3.75.0 ∫ 380x4+100e2e2x _____ x2 x4−400x5+100x6+ex(−40x2+80x3−20x4)+ee2x ____ x2 (e3x(40−40x)+400x4−200x5+e2x(−40x+40x2)+ex(−20x2+20x3)) ________________________________________________________________________________________________________________________________________________________________________________ e2xx2+x4−20x5+110x6+25e2e2x _____ x2 x6−100x7+25x8+ex(−2x3+20x4−10x5)+ee2x ___

Integrand size = 226, antiderivative size = 42 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=\frac {4}{-x+\frac {-e^x+x}{5 \left (2 x+\left (e^{\frac {e^{2 x}}{x^2}}-x\right ) x\right )}} \]

Rubi [F]

\[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=\int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx \]

Int[(380*x^4 + 100*E^((2*E^(2*x))/x^2)*x^4 - 400*x^5 + 100*x^6 + E^x*(-40*x^2 + 80*x^3 - 20*x^4) + E^(E^(2*x)/

x^2)*(E^(3*x)*(40 - 40*x) + 400*x^4 - 200*x^5 + E^(2*x)*(-40*x + 40*x^2) + E^x*(-20*x^2 + 20*x^3)))/(E^(2*x)*x

^2 + x^4 - 20*x^5 + 110*x^6 + 25*E^((2*E^(2*x))/x^2)*x^6 - 100*x^7 + 25*x^8 + E^x*(-2*x^3 + 20*x^4 - 10*x^5) +

-840*Defer[Int][E^(E^(2*x)/x^2), x] - 400*Defer[Int][E^((2*E^(2*x))/x^2), x] + 40*Defer[Int][E^(E^(2*x)/x^2 +

x)/x^2, x] + 40*Defer[Int][E^(E^(2*x)/x^2)/x, x] - 40*Defer[Int][E^(E^(2*x)/x^2 + x)/x, x] + 1200*Defer[Int][E

^(E^(2*x)/x^2)*x, x] + 400*Defer[Int][E^((2*E^(2*x))/x^2)*x, x] - 400*Defer[Int][E^(E^(2*x)/x^2)*x^2, x] - 20*

Defer[Int][(E^(E^(2*x)/x^2)*x)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] + 420*Defer[Int][(E^(E

^(2*x)/x^2)*x^2)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] + 7700*Defer[Int][(E^(E^(2*x)/x^2)*x

^3)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] + 8100*Defer[Int][(E^((2*E^(2*x))/x^2)*x^3)/(E^x

- x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] + 2000*Defer[Int][(E^((3*E^(2*x))/x^2)*x^3)/(E^x - x + 10*

x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] - 56000*Defer[Int][(E^(E^(2*x)/x^2)*x^4)/(E^x - x + 10*x^2 + 5*E^(E

^(2*x)/x^2)*x^2 - 5*x^3)^2, x] - 72000*Defer[Int][(E^((2*E^(2*x))/x^2)*x^4)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x

^2)*x^2 - 5*x^3)^2, x] - 32000*Defer[Int][(E^((3*E^(2*x))/x^2)*x^4)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2

- 5*x^3)^2, x] - 5000*Defer[Int][(E^((4*E^(2*x))/x^2)*x^4)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^

2, x] + 110000*Defer[Int][(E^(E^(2*x)/x^2)*x^5)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] + 124

000*Defer[Int][(E^((2*E^(2*x))/x^2)*x^5)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] + 45000*Defe

r[Int][(E^((3*E^(2*x))/x^2)*x^5)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] + 5000*Defer[Int][(E

^((4*E^(2*x))/x^2)*x^5)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] - 92000*Defer[Int][(E^(E^(2*x

)/x^2)*x^6)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] - 75000*Defer[Int][(E^((2*E^(2*x))/x^2)*x

^6)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] - 15000*Defer[Int][(E^((3*E^(2*x))/x^2)*x^6)/(E^x

- x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] + 35000*Defer[Int][(E^(E^(2*x)/x^2)*x^7)/(E^x - x + 10*x^

2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] + 15000*Defer[Int][(E^((2*E^(2*x))/x^2)*x^7)/(E^x - x + 10*x^2 + 5*E^

(E^(2*x)/x^2)*x^2 - 5*x^3)^2, x] - 5000*Defer[Int][(E^(E^(2*x)/x^2)*x^8)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)

