger than twice the leaf count of optimal. \(311\) vs. \(2(29)=58\).
Time = 3.74 (sec) , antiderivative size = 312, normalized size of antiderivative = 10.06
\[{\mathrm e}^{4 x^{3} {\mathrm e}^{\frac {x^{2}+4 \,{\mathrm e}^{3 x^{-x}}}{x}}-12 x^{3} {\mathrm e}^{\frac {x^{2}+3 \,{\mathrm e}^{3 x^{-x}}}{x}}+12 x^{3} {\mathrm e}^{\frac {x^{2}+2 \,{\mathrm e}^{3 x^{-x}}}{x}}-4 x^{3} {\mathrm e}^{\frac {x^{2}+{\mathrm e}^{3 x^{-x}}}{x}}+{\mathrm e}^{\frac {4 \,{\mathrm e}^{3 x^{-x}}}{x}} x^{4}-4 \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{3 x^{-x}}}{x}} x^{4}+6 \,{\mathrm e}^{\frac {2 \,{\mathrm e}^{3 x^{-x}}}{x}} x^{4}-4 \,{\mathrm e}^{\frac {{\mathrm e}^{3 x^{-x}}}{x}} x^{4}+6 x^{2} {\mathrm e}^{\frac {2 x^{2}+4 \,{\mathrm e}^{3 x^{-x}}}{x}}-12 x^{2} {\mathrm e}^{\frac {2 x^{2}+3 \,{\mathrm e}^{3 x^{-x}}}{x}}+6 x^{2} {\mathrm e}^{\frac {2 x^{2}+2 \,{\mathrm e}^{3 x^{-x}}}{x}}+x^{4}+4 x \,{\mathrm e}^{\frac {3 x^{2}+4 \,{\mathrm e}^{3 x^{-x}}}{x}}-4 x \,{\mathrm e}^{\frac {3 x^{2}+3 \,{\mathrm e}^{3 x^{-x}}}{x}}+{\mathrm e}^{\frac {4 x^{2}+4 \,{\mathrm e}^{3 x^{-x}}}{x}}-5}\]
int(((((-4*exp(x)^4-16*x*exp(x)^3-24*exp(x)^2*x^2-16*exp(x)*x^3-4*x^4)*exp (x*ln(x))+(-12*x*exp(x)^4-48*x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp(x)*x^4-12 *x^5)*ln(x)-12*x*exp(x)^4-48*x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp(x)*x^4-12 *x^5)*exp(3/exp(x*ln(x)))+(4*x^2*exp(x)^4+(12*x^3+4*x^2)*exp(x)^3+(12*x^4+ 12*x^3)*exp(x)^2+(4*x^5+12*x^4)*exp(x)+4*x^5)*exp(x*ln(x)))*exp(exp(3/exp( x*ln(x)))/x)^4+(((12*x*exp(x)^3+36*exp(x)^2*x^2+36*exp(x)*x^3+12*x^4)*exp( x*ln(x))+(36*x^2*exp(x)^3+108*exp(x)^2*x^3+108*exp(x)*x^4+36*x^5)*ln(x)+36 *x^2*exp(x)^3+108*exp(x)^2*x^3+108*exp(x)*x^4+36*x^5)*exp(3/exp(x*ln(x)))+ ((-12*x^3-4*x^2)*exp(x)^3+(-24*x^4-24*x^3)*exp(x)^2+(-12*x^5-36*x^4)*exp(x )-16*x^5)*exp(x*ln(x)))*exp(exp(3/exp(x*ln(x)))/x)^3+(((-12*exp(x)^2*x^2-2 4*exp(x)*x^3-12*x^4)*exp(x*ln(x))+(-36*exp(x)^2*x^3-72*exp(x)*x^4-36*x^5)* ln(x)-36*exp(x)^2*x^3-72*exp(x)*x^4-36*x^5)*exp(3/exp(x*ln(x)))+((12*x^4+1 2*x^3)*exp(x)^2+(12*x^5+36*x^4)*exp(x)+24*x^5)*exp(x*ln(x)))*exp(exp(3/exp (x*ln(x)))/x)^2+(((4*exp(x)*x^3+4*x^4)*exp(x*ln(x))+(12*exp(x)*x^4+12*x^5) *ln(x)+12*exp(x)*x^4+12*x^5)*exp(3/exp(x*ln(x)))+((-4*x^5-12*x^4)*exp(x)-1 6*x^5)*exp(x*ln(x)))*exp(exp(3/exp(x*ln(x)))/x)+4*x^5*exp(x*ln(x)))*exp((e xp(x)^4+4*x*exp(x)^3+6*exp(x)^2*x^2+4*exp(x)*x^3+x^4)*exp(exp(3/exp(x*ln(x )))/x)^4+(-4*x*exp(x)^3-12*exp(x)^2*x^2-12*exp(x)*x^3-4*x^4)*exp(exp(3/exp (x*ln(x)))/x)^3+(6*exp(x)^2*x^2+12*exp(x)*x^3+6*x^4)*exp(exp(3/exp(x*ln(x) ))/x)^2+(-4*exp(x)*x^3-4*x^4)*exp(exp(3/exp(x*ln(x)))/x)+x^4-5)/x^2/exp(x* ln(x)),x)
