\(\int \frac {200+100 x+e^{6 x^2-2 x^3} (8+4 x)+e^{3 x^2-x^3} (80+40 x)+e^{\frac {2 (39 x+8 e^{3 x^2-x^3} x)}{20+4 e^{3 x^2-x^3}}} (100 x+195 x^2+e^{6 x^2-2 x^3} (4 x+8 x^2)+e^{3 x^2-x^3} (40 x+79 x^2+6 x^4-3 x^5))+e^{\frac {39 x+8 e^{3 x^2-x^3} x}{20+4 e^{3 x^2-x^3}}} (-200-590 x-195 x^2+e^{6 x^2-2 x^3} (-8-24 x-8 x^2)+e^{3 x^2-x^3} (-80-238 x-79 x^2-12 x^3+3 x^5))}{50+2 e^{6 x^2-2 x^3}+20 e^{3 x^2-x^3}} \, dx\) [6849]

Optimal result

Integrand size = 298, antiderivative size = 34 \[ \int \frac {200+100 x+e^{6 x^2-2 x^3} (8+4 x)+e^{3 x^2-x^3} (80+40 x)+e^{\frac {2 \left (39 x+8 e^{3 x^2-x^3} x\right )}{20+4 e^{3 x^2-x^3}}} \left (100 x+195 x^2+e^{6 x^2-2 x^3} \left (4 x+8 x^2\right )+e^{3 x^2-x^3} \left (40 x+79 x^2+6 x^4-3 x^5\right )\right )+e^{\frac {39 x+8 e^{3 x^2-x^3} x}{20+4 e^{3 x^2-x^3}}} \left (-200-590 x-195 x^2+e^{6 x^2-2 x^3} \left (-8-24 x-8 x^2\right )+e^{3 x^2-x^3} \left (-80-238 x-79 x^2-12 x^3+3 x^5\right )\right )}{50+2 e^{6 x^2-2 x^3}+20 e^{3 x^2-x^3}} \, dx=\left (2+x-e^{2 x-\frac {x}{4 \left (5+e^{(3-x) x^2}\right )}} x\right )^2 \]

[Out]

(x+2-x*exp(2*x-1/4*x/(exp((-x+3)*x^2)+5)))^2

Rubi [F]

\[ \int \frac {200+100 x+e^{6 x^2-2 x^3} (8+4 x)+e^{3 x^2-x^3} (80+40 x)+e^{\frac {2 \left (39 x+8 e^{3 x^2-x^3} x\right )}{20+4 e^{3 x^2-x^3}}} \left (100 x+195 x^2+e^{6 x^2-2 x^3} \left (4 x+8 x^2\right )+e^{3 x^2-x^3} \left (40 x+79 x^2+6 x^4-3 x^5\right )\right )+e^{\frac {39 x+8 e^{3 x^2-x^3} x}{20+4 e^{3 x^2-x^3}}} \left (-200-590 x-195 x^2+e^{6 x^2-2 x^3} \left (-8-24 x-8 x^2\right )+e^{3 x^2-x^3} \left (-80-238 x-79 x^2-12 x^3+3 x^5\right )\right )}{50+2 e^{6 x^2-2 x^3}+20 e^{3 x^2-x^3}} \, dx=\int \frac {200+100 x+e^{6 x^2-2 x^3} (8+4 x)+e^{3 x^2-x^3} (80+40 x)+\exp \left (\frac {2 \left (39 x+8 e^{3 x^2-x^3} x\right )}{20+4 e^{3 x^2-x^3}}\right ) \left (100 x+195 x^2+e^{6 x^2-2 x^3} \left (4 x+8 x^2\right )+e^{3 x^2-x^3} \left (40 x+79 x^2+6 x^4-3 x^5\right )\right )+\exp \left (\frac {39 x+8 e^{3 x^2-x^3} x}{20+4 e^{3 x^2-x^3}}\right ) \left (-200-590 x-195 x^2+e^{6 x^2-2 x^3} \left (-8-24 x-8 x^2\right )+e^{3 x^2-x^3} \left (-80-238 x-79 x^2-12 x^3+3 x^5\right )\right )}{50+2 e^{6 x^2-2 x^3}+20 e^{3 x^2-x^3}} \, dx \]

[In]

Int[(200 + 100*x + E^(6*x^2 - 2*x^3)*(8 + 4*x) + E^(3*x^2 - x^3)*(80 + 40*x) + E^((2*(39*x + 8*E^(3*x^2 - x^3)
*x))/(20 + 4*E^(3*x^2 - x^3)))*(100*x + 195*x^2 + E^(6*x^2 - 2*x^3)*(4*x + 8*x^2) + E^(3*x^2 - x^3)*(40*x + 79
*x^2 + 6*x^4 - 3*x^5)) + E^((39*x + 8*E^(3*x^2 - x^3)*x)/(20 + 4*E^(3*x^2 - x^3)))*(-200 - 590*x - 195*x^2 + E
^(6*x^2 - 2*x^3)*(-8 - 24*x - 8*x^2) + E^(3*x^2 - x^3)*(-80 - 238*x - 79*x^2 - 12*x^3 + 3*x^5)))/(50 + 2*E^(6*
x^2 - 2*x^3) + 20*E^(3*x^2 - x^3)),x]

