\(\int \frac {e^{-\frac {e^{4 x}-16 e^{3 x} \log (2 x)+e^{2 x} (96-2 x) \log ^2(2 x)+e^x (-256+16 x) \log ^3(2 x)+(256-32 x+x^2) \log ^4(2 x)}{\log ^4(2 x)}} (e^{4 x} (20 x-4 x^2)+(e^{3 x} (-240 x+48 x^2)+e^{4 x} (-20 x^2+4 x^3)) \log (2 x)+(e^{3 x} (240 x^2-48 x^3)+e^{2 x} (960 x-212 x^2+4 x^3)) \log ^2(2 x)+(e^x (-1280 x+336 x^2-16 x^3)+e^{2 x} (-950 x^2+210 x^3-4 x^4)) \log ^3(2 x)+e^x (1200 x^2-320 x^3+16 x^4) \log ^4(2 x)+(10 x+157 x^2-42 x^3+2 x^4) \log ^5(2 x))}{\log ^5(2 x)} \, dx\) [1620]

Optimal result

Integrand size = 280, antiderivative size = 34 \[ \int \frac {e^{-\frac {e^{4 x}-16 e^{3 x} \log (2 x)+e^{2 x} (96-2 x) \log ^2(2 x)+e^x (-256+16 x) \log ^3(2 x)+\left (256-32 x+x^2\right ) \log ^4(2 x)}{\log ^4(2 x)}} \left (e^{4 x} \left (20 x-4 x^2\right )+\left (e^{3 x} \left (-240 x+48 x^2\right )+e^{4 x} \left (-20 x^2+4 x^3\right )\right ) \log (2 x)+\left (e^{3 x} \left (240 x^2-48 x^3\right )+e^{2 x} \left (960 x-212 x^2+4 x^3\right )\right ) \log ^2(2 x)+\left (e^x \left (-1280 x+336 x^2-16 x^3\right )+e^{2 x} \left (-950 x^2+210 x^3-4 x^4\right )\right ) \log ^3(2 x)+e^x \left (1200 x^2-320 x^3+16 x^4\right ) \log ^4(2 x)+\left (10 x+157 x^2-42 x^3+2 x^4\right ) \log ^5(2 x)\right )}{\log ^5(2 x)} \, dx=e^{-\left (x-\left (4-\frac {e^x}{\log (2 x)}\right )^2\right )^2} (5-x) x^2 \]

[Out]

x^2*(5-x)/exp((x-(4-exp(x)/ln(2*x))^2)^2)

Rubi [F]

\[ \int \frac {e^{-\frac {e^{4 x}-16 e^{3 x} \log (2 x)+e^{2 x} (96-2 x) \log ^2(2 x)+e^x (-256+16 x) \log ^3(2 x)+\left (256-32 x+x^2\right ) \log ^4(2 x)}{\log ^4(2 x)}} \left (e^{4 x} \left (20 x-4 x^2\right )+\left (e^{3 x} \left (-240 x+48 x^2\right )+e^{4 x} \left (-20 x^2+4 x^3\right )\right ) \log (2 x)+\left (e^{3 x} \left (240 x^2-48 x^3\right )+e^{2 x} \left (960 x-212 x^2+4 x^3\right )\right ) \log ^2(2 x)+\left (e^x \left (-1280 x+336 x^2-16 x^3\right )+e^{2 x} \left (-950 x^2+210 x^3-4 x^4\right )\right ) \log ^3(2 x)+e^x \left (1200 x^2-320 x^3+16 x^4\right ) \log ^4(2 x)+\left (10 x+157 x^2-42 x^3+2 x^4\right ) \log ^5(2 x)\right )}{\log ^5(2 x)} \, dx=\int \frac {\exp \left (-\frac {e^{4 x}-16 e^{3 x} \log (2 x)+e^{2 x} (96-2 x) \log ^2(2 x)+e^x (-256+16 x) \log ^3(2 x)+\left (256-32 x+x^2\right ) \log ^4(2 x)}{\log ^4(2 x)}\right ) \left (e^{4 x} \left (20 x-4 x^2\right )+\left (e^{3 x} \left (-240 x+48 x^2\right )+e^{4 x} \left (-20 x^2+4 x^3\right )\right ) \log (2 x)+\left (e^{3 x} \left (240 x^2-48 x^3\right )+e^{2 x} \left (960 x-212 x^2+4 x^3\right )\right ) \log ^2(2 x)+\left (e^x \left (-1280 x+336 x^2-16 x^3\right )+e^{2 x} \left (-950 x^2+210 x^3-4 x^4\right )\right ) \log ^3(2 x)+e^x \left (1200 x^2-320 x^3+16 x^4\right ) \log ^4(2 x)+\left (10 x+157 x^2-42 x^3+2 x^4\right ) \log ^5(2 x)\right )}{\log ^5(2 x)} \, dx \]

[In]