exp(4*x^3*exp((x^2+4*exp(3/(x^x)))/x)+exp(4*exp(3/(x^x))/x)*x^4-12*x^3*exp ((x^2+3*exp(3/(x^x)))/x)-4*exp(3*exp(3/(x^x))/x)*x^4+12*x^3*exp((x^2+2*exp (3/(x^x)))/x)+6*exp(2*exp(3/(x^x))/x)*x^4-4*x^3*exp((x^2+exp(3/(x^x)))/x)- 4*exp(exp(3/(x^x))/x)*x^4+6*x^2*exp(2*(x^2+2*exp(3/(x^x)))/x)-12*x^2*exp(( 2*x^2+3*exp(3/(x^x)))/x)+6*x^2*exp(2*(x^2+exp(3/(x^x)))/x)+x^4+4*x*exp((3* x^2+4*exp(3/(x^x)))/x)-4*x*exp(3*(x^2+exp(3/(x^x)))/x)+exp(4*(x^2+exp(3/(x ^x)))/x)-5)
Leaf count of result is larger than twice the leaf count of optimal. 154 vs. \(2 (27) = 54\).
Time = 0.28 (sec) , antiderivative size = 154, normalized size of antiderivative = 4.97 \[ \int e^{-5+x^4+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (-4 e^{3 x} x-12 e^{2 x} x^2-12 e^x x^3-4 x^4\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (-4 e^x x^3-4 x^4\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (e^{4 x}+4 e^{3 x} x+6 e^{2 x} x^2+4 e^x x^3+x^4\right )+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (6 e^{2 x} x^2+12 e^x x^3+6 x^4\right )} x^{-2-x} \left (4 x^{5+x}+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x^x \left (24 x^5+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (36 x^4+12 x^5\right )\right )+e^{3 x^{-x}} \left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5+x^x \left (-12 e^{2 x} x^2-24 e^x x^3-12 x^4\right )+\left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5\right ) \log (x)\right )\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x^x \left (4 e^{4 x} x^2+4 x^5+e^{3 x} \left (4 x^2+12 x^3\right )+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (12 x^4+4 x^5\right )\right )+e^{3 x^{-x}} \left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5+x^x \left (-4 e^{4 x}-16 e^{3 x} x-24 e^{2 x} x^2-16 e^x x^3-4 x^4\right )+\left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5\right ) \log (x)\right )\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^x \left (-12 x^4-4 x^5\right )\right )+e^{3 x^{-x}} \left (12 e^x x^4+12 x^5+x^x \left (4 e^x x^3+4 x^4\right )+\left (12 e^x x^4+12 x^5\right ) \log (x)\right )\right )+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^{3 x} \left (-4 x^2-12 x^3\right )+e^{2 x} \left (-24 x^3-24 x^4\right )+e^x \left (-36 x^4-12 x^5\right )\right )+e^{3 x^{-x}} \left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5+x^x \left (12 e^{3 x} x+36 e^{2 x} x^2+36 e^x x^3+12 x^4\right )+\left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5\right ) \log (x)\right )\right )\right ) \, dx=e^{\left (x^{4} + {\left (x^{4} + 4 \, x^{3} e^{x} + 6 \, x^{2} e^{\left (2 \, x\right )} + 4 \, x e^{\left (3 \, x\right )} + e^{\left (4 \, x\right )}\right )} e^{\left (\frac {4 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 4 \, {\left (x^{4} + 3 \, x^{3} e^{x} + 3 \, x^{2} e^{\left (2 \, x\right )} + x e^{\left (3 \, x\right )}\right )} e^{\left (\frac {3 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + 6 \, {\left (x^{4} + 2 \, x^{3} e^{x} + x^{2} e^{\left (2 \, x\right )}\right )} e^{\left (\frac {2 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 4 \, {\left (x^{4} + x^{3} e^{x}\right )} e^{\left (\frac {e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 5\right )} \]