[Out]

4*x + x^2 - 4*Defer[Int][E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(4*(E^(3*x^2) + 5*E^x^3))), x] - 12*Defer[Int][E^(((8
*E^(3*x^2) + 39*E^x^3)*x)/(4*(E^(3*x^2) + 5*E^x^3)))*x, x] + 2*Defer[Int][E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(2*(
E^(3*x^2) + 5*E^x^3)))*x, x] + Defer[Int][E^(2*x^3 - (x*(4*E^(3*x^2)*(-2 + 3*x + x^2) + E^x^3*(-39 + 60*x + 20
*x^2)))/(4*(E^(3*x^2) + 5*E^x^3)))*x, x] - 5*Defer[Int][(E^(2*x^3 - (x*(4*E^(3*x^2)*(-2 + 3*x) + E^x^3*(-39 +
60*x)))/(4*(E^(3*x^2) + 5*E^x^3)))*x)/(E^(3*x^2) + 5*E^x^3), x] - 4*Defer[Int][E^(((8*E^(3*x^2) + 39*E^x^3)*x)
/(4*(E^(3*x^2) + 5*E^x^3)))*x^2, x] + 4*Defer[Int][E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(2*(E^(3*x^2) + 5*E^x^3)))*
x^2, x] - Defer[Int][E^((x*(2*E^(3*x^2)*(4 - 3*x + x^2) + E^x^3*(39 - 30*x + 10*x^2)))/(2*(E^(3*x^2) + 5*E^x^3
)))*x^2, x]/2 + Defer[Int][E^(2*x^3 - (x*(4*E^(3*x^2)*(-2 + 3*x + x^2) + E^x^3*(-39 + 60*x + 20*x^2)))/(4*(E^(
3*x^2) + 5*E^x^3)))*x^2, x]/2 + (5*Defer[Int][(E^((x*(E^(3*x^2)*(8 - 6*x + 4*x^2) + E^x^3*(39 - 30*x + 20*x^2)
))/(2*(E^(3*x^2) + 5*E^x^3)))*x^2)/(E^(3*x^2) + 5*E^x^3), x])/2 - (5*Defer[Int][(E^(2*x^3 - (x*(4*E^(3*x^2)*(-
2 + 3*x) + E^x^3*(-39 + 60*x)))/(4*(E^(3*x^2) + 5*E^x^3)))*x^2)/(E^(3*x^2) + 5*E^x^3), x])/2 - 6*Defer[Int][E^
(2*x^3 - (x*(4*E^(3*x^2)*(-2 + 3*x + x^2) + E^x^3*(-39 + 60*x + 20*x^2)))/(4*(E^(3*x^2) + 5*E^x^3)))*x^3, x] +
30*Defer[Int][(E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(4*(E^(3*x^2) + 5*E^x^3)) + 2*x^3)*x^3)/(E^(3*x^2) + 5*E^x^3)^
2, x] + 30*Defer[Int][(E^(2*x^3 - (x*(4*E^(3*x^2)*(-2 + 3*x) + E^x^3*(-39 + 60*x)))/(4*(E^(3*x^2) + 5*E^x^3)))
*x^3)/(E^(3*x^2) + 5*E^x^3), x] + 3*Defer[Int][E^((x*(2*E^(3*x^2)*(4 - 3*x + x^2) + E^x^3*(39 - 30*x + 10*x^2)
))/(2*(E^(3*x^2) + 5*E^x^3)))*x^4, x] - 15*Defer[Int][(E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(2*(E^(3*x^2) + 5*E^x^3
)) + 2*x^3)*x^4)/(E^(3*x^2) + 5*E^x^3)^2, x] - 15*Defer[Int][(E^((x*(E^(3*x^2)*(8 - 6*x + 4*x^2) + E^x^3*(39 -
30*x + 20*x^2)))/(2*(E^(3*x^2) + 5*E^x^3)))*x^4)/(E^(3*x^2) + 5*E^x^3), x] - (3*Defer[Int][E^((x*(2*E^(3*x^2)
*(4 - 3*x + x^2) + E^x^3*(39 - 30*x + 10*x^2)))/(2*(E^(3*x^2) + 5*E^x^3)))*x^5, x])/2 + (3*Defer[Int][E^(2*x^3
- (x*(4*E^(3*x^2)*(-2 + 3*x + x^2) + E^x^3*(-39 + 60*x + 20*x^2)))/(4*(E^(3*x^2) + 5*E^x^3)))*x^5, x])/2 - (1
5*Defer[Int][(E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(4*(E^(3*x^2) + 5*E^x^3)) + 2*x^3)*x^5)/(E^(3*x^2) + 5*E^x^3)^2,
x])/2 + (15*Defer[Int][(E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(2*(E^(3*x^2) + 5*E^x^3)) + 2*x^3)*x^5)/(E^(3*x^2) +
5*E^x^3)^2, x])/2 + (15*Defer[Int][(E^((x*(E^(3*x^2)*(8 - 6*x + 4*x^2) + E^x^3*(39 - 30*x + 20*x^2)))/(2*(E^(3
*x^2) + 5*E^x^3)))*x^5)/(E^(3*x^2) + 5*E^x^3), x])/2 - (15*Defer[Int][(E^(2*x^3 - (x*(4*E^(3*x^2)*(-2 + 3*x) +
E^x^3*(-39 + 60*x)))/(4*(E^(3*x^2) + 5*E^x^3)))*x^5)/(E^(3*x^2) + 5*E^x^3), x])/2

Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{2 x^3} \left (200+100 x+e^{6 x^2-2 x^3} (8+4 x)+e^{3 x^2-x^3} (80+40 x)+\exp \left (\frac {2 \left (39 x+8 e^{3 x^2-x^3} x\right )}{20+4 e^{3 x^2-x^3}}\right ) \left (100 x+195 x^2+e^{6 x^2-2 x^3} \left (4 x+8 x^2\right )+e^{3 x^2-x^3} \left (40 x+79 x^2+6 x^4-3 x^5\right )\right )+\exp \left (\frac {39 x+8 e^{3 x^2-x^3} x}{20+4 e^{3 x^2-x^3}}\right ) \left (-200-590 x-195 x^2+e^{6 x^2-2 x^3} \left (-8-24 x-8 x^2\right )+e^{3 x^2-x^3} \left (-80-238 x-79 x^2-12 x^3+3 x^5\right )\right )\right )}{2 \left (e^{3 x^2}+5 e^{x^3}\right )^2} \, dx \\ & = \frac {1}{2} \int \frac {e^{2 x^3} \left (200+100 x+e^{6 x^2-2 x^3} (8+4 x)+e^{3 x^2-x^3} (80+40 x)+\exp \left (\frac {2 \left (39 x+8 e^{3 x^2-x^3} x\right )}{20+4 e^{3 x^2-x^3}}\right ) \left (100 x+195 x^2+e^{6 x^2-2 x^3} \left (4 x+8 x^2\right )+e^{3 x^2-x^3} \left (40 x+79 x^2+6 x^4-3 x^5\right )\right )+\exp \left (\frac {39 x+8 e^{3 x^2-x^3} x}{20+4 e^{3 x^2-x^3}}\right ) \left (-200-590 x-195 x^2+e^{6 x^2-2 x^3} \left (-8-24 x-8 x^2\right )+e^{3 x^2-x^3} \left (-80-238 x-79 x^2-12 x^3+3 x^5\right )\right )\right )}{\left (e^{3 x^2}+5 e^{x^3}\right )^2} \, dx \\ & = \frac {1}{2} \int \left (\frac {15 \exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}+2 x^3\right ) (-2+x) x^3 \left (-2-x+\exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x\right )}{\left (e^{3 x^2}+5 e^{x^3}\right )^2}+4 \left (-2-x+\exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x\right ) \left (-1+\exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right )+2 \exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x\right )-\exp \left (2 x^3-\frac {x \left (4 e^{3 x^2} \left (-2+3 x+x^2\right )+e^{x^3} \left (-39+60 x+20 x^2\right )\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x \left (-2-x+\exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x\right ) \left (1-6 x^2+3 x^3\right )+\frac {5 \exp \left (2 x^3-\frac {x \left (4 e^{3 x^2} (-2+3 x)+e^{x^3} (-39+60 x)\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x \left (-2-x+\exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x\right ) \left (1-6 x^2+3 x^3\right )}{e^{3 x^2}+5 e^{x^3}}\right ) \, dx \\ & = -\left (\frac {1}{2} \int \exp \left (2 x^3-\frac {x \left (4 e^{3 x^2} \left (-2+3 x+x^2\right )+e^{x^3} \left (-39+60 x+20 x^2\right )\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x \left (-2-x+\exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x\right ) \left (1-6 x^2+3 x^3\right ) \, dx\right )+2 \int \left (-2-x+\exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x\right ) \left (-1+\exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right )+2 \exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x\right ) \, dx+\frac {5}{2} \int \frac {\exp \left (2 x^3-\frac {x \left (4 e^{3 x^2} (-2+3 x)+e^{x^3} (-39+60 x)\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x \left (-2-x+\exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x\right ) \left (1-6 x^2+3 x^3\right )}{e^{3 x^2}+5 e^{x^3}} \, dx+\frac {15}{2} \int \frac {\exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}+2 x^3\right ) (-2+x) x^3 \left (-2-x+\exp \left (\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}\right ) x\right )}{\left (e^{3 x^2}+5 e^{x^3}\right )^2} \, dx \\ & = -\left (\frac {1}{2} \int \left (e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}+2 x^3-\frac {x \left (4 e^{3 x^2} \left (-2+3 x+x^2\right )+e^{x^3} \left (-39+60 x+20 x^2\right )\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x^2 \left (1-6 x^2+3 x^3\right )-e^{2 x^3-\frac {x \left (4 e^{3 x^2} \left (-2+3 x+x^2\right )+e^{x^3} \left (-39+60 x+20 x^2\right )\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x \left (2+x-12 x^2+3 x^4\right )\right ) \, dx\right )+2 \int \left (2-\left (-1+e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}}\right ) x\right ) \left (1-e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} (1+2 x)\right ) \, dx+\frac {5}{2} \int \left (\frac {e^{2 x^3-\frac {x \left (4 e^{3 x^2} (-2+3 x)+e^{x^3} (-39+60 x)\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x \left (-2-x+e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x\right )}{e^{3 x^2}+5 e^{x^3}}-\frac {6 e^{2 x^3-\frac {x \left (4 e^{3 x^2} (-2+3 x)+e^{x^3} (-39+60 x)\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x^3 \left (-2-x+e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x\right )}{e^{3 x^2}+5 e^{x^3}}+\frac {3 e^{2 x^3-\frac {x \left (4 e^{3 x^2} (-2+3 x)+e^{x^3} (-39+60 x)\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x^4 \left (-2-x+e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x\right )}{e^{3 x^2}+5 e^{x^3}}\right ) \, dx+\frac {15}{2} \int \left (-\frac {2 e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}+2 x^3} x^3 \left (-2-x+e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x\right )}{\left (e^{3 x^2}+5 e^{x^3}\right )^2}+\frac {e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}+2 x^3} x^4 \left (-2-x+e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x\right )}{\left (e^{3 x^2}+5 e^{x^3}\right )^2}\right ) \, dx \\ & = -\left (\frac {1}{2} \int e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}+2 x^3-\frac {x \left (4 e^{3 x^2} \left (-2+3 x+x^2\right )+e^{x^3} \left (-39+60 x+20 x^2\right )\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x^2 \left (1-6 x^2+3 x^3\right ) \, dx\right )+\frac {1}{2} \int e^{2 x^3-\frac {x \left (4 e^{3 x^2} \left (-2+3 x+x^2\right )+e^{x^3} \left (-39+60 x+20 x^2\right )\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x \left (2+x-12 x^2+3 x^4\right ) \, dx+2 \int \left (2+x+e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{2 \left (e^{3 x^2}+5 e^{x^3}\right )}} x (1+2 x)-2 e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} \left (1+3 x+x^2\right )\right ) \, dx+\frac {5}{2} \int \frac {e^{2 x^3-\frac {x \left (4 e^{3 x^2} (-2+3 x)+e^{x^3} (-39+60 x)\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x \left (-2-x+e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x\right )}{e^{3 x^2}+5 e^{x^3}} \, dx+\frac {15}{2} \int \frac {e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}+2 x^3} x^4 \left (-2-x+e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x\right )}{\left (e^{3 x^2}+5 e^{x^3}\right )^2} \, dx+\frac {15}{2} \int \frac {e^{2 x^3-\frac {x \left (4 e^{3 x^2} (-2+3 x)+e^{x^3} (-39+60 x)\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x^4 \left (-2-x+e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x\right )}{e^{3 x^2}+5 e^{x^3}} \, dx-15 \int \frac {e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}+2 x^3} x^3 \left (-2-x+e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x\right )}{\left (e^{3 x^2}+5 e^{x^3}\right )^2} \, dx-15 \int \frac {e^{2 x^3-\frac {x \left (4 e^{3 x^2} (-2+3 x)+e^{x^3} (-39+60 x)\right )}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x^3 \left (-2-x+e^{\frac {\left (8 e^{3 x^2}+39 e^{x^3}\right ) x}{4 \left (e^{3 x^2}+5 e^{x^3}\right )}} x\right )}{e^{3 x^2}+5 e^{x^3}} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [F]

