\(\int \frac {e^{1+(4+e^x (-10+2 x)) \log (\frac {3 x}{2})+(4+e^x (-20+4 x)+e^{2 x} (25-10 x+x^2)) \log ^2(\frac {3 x}{2})} (4+e^x (-10+2 x)+(8+e^x (-40+2 x^2)+e^{2 x} (50-20 x+2 x^2)) \log (\frac {3 x}{2})+(e^x (-16 x+4 x^2)+e^{2 x} (40 x-18 x^2+2 x^3)) \log ^2(\frac {3 x}{2}))}{x} \, dx\) [8057]

Optimal result

Integrand size = 150, antiderivative size = 28 \[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=e^5+e^{\left (-1+\left (-2+e^x (5-x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2} \]

[Out]

exp((-1+((5-x)*exp(x)-2)*ln(3/2*x))^2)+exp(5)

Rubi [F]

\[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=\int \frac {\exp \left (1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right ) \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx \]

[In]

Int[(E^(1 + (4 + E^x*(-10 + 2*x))*Log[(3*x)/2] + (4 + E^x*(-20 + 4*x) + E^(2*x)*(25 - 10*x + x^2))*Log[(3*x)/2
]^2)*(4 + E^x*(-10 + 2*x) + (8 + E^x*(-40 + 2*x^2) + E^(2*x)*(50 - 20*x + 2*x^2))*Log[(3*x)/2] + (E^x*(-16*x +
4*x^2) + E^(2*x)*(40*x - 18*x^2 + 2*x^3))*Log[(3*x)/2]^2))/x,x]

[Out]