integrate(((((-4*exp(x)^4-16*x*exp(x)^3-24*exp(x)^2*x^2-16*exp(x)*x^3-4*x^ 4)*exp(x*log(x))+(-12*x*exp(x)^4-48*x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp(x) *x^4-12*x^5)*log(x)-12*x*exp(x)^4-48*x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp(x )*x^4-12*x^5)*exp(3/exp(x*log(x)))+(4*x^2*exp(x)^4+(12*x^3+4*x^2)*exp(x)^3 +(12*x^4+12*x^3)*exp(x)^2+(4*x^5+12*x^4)*exp(x)+4*x^5)*exp(x*log(x)))*exp( exp(3/exp(x*log(x)))/x)^4+(((12*x*exp(x)^3+36*exp(x)^2*x^2+36*exp(x)*x^3+1 2*x^4)*exp(x*log(x))+(36*x^2*exp(x)^3+108*exp(x)^2*x^3+108*exp(x)*x^4+36*x ^5)*log(x)+36*x^2*exp(x)^3+108*exp(x)^2*x^3+108*exp(x)*x^4+36*x^5)*exp(3/e xp(x*log(x)))+((-12*x^3-4*x^2)*exp(x)^3+(-24*x^4-24*x^3)*exp(x)^2+(-12*x^5 -36*x^4)*exp(x)-16*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)^3+(((-1 2*exp(x)^2*x^2-24*exp(x)*x^3-12*x^4)*exp(x*log(x))+(-36*exp(x)^2*x^3-72*ex p(x)*x^4-36*x^5)*log(x)-36*exp(x)^2*x^3-72*exp(x)*x^4-36*x^5)*exp(3/exp(x* log(x)))+((12*x^4+12*x^3)*exp(x)^2+(12*x^5+36*x^4)*exp(x)+24*x^5)*exp(x*lo g(x)))*exp(exp(3/exp(x*log(x)))/x)^2+(((4*exp(x)*x^3+4*x^4)*exp(x*log(x))+ (12*exp(x)*x^4+12*x^5)*log(x)+12*exp(x)*x^4+12*x^5)*exp(3/exp(x*log(x)))+( (-4*x^5-12*x^4)*exp(x)-16*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)+ 4*x^5*exp(x*log(x)))*exp((exp(x)^4+4*x*exp(x)^3+6*exp(x)^2*x^2+4*exp(x)*x^ 3+x^4)*exp(exp(3/exp(x*log(x)))/x)^4+(-4*x*exp(x)^3-12*exp(x)^2*x^2-12*exp (x)*x^3-4*x^4)*exp(exp(3/exp(x*log(x)))/x)^3+(6*exp(x)^2*x^2+12*exp(x)*x^3 +6*x^4)*exp(exp(3/exp(x*log(x)))/x)^2+(-4*exp(x)*x^3-4*x^4)*exp(exp(3/exp( x*log(x)))/x)+x^4-5)/x^2/exp(x*log(x)),x, algorithm=\
e^(x^4 + (x^4 + 4*x^3*e^x + 6*x^2*e^(2*x) + 4*x*e^(3*x) + e^(4*x))*e^(4*e^ (3/x^x)/x) - 4*(x^4 + 3*x^3*e^x + 3*x^2*e^(2*x) + x*e^(3*x))*e^(3*e^(3/x^x )/x) + 6*(x^4 + 2*x^3*e^x + x^2*e^(2*x))*e^(2*e^(3/x^x)/x) - 4*(x^4 + x^3* e^x)*e^(e^(3/x^x)/x) - 5)
Timed out. \[ \int e^{-5+x^4+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (-4 e^{3 x} x-12 e^{2 x} x^2-12 e^x x^3-4 x^4\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (-4 e^x x^3-4 x^4\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (e^{4 x}+4 e^{3 x} x+6 e^{2 x} x^2+4 e^x x^3+x^4\right )+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (6 e^{2 x} x^2+12 e^x x^3+6 x^4\right )} x^{-2-x} \left (4 x^{5+x}+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x^x \left (24 x^5+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (36 x^4+12 x^5\right )\right )+e^{3 x^{-x}} \left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5+x^x \left (-12 e^{2 x} x^2-24 e^x x^3-12 x^4\right )+\left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5\right ) \log (x)\right )\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x^x \left (4 e^{4 x} x^2+4 x^5+e^{3 x} \left (4 x^2+12 x^3\right )+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (12 x^4+4 x^5\right )\right )+e^{3 x^{-x}} \left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5+x^x \left (-4 e^{4 x}-16 e^{3 x} x-24 e^{2 x} x^2-16 e^x x^3-4 x^4\right )+\left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5\right ) \log (x)\right )\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^x \left (-12 x^4-4 x^5\right )\right )+e^{3 x^{-x}} \left (12 e^x x^4+12 x^5+x^x \left (4 e^x x^3+4 x^4\right )+\left (12 e^x x^4+12 x^5\right ) \log (x)\right )\right )+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^{3 x} \left (-4 x^2-12 x^3\right )+e^{2 x} \left (-24 x^3-24 x^4\right )+e^x \left (-36 x^4-12 x^5\right )\right )+e^{3 x^{-x}} \left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5+x^x \left (12 e^{3 x} x+36 e^{2 x} x^2+36 e^x x^3+12 x^4\right )+\left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5\right ) \log (x)\right )\right )\right ) \, dx=\text {Timed out} \]
integrate(((((-4*exp(x)**4-16*x*exp(x)**3-24*exp(x)**2*x**2-16*exp(x)*x**3 -4*x**4)*exp(x*ln(x))+(-12*x*exp(x)**4-48*x**2*exp(x)**3-72*exp(x)**2*x**3 -48*exp(x)*x**4-12*x**5)*ln(x)-12*x*exp(x)**4-48*x**2*exp(x)**3-72*exp(x)* *2*x**3-48*exp(x)*x**4-12*x**5)*exp(3/exp(x*ln(x)))+(4*x**2*exp(x)**4+(12* x**3+4*x**2)*exp(x)**3+(12*x**4+12*x**3)*exp(x)**2+(4*x**5+12*x**4)*exp(x) +4*x**5)*exp(x*ln(x)))*exp(exp(3/exp(x*ln(x)))/x)**4+(((12*x*exp(x)**3+36* exp(x)**2*x**2+36*exp(x)*x**3+12*x**4)*exp(x*ln(x))+(36*x**2*exp(x)**3+108 *exp(x)**2*x**3+108*exp(x)*x**4+36*x**5)*ln(x)+36*x**2*exp(x)**3+108*exp(x )**2*x**3+108*exp(x)*x**4+36*x**5)*exp(3/exp(x*ln(x)))+((-12*x**3-4*x**2)* exp(x)**3+(-24*x**4-24*x**3)*exp(x)**2+(-12*x**5-36*x**4)*exp(x)-16*x**5)* exp(x*ln(x)))*exp(exp(3/exp(x*ln(x)))/x)**3+(((-12*exp(x)**2*x**2-24*exp(x )*x**3-12*x**4)*exp(x*ln(x))+(-36*exp(x)**2*x**3-72*exp(x)*x**4-36*x**5)*l n(x)-36*exp(x)**2*x**3-72*exp(x)*x**4-36*x**5)*exp(3/exp(x*ln(x)))+((12*x* *4+12*x**3)*exp(x)**2+(12*x**5+36*x**4)*exp(x)+24*x**5)*exp(x*ln(x)))*exp( exp(3/exp(x*ln(x)))/x)**2+(((4*exp(x)*x**3+4*x**4)*exp(x*ln(x))+(12*exp(x) *x**4+12*x**5)*ln(x)+12*exp(x)*x**4+12*x**5)*exp(3/exp(x*ln(x)))+((-4*x**5 -12*x**4)*exp(x)-16*x**5)*exp(x*ln(x)))*exp(exp(3/exp(x*ln(x)))/x)+4*x**5* exp(x*ln(x)))*exp((exp(x)**4+4*x*exp(x)**3+6*exp(x)**2*x**2+4*exp(x)*x**3+ x**4)*exp(exp(3/exp(x*ln(x)))/x)**4+(-4*x*exp(x)**3-12*exp(x)**2*x**2-12*e xp(x)*x**3-4*x**4)*exp(exp(3/exp(x*ln(x)))/x)**3+(6*exp(x)**2*x**2+12*exp( x)*x**3+6*x**4)*exp(exp(3/exp(x*ln(x)))/x)**2+(-4*exp(x)*x**3-4*x**4)*exp( exp(3/exp(x*ln(x)))/x)+x**4-5)/x**2/exp(x*ln(x)),x)
Leaf count of result is larger than twice the leaf count of optimal. 292 vs. \(2 (27) = 54\).