Int[(E^(4*x)*(20*x - 4*x^2) + (E^(3*x)*(-240*x + 48*x^2) + E^(4*x)*(-20*x^2 + 4*x^3))*Log[2*x] + (E^(3*x)*(240
*x^2 - 48*x^3) + E^(2*x)*(960*x - 212*x^2 + 4*x^3))*Log[2*x]^2 + (E^x*(-1280*x + 336*x^2 - 16*x^3) + E^(2*x)*(
-950*x^2 + 210*x^3 - 4*x^4))*Log[2*x]^3 + E^x*(1200*x^2 - 320*x^3 + 16*x^4)*Log[2*x]^4 + (10*x + 157*x^2 - 42*
x^3 + 2*x^4)*Log[2*x]^5)/(E^((E^(4*x) - 16*E^(3*x)*Log[2*x] + E^(2*x)*(96 - 2*x)*Log[2*x]^2 + E^x*(-256 + 16*x
)*Log[2*x]^3 + (256 - 32*x + x^2)*Log[2*x]^4)/Log[2*x]^4)*Log[2*x]^5),x]

[Out]

10*Defer[Int][x/E^((E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x]^4), x] + 157*Defer[Int][x^2/E^
((E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x]^4), x] - 42*Defer[Int][x^3/E^((E^(2*x) - 8*E^x*L
og[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x]^4), x] + 2*Defer[Int][x^4/E^((E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*
Log[2*x]^2)^2/Log[2*x]^4), x] + 20*Defer[Int][(E^(4*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Lo
g[2*x]^4)*x)/Log[2*x]^5, x] - 4*Defer[Int][(E^(4*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2
*x]^4)*x^2)/Log[2*x]^5, x] - 240*Defer[Int][(E^(3*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[
2*x]^4)*x)/Log[2*x]^4, x] + 48*Defer[Int][(E^(3*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*
x]^4)*x^2)/Log[2*x]^4, x] - 20*Defer[Int][(E^(4*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*
x]^4)*x^2)/Log[2*x]^4, x] + 4*Defer[Int][(E^(4*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x
]^4)*x^3)/Log[2*x]^4, x] + 960*Defer[Int][(E^(2*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*
x]^4)*x)/Log[2*x]^3, x] - 212*Defer[Int][(E^(2*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x
]^4)*x^2)/Log[2*x]^3, x] + 240*Defer[Int][(E^(3*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*
x]^4)*x^2)/Log[2*x]^3, x] + 4*Defer[Int][(E^(2*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x
]^4)*x^3)/Log[2*x]^3, x] - 48*Defer[Int][(E^(3*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x
]^4)*x^3)/Log[2*x]^3, x] - 1280*Defer[Int][(E^(x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x
]^4)*x)/Log[2*x]^2, x] + 336*Defer[Int][(E^(x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x]^4
)*x^2)/Log[2*x]^2, x] - 950*Defer[Int][(E^(2*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x]^
4)*x^2)/Log[2*x]^2, x] - 16*Defer[Int][(E^(x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x]^4)
*x^3)/Log[2*x]^2, x] + 210*Defer[Int][(E^(2*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x]^4
)*x^3)/Log[2*x]^2, x] - 4*Defer[Int][(E^(2*x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x]^4)
*x^4)/Log[2*x]^2, x] + 1200*Defer[Int][(E^(x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x]^4)
*x^2)/Log[2*x], x] - 320*Defer[Int][(E^(x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x]^4)*x^
3)/Log[2*x], x] + 16*Defer[Int][(E^(x - (E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x]^4)*x^4)/L
og[2*x], x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x \left (-4 e^{4 x} (-5+x)+4 e^{3 x} (-5+x) \left (12+e^x x\right ) \log (2 x)-4 e^{2 x} (-5+x) \left (48+\left (-1+12 e^x\right ) x\right ) \log ^2(2 x)-2 e^x (-5+x) \left (-128+\left (8-95 e^x\right ) x+2 e^x x^2\right ) \log ^3(2 x)+16 e^x x \left (75-20 x+x^2\right ) \log ^4(2 x)+\left (10+157 x-42 x^2+2 x^3\right ) \log ^5(2 x)\right )}{\log ^5(2 x)} \, dx \\ & = \int \left (\exp \left (-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x \left (10+157 x-42 x^2+2 x^3\right )+\frac {4 \exp \left (4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x (-1+x \log (2 x))}{\log ^5(2 x)}-\frac {48 \exp \left (3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x (-1+x \log (2 x))}{\log ^4(2 x)}+\frac {16 \exp \left (x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x \left (16-x-15 x \log (2 x)+x^2 \log (2 x)\right )}{\log ^2(2 x)}-\frac {2 \exp \left (2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x \left (96-2 x-95 x \log (2 x)+2 x^2 \log (2 x)\right )}{\log ^3(2 x)}\right ) \, dx \\ & = -\left (2 \int \frac {\exp \left (2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x \left (96-2 x-95 x \log (2 x)+2 x^2 \log (2 x)\right )}{\log ^3(2 x)} \, dx\right )+4 \int \frac {\exp \left (4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x (-1+x \log (2 x))}{\log ^5(2 x)} \, dx+16 \int \frac {\exp \left (x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x \left (16-x-15 x \log (2 x)+x^2 \log (2 x)\right )}{\log ^2(2 x)} \, dx-48 \int \frac {\exp \left (3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x (-1+x \log (2 x))}{\log ^4(2 x)} \, dx+\int \exp \left (-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x \left (10+157 x-42 x^2+2 x^3\right ) \, dx \\ & = -\left (2 \int \left (-\frac {2 \exp \left (2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x \left (240-53 x+x^2\right )}{\log ^3(2 x)}+\frac {\exp \left (2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x^2 \left (475-105 x+2 x^2\right )}{\log ^2(2 x)}\right ) \, dx\right )+4 \int \left (-\frac {\exp \left (4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x}{\log ^5(2 x)}+\frac {\exp \left (4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x^2}{\log ^4(2 x)}\right ) \, dx+16 \int \left (-\frac {\exp \left (x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x \left (80-21 x+x^2\right )}{\log ^2(2 x)}+\frac {\exp \left (x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x^2 \left (75-20 x+x^2\right )}{\log (2 x)}\right ) \, dx-48 \int \left (-\frac {\exp \left (3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x}{\log ^4(2 x)}+\frac {\exp \left (3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x^2}{\log ^3(2 x)}\right ) \, dx+\int \left (10 \exp \left (-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x+157 \exp \left (-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x^2-42 \exp \left (-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x^3+2 \exp \left (-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x^4\right ) \, dx \\ & = 2 \int \exp \left (-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x^4 \, dx-2 \int \frac {\exp \left (2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x^2 \left (475-105 x+2 x^2\right )}{\log ^2(2 x)} \, dx-4 \int \frac {\exp \left (4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x}{\log ^5(2 x)} \, dx+4 \int \frac {\exp \left (4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x^2}{\log ^4(2 x)} \, dx+4 \int \frac {\exp \left (2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x \left (240-53 x+x^2\right )}{\log ^3(2 x)} \, dx+10 \int \exp \left (-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x \, dx-16 \int \frac {\exp \left (x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x \left (80-21 x+x^2\right )}{\log ^2(2 x)} \, dx+16 \int \frac {\exp \left (x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x^2 \left (75-20 x+x^2\right )}{\log (2 x)} \, dx-42 \int \exp \left (-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x^3 \, dx+48 \int \frac {\exp \left (3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x}{\log ^4(2 x)} \, dx-48 \int \frac {\exp \left (3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) (-5+x) x^2}{\log ^3(2 x)} \, dx+157 \int \exp \left (-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}\right ) x^2 \, dx \\ & = 2 \int e^{-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^4 \, dx-2 \int \left (\frac {475 e^{2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^2(2 x)}-\frac {105 e^{2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3}{\log ^2(2 x)}+\frac {2 e^{2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^4}{\log ^2(2 x)}\right ) \, dx-4 \int \left (-\frac {5 e^{4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x}{\log ^5(2 x)}+\frac {e^{4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^5(2 x)}\right ) \, dx+4 \int \left (-\frac {5 e^{4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^4(2 x)}+\frac {e^{4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3}{\log ^4(2 x)}\right ) \, dx+4 \int \left (\frac {240 e^{2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x}{\log ^3(2 x)}-\frac {53 e^{2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^3(2 x)}+\frac {e^{2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3}{\log ^3(2 x)}\right ) \, dx+10 \int e^{-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x \, dx-16 \int \left (\frac {80 e^{x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x}{\log ^2(2 x)}-\frac {21 e^{x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^2(2 x)}+\frac {e^{x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3}{\log ^2(2 x)}\right ) \, dx+16 \int \left (\frac {75 e^{x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log (2 x)}-\frac {20 e^{x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3}{\log (2 x)}+\frac {e^{x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^4}{\log (2 x)}\right ) \, dx-42 \int e^{-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3 \, dx+48 \int \left (-\frac {5 e^{3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x}{\log ^4(2 x)}+\frac {e^{3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^4(2 x)}\right ) \, dx-48 \int \left (-\frac {5 e^{3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^3(2 x)}+\frac {e^{3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3}{\log ^3(2 x)}\right ) \, dx+157 \int e^{-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2 \, dx \\ & = 2 \int e^{-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^4 \, dx-4 \int \frac {e^{4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^5(2 x)} \, dx+4 \int \frac {e^{4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3}{\log ^4(2 x)} \, dx+4 \int \frac {e^{2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3}{\log ^3(2 x)} \, dx-4 \int \frac {e^{2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^4}{\log ^2(2 x)} \, dx+10 \int e^{-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x \, dx-16 \int \frac {e^{x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3}{\log ^2(2 x)} \, dx+16 \int \frac {e^{x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^4}{\log (2 x)} \, dx+20 \int \frac {e^{4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x}{\log ^5(2 x)} \, dx-20 \int \frac {e^{4 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^4(2 x)} \, dx-42 \int e^{-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3 \, dx+48 \int \frac {e^{3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^4(2 x)} \, dx-48 \int \frac {e^{3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3}{\log ^3(2 x)} \, dx+157 \int e^{-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2 \, dx+210 \int \frac {e^{2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3}{\log ^2(2 x)} \, dx-212 \int \frac {e^{2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^3(2 x)} \, dx-240 \int \frac {e^{3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x}{\log ^4(2 x)} \, dx+240 \int \frac {e^{3 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^3(2 x)} \, dx-320 \int \frac {e^{x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^3}{\log (2 x)} \, dx+336 \int \frac {e^{x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^2(2 x)} \, dx-950 \int \frac {e^{2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log ^2(2 x)} \, dx+960 \int \frac {e^{2 x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x}{\log ^3(2 x)} \, dx+1200 \int \frac {e^{x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x^2}{\log (2 x)} \, dx-1280 \int \frac {e^{x-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} x}{\log ^2(2 x)} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.38 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.35 \[ \int \frac {e^{-\frac {e^{4 x}-16 e^{3 x} \log (2 x)+e^{2 x} (96-2 x) \log ^2(2 x)+e^x (-256+16 x) \log ^3(2 x)+\left (256-32 x+x^2\right ) \log ^4(2 x)}{\log ^4(2 x)}} \left (e^{4 x} \left (20 x-4 x^2\right )+\left (e^{3 x} \left (-240 x+48 x^2\right )+e^{4 x} \left (-20 x^2+4 x^3\right )\right ) \log (2 x)+\left (e^{3 x} \left (240 x^2-48 x^3\right )+e^{2 x} \left (960 x-212 x^2+4 x^3\right )\right ) \log ^2(2 x)+\left (e^x \left (-1280 x+336 x^2-16 x^3\right )+e^{2 x} \left (-950 x^2+210 x^3-4 x^4\right )\right ) \log ^3(2 x)+e^x \left (1200 x^2-320 x^3+16 x^4\right ) \log ^4(2 x)+\left (10 x+157 x^2-42 x^3+2 x^4\right ) \log ^5(2 x)\right )}{\log ^5(2 x)} \, dx=-e^{-\frac {\left (e^{2 x}-8 e^x \log (2 x)-(-16+x) \log ^2(2 x)\right )^2}{\log ^4(2 x)}} (-5+x) x^2 \]