4*Defer[Int][E^(1 + (2 + E^x*(-5 + x))*Log[(3*x)/2])^2/x, x] - 10*Defer[Int][E^(x + (1 + (2 + E^x*(-5 + x))*Lo
g[(3*x)/2])^2)/x, x] + 8*Defer[Int][(E^(1 + (2 + E^x*(-5 + x))*Log[(3*x)/2])^2*Log[(3*x)/2])/x, x] - 40*Defer[
Int][(E^(x + (1 + (2 + E^x*(-5 + x))*Log[(3*x)/2])^2)*Log[(3*x)/2])/x, x] + 50*Defer[Int][(E^(2*x + (1 + (2 +
E^x*(-5 + x))*Log[(3*x)/2])^2)*Log[(3*x)/2])/x, x] + 2*Defer[Int][E^(x + (1 + (2 + E^x*(-5 + x))*Log[(3*x)/2])
^2)*x*Log[(3*x)/2], x] + 2*Defer[Int][E^(2*x + (1 + (2 + E^x*(-5 + x))*Log[(3*x)/2])^2)*x*Log[(3*x)/2], x] + 4
*Defer[Subst][Defer[Int][E^(2*x + (1 + (2 + E^(2*x)*(-5 + 2*x))*Log[3*x])^2), x], x, x/2] - 40*Defer[Subst][De
fer[Int][E^(4*x + (1 + (2 + E^(2*x)*(-5 + 2*x))*Log[3*x])^2)*Log[3*x], x], x, x/2] - 32*Defer[Subst][Defer[Int
][E^(2*x + (1 + (2 + E^(2*x)*(-5 + 2*x))*Log[3*x])^2)*Log[3*x]^2, x], x, x/2] + 80*Defer[Subst][Defer[Int][E^(
4*x + (1 + (2 + E^(2*x)*(-5 + 2*x))*Log[3*x])^2)*Log[3*x]^2, x], x, x/2] + 16*Defer[Subst][Defer[Int][E^(2*x +
(1 + (2 + E^(2*x)*(-5 + 2*x))*Log[3*x])^2)*x*Log[3*x]^2, x], x, x/2] - 72*Defer[Subst][Defer[Int][E^(4*x + (1
+ (2 + E^(2*x)*(-5 + 2*x))*Log[3*x])^2)*x*Log[3*x]^2, x], x, x/2] + 16*Defer[Subst][Defer[Int][E^(4*x + (1 +
(2 + E^(2*x)*(-5 + 2*x))*Log[3*x])^2)*x^2*Log[3*x]^2, x], x, x/2]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\left (1+2 \log \left (\frac {3 x}{2}\right )-5 e^x \log \left (\frac {3 x}{2}\right )+e^x x \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx \\ & = \int \frac {2 \exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (2+e^x (-5+x)+\left (4+e^{2 x} (-5+x)^2+e^x \left (-20+x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+e^x \left (2+e^x (-5+x)\right ) (-4+x) x \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx \\ & = 2 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (2+e^x (-5+x)+\left (4+e^{2 x} (-5+x)^2+e^x \left (-20+x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+e^x \left (2+e^x (-5+x)\right ) (-4+x) x \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx \\ & = 2 \int \left (\frac {2 \exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (1+2 \log \left (\frac {3 x}{2}\right )\right )}{x}+\frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-5+x) \log \left (\frac {3 x}{2}\right ) \left (-5+x-4 x \log \left (\frac {3 x}{2}\right )+x^2 \log \left (\frac {3 x}{2}\right )\right )}{x}+\frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (-5+x-20 \log \left (\frac {3 x}{2}\right )+x^2 \log \left (\frac {3 x}{2}\right )-8 x \log ^2\left (\frac {3 x}{2}\right )+2 x^2 \log ^2\left (\frac {3 x}{2}\right )\right )}{x}\right ) \, dx \\ & = 2 \int \frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-5+x) \log \left (\frac {3 x}{2}\right ) \left (-5+x-4 x \log \left (\frac {3 x}{2}\right )+x^2 \log \left (\frac {3 x}{2}\right )\right )}{x} \, dx+2 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (-5+x-20 \log \left (\frac {3 x}{2}\right )+x^2 \log \left (\frac {3 x}{2}\right )-8 x \log ^2\left (\frac {3 x}{2}\right )+2 x^2 \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx+4 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (1+2 \log \left (\frac {3 x}{2}\right )\right )}{x} \, dx \\ & = 2 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (-5+x+\left (-20+x^2\right ) \log \left (\frac {3 x}{2}\right )+2 (-4+x) x \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx+2 \int \left (\frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-5+x)^2 \log \left (\frac {3 x}{2}\right )}{x}+\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (20-9 x+x^2\right ) \log ^2\left (\frac {3 x}{2}\right )\right ) \, dx+4 \int \left (\frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x}+\frac {2 \exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x}\right ) \, dx \\ & = 2 \int \frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-5+x)^2 \log \left (\frac {3 x}{2}\right )}{x} \, dx+2 \int \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (20-9 x+x^2\right ) \log ^2\left (\frac {3 x}{2}\right ) \, dx+2 \int \left (\frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-5+x)}{x}+\frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (-20+x^2\right ) \log \left (\frac {3 x}{2}\right )}{x}+2 \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-4+x) \log ^2\left (\frac {3 x}{2}\right )\right ) \, dx+4 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+8 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx \\ & = 2 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-5+x)}{x} \, dx+2 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (-20+x^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx+2 \int \left (-10 \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )+\frac {25 \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x}+\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right )\right ) \, dx+4 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+4 \int \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-4+x) \log ^2\left (\frac {3 x}{2}\right ) \, dx+4 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \left (20-18 x+4 x^2\right ) \log ^2(3 x) \, dx,x,\frac {x}{2}\right )+8 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx \\ & = 2 \int \left (\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )-\frac {5 \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x}\right ) \, dx+2 \int \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right ) \, dx+2 \int \left (-\frac {20 \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x}+\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right )\right ) \, dx+4 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+4 \text {Subst}\left (\int \left (20 \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log ^2(3 x)-18 \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x \log ^2(3 x)+4 \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x^2 \log ^2(3 x)\right ) \, dx,x,\frac {x}{2}\right )+8 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx+8 \text {Subst}\left (\int \exp \left (2 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) (-4+2 x) \log ^2(3 x) \, dx,x,\frac {x}{2}\right )-20 \int \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right ) \, dx+50 \int \frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx \\ & = 2 \int \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \, dx+2 \int \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right ) \, dx+2 \int \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right ) \, dx+4 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+8 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx+8 \text {Subst}\left (\int \left (-4 \exp \left (2 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log ^2(3 x)+2 \exp \left (2 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x \log ^2(3 x)\right ) \, dx,x,\frac {x}{2}\right )-10 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+16 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x^2 \log ^2(3 x) \, dx,x,\frac {x}{2}\right )-40 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx-40 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log (3 x) \, dx,x,\frac {x}{2}\right )+50 \int \frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx-72 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x \log ^2(3 x) \, dx,x,\frac {x}{2}\right )+80 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log ^2(3 x) \, dx,x,\frac {x}{2}\right ) \\ & = 2 \int \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right ) \, dx+2 \int \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right ) \, dx+4 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+4 \text {Subst}\left (\int \exp \left (2 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \, dx,x,\frac {x}{2}\right )+8 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx-10 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+16 \text {Subst}\left (\int \exp \left (2 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x \log ^2(3 x) \, dx,x,\frac {x}{2}\right )+16 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x^2 \log ^2(3 x) \, dx,x,\frac {x}{2}\right )-32 \text {Subst}\left (\int \exp \left (2 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log ^2(3 x) \, dx,x,\frac {x}{2}\right )-40 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx-40 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log (3 x) \, dx,x,\frac {x}{2}\right )+50 \int \frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx-72 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x \log ^2(3 x) \, dx,x,\frac {x}{2}\right )+80 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log ^2(3 x) \, dx,x,\frac {x}{2}\right ) \\ \end{align*}