*x^2 - 5*x^3)^2, x] - 40*Defer[Int][(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3)^(-1), x] + 20*Defer[Int

][E^(E^(2*x)/x^2)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3), x] - 1620*Defer[Int][(E^(E^(2*x)/x^2)*x)

/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3), x] - 800*Defer[Int][(E^((2*E^(2*x))/x^2)*x)/(E^x - x + 10

*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3), x] + 14400*Defer[Int][(E^(E^(2*x)/x^2)*x^2)/(E^x - x + 10*x^2 + 5*E^(E^

(2*x)/x^2)*x^2 - 5*x^3), x] + 12800*Defer[Int][(E^((2*E^(2*x))/x^2)*x^2)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)

*x^2 - 5*x^3), x] + 3000*Defer[Int][(E^((3*E^(2*x))/x^2)*x^2)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^

3), x] - 24800*Defer[Int][(E^(E^(2*x)/x^2)*x^3)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3), x] - 18000

*Defer[Int][(E^((2*E^(2*x))/x^2)*x^3)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3), x] - 3000*Defer[Int]

[(E^((3*E^(2*x))/x^2)*x^3)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3), x] + 15000*Defer[Int][(E^(E^(2*

x)/x^2)*x^4)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3), x] + 6000*Defer[Int][(E^((2*E^(2*x))/x^2)*x^4

)/(E^x - x + 10*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3), x] - 3000*Defer[Int][(E^(E^(2*x)/x^2)*x^5)/(E^x - x + 10

*x^2 + 5*E^(E^(2*x)/x^2)*x^2 - 5*x^3), x] - 40*Defer[Int][x/(-E^x + x - 10*x^2 - 5*E^(E^(2*x)/x^2)*x^2 + 5*x^3

)^2, x] + 860*Defer[Int][x^2/(-E^x + x - 10*x^2 - 5*E^(E^(2*x)/x^2)*x^2 + 5*x^3)^2, x] - 1420*Defer[Int][x^3/(

-E^x + x - 10*x^2 - 5*E^(E^(2*x)/x^2)*x^2 + 5*x^3)^2, x] + 700*Defer[Int][x^4/(-E^x + x - 10*x^2 - 5*E^(E^(2*x

)/x^2)*x^2 + 5*x^3)^2, x] - 100*Defer[Int][x^5/(-E^x + x - 10*x^2 - 5*E^(E^(2*x)/x^2)*x^2 + 5*x^3)^2, x] - 80*

Defer[Int][x/(-E^x + x - 10*x^2 - 5*E^(E^(2*x)/x^2)*x^2 + 5*x^3), x] + 20*Defer[Int][x^2/(-E^x + x - 10*x^2 -

Mathematica [A] (veriﬁed)

Time = 0.17 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.26 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=\frac {20 x \left (-2-e^{\frac {e^{2 x}}{x^2}}+x\right )}{e^x+5 e^{\frac {e^{2 x}}{x^2}} x^2+x \left (-1+10 x-5 x^2\right )} \]

Integrate[(380*x^4 + 100*E^((2*E^(2*x))/x^2)*x^4 - 400*x^5 + 100*x^6 + E^x*(-40*x^2 + 80*x^3 - 20*x^4) + E^(E^

(2*x)/x^2)*(E^(3*x)*(40 - 40*x) + 400*x^4 - 200*x^5 + E^(2*x)*(-40*x + 40*x^2) + E^x*(-20*x^2 + 20*x^3)))/(E^(

2*x)*x^2 + x^4 - 20*x^5 + 110*x^6 + 25*E^((2*E^(2*x))/x^2)*x^6 - 100*x^7 + 25*x^8 + E^x*(-2*x^3 + 20*x^4 - 10*

(20*x*(-2 - E^(E^(2*x)/x^2) + x))/(E^x + 5*E^(E^(2*x)/x^2)*x^2 + x*(-1 + 10*x - 5*x^2))

Maple [A] (veriﬁed)