\[ \int \frac {200+100 x+e^{6 x^2-2 x^3} (8+4 x)+e^{3 x^2-x^3} (80+40 x)+e^{\frac {2 \left (39 x+8 e^{3 x^2-x^3} x\right )}{20+4 e^{3 x^2-x^3}}} \left (100 x+195 x^2+e^{6 x^2-2 x^3} \left (4 x+8 x^2\right )+e^{3 x^2-x^3} \left (40 x+79 x^2+6 x^4-3 x^5\right )\right )+e^{\frac {39 x+8 e^{3 x^2-x^3} x}{20+4 e^{3 x^2-x^3}}} \left (-200-590 x-195 x^2+e^{6 x^2-2 x^3} \left (-8-24 x-8 x^2\right )+e^{3 x^2-x^3} \left (-80-238 x-79 x^2-12 x^3+3 x^5\right )\right )}{50+2 e^{6 x^2-2 x^3}+20 e^{3 x^2-x^3}} \, dx=\int \frac {200+100 x+e^{6 x^2-2 x^3} (8+4 x)+e^{3 x^2-x^3} (80+40 x)+e^{\frac {2 \left (39 x+8 e^{3 x^2-x^3} x\right )}{20+4 e^{3 x^2-x^3}}} \left (100 x+195 x^2+e^{6 x^2-2 x^3} \left (4 x+8 x^2\right )+e^{3 x^2-x^3} \left (40 x+79 x^2+6 x^4-3 x^5\right )\right )+e^{\frac {39 x+8 e^{3 x^2-x^3} x}{20+4 e^{3 x^2-x^3}}} \left (-200-590 x-195 x^2+e^{6 x^2-2 x^3} \left (-8-24 x-8 x^2\right )+e^{3 x^2-x^3} \left (-80-238 x-79 x^2-12 x^3+3 x^5\right )\right )}{50+2 e^{6 x^2-2 x^3}+20 e^{3 x^2-x^3}} \, dx \]