Mathematica [F]

\[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=\int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx \]

[In]

Integrate[(E^(1 + (4 + E^x*(-10 + 2*x))*Log[(3*x)/2] + (4 + E^x*(-20 + 4*x) + E^(2*x)*(25 - 10*x + x^2))*Log[(
3*x)/2]^2)*(4 + E^x*(-10 + 2*x) + (8 + E^x*(-40 + 2*x^2) + E^(2*x)*(50 - 20*x + 2*x^2))*Log[(3*x)/2] + (E^x*(-
16*x + 4*x^2) + E^(2*x)*(40*x - 18*x^2 + 2*x^3))*Log[(3*x)/2]^2))/x,x]

[Out]

Integrate[(E^(1 + (4 + E^x*(-10 + 2*x))*Log[(3*x)/2] + (4 + E^x*(-20 + 4*x) + E^(2*x)*(25 - 10*x + x^2))*Log[(
3*x)/2]^2)*(4 + E^x*(-10 + 2*x) + (8 + E^x*(-40 + 2*x^2) + E^(2*x)*(50 - 20*x + 2*x^2))*Log[(3*x)/2] + (E^x*(-
16*x + 4*x^2) + E^(2*x)*(40*x - 18*x^2 + 2*x^3))*Log[(3*x)/2]^2))/x, x]

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(48\) vs. \(2(23)=46\).

Time = 241.78 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.75

method	result	size
parallelrisch	\({\mathrm e}^{\left (\left (x^{2}-10 x +25\right ) {\mathrm e}^{2 x}+\left (4 x -20\right ) {\mathrm e}^{x}+4\right ) \ln \left (\frac {3 x}{2}\right )^{2}+\left (\left (2 x -10\right ) {\mathrm e}^{x}+4\right ) \ln \left (\frac {3 x}{2}\right )+1}\)	\(49\)
risch	\(\left (\frac {3 x}{2}\right )^{2 \,{\mathrm e}^{x} x -10 \,{\mathrm e}^{x}+4} {\mathrm e}^{\ln \left (\frac {3 x}{2}\right )^{2} {\mathrm e}^{2 x} x^{2}+4 \,{\mathrm e}^{x} \ln \left (\frac {3 x}{2}\right )^{2} x -10 \ln \left (\frac {3 x}{2}\right )^{2} {\mathrm e}^{2 x} x -20 \,{\mathrm e}^{x} \ln \left (\frac {3 x}{2}\right )^{2}+25 \ln \left (\frac {3 x}{2}\right )^{2} {\mathrm e}^{2 x}+4 \ln \left (\frac {3 x}{2}\right )^{2}+1}\)	\(88\)