[In]

Integrate[(E^(4*x)*(20*x - 4*x^2) + (E^(3*x)*(-240*x + 48*x^2) + E^(4*x)*(-20*x^2 + 4*x^3))*Log[2*x] + (E^(3*x
)*(240*x^2 - 48*x^3) + E^(2*x)*(960*x - 212*x^2 + 4*x^3))*Log[2*x]^2 + (E^x*(-1280*x + 336*x^2 - 16*x^3) + E^(
2*x)*(-950*x^2 + 210*x^3 - 4*x^4))*Log[2*x]^3 + E^x*(1200*x^2 - 320*x^3 + 16*x^4)*Log[2*x]^4 + (10*x + 157*x^2
- 42*x^3 + 2*x^4)*Log[2*x]^5)/(E^((E^(4*x) - 16*E^(3*x)*Log[2*x] + E^(2*x)*(96 - 2*x)*Log[2*x]^2 + E^x*(-256
+ 16*x)*Log[2*x]^3 + (256 - 32*x + x^2)*Log[2*x]^4)/Log[2*x]^4)*Log[2*x]^5),x]

[Out]

-(((-5 + x)*x^2)/E^((E^(2*x) - 8*E^x*Log[2*x] - (-16 + x)*Log[2*x]^2)^2/Log[2*x]^4))

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(100\) vs. \(2(32)=64\).

Time = 10.91 (sec) , antiderivative size = 101, normalized size of antiderivative = 2.97

method	result	size
parallelrisch	\(-\frac {\left (\ln \left (2 x \right )^{4} x^{3}-5 \ln \left (2 x \right )^{4} x^{2}\right ) {\mathrm e}^{-\frac {\left (x^{2}-32 x +256\right ) \ln \left (2 x \right )^{4}+\left (16 x -256\right ) {\mathrm e}^{x} \ln \left (2 x \right )^{3}+\left (-2 x +96\right ) {\mathrm e}^{2 x} \ln \left (2 x \right )^{2}-16 \,{\mathrm e}^{3 x} \ln \left (2 x \right )+{\mathrm e}^{4 x}}{\ln \left (2 x \right )^{4}}}}{\ln \left (2 x \right )^{4}}\)	\(101\)
risch	\(\left (-x^{3}+5 x^{2}\right ) {\mathrm e}^{-\frac {\ln \left (2 x \right )^{4} x^{2}+16 \,{\mathrm e}^{x} \ln \left (2 x \right )^{3} x -32 \ln \left (2 x \right )^{4} x -256 \,{\mathrm e}^{x} \ln \left (2 x \right )^{3}+256 \ln \left (2 x \right )^{4}-2 \ln \left (2 x \right )^{2} {\mathrm e}^{2 x} x +96 \,{\mathrm e}^{2 x} \ln \left (2 x \right )^{2}-16 \,{\mathrm e}^{3 x} \ln \left (2 x \right )+{\mathrm e}^{4 x}}{\ln \left (2 x \right )^{4}}}\)	\(110\)