Time = 2.23 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.19


method	result	size

risch	\(-\frac {4}{x}+\frac {4 x -4 \,{\mathrm e}^{x}}{x \left (5 x^{3}-5 x^{2} {\mathrm e}^{\frac {{\mathrm e}^{2 x}}{x^{2}}}-10 x^{2}+x -{\mathrm e}^{x}\right )}\)	\(50\)
parallelrisch	\(-\frac {100 x^{2}-100 x \,{\mathrm e}^{\frac {{\mathrm e}^{2 x}}{x^{2}}}-200 x}{5 \left (5 x^{3}-5 x^{2} {\mathrm e}^{\frac {{\mathrm e}^{2 x}}{x^{2}}}-10 x^{2}+x -{\mathrm e}^{x}\right )}\)	\(56\)

int((100*x^4*exp(exp(x)^2/x^2)^2+((-40*x+40)*exp(x)^3+(40*x^2-40*x)*exp(x)^2+(20*x^3-20*x^2)*exp(x)-200*x^5+40

0*x^4)*exp(exp(x)^2/x^2)+(-20*x^4+80*x^3-40*x^2)*exp(x)+100*x^6-400*x^5+380*x^4)/(25*x^6*exp(exp(x)^2/x^2)^2+(

10*exp(x)*x^4-50*x^7+100*x^6-10*x^5)*exp(exp(x)^2/x^2)+exp(x)^2*x^2+(-10*x^5+20*x^4-2*x^3)*exp(x)+25*x^8-100*x

Fricas [A] (veriﬁcation not implemented)

Time = 0.26 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.26 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=-\frac {20 \, {\left (x^{2} - x e^{\left (\frac {e^{\left (2 \, x\right )}}{x^{2}}\right )} - 2 \, x\right )}}{5 \, x^{3} - 5 \, x^{2} e^{\left (\frac {e^{\left (2 \, x\right )}}{x^{2}}\right )} - 10 \, x^{2} + x - e^{x}} \]

integrate((100*x^4*exp(exp(x)^2/x^2)^2+((-40*x+40)*exp(x)^3+(40*x^2-40*x)*exp(x)^2+(20*x^3-20*x^2)*exp(x)-200*

x^5+400*x^4)*exp(exp(x)^2/x^2)+(-20*x^4+80*x^3-40*x^2)*exp(x)+100*x^6-400*x^5+380*x^4)/(25*x^6*exp(exp(x)^2/x^

2)^2+(10*exp(x)*x^4-50*x^7+100*x^6-10*x^5)*exp(exp(x)^2/x^2)+exp(x)^2*x^2+(-10*x^5+20*x^4-2*x^3)*exp(x)+25*x^8

-20*(x^2 - x*e^(e^(2*x)/x^2) - 2*x)/(5*x^3 - 5*x^2*e^(e^(2*x)/x^2) - 10*x^2 + x - e^x)

Sympy [A] (veriﬁcation not implemented)

Time = 0.21 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.05 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=\frac {- 4 x + 4 e^{x}}{- 5 x^{4} + 5 x^{3} e^{\frac {e^{2 x}}{x^{2}}} + 10 x^{3} - x^{2} + x e^{x}} - \frac {4}{x} \]

integrate((100*x**4*exp(exp(x)**2/x**2)**2+((-40*x+40)*exp(x)**3+(40*x**2-40*x)*exp(x)**2+(20*x**3-20*x**2)*ex

p(x)-200*x**5+400*x**4)*exp(exp(x)**2/x**2)+(-20*x**4+80*x**3-40*x**2)*exp(x)+100*x**6-400*x**5+380*x**4)/(25*

x**6*exp(exp(x)**2/x**2)**2+(10*exp(x)*x**4-50*x**7+100*x**6-10*x**5)*exp(exp(x)**2/x**2)+exp(x)**2*x**2+(-10*

(-4*x + 4*exp(x))/(-5*x**4 + 5*x**3*exp(exp(2*x)/x**2) + 10*x**3 - x**2 + x*exp(x)) - 4/x

Maxima [A] (veriﬁcation not implemented)

Time = 0.32 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.26 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=-\frac {20 \, {\left (x^{2} - x e^{\left (\frac {e^{\left (2 \, x\right )}}{x^{2}}\right )} - 2 \, x\right )}}{5 \, x^{3} - 5 \, x^{2} e^{\left (\frac {e^{\left (2 \, x\right )}}{x^{2}}\right )} - 10 \, x^{2} + x - e^{x}} \]

integrate((100*x^4*exp(exp(x)^2/x^2)^2+((-40*x+40)*exp(x)^3+(40*x^2-40*x)*exp(x)^2+(20*x^3-20*x^2)*exp(x)-200*

x^5+400*x^4)*exp(exp(x)^2/x^2)+(-20*x^4+80*x^3-40*x^2)*exp(x)+100*x^6-400*x^5+380*x^4)/(25*x^6*exp(exp(x)^2/x^

2)^2+(10*exp(x)*x^4-50*x^7+100*x^6-10*x^5)*exp(exp(x)^2/x^2)+exp(x)^2*x^2+(-10*x^5+20*x^4-2*x^3)*exp(x)+25*x^8

-20*(x^2 - x*e^(e^(2*x)/x^2) - 2*x)/(5*x^3 - 5*x^2*e^(e^(2*x)/x^2) - 10*x^2 + x - e^x)

Giac [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 708 vs. \(2 (36) = 72\).

