\(\int e^{-2 x+e^{-2 x} (225 x^6+90 x^7+9 x^8+e^{2 x} (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6)+e^x (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7))} (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5)+e^x (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7)) \, dx\) [4009]

Optimal result

Integrand size = 182, antiderivative size = 31 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{\left (-5-x^2+3 x (5+x) \left (3+2 x+e^{-x} x^2\right )\right )^2} \]

[Out]

exp(((5+x)*x*(6*x+3*x^2/exp(x)+9)-x^2-5)^2)

Rubi [F]

\[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=\int \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx \]

[In]

Int[E^(-2*x + (225*x^6 + 90*x^7 + 9*x^8 + E^(2*x)*(25 - 450*x + 1645*x^2 + 3360*x^3 + 1984*x^4 + 456*x^5 + 36*
x^6) + E^x*(-150*x^3 + 1320*x^4 + 1410*x^5 + 408*x^6 + 36*x^7))/E^(2*x))*(1350*x^5 + 180*x^6 - 108*x^7 - 18*x^
8 + E^(2*x)*(-450 + 3290*x + 10080*x^2 + 7936*x^3 + 2280*x^4 + 216*x^5) + E^x*(-450*x^2 + 5430*x^3 + 5730*x^4
+ 1038*x^5 - 156*x^6 - 36*x^7)),x]

[Out]

-450*Defer[Int][E^((3*x^3*(5 + x) + E^x*(-5 + 45*x + 38*x^2 + 6*x^3))^2/E^(2*x)), x] + 3290*Defer[Int][E^((3*x
^3*(5 + x) + E^x*(-5 + 45*x + 38*x^2 + 6*x^3))^2/E^(2*x))*x, x] + 10080*Defer[Int][E^((3*x^3*(5 + x) + E^x*(-5
+ 45*x + 38*x^2 + 6*x^3))^2/E^(2*x))*x^2, x] - 450*Defer[Int][E^(-x + (225*x^6 + 90*x^7 + 9*x^8 + E^(2*x)*(25
- 450*x + 1645*x^2 + 3360*x^3 + 1984*x^4 + 456*x^5 + 36*x^6) + E^x*(-150*x^3 + 1320*x^4 + 1410*x^5 + 408*x^6
+ 36*x^7))/E^(2*x))*x^2, x] + 7936*Defer[Int][E^((3*x^3*(5 + x) + E^x*(-5 + 45*x + 38*x^2 + 6*x^3))^2/E^(2*x))
*x^3, x] + 5430*Defer[Int][E^(-x + (225*x^6 + 90*x^7 + 9*x^8 + E^(2*x)*(25 - 450*x + 1645*x^2 + 3360*x^3 + 198
4*x^4 + 456*x^5 + 36*x^6) + E^x*(-150*x^3 + 1320*x^4 + 1410*x^5 + 408*x^6 + 36*x^7))/E^(2*x))*x^3, x] + 2280*D
efer[Int][E^((3*x^3*(5 + x) + E^x*(-5 + 45*x + 38*x^2 + 6*x^3))^2/E^(2*x))*x^4, x] + 5730*Defer[Int][E^(-x + (
225*x^6 + 90*x^7 + 9*x^8 + E^(2*x)*(25 - 450*x + 1645*x^2 + 3360*x^3 + 1984*x^4 + 456*x^5 + 36*x^6) + E^x*(-15
0*x^3 + 1320*x^4 + 1410*x^5 + 408*x^6 + 36*x^7))/E^(2*x))*x^4, x] + 216*Defer[Int][E^((3*x^3*(5 + x) + E^x*(-5
+ 45*x + 38*x^2 + 6*x^3))^2/E^(2*x))*x^5, x] + 1350*Defer[Int][E^(-2*x + (225*x^6 + 90*x^7 + 9*x^8 + E^(2*x)*
(25 - 450*x + 1645*x^2 + 3360*x^3 + 1984*x^4 + 456*x^5 + 36*x^6) + E^x*(-150*x^3 + 1320*x^4 + 1410*x^5 + 408*x
^6 + 36*x^7))/E^(2*x))*x^5, x] + 1038*Defer[Int][E^(-x + (225*x^6 + 90*x^7 + 9*x^8 + E^(2*x)*(25 - 450*x + 164
5*x^2 + 3360*x^3 + 1984*x^4 + 456*x^5 + 36*x^6) + E^x*(-150*x^3 + 1320*x^4 + 1410*x^5 + 408*x^6 + 36*x^7))/E^(
2*x))*x^5, x] + 180*Defer[Int][E^(-2*x + (225*x^6 + 90*x^7 + 9*x^8 + E^(2*x)*(25 - 450*x + 1645*x^2 + 3360*x^3
+ 1984*x^4 + 456*x^5 + 36*x^6) + E^x*(-150*x^3 + 1320*x^4 + 1410*x^5 + 408*x^6 + 36*x^7))/E^(2*x))*x^6, x] -
156*Defer[Int][E^(-x + (225*x^6 + 90*x^7 + 9*x^8 + E^(2*x)*(25 - 450*x + 1645*x^2 + 3360*x^3 + 1984*x^4 + 456*
x^5 + 36*x^6) + E^x*(-150*x^3 + 1320*x^4 + 1410*x^5 + 408*x^6 + 36*x^7))/E^(2*x))*x^6, x] - 108*Defer[Int][E^(
-2*x + (225*x^6 + 90*x^7 + 9*x^8 + E^(2*x)*(25 - 450*x + 1645*x^2 + 3360*x^3 + 1984*x^4 + 456*x^5 + 36*x^6) +
E^x*(-150*x^3 + 1320*x^4 + 1410*x^5 + 408*x^6 + 36*x^7))/E^(2*x))*x^7, x] - 36*Defer[Int][E^(-x + (225*x^6 + 9
0*x^7 + 9*x^8 + E^(2*x)*(25 - 450*x + 1645*x^2 + 3360*x^3 + 1984*x^4 + 456*x^5 + 36*x^6) + E^x*(-150*x^3 + 132
0*x^4 + 1410*x^5 + 408*x^6 + 36*x^7))/E^(2*x))*x^7, x] - 18*Defer[Int][E^(-2*x + (225*x^6 + 90*x^7 + 9*x^8 + E
^(2*x)*(25 - 450*x + 1645*x^2 + 3360*x^3 + 1984*x^4 + 456*x^5 + 36*x^6) + E^x*(-150*x^3 + 1320*x^4 + 1410*x^5
+ 408*x^6 + 36*x^7))/E^(2*x))*x^8, x]

