\(\int e^{100 x^2-40 x \log (4)+4 \log ^2(4)+4 (-10 x^3-20 x^4-10 x^5+(2 x^2+4 x^3+2 x^4) \log (4)) \log (x)+4 (x^4+4 x^5+6 x^6+4 x^7+x^8) \log ^2(x)} (200 x-40 x^2-80 x^3-40 x^4+(-40+8 x+16 x^2+8 x^3) \log (4)+(-120 x^2-312 x^3-168 x^4+48 x^5+32 x^6+8 x^7+(16 x+48 x^2+32 x^3) \log (4)) \log (x)+(16 x^3+80 x^4+144 x^5+112 x^6+32 x^7) \log ^2(x)) \, dx\) [4251]

Optimal result

Integrand size = 206, antiderivative size = 22 \[ \int e^{100 x^2-40 x \log (4)+4 \log ^2(4)+4 \left (-10 x^3-20 x^4-10 x^5+\left (2 x^2+4 x^3+2 x^4\right ) \log (4)\right ) \log (x)+4 \left (x^4+4 x^5+6 x^6+4 x^7+x^8\right ) \log ^2(x)} \left (200 x-40 x^2-80 x^3-40 x^4+\left (-40+8 x+16 x^2+8 x^3\right ) \log (4)+\left (-120 x^2-312 x^3-168 x^4+48 x^5+32 x^6+8 x^7+\left (16 x+48 x^2+32 x^3\right ) \log (4)\right ) \log (x)+\left (16 x^3+80 x^4+144 x^5+112 x^6+32 x^7\right ) \log ^2(x)\right ) \, dx=e^{4 \left (-5 x+\log (4)+\left (x+x^2\right )^2 \log (x)\right )^2} \]

[Out]

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

Rubi [F]

\[ \int e^{100 x^2-40 x \log (4)+4 \log ^2(4)+4 \left (-10 x^3-20 x^4-10 x^5+\left (2 x^2+4 x^3+2 x^4\right ) \log (4)\right ) \log (x)+4 \left (x^4+4 x^5+6 x^6+4 x^7+x^8\right ) \log ^2(x)} \left (200 x-40 x^2-80 x^3-40 x^4+\left (-40+8 x+16 x^2+8 x^3\right ) \log (4)+\left (-120 x^2-312 x^3-168 x^4+48 x^5+32 x^6+8 x^7+\left (16 x+48 x^2+32 x^3\right ) \log (4)\right ) \log (x)+\left (16 x^3+80 x^4+144 x^5+112 x^6+32 x^7\right ) \log ^2(x)\right ) \, dx=\int \exp \left (100 x^2-40 x \log (4)+4 \log ^2(4)+4 \left (-10 x^3-20 x^4-10 x^5+\left (2 x^2+4 x^3+2 x^4\right ) \log (4)\right ) \log (x)+4 \left (x^4+4 x^5+6 x^6+4 x^7+x^8\right ) \log ^2(x)\right ) \left (200 x-40 x^2-80 x^3-40 x^4+\left (-40+8 x+16 x^2+8 x^3\right ) \log (4)+\left (-120 x^2-312 x^3-168 x^4+48 x^5+32 x^6+8 x^7+\left (16 x+48 x^2+32 x^3\right ) \log (4)\right ) \log (x)+\left (16 x^3+80 x^4+144 x^5+112 x^6+32 x^7\right ) \log ^2(x)\right ) \, dx \]

[In]

Int[E^(100*x^2 - 40*x*Log[4] + 4*Log[4]^2 + 4*(-10*x^3 - 20*x^4 - 10*x^5 + (2*x^2 + 4*x^3 + 2*x^4)*Log[4])*Log
[x] + 4*(x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8)*Log[x]^2)*(200*x - 40*x^2 - 80*x^3 - 40*x^4 + (-40 + 8*x + 16*x^2
+ 8*x^3)*Log[4] + (-120*x^2 - 312*x^3 - 168*x^4 + 48*x^5 + 32*x^6 + 8*x^7 + (16*x + 48*x^2 + 32*x^3)*Log[4])*L
og[x] + (16*x^3 + 80*x^4 + 144*x^5 + 112*x^6 + 32*x^7)*Log[x]^2),x]

[Out]