[In]

int(((2*x^4-42*x^3+157*x^2+10*x)*ln(2*x)^5+(16*x^4-320*x^3+1200*x^2)*exp(x)*ln(2*x)^4+((-4*x^4+210*x^3-950*x^2
)*exp(x)^2+(-16*x^3+336*x^2-1280*x)*exp(x))*ln(2*x)^3+((-48*x^3+240*x^2)*exp(x)^3+(4*x^3-212*x^2+960*x)*exp(x)
^2)*ln(2*x)^2+((4*x^3-20*x^2)*exp(x)^4+(48*x^2-240*x)*exp(x)^3)*ln(2*x)+(-4*x^2+20*x)*exp(x)^4)/ln(2*x)^5/exp(
((x^2-32*x+256)*ln(2*x)^4+(16*x-256)*exp(x)*ln(2*x)^3+(-2*x+96)*exp(x)^2*ln(2*x)^2-16*exp(x)^3*ln(2*x)+exp(x)^
4)/ln(2*x)^4),x,method=_RETURNVERBOSE)

[Out]

-1/ln(2*x)^4*(ln(2*x)^4*x^3-5*ln(2*x)^4*x^2)/exp(((x^2-32*x+256)*ln(2*x)^4+(16*x-256)*exp(x)*ln(2*x)^3+(-2*x+9
6)*exp(x)^2*ln(2*x)^2-16*exp(x)^3*ln(2*x)+exp(x)^4)/ln(2*x)^4)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 78 vs. \(2 (30) = 60\).

Time = 0.27 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.29 \[ \int \frac {e^{-\frac {e^{4 x}-16 e^{3 x} \log (2 x)+e^{2 x} (96-2 x) \log ^2(2 x)+e^x (-256+16 x) \log ^3(2 x)+\left (256-32 x+x^2\right ) \log ^4(2 x)}{\log ^4(2 x)}} \left (e^{4 x} \left (20 x-4 x^2\right )+\left (e^{3 x} \left (-240 x+48 x^2\right )+e^{4 x} \left (-20 x^2+4 x^3\right )\right ) \log (2 x)+\left (e^{3 x} \left (240 x^2-48 x^3\right )+e^{2 x} \left (960 x-212 x^2+4 x^3\right )\right ) \log ^2(2 x)+\left (e^x \left (-1280 x+336 x^2-16 x^3\right )+e^{2 x} \left (-950 x^2+210 x^3-4 x^4\right )\right ) \log ^3(2 x)+e^x \left (1200 x^2-320 x^3+16 x^4\right ) \log ^4(2 x)+\left (10 x+157 x^2-42 x^3+2 x^4\right ) \log ^5(2 x)\right )}{\log ^5(2 x)} \, dx=-{\left (x^{3} - 5 \, x^{2}\right )} e^{\left (-\frac {16 \, {\left (x - 16\right )} e^{x} \log \left (2 \, x\right )^{3} + {\left (x^{2} - 32 \, x + 256\right )} \log \left (2 \, x\right )^{4} - 2 \, {\left (x - 48\right )} e^{\left (2 \, x\right )} \log \left (2 \, x\right )^{2} - 16 \, e^{\left (3 \, x\right )} \log \left (2 \, x\right ) + e^{\left (4 \, x\right )}}{\log \left (2 \, x\right )^{4}}\right )} \]

[In]

integrate(((2*x^4-42*x^3+157*x^2+10*x)*log(2*x)^5+(16*x^4-320*x^3+1200*x^2)*exp(x)*log(2*x)^4+((-4*x^4+210*x^3
-950*x^2)*exp(x)^2+(-16*x^3+336*x^2-1280*x)*exp(x))*log(2*x)^3+((-48*x^3+240*x^2)*exp(x)^3+(4*x^3-212*x^2+960*
x)*exp(x)^2)*log(2*x)^2+((4*x^3-20*x^2)*exp(x)^4+(48*x^2-240*x)*exp(x)^3)*log(2*x)+(-4*x^2+20*x)*exp(x)^4)/log
(2*x)^5/exp(((x^2-32*x+256)*log(2*x)^4+(16*x-256)*exp(x)*log(2*x)^3+(-2*x+96)*exp(x)^2*log(2*x)^2-16*exp(x)^3*
log(2*x)+exp(x)^4)/log(2*x)^4),x, algorithm="fricas")

[Out]

-(x^3 - 5*x^2)*e^(-(16*(x - 16)*e^x*log(2*x)^3 + (x^2 - 32*x + 256)*log(2*x)^4 - 2*(x - 48)*e^(2*x)*log(2*x)^2
- 16*e^(3*x)*log(2*x) + e^(4*x))/log(2*x)^4)

Sympy [F(-1)]

Timed out. \[ \int \frac {e^{-\frac {e^{4 x}-16 e^{3 x} \log (2 x)+e^{2 x} (96-2 x) \log ^2(2 x)+e^x (-256+16 x) \log ^3(2 x)+\left (256-32 x+x^2\right ) \log ^4(2 x)}{\log ^4(2 x)}} \left (e^{4 x} \left (20 x-4 x^2\right )+\left (e^{3 x} \left (-240 x+48 x^2\right )+e^{4 x} \left (-20 x^2+4 x^3\right )\right ) \log (2 x)+\left (e^{3 x} \left (240 x^2-48 x^3\right )+e^{2 x} \left (960 x-212 x^2+4 x^3\right )\right ) \log ^2(2 x)+\left (e^x \left (-1280 x+336 x^2-16 x^3\right )+e^{2 x} \left (-950 x^2+210 x^3-4 x^4\right )\right ) \log ^3(2 x)+e^x \left (1200 x^2-320 x^3+16 x^4\right ) \log ^4(2 x)+\left (10 x+157 x^2-42 x^3+2 x^4\right ) \log ^5(2 x)\right )}{\log ^5(2 x)} \, dx=\text {Timed out} \]