Rubi steps \begin{align*} \text {integral}& = \int \left (1350 \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^5+180 \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^6-108 \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^7-18 \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^8-6 \exp \left (-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^2 \left (75-905 x-955 x^2-173 x^3+26 x^4+6 x^5\right )+2 \exp \left (e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) \left (-225+1645 x+5040 x^2+3968 x^3+1140 x^4+108 x^5\right )\right ) \, dx \\ & = 2 \int \exp \left (e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) \left (-225+1645 x+5040 x^2+3968 x^3+1140 x^4+108 x^5\right ) \, dx-6 \int \exp \left (-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^2 \left (75-905 x-955 x^2-173 x^3+26 x^4+6 x^5\right ) \, dx-18 \int \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^8 \, dx-108 \int \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^7 \, dx+180 \int \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^6 \, dx+1350 \int \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^5 \, dx \\ & = 2 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} \left (-225+1645 x+5040 x^2+3968 x^3+1140 x^4+108 x^5\right ) \, dx-6 \int \left (75 e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^2-905 e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^3-955 e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^4-173 e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^5+26 e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^6+6 e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^7\right ) \, dx-18 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^8 \, dx-108 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^7 \, dx+180 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^6 \, dx+1350 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^5 \, dx \\ & = 2 \int \left (-225 e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2}+1645 e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x+5040 e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^2+3968 e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^3+1140 e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^4+108 e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^5\right ) \, dx-18 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^8 \, dx-36 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^7 \, dx-108 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^7 \, dx-156 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^6 \, dx+180 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^6 \, dx-450 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^2 \, dx+1038 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^5 \, dx+1350 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^5 \, dx+5430 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^3 \, dx+5730 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^4 \, dx \\ & = -\left (18 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^8 \, dx\right )-36 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^7 \, dx-108 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^7 \, dx-156 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^6 \, dx+180 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^6 \, dx+216 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^5 \, dx-450 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} \, dx-450 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^2 \, dx+1038 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^5 \, dx+1350 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^5 \, dx+2280 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^4 \, dx+3290 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x \, dx+5430 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^3 \, dx+5730 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^4 \, dx+7936 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^3 \, dx+10080 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^2 \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.22 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.23 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} \]

[In]