(25 + Log[4])*Defer[Int][2^(3 - 80*x)*E^(4*(25*x^2 + Log[4]^2 + x^4*(1 + x)^4*Log[x]^2))*x^(1 - 8*x^2*(1 + x)^
2*(5*x - Log[4])), x] - (5 - Log[16])*Defer[Int][2^(3 - 80*x)*E^(4*(25*x^2 + Log[4]^2 + x^4*(1 + x)^4*Log[x]^2
))*x^(2 - 8*x^2*(1 + x)^2*(5*x - Log[4])), x] - (10 - Log[4])*Defer[Int][2^(3 - 80*x)*E^(4*(25*x^2 + Log[4]^2
+ x^4*(1 + x)^4*Log[x]^2))*x^(3 - 8*x^2*(1 + x)^2*(5*x - Log[4])), x] - 5*Defer[Int][2^(3 - 80*x)*E^(4*(25*x^2
+ Log[4]^2 + x^4*(1 + x)^4*Log[x]^2))*x^(4 - 8*x^2*(1 + x)^2*(5*x - Log[4])), x] - 5*Log[4]*Defer[Int][(2^(3
- 80*x)*E^(4*(25*x^2 + Log[4]^2 + x^4*(1 + x)^4*Log[x]^2)))/x^(8*x^2*(1 + x)^2*(5*x - Log[4])), x] + Log[16]*D
efer[Int][2^(3 - 80*x)*E^(4*(25*x^2 + Log[4]^2 + x^4*(1 + x)^4*Log[x]^2))*x^(1 - 8*x^2*(1 + x)^2*(5*x - Log[4]
))*Log[x], x] - (15 - Log[4096])*Defer[Int][2^(3 - 80*x)*E^(4*(25*x^2 + Log[4]^2 + x^4*(1 + x)^4*Log[x]^2))*x^
(2 - 8*x^2*(1 + x)^2*(5*x - Log[4]))*Log[x], x] - (39 - Log[256])*Defer[Int][2^(3 - 80*x)*E^(4*(25*x^2 + Log[4
]^2 + x^4*(1 + x)^4*Log[x]^2))*x^(3 - 8*x^2*(1 + x)^2*(5*x - Log[4]))*Log[x], x] - 21*Defer[Int][2^(3 - 80*x)*
E^(4*(25*x^2 + Log[4]^2 + x^4*(1 + x)^4*Log[x]^2))*x^(4 - 8*x^2*(1 + x)^2*(5*x - Log[4]))*Log[x], x] + 3*Defer
[Int][2^(4 - 80*x)*E^(4*(25*x^2 + Log[4]^2 + x^4*(1 + x)^4*Log[x]^2))*x^(5 - 8*x^2*(1 + x)^2*(5*x - Log[4]))*L
og[x], x] + Defer[Int][2^(5 - 80*x)*E^(4*(25*x^2 + Log[4]^2 + x^4*(1 + x)^4*Log[x]^2))*x^(6 - 8*x^2*(1 + x)^2*
(5*x - Log[4]))*Log[x], x] + Defer[Int][2^(3 - 80*x)*E^(4*(25*x^2 + Log[4]^2 + x^4*(1 + x)^4*Log[x]^2))*x^(7 -
8*x^2*(1 + x)^2*(5*x - Log[4]))*Log[x], x] + Defer[Int][2^(4 - 80*x)*E^(4*(25*x^2 + Log[4]^2 + x^4*(1 + x)^4*
Log[x]^2))*x^(3 - 8*x^2*(1 + x)^2*(5*x - Log[4]))*Log[x]^2, x] + 5*Defer[Int][2^(4 - 80*x)*E^(4*(25*x^2 + Log[
4]^2 + x^4*(1 + x)^4*Log[x]^2))*x^(4 - 8*x^2*(1 + x)^2*(5*x - Log[4]))*Log[x]^2, x] + 9*Defer[Int][2^(4 - 80*x
)*E^(4*(25*x^2 + Log[4]^2 + x^4*(1 + x)^4*Log[x]^2))*x^(5 - 8*x^2*(1 + x)^2*(5*x - Log[4]))*Log[x]^2, x] + 7*D
efer[Int][2^(4 - 80*x)*E^(4*(25*x^2 + Log[4]^2 + x^4*(1 + x)^4*Log[x]^2))*x^(6 - 8*x^2*(1 + x)^2*(5*x - Log[4]
))*Log[x]^2, x] + Defer[Int][2^(5 - 80*x)*E^(4*(25*x^2 + Log[4]^2 + x^4*(1 + x)^4*Log[x]^2))*x^(7 - 8*x^2*(1 +
x)^2*(5*x - Log[4]))*Log[x]^2, x]