[In]

Integrate[(200 + 100*x + E^(6*x^2 - 2*x^3)*(8 + 4*x) + E^(3*x^2 - x^3)*(80 + 40*x) + E^((2*(39*x + 8*E^(3*x^2
- x^3)*x))/(20 + 4*E^(3*x^2 - x^3)))*(100*x + 195*x^2 + E^(6*x^2 - 2*x^3)*(4*x + 8*x^2) + E^(3*x^2 - x^3)*(40*
x + 79*x^2 + 6*x^4 - 3*x^5)) + E^((39*x + 8*E^(3*x^2 - x^3)*x)/(20 + 4*E^(3*x^2 - x^3)))*(-200 - 590*x - 195*x
^2 + E^(6*x^2 - 2*x^3)*(-8 - 24*x - 8*x^2) + E^(3*x^2 - x^3)*(-80 - 238*x - 79*x^2 - 12*x^3 + 3*x^5)))/(50 + 2
*E^(6*x^2 - 2*x^3) + 20*E^(3*x^2 - x^3)),x]

[Out]

Integrate[(200 + 100*x + E^(6*x^2 - 2*x^3)*(8 + 4*x) + E^(3*x^2 - x^3)*(80 + 40*x) + E^((2*(39*x + 8*E^(3*x^2
- x^3)*x))/(20 + 4*E^(3*x^2 - x^3)))*(100*x + 195*x^2 + E^(6*x^2 - 2*x^3)*(4*x + 8*x^2) + E^(3*x^2 - x^3)*(40*
x + 79*x^2 + 6*x^4 - 3*x^5)) + E^((39*x + 8*E^(3*x^2 - x^3)*x)/(20 + 4*E^(3*x^2 - x^3)))*(-200 - 590*x - 195*x
^2 + E^(6*x^2 - 2*x^3)*(-8 - 24*x - 8*x^2) + E^(3*x^2 - x^3)*(-80 - 238*x - 79*x^2 - 12*x^3 + 3*x^5)))/(50 + 2
*E^(6*x^2 - 2*x^3) + 20*E^(3*x^2 - x^3)), x]

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(81\) vs. \(2(30)=60\).

Time = 0.80 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.41

method	result	size
risch	\(x^{2} {\mathrm e}^{\frac {\left (8 \,{\mathrm e}^{-x^{2} \left (-3+x \right )}+39\right ) x}{2 \,{\mathrm e}^{-x^{2} \left (-3+x \right )}+10}}+x^{2}+4 x +\left (-2 x^{2}-4 x \right ) {\mathrm e}^{\frac {\left (8 \,{\mathrm e}^{-x^{2} \left (-3+x \right )}+39\right ) x}{4 \,{\mathrm e}^{-x^{2} \left (-3+x \right )}+20}}\)	\(82\)
parallelrisch	\({\mathrm e}^{\frac {x \left (8 \,{\mathrm e}^{-x^{3}+3 x^{2}}+39\right )}{2 \,{\mathrm e}^{-x^{3}+3 x^{2}}+10}} x^{2}-2 \,{\mathrm e}^{\frac {x \left (8 \,{\mathrm e}^{-x^{3}+3 x^{2}}+39\right )}{4 \,{\mathrm e}^{-x^{3}+3 x^{2}}+20}} x^{2}+x^{2}-4 \,{\mathrm e}^{\frac {x \left (8 \,{\mathrm e}^{-x^{3}+3 x^{2}}+39\right )}{4 \,{\mathrm e}^{-x^{3}+3 x^{2}}+20}} x +4 x\)	\(130\)

[In]

int((((8*x^2+4*x)*exp(-x^3+3*x^2)^2+(-3*x^5+6*x^4+79*x^2+40*x)*exp(-x^3+3*x^2)+195*x^2+100*x)*exp((8*x*exp(-x^
3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))^2+((-8*x^2-24*x-8)*exp(-x^3+3*x^2)^2+(3*x^5-12*x^3-79*x^2-238*x-80)*exp
(-x^3+3*x^2)-195*x^2-590*x-200)*exp((8*x*exp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))+(4*x+8)*exp(-x^3+3*x^2)
^2+(40*x+80)*exp(-x^3+3*x^2)+100*x+200)/(2*exp(-x^3+3*x^2)^2+20*exp(-x^3+3*x^2)+50),x,method=_RETURNVERBOSE)

[Out]

x^2*exp(1/2*x*(8*exp(-x^2*(-3+x))+39)/(exp(-x^2*(-3+x))+5))+x^2+4*x+(-2*x^2-4*x)*exp(1/4*x*(8*exp(-x^2*(-3+x))
+39)/(exp(-x^2*(-3+x))+5))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 96 vs. \(2 (30) = 60\).