Time = 3.89 (sec) , antiderivative size = 292, normalized size of antiderivative = 9.42 \[ \int e^{-5+x^4+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (-4 e^{3 x} x-12 e^{2 x} x^2-12 e^x x^3-4 x^4\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (-4 e^x x^3-4 x^4\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (e^{4 x}+4 e^{3 x} x+6 e^{2 x} x^2+4 e^x x^3+x^4\right )+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (6 e^{2 x} x^2+12 e^x x^3+6 x^4\right )} x^{-2-x} \left (4 x^{5+x}+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x^x \left (24 x^5+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (36 x^4+12 x^5\right )\right )+e^{3 x^{-x}} \left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5+x^x \left (-12 e^{2 x} x^2-24 e^x x^3-12 x^4\right )+\left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5\right ) \log (x)\right )\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x^x \left (4 e^{4 x} x^2+4 x^5+e^{3 x} \left (4 x^2+12 x^3\right )+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (12 x^4+4 x^5\right )\right )+e^{3 x^{-x}} \left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5+x^x \left (-4 e^{4 x}-16 e^{3 x} x-24 e^{2 x} x^2-16 e^x x^3-4 x^4\right )+\left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5\right ) \log (x)\right )\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^x \left (-12 x^4-4 x^5\right )\right )+e^{3 x^{-x}} \left (12 e^x x^4+12 x^5+x^x \left (4 e^x x^3+4 x^4\right )+\left (12 e^x x^4+12 x^5\right ) \log (x)\right )\right )+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^{3 x} \left (-4 x^2-12 x^3\right )+e^{2 x} \left (-24 x^3-24 x^4\right )+e^x \left (-36 x^4-12 x^5\right )\right )+e^{3 x^{-x}} \left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5+x^x \left (12 e^{3 x} x+36 e^{2 x} x^2+36 e^x x^3+12 x^4\right )+\left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5\right ) \log (x)\right )\right )\right ) \, dx=e^{\left (x^{4} e^{\left (\frac {4 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 4 \, x^{4} e^{\left (\frac {3 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + 6 \, x^{4} e^{\left (\frac {2 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 4 \, x^{4} e^{\left (\frac {e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + x^{4} + 4 \, x^{3} e^{\left (x + \frac {4 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 12 \, x^{3} e^{\left (x + \frac {3 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + 12 \, x^{3} e^{\left (x + \frac {2 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 4 \, x^{3} e^{\left (x + \frac {e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + 6 \, x^{2} e^{\left (2 \, x + \frac {4 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 12 \, x^{2} e^{\left (2 \, x + \frac {3 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + 6 \, x^{2} e^{\left (2 \, x + \frac {2 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + 4 \, x e^{\left (3 \, x + \frac {4 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 4 \, x e^{\left (3 \, x + \frac {3 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + e^{\left (4 \, x + \frac {4 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 5\right )} \]