Rubi steps \begin{align*} \text {integral}& = \int 2^{3-80 x} \exp \left (4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )\right ) x^{-8 x^2 (1+x)^2 (5 x-\log (4))} \left (5 x-\log (4)-x^2 (1+x)^2 \log (x)\right ) \left (5-x-2 x^2-x^3-2 x \left (1+3 x+2 x^2\right ) \log (x)\right ) \, dx \\ & = \int \left (-2^{3-80 x} \exp \left (4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )\right ) x^{-8 x^2 (1+x)^2 (5 x-\log (4))} \left (-5+x+2 x^2+x^3\right ) (5 x-\log (4))+2^{3-80 x} \exp \left (4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )\right ) x^{1-8 x^2 (1+x)^2 (5 x-\log (4))} (1+x) \left (-24 x^2+3 x^3+3 x^4+x^5-15 x \left (1-\frac {8 \log (2)}{15}\right )+\log (16)\right ) \log (x)+2^{4-80 x} \exp \left (4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )\right ) x^{3-8 x^2 (1+x)^2 (5 x-\log (4))} (1+x)^3 (1+2 x) \log ^2(x)\right ) \, dx \\ & = -\int 2^{3-80 x} \exp \left (4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )\right ) x^{-8 x^2 (1+x)^2 (5 x-\log (4))} \left (-5+x+2 x^2+x^3\right ) (5 x-\log (4)) \, dx+\int 2^{3-80 x} \exp \left (4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )\right ) x^{1-8 x^2 (1+x)^2 (5 x-\log (4))} (1+x) \left (-24 x^2+3 x^3+3 x^4+x^5-15 x \left (1-\frac {8 \log (2)}{15}\right )+\log (16)\right ) \log (x) \, dx+\int 2^{4-80 x} \exp \left (4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )\right ) x^{3-8 x^2 (1+x)^2 (5 x-\log (4))} (1+x)^3 (1+2 x) \log ^2(x) \, dx \\ & = -\int \left (5\ 2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{4-8 x^2 (1+x)^2 (5 x-\log (4))}+2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{2-8 x^2 (1+x)^2 (5 x-\log (4))} (5-2 \log (4))+2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{3-8 x^2 (1+x)^2 (5 x-\log (4))} (10-\log (4))+5\ 2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{-8 x^2 (1+x)^2 (5 x-\log (4))} \log (4)-2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{1-8 x^2 (1+x)^2 (5 x-\log (4))} (25+\log (4))\right ) \, dx+\int \left (-21 2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{4-8 x^2 (1+x)^2 (5 x-\log (4))} \log (x)+3\ 2^{4-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{5-8 x^2 (1+x)^2 (5 x-\log (4))} \log (x)+2^{5-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{6-8 x^2 (1+x)^2 (5 x-\log (4))} \log (x)+2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{7-8 x^2 (1+x)^2 (5 x-\log (4))} \log (x)+2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{1-8 x^2 (1+x)^2 (5 x-\log (4))} \log (16) \log (x)+2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{3-8 x^2 (1+x)^2 (5 x-\log (4))} (-39+\log (256)) \log (x)+2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{2-8 x^2 (1+x)^2 (5 x-\log (4))} (-15+\log (4096)) \log (x)\right ) \, dx+\int \left (2^{4-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{3-8 x^2 (1+x)^2 (5 x-\log (4))} \log ^2(x)+5\ 2^{4-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{4-8 x^2 (1+x)^2 (5 x-\log (4))} \log ^2(x)+9\ 2^{4-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{5-8 x^2 (1+x)^2 (5 x-\log (4))} \log ^2(x)+7\ 2^{4-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{6-8 x^2 (1+x)^2 (5 x-\log (4))} \log ^2(x)+2^{5-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{7-8 x^2 (1+x)^2 (5 x-\log (4))} \log ^2(x)\right ) \, dx \\ & = 3 \int 2^{4-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{5-8 x^2 (1+x)^2 (5 x-\log (4))} \log (x) \, dx-5 \int 2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{4-8 x^2 (1+x)^2 (5 x-\log (4))} \, dx+5 \int 2^{4-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{4-8 x^2 (1+x)^2 (5 x-\log (4))} \log ^2(x) \, dx+7 \int 2^{4-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{6-8 x^2 (1+x)^2 (5 x-\log (4))} \log ^2(x) \, dx+9 \int 2^{4-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{5-8 x^2 (1+x)^2 (5 x-\log (4))} \log ^2(x) \, dx-21 \int 2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{4-8 x^2 (1+x)^2 (5 x-\log (4))} \log (x) \, dx-(5-2 \log (4)) \int 2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{2-8 x^2 (1+x)^2 (5 x-\log (4))} \, dx-(-25-\log (4)) \int 2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{1-8 x^2 (1+x)^2 (5 x-\log (4))} \, dx-(10-\log (4)) \int 2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{3-8 x^2 (1+x)^2 (5 x-\log (4))} \, dx-(5 \log (4)) \int 2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{-8 x^2 (1+x)^2 (5 x-\log (4))} \, dx+\log (16) \int 2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{1-8 x^2 (1+x)^2 (5 x-\log (4))} \log (x) \, dx+(-39+\log (256)) \int 2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{3-8 x^2 (1+x)^2 (5 x-\log (4))} \log (x) \, dx+(-15+\log (4096)) \int 2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{2-8 x^2 (1+x)^2 (5 x-\log (4))} \log (x) \, dx+\int 2^{5-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{6-8 x^2 (1+x)^2 (5 x-\log (4))} \log (x) \, dx+\int 2^{3-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{7-8 x^2 (1+x)^2 (5 x-\log (4))} \log (x) \, dx+\int 2^{4-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{3-8 x^2 (1+x)^2 (5 x-\log (4))} \log ^2(x) \, dx+\int 2^{5-80 x} e^{4 \left (25 x^2+\log ^2(4)+x^4 (1+x)^4 \log ^2(x)\right )} x^{7-8 x^2 (1+x)^2 (5 x-\log (4))} \log ^2(x) \, dx \\ \end{align*}