Time = 0.49 (sec) , antiderivative size = 708, normalized size of antiderivative = 16.86 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=-\frac {20 \, {\left (5 \, x^{8} e^{x} - 10 \, x^{7} e^{\left (3 \, x\right )} - 10 \, x^{7} e^{x} - 5 \, x^{7} e^{\left (\frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} + 50 \, x^{6} e^{\left (3 \, x\right )} - x^{6} e^{\left (2 \, x\right )} + 10 \, x^{6} e^{\left (2 \, x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} - x^{6} e^{x} - 82 \, x^{5} e^{\left (3 \, x\right )} + 4 \, x^{5} e^{\left (2 \, x\right )} - 30 \, x^{5} e^{\left (2 \, x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} + x^{5} e^{\left (x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} + 2 \, x^{5} e^{x} + x^{5} e^{\left (\frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} + 2 \, x^{4} e^{\left (4 \, x\right )} + 46 \, x^{4} e^{\left (3 \, x\right )} - 4 \, x^{4} e^{\left (2 \, x\right )} + 22 \, x^{4} e^{\left (2 \, x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} - 2 \, x^{4} e^{\left (x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} - 6 \, x^{3} e^{\left (4 \, x\right )} - 4 \, x^{3} e^{\left (3 \, x\right )} - 2 \, x^{3} e^{\left (3 \, x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} - 2 \, x^{3} e^{\left (2 \, x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} + 4 \, x^{2} e^{\left (4 \, x\right )} + 2 \, x^{2} e^{\left (3 \, x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )}\right )}}{25 \, x^{9} e^{x} - 50 \, x^{8} e^{\left (3 \, x\right )} - 50 \, x^{8} e^{x} - 25 \, x^{8} e^{\left (\frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} + 250 \, x^{7} e^{\left (3 \, x\right )} - 5 \, x^{7} e^{\left (2 \, x\right )} + 50 \, x^{7} e^{\left (2 \, x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} - 420 \, x^{6} e^{\left (3 \, x\right )} + 15 \, x^{6} e^{\left (2 \, x\right )} - 150 \, x^{6} e^{\left (2 \, x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} + 5 \, x^{6} e^{\left (x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} + 10 \, x^{6} e^{x} + 5 \, x^{6} e^{\left (\frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} + 20 \, x^{5} e^{\left (4 \, x\right )} + 260 \, x^{5} e^{\left (3 \, x\right )} - 21 \, x^{5} e^{\left (2 \, x\right )} + 110 \, x^{5} e^{\left (2 \, x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} - 10 \, x^{5} e^{\left (x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} - x^{5} e^{x} - 60 \, x^{4} e^{\left (4 \, x\right )} - 41 \, x^{4} e^{\left (3 \, x\right )} + 3 \, x^{4} e^{\left (2 \, x\right )} - 10 \, x^{4} e^{\left (3 \, x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} - 10 \, x^{4} e^{\left (2 \, x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} + 44 \, x^{3} e^{\left (4 \, x\right )} + 10 \, x^{3} e^{\left (3 \, x + \frac {x^{3} + e^{\left (2 \, x\right )}}{x^{2}}\right )} - 2 \, x^{2} e^{\left (5 \, x\right )} - 4 \, x^{2} e^{\left (4 \, x\right )} + 2 \, x e^{\left (5 \, x\right )}} \]

integrate((100*x^4*exp(exp(x)^2/x^2)^2+((-40*x+40)*exp(x)^3+(40*x^2-40*x)*exp(x)^2+(20*x^3-20*x^2)*exp(x)-200*

x^5+400*x^4)*exp(exp(x)^2/x^2)+(-20*x^4+80*x^3-40*x^2)*exp(x)+100*x^6-400*x^5+380*x^4)/(25*x^6*exp(exp(x)^2/x^