integrate(((((-4*exp(x)^4-16*x*exp(x)^3-24*exp(x)^2*x^2-16*exp(x)*x^3-4*x^ 4)*exp(x*log(x))+(-12*x*exp(x)^4-48*x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp(x) *x^4-12*x^5)*log(x)-12*x*exp(x)^4-48*x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp(x )*x^4-12*x^5)*exp(3/exp(x*log(x)))+(4*x^2*exp(x)^4+(12*x^3+4*x^2)*exp(x)^3 +(12*x^4+12*x^3)*exp(x)^2+(4*x^5+12*x^4)*exp(x)+4*x^5)*exp(x*log(x)))*exp( exp(3/exp(x*log(x)))/x)^4+(((12*x*exp(x)^3+36*exp(x)^2*x^2+36*exp(x)*x^3+1 2*x^4)*exp(x*log(x))+(36*x^2*exp(x)^3+108*exp(x)^2*x^3+108*exp(x)*x^4+36*x ^5)*log(x)+36*x^2*exp(x)^3+108*exp(x)^2*x^3+108*exp(x)*x^4+36*x^5)*exp(3/e xp(x*log(x)))+((-12*x^3-4*x^2)*exp(x)^3+(-24*x^4-24*x^3)*exp(x)^2+(-12*x^5 -36*x^4)*exp(x)-16*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)^3+(((-1 2*exp(x)^2*x^2-24*exp(x)*x^3-12*x^4)*exp(x*log(x))+(-36*exp(x)^2*x^3-72*ex p(x)*x^4-36*x^5)*log(x)-36*exp(x)^2*x^3-72*exp(x)*x^4-36*x^5)*exp(3/exp(x* log(x)))+((12*x^4+12*x^3)*exp(x)^2+(12*x^5+36*x^4)*exp(x)+24*x^5)*exp(x*lo g(x)))*exp(exp(3/exp(x*log(x)))/x)^2+(((4*exp(x)*x^3+4*x^4)*exp(x*log(x))+ (12*exp(x)*x^4+12*x^5)*log(x)+12*exp(x)*x^4+12*x^5)*exp(3/exp(x*log(x)))+( (-4*x^5-12*x^4)*exp(x)-16*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)+ 4*x^5*exp(x*log(x)))*exp((exp(x)^4+4*x*exp(x)^3+6*exp(x)^2*x^2+4*exp(x)*x^ 3+x^4)*exp(exp(3/exp(x*log(x)))/x)^4+(-4*x*exp(x)^3-12*exp(x)^2*x^2-12*exp (x)*x^3-4*x^4)*exp(exp(3/exp(x*log(x)))/x)^3+(6*exp(x)^2*x^2+12*exp(x)*x^3 +6*x^4)*exp(exp(3/exp(x*log(x)))/x)^2+(-4*exp(x)*x^3-4*x^4)*exp(exp(3/exp( x*log(x)))/x)+x^4-5)/x^2/exp(x*log(x)),x, algorithm=\
e^(x^4*e^(4*e^(3/x^x)/x) - 4*x^4*e^(3*e^(3/x^x)/x) + 6*x^4*e^(2*e^(3/x^x)/ x) - 4*x^4*e^(e^(3/x^x)/x) + x^4 + 4*x^3*e^(x + 4*e^(3/x^x)/x) - 12*x^3*e^ (x + 3*e^(3/x^x)/x) + 12*x^3*e^(x + 2*e^(3/x^x)/x) - 4*x^3*e^(x + e^(3/x^x )/x) + 6*x^2*e^(2*x + 4*e^(3/x^x)/x) - 12*x^2*e^(2*x + 3*e^(3/x^x)/x) + 6* x^2*e^(2*x + 2*e^(3/x^x)/x) + 4*x*e^(3*x + 4*e^(3/x^x)/x) - 4*x*e^(3*x + 3 *e^(3/x^x)/x) + e^(4*x + 4*e^(3/x^x)/x) - 5)
Timed out. \[ \int e^{-5+x^4+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (-4 e^{3 x} x-12 e^{2 x} x^2-12 e^x x^3-4 x^4\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (-4 e^x x^3-4 x^4\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (e^{4 x}+4 e^{3 x} x+6 e^{2 x} x^2+4 e^x x^3+x^4\right )+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (6 e^{2 x} x^2+12 e^x x^3+6 x^4\right )} x^{-2-x} \left (4 x^{5+x}+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x^x \left (24 x^5+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (36 x^4+12 x^5\right )\right )+e^{3 x^{-x}} \left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5+x^x \left (-12 e^{2 x} x^2-24 e^x x^3-12 x^4\right )+\left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5\right ) \log (x)\right )\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x^x \left (4 e^{4 x} x^2+4 x^5+e^{3 x} \left (4 x^2+12 x^3\right )+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (12 x^4+4 x^5\right )\right )+e^{3 x^{-x}} \left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5+x^x \left (-4 e^{4 x}-16 e^{3 x} x-24 e^{2 x} x^2-16 e^x x^3-4 x^4\right )+\left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5\right ) \log (x)\right )\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^x \left (-12 x^4-4 x^5\right )\right )+e^{3 x^{-x}} \left (12 e^x x^4+12 x^5+x^x \left (4 e^x x^3+4 x^4\right )+\left (12 e^x x^4+12 x^5\right ) \log (x)\right )\right )+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^{3 x} \left (-4 x^2-12 x^3\right )+e^{2 x} \left (-24 x^3-24 x^4\right )+e^x \left (-36 x^4-12 x^5\right )\right )+e^{3 x^{-x}} \left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5+x^x \left (12 e^{3 x} x+36 e^{2 x} x^2+36 e^x x^3+12 x^4\right )+\left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5\right ) \log (x)\right )\right )\right ) \, dx=\text {Timed out} \]