Mathematica [F]

\[ \int e^{100 x^2-40 x \log (4)+4 \log ^2(4)+4 \left (-10 x^3-20 x^4-10 x^5+\left (2 x^2+4 x^3+2 x^4\right ) \log (4)\right ) \log (x)+4 \left (x^4+4 x^5+6 x^6+4 x^7+x^8\right ) \log ^2(x)} \left (200 x-40 x^2-80 x^3-40 x^4+\left (-40+8 x+16 x^2+8 x^3\right ) \log (4)+\left (-120 x^2-312 x^3-168 x^4+48 x^5+32 x^6+8 x^7+\left (16 x+48 x^2+32 x^3\right ) \log (4)\right ) \log (x)+\left (16 x^3+80 x^4+144 x^5+112 x^6+32 x^7\right ) \log ^2(x)\right ) \, dx=\int e^{100 x^2-40 x \log (4)+4 \log ^2(4)+4 \left (-10 x^3-20 x^4-10 x^5+\left (2 x^2+4 x^3+2 x^4\right ) \log (4)\right ) \log (x)+4 \left (x^4+4 x^5+6 x^6+4 x^7+x^8\right ) \log ^2(x)} \left (200 x-40 x^2-80 x^3-40 x^4+\left (-40+8 x+16 x^2+8 x^3\right ) \log (4)+\left (-120 x^2-312 x^3-168 x^4+48 x^5+32 x^6+8 x^7+\left (16 x+48 x^2+32 x^3\right ) \log (4)\right ) \log (x)+\left (16 x^3+80 x^4+144 x^5+112 x^6+32 x^7\right ) \log ^2(x)\right ) \, dx \]

[In]

Integrate[E^(100*x^2 - 40*x*Log[4] + 4*Log[4]^2 + 4*(-10*x^3 - 20*x^4 - 10*x^5 + (2*x^2 + 4*x^3 + 2*x^4)*Log[4
])*Log[x] + 4*(x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8)*Log[x]^2)*(200*x - 40*x^2 - 80*x^3 - 40*x^4 + (-40 + 8*x + 1
6*x^2 + 8*x^3)*Log[4] + (-120*x^2 - 312*x^3 - 168*x^4 + 48*x^5 + 32*x^6 + 8*x^7 + (16*x + 48*x^2 + 32*x^3)*Log
[4])*Log[x] + (16*x^3 + 80*x^4 + 144*x^5 + 112*x^6 + 32*x^7)*Log[x]^2),x]

[Out]