Integrate[E^(-2*x + (225*x^6 + 90*x^7 + 9*x^8 + E^(2*x)*(25 - 450*x + 1645*x^2 + 3360*x^3 + 1984*x^4 + 456*x^5
+ 36*x^6) + E^x*(-150*x^3 + 1320*x^4 + 1410*x^5 + 408*x^6 + 36*x^7))/E^(2*x))*(1350*x^5 + 180*x^6 - 108*x^7 -
18*x^8 + E^(2*x)*(-450 + 3290*x + 10080*x^2 + 7936*x^3 + 2280*x^4 + 216*x^5) + E^x*(-450*x^2 + 5430*x^3 + 573
0*x^4 + 1038*x^5 - 156*x^6 - 36*x^7)),x]

[Out]

E^((3*x^3*(5 + x) + E^x*(-5 + 45*x + 38*x^2 + 6*x^3))^2/E^(2*x))

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(86\) vs. \(2(29)=58\).

Time = 2.07 (sec) , antiderivative size = 87, normalized size of antiderivative = 2.81

method	result	size
parallelrisch	\({\mathrm e}^{\left (\left (36 x^{6}+456 x^{5}+1984 x^{4}+3360 x^{3}+1645 x^{2}-450 x +25\right ) {\mathrm e}^{2 x}+\left (36 x^{7}+408 x^{6}+1410 x^{5}+1320 x^{4}-150 x^{3}\right ) {\mathrm e}^{x}+9 x^{8}+90 x^{7}+225 x^{6}\right ) {\mathrm e}^{-2 x}}\)	\(87\)
risch	\({\mathrm e}^{\left (36 x^{7} {\mathrm e}^{x}+9 x^{8}+408 x^{6} {\mathrm e}^{x}+36 \,{\mathrm e}^{2 x} x^{6}+90 x^{7}+1410 x^{5} {\mathrm e}^{x}+456 x^{5} {\mathrm e}^{2 x}+225 x^{6}+1320 \,{\mathrm e}^{x} x^{4}+1984 \,{\mathrm e}^{2 x} x^{4}-150 \,{\mathrm e}^{x} x^{3}+3360 \,{\mathrm e}^{2 x} x^{3}+1645 \,{\mathrm e}^{2 x} x^{2}-450 x \,{\mathrm e}^{2 x}+25 \,{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x}}\)	\(116\)

[In]

int(((216*x^5+2280*x^4+7936*x^3+10080*x^2+3290*x-450)*exp(x)^2+(-36*x^7-156*x^6+1038*x^5+5730*x^4+5430*x^3-450
*x^2)*exp(x)-18*x^8-108*x^7+180*x^6+1350*x^5)*exp(((36*x^6+456*x^5+1984*x^4+3360*x^3+1645*x^2-450*x+25)*exp(x)
^2+(36*x^7+408*x^6+1410*x^5+1320*x^4-150*x^3)*exp(x)+9*x^8+90*x^7+225*x^6)/exp(x)^2)/exp(x)^2,x,method=_RETURN
VERBOSE)

[Out]

exp(((36*x^6+456*x^5+1984*x^4+3360*x^3+1645*x^2-450*x+25)*exp(x)^2+(36*x^7+408*x^6+1410*x^5+1320*x^4-150*x^3)*
exp(x)+9*x^8+90*x^7+225*x^6)/exp(x)^2)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 91 vs. \(2 (29) = 58\).

Time = 0.26 (sec) , antiderivative size = 91, normalized size of antiderivative = 2.94 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{\left ({\left (9 \, x^{8} + 90 \, x^{7} + 225 \, x^{6} + {\left (36 \, x^{6} + 456 \, x^{5} + 1984 \, x^{4} + 3360 \, x^{3} + 1645 \, x^{2} - 452 \, x + 25\right )} e^{\left (2 \, x\right )} + 6 \, {\left (6 \, x^{7} + 68 \, x^{6} + 235 \, x^{5} + 220 \, x^{4} - 25 \, x^{3}\right )} e^{x}\right )} e^{\left (-2 \, x\right )} + 2 \, x\right )} \]

[In]

integrate(((216*x^5+2280*x^4+7936*x^3+10080*x^2+3290*x-450)*exp(x)^2+(-36*x^7-156*x^6+1038*x^5+5730*x^4+5430*x
^3-450*x^2)*exp(x)-18*x^8-108*x^7+180*x^6+1350*x^5)*exp(((36*x^6+456*x^5+1984*x^4+3360*x^3+1645*x^2-450*x+25)*
exp(x)^2+(36*x^7+408*x^6+1410*x^5+1320*x^4-150*x^3)*exp(x)+9*x^8+90*x^7+225*x^6)/exp(x)^2)/exp(x)^2,x, algorit
hm="fricas")

[Out]

e^((9*x^8 + 90*x^7 + 225*x^6 + (36*x^6 + 456*x^5 + 1984*x^4 + 3360*x^3 + 1645*x^2 - 452*x + 25)*e^(2*x) + 6*(6
*x^7 + 68*x^6 + 235*x^5 + 220*x^4 - 25*x^3)*e^x)*e^(-2*x) + 2*x)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (26) = 52\).