integrate(((((-4*exp(x)^4-16*x*exp(x)^3-24*exp(x)^2*x^2-16*exp(x)*x^3-4*x^ 4)*exp(x*log(x))+(-12*x*exp(x)^4-48*x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp(x) *x^4-12*x^5)*log(x)-12*x*exp(x)^4-48*x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp(x )*x^4-12*x^5)*exp(3/exp(x*log(x)))+(4*x^2*exp(x)^4+(12*x^3+4*x^2)*exp(x)^3 +(12*x^4+12*x^3)*exp(x)^2+(4*x^5+12*x^4)*exp(x)+4*x^5)*exp(x*log(x)))*exp( exp(3/exp(x*log(x)))/x)^4+(((12*x*exp(x)^3+36*exp(x)^2*x^2+36*exp(x)*x^3+1 2*x^4)*exp(x*log(x))+(36*x^2*exp(x)^3+108*exp(x)^2*x^3+108*exp(x)*x^4+36*x ^5)*log(x)+36*x^2*exp(x)^3+108*exp(x)^2*x^3+108*exp(x)*x^4+36*x^5)*exp(3/e xp(x*log(x)))+((-12*x^3-4*x^2)*exp(x)^3+(-24*x^4-24*x^3)*exp(x)^2+(-12*x^5 -36*x^4)*exp(x)-16*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)^3+(((-1 2*exp(x)^2*x^2-24*exp(x)*x^3-12*x^4)*exp(x*log(x))+(-36*exp(x)^2*x^3-72*ex p(x)*x^4-36*x^5)*log(x)-36*exp(x)^2*x^3-72*exp(x)*x^4-36*x^5)*exp(3/exp(x* log(x)))+((12*x^4+12*x^3)*exp(x)^2+(12*x^5+36*x^4)*exp(x)+24*x^5)*exp(x*lo g(x)))*exp(exp(3/exp(x*log(x)))/x)^2+(((4*exp(x)*x^3+4*x^4)*exp(x*log(x))+ (12*exp(x)*x^4+12*x^5)*log(x)+12*exp(x)*x^4+12*x^5)*exp(3/exp(x*log(x)))+( (-4*x^5-12*x^4)*exp(x)-16*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)+ 4*x^5*exp(x*log(x)))*exp((exp(x)^4+4*x*exp(x)^3+6*exp(x)^2*x^2+4*exp(x)*x^ 3+x^4)*exp(exp(3/exp(x*log(x)))/x)^4+(-4*x*exp(x)^3-12*exp(x)^2*x^2-12*exp (x)*x^3-4*x^4)*exp(exp(3/exp(x*log(x)))/x)^3+(6*exp(x)^2*x^2+12*exp(x)*x^3 +6*x^4)*exp(exp(3/exp(x*log(x)))/x)^2+(-4*exp(x)*x^3-4*x^4)*exp(exp(3/exp( x*log(x)))/x)+x^4-5)/x^2/exp(x*log(x)),x, algorithm=\
Time = 12.71 (sec) , antiderivative size = 308, normalized size of antiderivative = 9.94 \[ \int e^{-5+x^4+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (-4 e^{3 x} x-12 e^{2 x} x^2-12 e^x x^3-4 x^4\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (-4 e^x x^3-4 x^4\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (e^{4 x}+4 e^{3 x} x+6 e^{2 x} x^2+4 e^x x^3+x^4\right )+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (6 e^{2 x} x^2+12 e^x x^3+6 x^4\right )} x^{-2-x} \left (4 x^{5+x}+e^{\frac {2 e^{3 x^{-x}}}{x}} \left (x^x \left (24 x^5+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (36 x^4+12 x^5\right )\right )+e^{3 x^{-x}} \left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5+x^x \left (-12 e^{2 x} x^2-24 e^x x^3-12 x^4\right )+\left (-36 e^{2 x} x^3-72 e^x x^4-36 x^5\right ) \log (x)\right )\right )+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (x^x \left (4 e^{4 x} x^2+4 x^5+e^{3 x} \left (4 x^2+12 x^3\right )+e^{2 x} \left (12 x^3+12 x^4\right )+e^x \left (12 x^4+4 x^5\right )\right )+e^{3 x^{-x}} \left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5+x^x \left (-4 e^{4 x}-16 e^{3 x} x-24 e^{2 x} x^2-16 e^x x^3-4 x^4\right )+\left (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5\right ) \log (x)\right )\right )+e^{\frac {e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^x \left (-12 x^4-4 x^5\right )\right )+e^{3 x^{-x}} \left (12 e^x x^4+12 x^5+x^x \left (4 e^x x^3+4 x^4\right )+\left (12 e^x x^4+12 x^5\right ) \log (x)\right )\right )+e^{\frac {3 e^{3 x^{-x}}}{x}} \left (x^x \left (-16 x^5+e^{3 x} \left (-4 x^2-12 x^3\right )+e^{2 x} \left (-24 x^3-24 x^4\right )+e^x \left (-36 x^4-12 x^5\right )\right )+e^{3 