Time = 0.25 (sec) , antiderivative size = 96, normalized size of antiderivative = 2.82 \[ \int \frac {200+100 x+e^{6 x^2-2 x^3} (8+4 x)+e^{3 x^2-x^3} (80+40 x)+e^{\frac {2 \left (39 x+8 e^{3 x^2-x^3} x\right )}{20+4 e^{3 x^2-x^3}}} \left (100 x+195 x^2+e^{6 x^2-2 x^3} \left (4 x+8 x^2\right )+e^{3 x^2-x^3} \left (40 x+79 x^2+6 x^4-3 x^5\right )\right )+e^{\frac {39 x+8 e^{3 x^2-x^3} x}{20+4 e^{3 x^2-x^3}}} \left (-200-590 x-195 x^2+e^{6 x^2-2 x^3} \left (-8-24 x-8 x^2\right )+e^{3 x^2-x^3} \left (-80-238 x-79 x^2-12 x^3+3 x^5\right )\right )}{50+2 e^{6 x^2-2 x^3}+20 e^{3 x^2-x^3}} \, dx=x^{2} e^{\left (\frac {8 \, x e^{\left (-x^{3} + 3 \, x^{2}\right )} + 39 \, x}{2 \, {\left (e^{\left (-x^{3} + 3 \, x^{2}\right )} + 5\right )}}\right )} + x^{2} - 2 \, {\left (x^{2} + 2 \, x\right )} e^{\left (\frac {8 \, x e^{\left (-x^{3} + 3 \, x^{2}\right )} + 39 \, x}{4 \, {\left (e^{\left (-x^{3} + 3 \, x^{2}\right )} + 5\right )}}\right )} + 4 \, x \]

[In]

integrate((((8*x^2+4*x)*exp(-x^3+3*x^2)^2+(-3*x^5+6*x^4+79*x^2+40*x)*exp(-x^3+3*x^2)+195*x^2+100*x)*exp((8*x*e
xp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))^2+((-8*x^2-24*x-8)*exp(-x^3+3*x^2)^2+(3*x^5-12*x^3-79*x^2-238*x-8
0)*exp(-x^3+3*x^2)-195*x^2-590*x-200)*exp((8*x*exp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))+(4*x+8)*exp(-x^3+
3*x^2)^2+(40*x+80)*exp(-x^3+3*x^2)+100*x+200)/(2*exp(-x^3+3*x^2)^2+20*exp(-x^3+3*x^2)+50),x, algorithm="fricas
")

[Out]

x^2*e^(1/2*(8*x*e^(-x^3 + 3*x^2) + 39*x)/(e^(-x^3 + 3*x^2) + 5)) + x^2 - 2*(x^2 + 2*x)*e^(1/4*(8*x*e^(-x^3 + 3
*x^2) + 39*x)/(e^(-x^3 + 3*x^2) + 5)) + 4*x

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (24) = 48\).

Time = 24.56 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.44 \[ \int \frac {200+100 x+e^{6 x^2-2 x^3} (8+4 x)+e^{3 x^2-x^3} (80+40 x)+e^{\frac {2 \left (39 x+8 e^{3 x^2-x^3} x\right )}{20+4 e^{3 x^2-x^3}}} \left (100 x+195 x^2+e^{6 x^2-2 x^3} \left (4 x+8 x^2\right )+e^{3 x^2-x^3} \left (40 x+79 x^2+6 x^4-3 x^5\right )\right )+e^{\frac {39 x+8 e^{3 x^2-x^3} x}{20+4 e^{3 x^2-x^3}}} \left (-200-590 x-195 x^2+e^{6 x^2-2 x^3} \left (-8-24 x-8 x^2\right )+e^{3 x^2-x^3} \left (-80-238 x-79 x^2-12 x^3+3 x^5\right )\right )}{50+2 e^{6 x^2-2 x^3}+20 e^{3 x^2-x^3}} \, dx=x^{2} e^{\frac {2 \cdot \left (8 x e^{- x^{3} + 3 x^{2}} + 39 x\right )}{4 e^{- x^{3} + 3 x^{2}} + 20}} + x^{2} + 4 x + \left (- 2 x^{2} - 4 x\right ) e^{\frac {8 x e^{- x^{3} + 3 x^{2}} + 39 x}{4 e^{- x^{3} + 3 x^{2}} + 20}} \]