[In]

int((((2*x^3-18*x^2+40*x)*exp(x)^2+(4*x^2-16*x)*exp(x))*ln(3/2*x)^2+((2*x^2-20*x+50)*exp(x)^2+(2*x^2-40)*exp(x
)+8)*ln(3/2*x)+(2*x-10)*exp(x)+4)*exp(((x^2-10*x+25)*exp(x)^2+(4*x-20)*exp(x)+4)*ln(3/2*x)^2+((2*x-10)*exp(x)+
4)*ln(3/2*x)+1)/x,x,method=_RETURNVERBOSE)

[Out]

exp(((x^2-10*x+25)*exp(x)^2+(4*x-20)*exp(x)+4)*ln(3/2*x)^2+((2*x-10)*exp(x)+4)*ln(3/2*x)+1)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (21) = 42\).

Time = 0.29 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.64 \[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=e^{\left ({\left ({\left (x^{2} - 10 \, x + 25\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x - 5\right )} e^{x} + 4\right )} \log \left (\frac {3}{2} \, x\right )^{2} + 2 \, {\left ({\left (x - 5\right )} e^{x} + 2\right )} \log \left (\frac {3}{2} \, x\right ) + 1\right )} \]

[In]

integrate((((2*x^3-18*x^2+40*x)*exp(x)^2+(4*x^2-16*x)*exp(x))*log(3/2*x)^2+((2*x^2-20*x+50)*exp(x)^2+(2*x^2-40
)*exp(x)+8)*log(3/2*x)+(2*x-10)*exp(x)+4)*exp(((x^2-10*x+25)*exp(x)^2+(4*x-20)*exp(x)+4)*log(3/2*x)^2+((2*x-10
)*exp(x)+4)*log(3/2*x)+1)/x,x, algorithm="fricas")

[Out]

e^(((x^2 - 10*x + 25)*e^(2*x) + 4*(x - 5)*e^x + 4)*log(3/2*x)^2 + 2*((x - 5)*e^x + 2)*log(3/2*x) + 1)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (22) = 44\).

Time = 1.13 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.82 \[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=e^{\left (\left (2 x - 10\right ) e^{x} + 4\right ) \log {\left (\frac {3 x}{2} \right )} + \left (\left (4 x - 20\right ) e^{x} + \left (x^{2} - 10 x + 25\right ) e^{2 x} + 4\right ) \log {\left (\frac {3 x}{2} \right )}^{2} + 1} \]

[In]

integrate((((2*x**3-18*x**2+40*x)*exp(x)**2+(4*x**2-16*x)*exp(x))*ln(3/2*x)**2+((2*x**2-20*x+50)*exp(x)**2+(2*
x**2-40)*exp(x)+8)*ln(3/2*x)+(2*x-10)*exp(x)+4)*exp(((x**2-10*x+25)*exp(x)**2+(4*x-20)*exp(x)+4)*ln(3/2*x)**2+
((2*x-10)*exp(x)+4)*ln(3/2*x)+1)/x,x)

[Out]

exp(((2*x - 10)*exp(x) + 4)*log(3*x/2) + ((4*x - 20)*exp(x) + (x**2 - 10*x + 25)*exp(2*x) + 4)*log(3*x/2)**2 +
1)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 388 vs. \(2 (21) = 42\).