2)^2+(10*exp(x)*x^4-50*x^7+100*x^6-10*x^5)*exp(exp(x)^2/x^2)+exp(x)^2*x^2+(-10*x^5+20*x^4-2*x^3)*exp(x)+25*x^8

-20*(5*x^8*e^x - 10*x^7*e^(3*x) - 10*x^7*e^x - 5*x^7*e^((x^3 + e^(2*x))/x^2) + 50*x^6*e^(3*x) - x^6*e^(2*x) +

10*x^6*e^(2*x + (x^3 + e^(2*x))/x^2) - x^6*e^x - 82*x^5*e^(3*x) + 4*x^5*e^(2*x) - 30*x^5*e^(2*x + (x^3 + e^(2*

x))/x^2) + x^5*e^(x + (x^3 + e^(2*x))/x^2) + 2*x^5*e^x + x^5*e^((x^3 + e^(2*x))/x^2) + 2*x^4*e^(4*x) + 46*x^4*

e^(3*x) - 4*x^4*e^(2*x) + 22*x^4*e^(2*x + (x^3 + e^(2*x))/x^2) - 2*x^4*e^(x + (x^3 + e^(2*x))/x^2) - 6*x^3*e^(

4*x) - 4*x^3*e^(3*x) - 2*x^3*e^(3*x + (x^3 + e^(2*x))/x^2) - 2*x^3*e^(2*x + (x^3 + e^(2*x))/x^2) + 4*x^2*e^(4*

x) + 2*x^2*e^(3*x + (x^3 + e^(2*x))/x^2))/(25*x^9*e^x - 50*x^8*e^(3*x) - 50*x^8*e^x - 25*x^8*e^((x^3 + e^(2*x)

)/x^2) + 250*x^7*e^(3*x) - 5*x^7*e^(2*x) + 50*x^7*e^(2*x + (x^3 + e^(2*x))/x^2) - 420*x^6*e^(3*x) + 15*x^6*e^(

2*x) - 150*x^6*e^(2*x + (x^3 + e^(2*x))/x^2) + 5*x^6*e^(x + (x^3 + e^(2*x))/x^2) + 10*x^6*e^x + 5*x^6*e^((x^3

+ e^(2*x))/x^2) + 20*x^5*e^(4*x) + 260*x^5*e^(3*x) - 21*x^5*e^(2*x) + 110*x^5*e^(2*x + (x^3 + e^(2*x))/x^2) -

10*x^5*e^(x + (x^3 + e^(2*x))/x^2) - x^5*e^x - 60*x^4*e^(4*x) - 41*x^4*e^(3*x) + 3*x^4*e^(2*x) - 10*x^4*e^(3*x

+ (x^3 + e^(2*x))/x^2) - 10*x^4*e^(2*x + (x^3 + e^(2*x))/x^2) + 44*x^3*e^(4*x) + 10*x^3*e^(3*x + (x^3 + e^(2*

Mupad [B] (veriﬁcation not implemented)

Time = 13.57 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.17 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=-\frac {20\,x\,\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x}}{x^2}}-x+2\right )}{{\mathrm {e}}^x-x+5\,x^2\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x}}{x^2}}+10\,x^2-5\,x^3} \]

int((100*x^4*exp((2*exp(2*x))/x^2) - exp(x)*(40*x^2 - 80*x^3 + 20*x^4) + 380*x^4 - 400*x^5 + 100*x^6 - exp(exp

(2*x)/x^2)*(exp(2*x)*(40*x - 40*x^2) + exp(x)*(20*x^2 - 20*x^3) + exp(3*x)*(40*x - 40) - 400*x^4 + 200*x^5))/(

25*x^6*exp((2*exp(2*x))/x^2) - exp(x)*(2*x^3 - 20*x^4 + 10*x^5) + exp(exp(2*x)/x^2)*(10*x^4*exp(x) - 10*x^5 +

-(20*x*(exp(exp(2*x)/x^2) - x + 2))/(exp(x) - x + 5*x^2*exp(exp(2*x)/x^2) + 10*x^2 - 5*x^3)

Optimal result

Rubi [F]

Mathematica [A] (veriﬁed)

Maple [A] (veriﬁed)

Fricas [A] (veriﬁcation not implemented)

Sympy [A] (veriﬁcation not implemented)

Maxima [A] (veriﬁcation not implemented)

Giac [B] (veriﬁcation not implemented)

Mupad [B] (veriﬁcation not implemented)