x^{-x}} \left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5+x^x \left (12 e^{3 x} x+36 e^{2 x} x^2+36 e^x x^3+12 x^4\right )+\left (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5\right ) \log (x)\right )\right )\right ) \, dx={\mathrm {e}}^{{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^{-4\,x\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^{3\,x}}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^{3\,x}}\,{\mathrm {e}}^{-4\,x^3\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{4\,x^3\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{12\,x^3\,{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-12\,x^3\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{x^4\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}}\,{\mathrm {e}}^{-4\,x^4\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{\frac {3}{x^x}}}{x}}}\,{\mathrm {e}}^{-4\,x^4\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}}\,{\mathrm {e}}^{6\,x^4\,{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}}\,{\mathrm {e}}^{6\,x^2\,{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{6\,x^2\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-12\,x^2\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^{2\,x}} \]
int((exp(-x*log(x))*exp(exp((2*exp(3*exp(-x*log(x))))/x)*(12*x^3*exp(x) + 6*x^2*exp(2*x) + 6*x^4) - exp((3*exp(3*exp(-x*log(x))))/x)*(4*x*exp(3*x) + 12*x^3*exp(x) + 12*x^2*exp(2*x) + 4*x^4) - exp(exp(3*exp(-x*log(x)))/x)*( 4*x^3*exp(x) + 4*x^4) + x^4 + exp((4*exp(3*exp(-x*log(x))))/x)*(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4) - 5)*(4*x^5*exp(x*log (x)) - exp((2*exp(3*exp(-x*log(x))))/x)*(exp(3*exp(-x*log(x)))*(72*x^4*exp (x) + log(x)*(72*x^4*exp(x) + 36*x^3*exp(2*x) + 36*x^5) + 36*x^3*exp(2*x) + exp(x*log(x))*(24*x^3*exp(x) + 12*x^2*exp(2*x) + 12*x^4) + 36*x^5) - exp (x*log(x))*(exp(x)*(36*x^4 + 12*x^5) + exp(2*x)*(12*x^3 + 12*x^4) + 24*x^5 )) + exp(exp(3*exp(-x*log(x)))/x)*(exp(3*exp(-x*log(x)))*(12*x^4*exp(x) + exp(x*log(x))*(4*x^3*exp(x) + 4*x^4) + 12*x^5 + log(x)*(12*x^4*exp(x) + 12 *x^5)) - exp(x*log(x))*(exp(x)*(12*x^4 + 4*x^5) + 16*x^5)) + exp((3*exp(3* exp(-x*log(x))))/x)*(exp(3*exp(-x*log(x)))*(108*x^4*exp(x) + 36*x^2*exp(3* x) + 108*x^3*exp(2*x) + exp(x*log(x))*(12*x*exp(3*x) + 36*x^3*exp(x) + 36* x^2*exp(2*x) + 12*x^4) + log(x)*(108*x^4*exp(x) + 36*x^2*exp(3*x) + 108*x^ 3*exp(2*x) + 36*x^5) + 36*x^5) - exp(x*log(x))*(exp(x)*(36*x^4 + 12*x^5) + exp(3*x)*(4*x^2 + 12*x^3) + exp(2*x)*(24*x^3 + 24*x^4) + 16*x^5)) - exp(( 4*exp(3*exp(-x*log(x))))/x)*(exp(3*exp(-x*log(x)))*(12*x*exp(4*x) + 48*x^4 *exp(x) + exp(x*log(x))*(4*exp(4*x) + 16*x*exp(3*x) + 16*x^3*exp(x) + 24*x ^2*exp(2*x) + 4*x^4) + 48*x^2*exp(3*x) + 72*x^3*exp(2*x) + 12*x^5 + log(x) *(12*x*exp(4*x) + 48*x^4*exp(x) + 48*x^2*exp(3*x) + 72*x^3*exp(2*x) + 12*x ^5)) - exp(x*log(x))*(exp(x)*(12*x^4 + 4*x^5) + exp(3*x)*(4*x^2 + 12*x^3) + exp(2*x)*(12*x^3 + 12*x^4) + 4*x^2*exp(4*x) + 4*x^5))))/x^2,x)
exp(exp((4*exp(3/x^x))/x)*exp(4*x))*exp(x^4)*exp(-5)*exp(-4*x*exp((3*exp(3 /x^x))/x)*exp(3*x))*exp(4*x*exp((4*exp(3/x^x))/x)*exp(3*x))*exp(-4*x^3*exp (exp(3/x^x)/x)*exp(x))*exp(4*x^3*exp((4*exp(3/x^x))/x)*exp(x))*exp(12*x^3* exp((2*exp(3/x^x))/x)*exp(x))*exp(-12*x^3*exp((3*exp(3/x^x))/x)*exp(x))*ex p(x^4*exp((4*exp(3/x^x))/x))*exp(-4*x^4*exp(exp(3/x^x)/x))*exp(-4*x^4*exp( (3*exp(3/x^x))/x))*exp(6*x^4*exp((2*exp(3/x^x))/x))*exp(6*x^2*exp((2*exp(3 /x^x))/x)*exp(2*x))*exp(6*x^2*exp((4*exp(3/x^x))/x)*exp(2*x))*exp(-12*x^2* exp((3*exp(3/x^x))/x)*exp(2*x))