Integrate[E^(100*x^2 - 40*x*Log[4] + 4*Log[4]^2 + 4*(-10*x^3 - 20*x^4 - 10*x^5 + (2*x^2 + 4*x^3 + 2*x^4)*Log[4
])*Log[x] + 4*(x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8)*Log[x]^2)*(200*x - 40*x^2 - 80*x^3 - 40*x^4 + (-40 + 8*x + 1
6*x^2 + 8*x^3)*Log[4] + (-120*x^2 - 312*x^3 - 168*x^4 + 48*x^5 + 32*x^6 + 8*x^7 + (16*x + 48*x^2 + 32*x^3)*Log
[4])*Log[x] + (16*x^3 + 80*x^4 + 144*x^5 + 112*x^6 + 32*x^7)*Log[x]^2), x]

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(86\) vs. \(2(23)=46\).

Time = 42.80 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.95

method	result	size
risch	\(1048576^{-4 x} x^{8 x^{2} \left (1+x \right )^{2} \left (2 \ln \left (2\right )-5 x \right )} {\mathrm e}^{4 x^{8} \ln \left (x \right )^{2}+16 x^{7} \ln \left (x \right )^{2}+24 x^{6} \ln \left (x \right )^{2}+16 x^{5} \ln \left (x \right )^{2}+4 x^{4} \ln \left (x \right )^{2}+16 \ln \left (2\right )^{2}+100 x^{2}}\)	\(87\)
parallelrisch	\({\mathrm e}^{4 \left (x^{8}+4 x^{7}+6 x^{6}+4 x^{5}+x^{4}\right ) \ln \left (x \right )^{2}+\left (8 \left (2 x^{4}+4 x^{3}+2 x^{2}\right ) \ln \left (2\right )-40 x^{5}-80 x^{4}-40 x^{3}\right ) \ln \left (x \right )+16 \ln \left (2\right )^{2}-80 x \ln \left (2\right )+100 x^{2}}\)	\(87\)

[In]

int(((32*x^7+112*x^6+144*x^5+80*x^4+16*x^3)*ln(x)^2+(2*(32*x^3+48*x^2+16*x)*ln(2)+8*x^7+32*x^6+48*x^5-168*x^4-
312*x^3-120*x^2)*ln(x)+2*(8*x^3+16*x^2+8*x-40)*ln(2)-40*x^4-80*x^3-40*x^2+200*x)*exp((x^8+4*x^7+6*x^6+4*x^5+x^
4)*ln(x)^2+(2*(2*x^4+4*x^3+2*x^2)*ln(2)-10*x^5-20*x^4-10*x^3)*ln(x)+4*ln(2)^2-20*x*ln(2)+25*x^2)^4,x,method=_R
ETURNVERBOSE)

[Out]

((1/1048576)^x)^4*(x^(2*x^2*(1+x)^2*(2*ln(2)-5*x)))^4*exp(4*x^8*ln(x)^2+16*x^7*ln(x)^2+24*x^6*ln(x)^2+16*x^5*l
n(x)^2+4*x^4*ln(x)^2+16*ln(2)^2+100*x^2)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (23) = 46\).

Time = 0.25 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.73 \[ \int e^{100 x^2-40 x \log (4)+4 \log ^2(4)+4 \left (-10 x^3-20 x^4-10 x^5+\left (2 x^2+4 x^3+2 x^4\right ) \log (4)\right ) \log (x)+4 \left (x^4+4 x^5+6 x^6+4 x^7+x^8\right ) \log ^2(x)} \left (200 x-40 x^2-80 x^3-40 x^4+\left (-40+8 x+16 x^2+8 x^3\right ) \log (4)+\left (-120 x^2-312 x^3-168 x^4+48 x^5+32 x^6+8 x^7+\left (16 x+48 x^2+32 x^3\right ) \log (4)\right ) \log (x)+\left (16 x^3+80 x^4+144 x^5+112 x^6+32 x^7\right ) \log ^2(x)\right ) \, dx=e^{\left (4 \, {\left (x^{8} + 4 \, x^{7} + 6 \, x^{6} + 4 \, x^{5} + x^{4}\right )} \log \left (x\right )^{2} + 100 \, x^{2} - 80 \, x \log \left (2\right ) + 16 \, \log \left (2\right )^{2} - 8 \, {\left (5 \, x^{5} + 10 \, x^{4} + 5 \, x^{3} - 2 \, {\left (x^{4} + 2 \, x^{3} + x^{2}\right )} \log \left (2\right )\right )} \log \left (x\right )\right )} \]