[In]

integrate(((2*x**4-42*x**3+157*x**2+10*x)*ln(2*x)**5+(16*x**4-320*x**3+1200*x**2)*exp(x)*ln(2*x)**4+((-4*x**4+
210*x**3-950*x**2)*exp(x)**2+(-16*x**3+336*x**2-1280*x)*exp(x))*ln(2*x)**3+((-48*x**3+240*x**2)*exp(x)**3+(4*x
**3-212*x**2+960*x)*exp(x)**2)*ln(2*x)**2+((4*x**3-20*x**2)*exp(x)**4+(48*x**2-240*x)*exp(x)**3)*ln(2*x)+(-4*x
**2+20*x)*exp(x)**4)/ln(2*x)**5/exp(((x**2-32*x+256)*ln(2*x)**4+(16*x-256)*exp(x)*ln(2*x)**3+(-2*x+96)*exp(x)*
*2*ln(2*x)**2-16*exp(x)**3*ln(2*x)+exp(x)**4)/ln(2*x)**4),x)

[Out]

Timed out

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 168 vs. \(2 (30) = 60\).

Time = 57.81 (sec) , antiderivative size = 168, normalized size of antiderivative = 4.94 \[ \int \frac {e^{-\frac {e^{4 x}-16 e^{3 x} \log (2 x)+e^{2 x} (96-2 x) \log ^2(2 x)+e^x (-256+16 x) \log ^3(2 x)+\left (256-32 x+x^2\right ) \log ^4(2 x)}{\log ^4(2 x)}} \left (e^{4 x} \left (20 x-4 x^2\right )+\left (e^{3 x} \left (-240 x+48 x^2\right )+e^{4 x} \left (-20 x^2+4 x^3\right )\right ) \log (2 x)+\left (e^{3 x} \left (240 x^2-48 x^3\right )+e^{2 x} \left (960 x-212 x^2+4 x^3\right )\right ) \log ^2(2 x)+\left (e^x \left (-1280 x+336 x^2-16 x^3\right )+e^{2 x} \left (-950 x^2+210 x^3-4 x^4\right )\right ) \log ^3(2 x)+e^x \left (1200 x^2-320 x^3+16 x^4\right ) \log ^4(2 x)+\left (10 x+157 x^2-42 x^3+2 x^4\right ) \log ^5(2 x)\right )}{\log ^5(2 x)} \, dx=-{\left (x^{3} - 5 \, x^{2}\right )} e^{\left (-x^{2} + 32 \, x + \frac {2 \, x e^{\left (2 \, x\right )}}{\log \left (2\right )^{2} + 2 \, \log \left (2\right ) \log \left (x\right ) + \log \left (x\right )^{2}} - \frac {16 \, x e^{x}}{\log \left (2\right ) + \log \left (x\right )} - \frac {e^{\left (4 \, x\right )}}{\log \left (2\right )^{4} + 4 \, \log \left (2\right )^{3} \log \left (x\right ) + 6 \, \log \left (2\right )^{2} \log \left (x\right )^{2} + 4 \, \log \left (2\right ) \log \left (x\right )^{3} + \log \left (x\right )^{4}} + \frac {16 \, e^{\left (3 \, x\right )}}{\log \left (2\right )^{3} + 3 \, \log \left (2\right )^{2} \log \left (x\right ) + 3 \, \log \left (2\right ) \log \left (x\right )^{2} + \log \left (x\right )^{3}} - \frac {96 \, e^{\left (2 \, x\right )}}{\log \left (2\right )^{2} + 2 \, \log \left (2\right ) \log \left (x\right ) + \log \left (x\right )^{2}} + \frac {256 \, e^{x}}{\log \left (2\right ) + \log \left (x\right )} - 256\right )} \]

[In]

integrate(((2*x^4-42*x^3+157*x^2+10*x)*log(2*x)^5+(16*x^4-320*x^3+1200*x^2)*exp(x)*log(2*x)^4+((-4*x^4+210*x^3
-950*x^2)*exp(x)^2+(-16*x^3+336*x^2-1280*x)*exp(x))*log(2*x)^3+((-48*x^3+240*x^2)*exp(x)^3+(4*x^3-212*x^2+960*
x)*exp(x)^2)*log(2*x)^2+((4*x^3-20*x^2)*exp(x)^4+(48*x^2-240*x)*exp(x)^3)*log(2*x)+(-4*x^2+20*x)*exp(x)^4)/log
(2*x)^5/exp(((x^2-32*x+256)*log(2*x)^4+(16*x-256)*exp(x)*log(2*x)^3+(-2*x+96)*exp(x)^2*log(2*x)^2-16*exp(x)^3*
log(2*x)+exp(x)^4)/log(2*x)^4),x, algorithm="maxima")