[In]

integrate((((8*x**2+4*x)*exp(-x**3+3*x**2)**2+(-3*x**5+6*x**4+79*x**2+40*x)*exp(-x**3+3*x**2)+195*x**2+100*x)*
exp((8*x*exp(-x**3+3*x**2)+39*x)/(4*exp(-x**3+3*x**2)+20))**2+((-8*x**2-24*x-8)*exp(-x**3+3*x**2)**2+(3*x**5-1
2*x**3-79*x**2-238*x-80)*exp(-x**3+3*x**2)-195*x**2-590*x-200)*exp((8*x*exp(-x**3+3*x**2)+39*x)/(4*exp(-x**3+3
*x**2)+20))+(4*x+8)*exp(-x**3+3*x**2)**2+(40*x+80)*exp(-x**3+3*x**2)+100*x+200)/(2*exp(-x**3+3*x**2)**2+20*exp
(-x**3+3*x**2)+50),x)

[Out]

x**2*exp(2*(8*x*exp(-x**3 + 3*x**2) + 39*x)/(4*exp(-x**3 + 3*x**2) + 20)) + x**2 + 4*x + (-2*x**2 - 4*x)*exp((
8*x*exp(-x**3 + 3*x**2) + 39*x)/(4*exp(-x**3 + 3*x**2) + 20))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (30) = 60\).

Time = 0.30 (sec) , antiderivative size = 116, normalized size of antiderivative = 3.41 \[ \int \frac {200+100 x+e^{6 x^2-2 x^3} (8+4 x)+e^{3 x^2-x^3} (80+40 x)+e^{\frac {2 \left (39 x+8 e^{3 x^2-x^3} x\right )}{20+4 e^{3 x^2-x^3}}} \left (100 x+195 x^2+e^{6 x^2-2 x^3} \left (4 x+8 x^2\right )+e^{3 x^2-x^3} \left (40 x+79 x^2+6 x^4-3 x^5\right )\right )+e^{\frac {39 x+8 e^{3 x^2-x^3} x}{20+4 e^{3 x^2-x^3}}} \left (-200-590 x-195 x^2+e^{6 x^2-2 x^3} \left (-8-24 x-8 x^2\right )+e^{3 x^2-x^3} \left (-80-238 x-79 x^2-12 x^3+3 x^5\right )\right )}{50+2 e^{6 x^2-2 x^3}+20 e^{3 x^2-x^3}} \, dx=x^{2} e^{\left (\frac {39 \, x e^{\left (x^{3}\right )}}{2 \, {\left (5 \, e^{\left (x^{3}\right )} + e^{\left (3 \, x^{2}\right )}\right )}} + \frac {4 \, x e^{\left (3 \, x^{2}\right )}}{5 \, e^{\left (x^{3}\right )} + e^{\left (3 \, x^{2}\right )}}\right )} + x^{2} - 2 \, {\left (x^{2} + 2 \, x\right )} e^{\left (\frac {39 \, x e^{\left (x^{3}\right )}}{4 \, {\left (5 \, e^{\left (x^{3}\right )} + e^{\left (3 \, x^{2}\right )}\right )}} + \frac {2 \, x e^{\left (3 \, x^{2}\right )}}{5 \, e^{\left (x^{3}\right )} + e^{\left (3 \, x^{2}\right )}}\right )} + 4 \, x \]

[In]

integrate((((8*x^2+4*x)*exp(-x^3+3*x^2)^2+(-3*x^5+6*x^4+79*x^2+40*x)*exp(-x^3+3*x^2)+195*x^2+100*x)*exp((8*x*e
xp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))^2+((-8*x^2-24*x-8)*exp(-x^3+3*x^2)^2+(3*x^5-12*x^3-79*x^2-238*x-8
0)*exp(-x^3+3*x^2)-195*x^2-590*x-200)*exp((8*x*exp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))+(4*x+8)*exp(-x^3+
3*x^2)^2+(40*x+80)*exp(-x^3+3*x^2)+100*x+200)/(2*exp(-x^3+3*x^2)^2+20*exp(-x^3+3*x^2)+50),x, algorithm="maxima
")

[Out]

x^2*e^(39/2*x*e^(x^3)/(5*e^(x^3) + e^(3*x^2)) + 4*x*e^(3*x^2)/(5*e^(x^3) + e^(3*x^2))) + x^2 - 2*(x^2 + 2*x)*e
^(39/4*x*e^(x^3)/(5*e^(x^3) + e^(3*x^2)) + 2*x*e^(3*x^2)/(5*e^(x^3) + e^(3*x^2))) + 4*x

Giac [F(-1)]