[In]

integrate(((32*x^7+112*x^6+144*x^5+80*x^4+16*x^3)*log(x)^2+(2*(32*x^3+48*x^2+16*x)*log(2)+8*x^7+32*x^6+48*x^5-
168*x^4-312*x^3-120*x^2)*log(x)+2*(8*x^3+16*x^2+8*x-40)*log(2)-40*x^4-80*x^3-40*x^2+200*x)*exp((x^8+4*x^7+6*x^
6+4*x^5+x^4)*log(x)^2+(2*(2*x^4+4*x^3+2*x^2)*log(2)-10*x^5-20*x^4-10*x^3)*log(x)+4*log(2)^2-20*x*log(2)+25*x^2
)^4,x, algorithm="fricas")

[Out]

e^(4*(x^8 + 4*x^7 + 6*x^6 + 4*x^5 + x^4)*log(x)^2 + 100*x^2 - 80*x*log(2) + 16*log(2)^2 - 8*(5*x^5 + 10*x^4 +
5*x^3 - 2*(x^4 + 2*x^3 + x^2)*log(2))*log(x))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (22) = 44\).

Time = 0.39 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.95 \[ \int e^{100 x^2-40 x \log (4)+4 \log ^2(4)+4 \left (-10 x^3-20 x^4-10 x^5+\left (2 x^2+4 x^3+2 x^4\right ) \log (4)\right ) \log (x)+4 \left (x^4+4 x^5+6 x^6+4 x^7+x^8\right ) \log ^2(x)} \left (200 x-40 x^2-80 x^3-40 x^4+\left (-40+8 x+16 x^2+8 x^3\right ) \log (4)+\left (-120 x^2-312 x^3-168 x^4+48 x^5+32 x^6+8 x^7+\left (16 x+48 x^2+32 x^3\right ) \log (4)\right ) \log (x)+\left (16 x^3+80 x^4+144 x^5+112 x^6+32 x^7\right ) \log ^2(x)\right ) \, dx=e^{100 x^{2} - 80 x \log {\left (2 \right )} + 4 \left (- 10 x^{5} - 20 x^{4} - 10 x^{3} + \left (4 x^{4} + 8 x^{3} + 4 x^{2}\right ) \log {\left (2 \right )}\right ) \log {\left (x \right )} + 4 \left (x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + x^{4}\right ) \log {\left (x \right )}^{2} + 16 \log {\left (2 \right )}^{2}} \]

[In]

integrate(((32*x**7+112*x**6+144*x**5+80*x**4+16*x**3)*ln(x)**2+(2*(32*x**3+48*x**2+16*x)*ln(2)+8*x**7+32*x**6
+48*x**5-168*x**4-312*x**3-120*x**2)*ln(x)+2*(8*x**3+16*x**2+8*x-40)*ln(2)-40*x**4-80*x**3-40*x**2+200*x)*exp(
(x**8+4*x**7+6*x**6+4*x**5+x**4)*ln(x)**2+(2*(2*x**4+4*x**3+2*x**2)*ln(2)-10*x**5-20*x**4-10*x**3)*ln(x)+4*ln(
2)**2-20*x*ln(2)+25*x**2)**4,x)

[Out]

exp(100*x**2 - 80*x*log(2) + 4*(-10*x**5 - 20*x**4 - 10*x**3 + (4*x**4 + 8*x**3 + 4*x**2)*log(2))*log(x) + 4*(
x**8 + 4*x**7 + 6*x**6 + 4*x**5 + x**4)*log(x)**2 + 16*log(2)**2)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 111 vs. \(2 (23) = 46\).