[Out]

-(x^3 - 5*x^2)*e^(-x^2 + 32*x + 2*x*e^(2*x)/(log(2)^2 + 2*log(2)*log(x) + log(x)^2) - 16*x*e^x/(log(2) + log(x
)) - e^(4*x)/(log(2)^4 + 4*log(2)^3*log(x) + 6*log(2)^2*log(x)^2 + 4*log(2)*log(x)^3 + log(x)^4) + 16*e^(3*x)/
(log(2)^3 + 3*log(2)^2*log(x) + 3*log(2)*log(x)^2 + log(x)^3) - 96*e^(2*x)/(log(2)^2 + 2*log(2)*log(x) + log(x
)^2) + 256*e^x/(log(2) + log(x)) - 256)

Giac [F]

\[ \int \frac {e^{-\frac {e^{4 x}-16 e^{3 x} \log (2 x)+e^{2 x} (96-2 x) \log ^2(2 x)+e^x (-256+16 x) \log ^3(2 x)+\left (256-32 x+x^2\right ) \log ^4(2 x)}{\log ^4(2 x)}} \left (e^{4 x} \left (20 x-4 x^2\right )+\left (e^{3 x} \left (-240 x+48 x^2\right )+e^{4 x} \left (-20 x^2+4 x^3\right )\right ) \log (2 x)+\left (e^{3 x} \left (240 x^2-48 x^3\right )+e^{2 x} \left (960 x-212 x^2+4 x^3\right )\right ) \log ^2(2 x)+\left (e^x \left (-1280 x+336 x^2-16 x^3\right )+e^{2 x} \left (-950 x^2+210 x^3-4 x^4\right )\right ) \log ^3(2 x)+e^x \left (1200 x^2-320 x^3+16 x^4\right ) \log ^4(2 x)+\left (10 x+157 x^2-42 x^3+2 x^4\right ) \log ^5(2 x)\right )}{\log ^5(2 x)} \, dx=\int { \frac {{\left (16 \, {\left (x^{4} - 20 \, x^{3} + 75 \, x^{2}\right )} e^{x} \log \left (2 \, x\right )^{4} + {\left (2 \, x^{4} - 42 \, x^{3} + 157 \, x^{2} + 10 \, x\right )} \log \left (2 \, x\right )^{5} - 2 \, {\left ({\left (2 \, x^{4} - 105 \, x^{3} + 475 \, x^{2}\right )} e^{\left (2 \, x\right )} + 8 \, {\left (x^{3} - 21 \, x^{2} + 80 \, x\right )} e^{x}\right )} \log \left (2 \, x\right )^{3} - 4 \, {\left (12 \, {\left (x^{3} - 5 \, x^{2}\right )} e^{\left (3 \, x\right )} - {\left (x^{3} - 53 \, x^{2} + 240 \, x\right )} e^{\left (2 \, x\right )}\right )} \log \left (2 \, x\right )^{2} - 4 \, {\left (x^{2} - 5 \, x\right )} e^{\left (4 \, x\right )} + 4 \, {\left ({\left (x^{3} - 5 \, x^{2}\right )} e^{\left (4 \, x\right )} + 12 \, {\left (x^{2} - 5 \, x\right )} e^{\left (3 \, x\right )}\right )} \log \left (2 \, x\right )\right )} e^{\left (-\frac {16 \, {\left (x - 16\right )} e^{x} \log \left (2 \, x\right )^{3} + {\left (x^{2} - 32 \, x + 256\right )} \log \left (2 \, x\right )^{4} - 2 \, {\left (x - 48\right )} e^{\left (2 \, x\right )} \log \left (2 \, x\right )^{2} - 16 \, e^{\left (3 \, x\right )} \log \left (2 \, x\right ) + e^{\left (4 \, x\right )}}{\log \left (2 \, x\right )^{4}}\right )}}{\log \left (2 \, x\right )^{5}} \,d x } \]

[In]

integrate(((2*x^4-42*x^3+157*x^2+10*x)*log(2*x)^5+(16*x^4-320*x^3+1200*x^2)*exp(x)*log(2*x)^4+((-4*x^4+210*x^3
-950*x^2)*exp(x)^2+(-16*x^3+336*x^2-1280*x)*exp(x))*log(2*x)^3+((-48*x^3+240*x^2)*exp(x)^3+(4*x^3-212*x^2+960*
x)*exp(x)^2)*log(2*x)^2+((4*x^3-20*x^2)*exp(x)^4+(48*x^2-240*x)*exp(x)^3)*log(2*x)+(-4*x^2+20*x)*exp(x)^4)/log
(2*x)^5/exp(((x^2-32*x+256)*log(2*x)^4+(16*x-256)*exp(x)*log(2*x)^3+(-2*x+96)*exp(x)^2*log(2*x)^2-16*exp(x)^3*
log(2*x)+exp(x)^4)/log(2*x)^4),x, algorithm="giac")