Time = 0.35 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.74 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{\left (9 x^{8} + 90 x^{7} + 225 x^{6} + \left (36 x^{7} + 408 x^{6} + 1410 x^{5} + 1320 x^{4} - 150 x^{3}\right ) e^{x} + \left (36 x^{6} + 456 x^{5} + 1984 x^{4} + 3360 x^{3} + 1645 x^{2} - 450 x + 25\right ) e^{2 x}\right ) e^{- 2 x}} \]

[In]

integrate(((216*x**5+2280*x**4+7936*x**3+10080*x**2+3290*x-450)*exp(x)**2+(-36*x**7-156*x**6+1038*x**5+5730*x*
*4+5430*x**3-450*x**2)*exp(x)-18*x**8-108*x**7+180*x**6+1350*x**5)*exp(((36*x**6+456*x**5+1984*x**4+3360*x**3+
1645*x**2-450*x+25)*exp(x)**2+(36*x**7+408*x**6+1410*x**5+1320*x**4-150*x**3)*exp(x)+9*x**8+90*x**7+225*x**6)/
exp(x)**2)/exp(x)**2,x)

[Out]

exp((9*x**8 + 90*x**7 + 225*x**6 + (36*x**7 + 408*x**6 + 1410*x**5 + 1320*x**4 - 150*x**3)*exp(x) + (36*x**6 +
456*x**5 + 1984*x**4 + 3360*x**3 + 1645*x**2 - 450*x + 25)*exp(2*x))*exp(-2*x))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 103 vs. \(2 (29) = 58\).

Time = 1.26 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.32 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{\left (9 \, x^{8} e^{\left (-2 \, x\right )} + 36 \, x^{7} e^{\left (-x\right )} + 90 \, x^{7} e^{\left (-2 \, x\right )} + 408 \, x^{6} e^{\left (-x\right )} + 225 \, x^{6} e^{\left (-2 \, x\right )} + 36 \, x^{6} + 1410 \, x^{5} e^{\left (-x\right )} + 456 \, x^{5} + 1320 \, x^{4} e^{\left (-x\right )} + 1984 \, x^{4} - 150 \, x^{3} e^{\left (-x\right )} + 3360 \, x^{3} + 1645 \, x^{2} - 450 \, x + 25\right )} \]

[In]

integrate(((216*x^5+2280*x^4+7936*x^3+10080*x^2+3290*x-450)*exp(x)^2+(-36*x^7-156*x^6+1038*x^5+5730*x^4+5430*x
^3-450*x^2)*exp(x)-18*x^8-108*x^7+180*x^6+1350*x^5)*exp(((36*x^6+456*x^5+1984*x^4+3360*x^3+1645*x^2-450*x+25)*
exp(x)^2+(36*x^7+408*x^6+1410*x^5+1320*x^4-150*x^3)*exp(x)+9*x^8+90*x^7+225*x^6)/exp(x)^2)/exp(x)^2,x, algorit
hm="maxima")

[Out]

e^(9*x^8*e^(-2*x) + 36*x^7*e^(-x) + 90*x^7*e^(-2*x) + 408*x^6*e^(-x) + 225*x^6*e^(-2*x) + 36*x^6 + 1410*x^5*e^
(-x) + 456*x^5 + 1320*x^4*e^(-x) + 1984*x^4 - 150*x^3*e^(-x) + 3360*x^3 + 1645*x^2 - 450*x + 25)