Time = 2.04 (sec) , antiderivative size = 388, normalized size of antiderivative = 13.86 \[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=81 \cdot 2^{-8 \, \log \left (3\right ) - 4} x^{4} e^{\left (x^{2} e^{\left (2 \, x\right )} \log \left (3\right )^{2} - 2 \, x^{2} e^{\left (2 \, x\right )} \log \left (3\right ) \log \left (2\right ) + x^{2} e^{\left (2 \, x\right )} \log \left (2\right )^{2} + 2 \, x^{2} e^{\left (2 \, x\right )} \log \left (3\right ) \log \left (x\right ) - 2 \, x^{2} e^{\left (2 \, x\right )} \log \left (2\right ) \log \left (x\right ) + x^{2} e^{\left (2 \, x\right )} \log \left (x\right )^{2} - 10 \, x e^{\left (2 \, x\right )} \log \left (3\right )^{2} + 4 \, x e^{x} \log \left (3\right )^{2} + 20 \, x e^{\left (2 \, x\right )} \log \left (3\right ) \log \left (2\right ) - 8 \, x e^{x} \log \left (3\right ) \log \left (2\right ) - 10 \, x e^{\left (2 \, x\right )} \log \left (2\right )^{2} + 4 \, x e^{x} \log \left (2\right )^{2} - 20 \, x e^{\left (2 \, x\right )} \log \left (3\right ) \log \left (x\right ) + 8 \, x e^{x} \log \left (3\right ) \log \left (x\right ) + 20 \, x e^{\left (2 \, x\right )} \log \left (2\right ) \log \left (x\right ) - 8 \, x e^{x} \log \left (2\right ) \log \left (x\right ) - 10 \, x e^{\left (2 \, x\right )} \log \left (x\right )^{2} + 4 \, x e^{x} \log \left (x\right )^{2} + 2 \, x e^{x} \log \left (3\right ) + 25 \, e^{\left (2 \, x\right )} \log \left (3\right )^{2} - 20 \, e^{x} \log \left (3\right )^{2} - 2 \, x e^{x} \log \left (2\right ) - 50 \, e^{\left (2 \, x\right )} \log \left (3\right ) \log \left (2\right ) + 40 \, e^{x} \log \left (3\right ) \log \left (2\right ) + 25 \, e^{\left (2 \, x\right )} \log \left (2\right )^{2} - 20 \, e^{x} \log \left (2\right )^{2} + 2 \, x e^{x} \log \left (x\right ) + 50 \, e^{\left (2 \, x\right )} \log \left (3\right ) \log \left (x\right ) - 40 \, e^{x} \log \left (3\right ) \log \left (x\right ) - 50 \, e^{\left (2 \, x\right )} \log \left (2\right ) \log \left (x\right ) + 40 \, e^{x} \log \left (2\right ) \log \left (x\right ) + 25 \, e^{\left (2 \, x\right )} \log \left (x\right )^{2} - 20 \, e^{x} \log \left (x\right )^{2} - 10 \, e^{x} \log \left (3\right ) + 4 \, \log \left (3\right )^{2} + 10 \, e^{x} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 10 \, e^{x} \log \left (x\right ) + 8 \, \log \left (3\right ) \log \left (x\right ) - 8 \, \log \left (2\right ) \log \left (x\right ) + 4 \, \log \left (x\right )^{2} + 1\right )} \]

[In]

integrate((((2*x^3-18*x^2+40*x)*exp(x)^2+(4*x^2-16*x)*exp(x))*log(3/2*x)^2+((2*x^2-20*x+50)*exp(x)^2+(2*x^2-40
)*exp(x)+8)*log(3/2*x)+(2*x-10)*exp(x)+4)*exp(((x^2-10*x+25)*exp(x)^2+(4*x-20)*exp(x)+4)*log(3/2*x)^2+((2*x-10
)*exp(x)+4)*log(3/2*x)+1)/x,x, algorithm="maxima")

[Out]

81*2^(-8*log(3) - 4)*x^4*e^(x^2*e^(2*x)*log(3)^2 - 2*x^2*e^(2*x)*log(3)*log(2) + x^2*e^(2*x)*log(2)^2 + 2*x^2*
e^(2*x)*log(3)*log(x) - 2*x^2*e^(2*x)*log(2)*log(x) + x^2*e^(2*x)*log(x)^2 - 10*x*e^(2*x)*log(3)^2 + 4*x*e^x*l
og(3)^2 + 20*x*e^(2*x)*log(3)*log(2) - 8*x*e^x*log(3)*log(2) - 10*x*e^(2*x)*log(2)^2 + 4*x*e^x*log(2)^2 - 20*x
*e^(2*x)*log(3)*log(x) + 8*x*e^x*log(3)*log(x) + 20*x*e^(2*x)*log(2)*log(x) - 8*x*e^x*log(2)*log(x) - 10*x*e^(
2*x)*log(x)^2 + 4*x*e^x*log(x)^2 + 2*x*e^x*log(3) + 25*e^(2*x)*log(3)^2 - 20*e^x*log(3)^2 - 2*x*e^x*log(2) - 5
0*e^(2*x)*log(3)*log(2) + 40*e^x*log(3)*log(2) + 25*e^(2*x)*log(2)^2 - 20*e^x*log(2)^2 + 2*x*e^x*log(x) + 50*e
^(2*x)*log(3)*log(x) - 40*e^x*log(3)*log(x) - 50*e^(2*x)*log(2)*log(x) + 40*e^x*log(2)*log(x) + 25*e^(2*x)*log
(x)^2 - 20*e^x*log(x)^2 - 10*e^x*log(3) + 4*log(3)^2 + 10*e^x*log(2) + 4*log(2)^2 - 10*e^x*log(x) + 8*log(3)*l
og(x) - 8*log(2)*log(x) + 4*log(x)^2 + 1)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (21) = 42\).