[Out]

undef

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{-\frac {e^{4 x}-16 e^{3 x} \log (2 x)+e^{2 x} (96-2 x) \log ^2(2 x)+e^x (-256+16 x) \log ^3(2 x)+\left (256-32 x+x^2\right ) \log ^4(2 x)}{\log ^4(2 x)}} \left (e^{4 x} \left (20 x-4 x^2\right )+\left (e^{3 x} \left (-240 x+48 x^2\right )+e^{4 x} \left (-20 x^2+4 x^3\right )\right ) \log (2 x)+\left (e^{3 x} \left (240 x^2-48 x^3\right )+e^{2 x} \left (960 x-212 x^2+4 x^3\right )\right ) \log ^2(2 x)+\left (e^x \left (-1280 x+336 x^2-16 x^3\right )+e^{2 x} \left (-950 x^2+210 x^3-4 x^4\right )\right ) \log ^3(2 x)+e^x \left (1200 x^2-320 x^3+16 x^4\right ) \log ^4(2 x)+\left (10 x+157 x^2-42 x^3+2 x^4\right ) \log ^5(2 x)\right )}{\log ^5(2 x)} \, dx=\int \frac {{\mathrm {e}}^{-\frac {\left (x^2-32\,x+256\right )\,{\ln \left (2\,x\right )}^4+{\mathrm {e}}^x\,\left (16\,x-256\right )\,{\ln \left (2\,x\right )}^3-{\mathrm {e}}^{2\,x}\,\left (2\,x-96\right )\,{\ln \left (2\,x\right )}^2-16\,{\mathrm {e}}^{3\,x}\,\ln \left (2\,x\right )+{\mathrm {e}}^{4\,x}}{{\ln \left (2\,x\right )}^4}}\,\left (\left (2\,x^4-42\,x^3+157\,x^2+10\,x\right )\,{\ln \left (2\,x\right )}^5+{\mathrm {e}}^x\,\left (16\,x^4-320\,x^3+1200\,x^2\right )\,{\ln \left (2\,x\right )}^4+\left (-{\mathrm {e}}^{2\,x}\,\left (4\,x^4-210\,x^3+950\,x^2\right )-{\mathrm {e}}^x\,\left (16\,x^3-336\,x^2+1280\,x\right )\right )\,{\ln \left (2\,x\right )}^3+\left ({\mathrm {e}}^{2\,x}\,\left (4\,x^3-212\,x^2+960\,x\right )+{\mathrm {e}}^{3\,x}\,\left (240\,x^2-48\,x^3\right )\right )\,{\ln \left (2\,x\right )}^2+\left (-{\mathrm {e}}^{3\,x}\,\left (240\,x-48\,x^2\right )-{\mathrm {e}}^{4\,x}\,\left (20\,x^2-4\,x^3\right )\right )\,\ln \left (2\,x\right )+{\mathrm {e}}^{4\,x}\,\left (20\,x-4\,x^2\right )\right )}{{\ln \left (2\,x\right )}^5} \,d x \]

[In]

int((exp(-(exp(4*x) + log(2*x)^4*(x^2 - 32*x + 256) - 16*log(2*x)*exp(3*x) + log(2*x)^3*exp(x)*(16*x - 256) -
log(2*x)^2*exp(2*x)*(2*x - 96))/log(2*x)^4)*(exp(4*x)*(20*x - 4*x^2) + log(2*x)^2*(exp(2*x)*(960*x - 212*x^2 +
4*x^3) + exp(3*x)*(240*x^2 - 48*x^3)) - log(2*x)*(exp(3*x)*(240*x - 48*x^2) + exp(4*x)*(20*x^2 - 4*x^3)) + lo
g(2*x)^5*(10*x + 157*x^2 - 42*x^3 + 2*x^4) - log(2*x)^3*(exp(2*x)*(950*x^2 - 210*x^3 + 4*x^4) + exp(x)*(1280*x
- 336*x^2 + 16*x^3)) + log(2*x)^4*exp(x)*(1200*x^2 - 320*x^3 + 16*x^4)))/log(2*x)^5,x)

[Out]

int((exp(-(exp(4*x) + log(2*x)^4*(x^2 - 32*x + 256) - 16*log(2*x)*exp(3*x) + log(2*x)^3*exp(x)*(16*x - 256) -
log(2*x)^2*exp(2*x)*(2*x - 96))/log(2*x)^4)*(exp(4*x)*(20*x - 4*x^2) + log(2*x)^2*(exp(2*x)*(960*x - 212*x^2 +
4*x^3) + exp(3*x)*(240*x^2 - 48*x^3)) - log(2*x)*(exp(3*x)*(240*x - 48*x^2) + exp(4*x)*(20*x^2 - 4*x^3)) + lo
g(2*x)^5*(10*x + 157*x^2 - 42*x^3 + 2*x^4) - log(2*x)^3*(exp(2*x)*(950*x^2 - 210*x^3 + 4*x^4) + exp(x)*(1280*x
- 336*x^2 + 16*x^3)) + log(2*x)^4*exp(x)*(1200*x^2 - 320*x^3 + 16*x^4)))/log(2*x)^5, x)