Giac [F]

\[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=\int { -2 \, {\left (9 \, x^{8} + 54 \, x^{7} - 90 \, x^{6} - 675 \, x^{5} - {\left (108 \, x^{5} + 1140 \, x^{4} + 3968 \, x^{3} + 5040 \, x^{2} + 1645 \, x - 225\right )} e^{\left (2 \, x\right )} + 3 \, {\left (6 \, x^{7} + 26 \, x^{6} - 173 \, x^{5} - 955 \, x^{4} - 905 \, x^{3} + 75 \, x^{2}\right )} e^{x}\right )} e^{\left ({\left (9 \, x^{8} + 90 \, x^{7} + 225 \, x^{6} + {\left (36 \, x^{6} + 456 \, x^{5} + 1984 \, x^{4} + 3360 \, x^{3} + 1645 \, x^{2} - 450 \, x + 25\right )} e^{\left (2 \, x\right )} + 6 \, {\left (6 \, x^{7} + 68 \, x^{6} + 235 \, x^{5} + 220 \, x^{4} - 25 \, x^{3}\right )} e^{x}\right )} e^{\left (-2 \, x\right )} - 2 \, x\right )} \,d x } \]

[In]

integrate(((216*x^5+2280*x^4+7936*x^3+10080*x^2+3290*x-450)*exp(x)^2+(-36*x^7-156*x^6+1038*x^5+5730*x^4+5430*x
^3-450*x^2)*exp(x)-18*x^8-108*x^7+180*x^6+1350*x^5)*exp(((36*x^6+456*x^5+1984*x^4+3360*x^3+1645*x^2-450*x+25)*
exp(x)^2+(36*x^7+408*x^6+1410*x^5+1320*x^4-150*x^3)*exp(x)+9*x^8+90*x^7+225*x^6)/exp(x)^2)/exp(x)^2,x, algorit
hm="giac")

[Out]

integrate(-2*(9*x^8 + 54*x^7 - 90*x^6 - 675*x^5 - (108*x^5 + 1140*x^4 + 3968*x^3 + 5040*x^2 + 1645*x - 225)*e^
(2*x) + 3*(6*x^7 + 26*x^6 - 173*x^5 - 955*x^4 - 905*x^3 + 75*x^2)*e^x)*e^((9*x^8 + 90*x^7 + 225*x^6 + (36*x^6
+ 456*x^5 + 1984*x^4 + 3360*x^3 + 1645*x^2 - 450*x + 25)*e^(2*x) + 6*(6*x^7 + 68*x^6 + 235*x^5 + 220*x^4 - 25*
x^3)*e^x)*e^(-2*x) - 2*x), x)

Mupad [B] (verification not implemented)

Time = 9.70 (sec) , antiderivative size = 117, normalized size of antiderivative = 3.77 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx={\mathrm {e}}^{-450\,x}\,{\mathrm {e}}^{25}\,{\mathrm {e}}^{36\,x^6}\,{\mathrm {e}}^{456\,x^5}\,{\mathrm {e}}^{1645\,x^2}\,{\mathrm {e}}^{1984\,x^4}\,{\mathrm {e}}^{3360\,x^3}\,{\mathrm {e}}^{9\,x^8\,{\mathrm {e}}^{-2\,x}}\,{\mathrm {e}}^{36\,x^7\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{90\,x^7\,{\mathrm {e}}^{-2\,x}}\,{\mathrm {e}}^{-150\,x^3\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{225\,x^6\,{\mathrm {e}}^{-2\,x}}\,{\mathrm {e}}^{408\,x^6\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{1320\,x^4\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{1410\,x^5\,{\mathrm {e}}^{-x}} \]

[In]

int(exp(-2*x)*exp(exp(-2*x)*(exp(x)*(1320*x^4 - 150*x^3 + 1410*x^5 + 408*x^6 + 36*x^7) + 225*x^6 + 90*x^7 + 9*
x^8 + exp(2*x)*(1645*x^2 - 450*x + 3360*x^3 + 1984*x^4 + 456*x^5 + 36*x^6 + 25)))*(exp(2*x)*(3290*x + 10080*x^
2 + 7936*x^3 + 2280*x^4 + 216*x^5 - 450) + 1350*x^5 + 180*x^6 - 108*x^7 - 18*x^8 - exp(x)*(450*x^2 - 5430*x^3
- 5730*x^4 - 1038*x^5 + 156*x^6 + 36*x^7)),x)

[Out]

exp(-450*x)*exp(25)*exp(36*x^6)*exp(456*x^5)*exp(1645*x^2)*exp(1984*x^4)*exp(3360*x^3)*exp(9*x^8*exp(-2*x))*ex
p(36*x^7*exp(-x))*exp(90*x^7*exp(-2*x))*exp(-150*x^3*exp(-x))*exp(225*x^6*exp(-2*x))*exp(408*x^6*exp(-x))*exp(
1320*x^4*exp(-x))*exp(1410*x^5*exp(-x))