Time = 1.96 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.36 \[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=e^{\left (x^{2} e^{\left (2 \, x\right )} \log \left (\frac {3}{2} \, x\right )^{2} - 10 \, x e^{\left (2 \, x\right )} \log \left (\frac {3}{2} \, x\right )^{2} + 4 \, x e^{x} \log \left (\frac {3}{2} \, x\right )^{2} + 2 \, x e^{x} \log \left (\frac {3}{2} \, x\right ) + 25 \, e^{\left (2 \, x\right )} \log \left (\frac {3}{2} \, x\right )^{2} - 20 \, e^{x} \log \left (\frac {3}{2} \, x\right )^{2} - 10 \, e^{x} \log \left (\frac {3}{2} \, x\right ) + 4 \, \log \left (\frac {3}{2} \, x\right )^{2} + 4 \, \log \left (\frac {3}{2} \, x\right ) + 1\right )} \]

[In]

integrate((((2*x^3-18*x^2+40*x)*exp(x)^2+(4*x^2-16*x)*exp(x))*log(3/2*x)^2+((2*x^2-20*x+50)*exp(x)^2+(2*x^2-40
)*exp(x)+8)*log(3/2*x)+(2*x-10)*exp(x)+4)*exp(((x^2-10*x+25)*exp(x)^2+(4*x-20)*exp(x)+4)*log(3/2*x)^2+((2*x-10
)*exp(x)+4)*log(3/2*x)+1)/x,x, algorithm="giac")

[Out]

e^(x^2*e^(2*x)*log(3/2*x)^2 - 10*x*e^(2*x)*log(3/2*x)^2 + 4*x*e^x*log(3/2*x)^2 + 2*x*e^x*log(3/2*x) + 25*e^(2*
x)*log(3/2*x)^2 - 20*e^x*log(3/2*x)^2 - 10*e^x*log(3/2*x) + 4*log(3/2*x)^2 + 4*log(3/2*x) + 1)

Mupad [B] (verification not implemented)