Timed out. \[ \int \frac {200+100 x+e^{6 x^2-2 x^3} (8+4 x)+e^{3 x^2-x^3} (80+40 x)+e^{\frac {2 \left (39 x+8 e^{3 x^2-x^3} x\right )}{20+4 e^{3 x^2-x^3}}} \left (100 x+195 x^2+e^{6 x^2-2 x^3} \left (4 x+8 x^2\right )+e^{3 x^2-x^3} \left (40 x+79 x^2+6 x^4-3 x^5\right )\right )+e^{\frac {39 x+8 e^{3 x^2-x^3} x}{20+4 e^{3 x^2-x^3}}} \left (-200-590 x-195 x^2+e^{6 x^2-2 x^3} \left (-8-24 x-8 x^2\right )+e^{3 x^2-x^3} \left (-80-238 x-79 x^2-12 x^3+3 x^5\right )\right )}{50+2 e^{6 x^2-2 x^3}+20 e^{3 x^2-x^3}} \, dx=\text {Timed out} \]

[In]

integrate((((8*x^2+4*x)*exp(-x^3+3*x^2)^2+(-3*x^5+6*x^4+79*x^2+40*x)*exp(-x^3+3*x^2)+195*x^2+100*x)*exp((8*x*e
xp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))^2+((-8*x^2-24*x-8)*exp(-x^3+3*x^2)^2+(3*x^5-12*x^3-79*x^2-238*x-8
0)*exp(-x^3+3*x^2)-195*x^2-590*x-200)*exp((8*x*exp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))+(4*x+8)*exp(-x^3+
3*x^2)^2+(40*x+80)*exp(-x^3+3*x^2)+100*x+200)/(2*exp(-x^3+3*x^2)^2+20*exp(-x^3+3*x^2)+50),x, algorithm="giac")

[Out]

Timed out

Mupad [B] (verification not implemented)

Time = 0.53 (sec) , antiderivative size = 134, normalized size of antiderivative = 3.94 \[ \int \frac {200+100 x+e^{6 x^2-2 x^3} (8+4 x)+e^{3 x^2-x^3} (80+40 x)+e^{\frac {2 \left (39 x+8 e^{3 x^2-x^3} x\right )}{20+4 e^{3 x^2-x^3}}} \left (100 x+195 x^2+e^{6 x^2-2 x^3} \left (4 x+8 x^2\right )+e^{3 x^2-x^3} \left (40 x+79 x^2+6 x^4-3 x^5\right )\right )+e^{\frac {39 x+8 e^{3 x^2-x^3} x}{20+4 e^{3 x^2-x^3}}} \left (-200-590 x-195 x^2+e^{6 x^2-2 x^3} \left (-8-24 x-8 x^2\right )+e^{3 x^2-x^3} \left (-80-238 x-79 x^2-12 x^3+3 x^5\right )\right )}{50+2 e^{6 x^2-2 x^3}+20 e^{3 x^2-x^3}} \, dx=4\,x-{\mathrm {e}}^{\frac {39\,x}{4\,{\mathrm {e}}^{-x^3}\,{\mathrm {e}}^{3\,x^2}+20}+\frac {8\,x\,{\mathrm {e}}^{-x^3}\,{\mathrm {e}}^{3\,x^2}}{4\,{\mathrm {e}}^{-x^3}\,{\mathrm {e}}^{3\,x^2}+20}}\,\left (2\,x^2+4\,x\right )+x^2\,{\mathrm {e}}^{\frac {78\,x}{4\,{\mathrm {e}}^{-x^3}\,{\mathrm {e}}^{3\,x^2}+20}+\frac {16\,x\,{\mathrm {e}}^{-x^3}\,{\mathrm {e}}^{3\,x^2}}{4\,{\mathrm {e}}^{-x^3}\,{\mathrm {e}}^{3\,x^2}+20}}+x^2 \]

[In]

int((100*x + exp((2*(39*x + 8*x*exp(3*x^2 - x^3)))/(4*exp(3*x^2 - x^3) + 20))*(100*x + exp(3*x^2 - x^3)*(40*x
+ 79*x^2 + 6*x^4 - 3*x^5) + 195*x^2 + exp(6*x^2 - 2*x^3)*(4*x + 8*x^2)) - exp((39*x + 8*x*exp(3*x^2 - x^3))/(4
*exp(3*x^2 - x^3) + 20))*(590*x + exp(3*x^2 - x^3)*(238*x + 79*x^2 + 12*x^3 - 3*x^5 + 80) + 195*x^2 + exp(6*x^
2 - 2*x^3)*(24*x + 8*x^2 + 8) + 200) + exp(6*x^2 - 2*x^3)*(4*x + 8) + exp(3*x^2 - x^3)*(40*x + 80) + 200)/(20*
exp(3*x^2 - x^3) + 2*exp(6*x^2 - 2*x^3) + 50),x)

[Out]

4*x - exp((39*x)/(4*exp(-x^3)*exp(3*x^2) + 20) + (8*x*exp(-x^3)*exp(3*x^2))/(4*exp(-x^3)*exp(3*x^2) + 20))*(4*
x + 2*x^2) + x^2*exp((78*x)/(4*exp(-x^3)*exp(3*x^2) + 20) + (16*x*exp(-x^3)*exp(3*x^2))/(4*exp(-x^3)*exp(3*x^2
) + 20)) + x^2