Time = 0.60 (sec) , antiderivative size = 111, normalized size of antiderivative = 5.05 \[ \int e^{100 x^2-40 x \log (4)+4 \log ^2(4)+4 \left (-10 x^3-20 x^4-10 x^5+\left (2 x^2+4 x^3+2 x^4\right ) \log (4)\right ) \log (x)+4 \left (x^4+4 x^5+6 x^6+4 x^7+x^8\right ) \log ^2(x)} \left (200 x-40 x^2-80 x^3-40 x^4+\left (-40+8 x+16 x^2+8 x^3\right ) \log (4)+\left (-120 x^2-312 x^3-168 x^4+48 x^5+32 x^6+8 x^7+\left (16 x+48 x^2+32 x^3\right ) \log (4)\right ) \log (x)+\left (16 x^3+80 x^4+144 x^5+112 x^6+32 x^7\right ) \log ^2(x)\right ) \, dx=e^{\left (4 \, x^{8} \log \left (x\right )^{2} + 16 \, x^{7} \log \left (x\right )^{2} + 24 \, x^{6} \log \left (x\right )^{2} + 16 \, x^{5} \log \left (x\right )^{2} - 40 \, x^{5} \log \left (x\right ) + 16 \, x^{4} \log \left (2\right ) \log \left (x\right ) + 4 \, x^{4} \log \left (x\right )^{2} - 80 \, x^{4} \log \left (x\right ) + 32 \, x^{3} \log \left (2\right ) \log \left (x\right ) - 40 \, x^{3} \log \left (x\right ) + 16 \, x^{2} \log \left (2\right ) \log \left (x\right ) + 100 \, x^{2} - 80 \, x \log \left (2\right ) + 16 \, \log \left (2\right )^{2}\right )} \]

[In]

integrate(((32*x^7+112*x^6+144*x^5+80*x^4+16*x^3)*log(x)^2+(2*(32*x^3+48*x^2+16*x)*log(2)+8*x^7+32*x^6+48*x^5-
168*x^4-312*x^3-120*x^2)*log(x)+2*(8*x^3+16*x^2+8*x-40)*log(2)-40*x^4-80*x^3-40*x^2+200*x)*exp((x^8+4*x^7+6*x^
6+4*x^5+x^4)*log(x)^2+(2*(2*x^4+4*x^3+2*x^2)*log(2)-10*x^5-20*x^4-10*x^3)*log(x)+4*log(2)^2-20*x*log(2)+25*x^2
)^4,x, algorithm="maxima")

[Out]

e^(4*x^8*log(x)^2 + 16*x^7*log(x)^2 + 24*x^6*log(x)^2 + 16*x^5*log(x)^2 - 40*x^5*log(x) + 16*x^4*log(2)*log(x)
+ 4*x^4*log(x)^2 - 80*x^4*log(x) + 32*x^3*log(2)*log(x) - 40*x^3*log(x) + 16*x^2*log(2)*log(x) + 100*x^2 - 80
*x*log(2) + 16*log(2)^2)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 111 vs. \(2 (23) = 46\).

Time = 0.38 (sec) , antiderivative size = 111, normalized size of antiderivative = 5.05 \[ \int e^{100 x^2-40 x \log (4)+4 \log ^2(4)+4 \left (-10 x^3-20 x^4-10 x^5+\left (2 x^2+4 x^3+2 x^4\right ) \log (4)\right ) \log (x)+4 \left (x^4+4 x^5+6 x^6+4 x^7+x^8\right ) \log ^2(x)} \left (200 x-40 x^2-80 x^3-40 x^4+\left (-40+8 x+16 x^2+8 x^3\right ) \log (4)+\left (-120 x^2-312 x^3-168 x^4+48 x^5+32 x^6+8 x^7+\left (16 x+48 x^2+32 x^3\right ) \log (4)\right ) \log (x)+\left (16 x^3+80 x^4+144 x^5+112 x^6+32 x^7\right ) \log ^2(x)\right ) \, dx=e^{\left (4 \, x^{8} \log \left (x\right )^{2} + 16 \, x^{7} \log \left (x\right )^{2} + 24 \, x^{6} \log \left (x\right )^{2} + 16 \, x^{5} \log \left (x\right )^{2} - 40 \, x^{5} \log \left (x\right ) + 16 \, x^{4} \log \left (2\right ) \log \left (x\right ) + 4 \, x^{4} \log \left (x\right )^{2} - 80 \, x^{4} \log \left (x\right ) + 32 \, x^{3} \log \left (2\right ) \log \left (x\right ) - 40 \, x^{3} \log \left (x\right ) + 16 \, x^{2} \log \left (2\right ) \log \left (x\right ) + 100 \, x^{2} - 80 \, x \log \left (2\right ) + 16 \, \log \left (2\right )^{2}\right )} \]