Time = 13.37 (sec) , antiderivative size = 429, normalized size of antiderivative = 15.32 \[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=\frac {81\,2^{40\,{\mathrm {e}}^x\,\ln \left (3\right )}\,2^{10\,{\mathrm {e}}^x}\,2^{20\,x\,{\mathrm {e}}^{2\,x}\,\ln \left (3\right )}\,3^{2\,x\,{\mathrm {e}}^x}\,x^{20\,x\,{\mathrm {e}}^{2\,x}\,\ln \left (2\right )}\,x^{40\,{\mathrm {e}}^x\,\ln \left (2\right )}\,x^{2\,x\,{\mathrm {e}}^x}\,x^{8\,\ln \left (3\right )}\,x^{2\,x^2\,{\mathrm {e}}^{2\,x}\,\ln \left (3\right )}\,x^4\,x^{50\,{\mathrm {e}}^{2\,x}\,\ln \left (3\right )}\,x^{8\,x\,{\mathrm {e}}^x\,\ln \left (3\right )}\,{\mathrm {e}}^{4\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{2\,x}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{-10\,x\,{\mathrm {e}}^{2\,x}\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{-10\,x\,{\mathrm {e}}^{2\,x}\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{25\,{\mathrm {e}}^{2\,x}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^x\,{\ln \left (x\right )}^2}\,\mathrm {e}\,{\mathrm {e}}^{-20\,{\mathrm {e}}^x\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{-20\,{\mathrm {e}}^x\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{4\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{2\,x}\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{2\,x}\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{-10\,x\,{\mathrm {e}}^{2\,x}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{25\,{\mathrm {e}}^{2\,x}\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{25\,{\mathrm {e}}^{2\,x}\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^x\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^x\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{-20\,{\mathrm {e}}^x\,{\ln \left (x\right )}^2}}{16\,2^{2\,x\,{\mathrm {e}}^x}\,2^{8\,\ln \left (3\right )}\,2^{2\,x^2\,{\mathrm {e}}^{2\,x}\,\ln \left (3\right )}\,2^{50\,{\mathrm {e}}^{2\,x}\,\ln \left (3\right )}\,2^{8\,x\,{\mathrm {e}}^x\,\ln \left (3\right )}\,3^{10\,{\mathrm {e}}^x}\,x^{10\,{\mathrm {e}}^x}\,x^{20\,x\,{\mathrm {e}}^{2\,x}\,\ln \left (3\right )}\,x^{40\,{\mathrm {e}}^x\,\ln \left (3\right )}\,x^{8\,\ln \left (2\right )}\,x^{2\,x^2\,{\mathrm {e}}^{2\,x}\,\ln \left (2\right )}\,x^{50\,{\mathrm {e}}^{2\,x}\,\ln \left (2\right )}\,x^{8\,x\,{\mathrm {e}}^x\,\ln \left (2\right )}} \]

[In]

int((exp(log((3*x)/2)*(exp(x)*(2*x - 10) + 4) + log((3*x)/2)^2*(exp(x)*(4*x - 20) + exp(2*x)*(x^2 - 10*x + 25)
+ 4) + 1)*(log((3*x)/2)^2*(exp(2*x)*(40*x - 18*x^2 + 2*x^3) - exp(x)*(16*x - 4*x^2)) + exp(x)*(2*x - 10) + lo
g((3*x)/2)*(exp(2*x)*(2*x^2 - 20*x + 50) + exp(x)*(2*x^2 - 40) + 8) + 4))/x,x)

[Out]

(81*2^(40*exp(x)*log(3))*2^(10*exp(x))*2^(20*x*exp(2*x)*log(3))*3^(2*x*exp(x))*x^(20*x*exp(2*x)*log(2))*x^(40*
exp(x)*log(2))*x^(2*x*exp(x))*x^(8*log(3))*x^(2*x^2*exp(2*x)*log(3))*x^4*x^(50*exp(2*x)*log(3))*x^(8*x*exp(x)*
log(3))*exp(4*log(x)^2)*exp(x^2*exp(2*x)*log(x)^2)*exp(-10*x*exp(2*x)*log(2)^2)*exp(-10*x*exp(2*x)*log(3)^2)*e
xp(25*exp(2*x)*log(x)^2)*exp(4*x*exp(x)*log(x)^2)*exp(1)*exp(-20*exp(x)*log(2)^2)*exp(-20*exp(x)*log(3)^2)*exp
(4*log(2)^2)*exp(4*log(3)^2)*exp(x^2*exp(2*x)*log(2)^2)*exp(x^2*exp(2*x)*log(3)^2)*exp(-10*x*exp(2*x)*log(x)^2
)*exp(25*exp(2*x)*log(2)^2)*exp(25*exp(2*x)*log(3)^2)*exp(4*x*exp(x)*log(2)^2)*exp(4*x*exp(x)*log(3)^2)*exp(-2
0*exp(x)*log(x)^2))/(16*2^(2*x*exp(x))*2^(8*log(3))*2^(2*x^2*exp(2*x)*log(3))*2^(50*exp(2*x)*log(3))*2^(8*x*ex
p(x)*log(3))*3^(10*exp(x))*x^(10*exp(x))*x^(20*x*exp(2*x)*log(3))*x^(40*exp(x)*log(3))*x^(8*log(2))*x^(2*x^2*e
xp(2*x)*log(2))*x^(50*exp(2*x)*log(2))*x^(8*x*exp(x)*log(2)))