[In]

integrate(((32*x^7+112*x^6+144*x^5+80*x^4+16*x^3)*log(x)^2+(2*(32*x^3+48*x^2+16*x)*log(2)+8*x^7+32*x^6+48*x^5-
168*x^4-312*x^3-120*x^2)*log(x)+2*(8*x^3+16*x^2+8*x-40)*log(2)-40*x^4-80*x^3-40*x^2+200*x)*exp((x^8+4*x^7+6*x^
6+4*x^5+x^4)*log(x)^2+(2*(2*x^4+4*x^3+2*x^2)*log(2)-10*x^5-20*x^4-10*x^3)*log(x)+4*log(2)^2-20*x*log(2)+25*x^2
)^4,x, algorithm="giac")

[Out]

e^(4*x^8*log(x)^2 + 16*x^7*log(x)^2 + 24*x^6*log(x)^2 + 16*x^5*log(x)^2 - 40*x^5*log(x) + 16*x^4*log(2)*log(x)
+ 4*x^4*log(x)^2 - 80*x^4*log(x) + 32*x^3*log(2)*log(x) - 40*x^3*log(x) + 16*x^2*log(2)*log(x) + 100*x^2 - 80
*x*log(2) + 16*log(2)^2)

Mupad [F(-1)]

Timed out. \[ \int e^{100 x^2-40 x \log (4)+4 \log ^2(4)+4 \left (-10 x^3-20 x^4-10 x^5+\left (2 x^2+4 x^3+2 x^4\right ) \log (4)\right ) \log (x)+4 \left (x^4+4 x^5+6 x^6+4 x^7+x^8\right ) \log ^2(x)} \left (200 x-40 x^2-80 x^3-40 x^4+\left (-40+8 x+16 x^2+8 x^3\right ) \log (4)+\left (-120 x^2-312 x^3-168 x^4+48 x^5+32 x^6+8 x^7+\left (16 x+48 x^2+32 x^3\right ) \log (4)\right ) \log (x)+\left (16 x^3+80 x^4+144 x^5+112 x^6+32 x^7\right ) \log ^2(x)\right ) \, dx=\int {\mathrm {e}}^{4\,{\ln \left (x\right )}^2\,\left (x^8+4\,x^7+6\,x^6+4\,x^5+x^4\right )-80\,x\,\ln \left (2\right )-4\,\ln \left (x\right )\,\left (10\,x^3-2\,\ln \left (2\right )\,\left (2\,x^4+4\,x^3+2\,x^2\right )+20\,x^4+10\,x^5\right )+16\,{\ln \left (2\right )}^2+100\,x^2}\,\left (200\,x+{\ln \left (x\right )}^2\,\left (32\,x^7+112\,x^6+144\,x^5+80\,x^4+16\,x^3\right )+\ln \left (x\right )\,\left (2\,\ln \left (2\right )\,\left (32\,x^3+48\,x^2+16\,x\right )-120\,x^2-312\,x^3-168\,x^4+48\,x^5+32\,x^6+8\,x^7\right )+2\,\ln \left (2\right )\,\left (8\,x^3+16\,x^2+8\,x-40\right )-40\,x^2-80\,x^3-40\,x^4\right ) \,d x \]

[In]

int(exp(4*log(x)^2*(x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8) - 80*x*log(2) - 4*log(x)*(10*x^3 - 2*log(2)*(2*x^2 + 4*
x^3 + 2*x^4) + 20*x^4 + 10*x^5) + 16*log(2)^2 + 100*x^2)*(200*x + log(x)^2*(16*x^3 + 80*x^4 + 144*x^5 + 112*x^
6 + 32*x^7) + log(x)*(2*log(2)*(16*x + 48*x^2 + 32*x^3) - 120*x^2 - 312*x^3 - 168*x^4 + 48*x^5 + 32*x^6 + 8*x^
7) + 2*log(2)*(8*x + 16*x^2 + 8*x^3 - 40) - 40*x^2 - 80*x^3 - 40*x^4),x)

[Out]

int(exp(4*log(x)^2*(x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8) - 80*x*log(2) - 4*log(x)*(10*x^3 - 2*log(2)*(2*x^2 + 4*
x^3 + 2*x^4) + 20*x^4 + 10*x^5) + 16*log(2)^2 + 100*x^2)*(200*x + log(x)^2*(16*x^3 + 80*x^4 + 144*x^5 + 112*x^
6 + 32*x^7) + log(x)*(2*log(2)*(16*x + 48*x^2 + 32*x^3) - 120*x^2 - 312*x^3 - 168*x^4 + 48*x^5 + 32*x^6 + 8*x^
7) + 2*log(2)*(8*x + 16*x^2 + 8*x^3 - 40) - 40*x^2 - 80*x^3 - 40*x^4), x)