\(\int e^{-2 x+e^{-2 x} (225 x^6+90 x^7+9 x^8+e^{2 x} (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6)+e^x (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7))} (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5)+e^x (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7)) \, dx\) [1009]

Optimal result

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

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

Mathematica [A] (verified)

Time = 0.13 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.23 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} \] Input:

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 - 1 
8*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]
 

Output:

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

Rubi [F]

Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.

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

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-18 x^8 \exp \left (e^{-2 x} \left (9 x^8+90 x^7+225 x^6+e^x \left (36 x^7+408 x^6+1410 x^5+1320 x^4-150 x^3\right )+e^{2 x} \left (36 x^6+456 x^5+1984 x^4+3360 x^3+1645 x^2-450 x+25\right )\right )-2 x\right )-108 x^7 \exp \left (e^{-2 x} \left (9 x^8+90 x^7+225 x^6+e^x \left (36 x^7+408 x^6+1410 x^5+1320 x^4-150 x^3\right )+e^{2 x} \left (36 x^6+456 x^5+1984 x^4+3360 x^3+1645 x^2-450 x+25\right )\right )-2 x\right )+180 x^6 \exp \left (e^{-2 x} \left (9 x^8+90 x^7+225 x^6+e^x \left (36 x^7+408 x^6+1410 x^5+1320 x^4-150 x^3\right )+e^{2 x} \left (36 x^6+456 x^5+1984 x^4+3360 x^3+1645 x^2-450 x+25\right )\right )-2 x\right )+1350 x^5 \exp \left (e^{-2 x} \left (9 x^8+90 x^7+225 x^6+e^x \left (36 x^7+408 x^6+1410 x^5+1320 x^4-150 x^3\right )+e^{2 x} \left (36 x^6+456 x^5+1984 x^4+3360 x^3+1645 x^2-450 x+25\right )\right )-2 x\right )-6 \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2 \exp \left (e^{-2 x} \left (9 x^8+90 x^7+225 x^6+e^x \left (36 x^7+408 x^6+1410 x^5+1320 x^4-150 x^3\right )+e^{2 x} \left (36 x^6+456 x^5+1984 x^4+3360 x^3+1645 x^2-450 x+25\right )\right )-x\right )+2 \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right ) \exp \left (e^{-2 x} \left (9 x^8+90 x^7+225 x^6+e^x \left (36 x^7+408 x^6+1410 x^5+1320 x^4-150 x^3\right )+e^{2 x} \left (36 x^6+456 x^5+1984 x^4+3360 x^3+1645 x^2-450 x+25\right )\right )\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 2 \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right ) \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+3360 x^3+1645 x^2+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3-452 x+25\right )dx\)

\(\Big \downarrow \) 27

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4-6 e^{-x} \left (-6 x^4-68 x^3-235 x^2-220 x+25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (9 \left (-x^3-6 x^2+10 x+75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2-e^{2 x} \left (-108 x^5-1140 x^4-3968 x^3-5040 x^2-1645 x+225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4-6 e^{-x} \left (-6 x^4-68 x^3-235 x^2-220 x+25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4-6 e^{-x} \left (-6 x^4-68 x^3-235 x^2-220 x+25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4-6 e^{-x} \left (-6 x^4-68 x^3-235 x^2-220 x+25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (-9 \left (x^3+6 x^2-10 x-75\right ) x^5-3 e^x \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+e^{2 x} \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (-9 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-452 x+25\right ) \left (x^3+6 x^2-10 x-75\right ) x^5-3 \exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-451 x+25\right ) \left (6 x^5+26 x^4-173 x^3-955 x^2-905 x+75\right ) x^2+\exp \left (9 e^{-2 x} (x+5)^2 x^6+36 x^6+456 x^5+1984 x^4+6 e^{-x} \left (6 x^4+68 x^3+235 x^2+220 x-25\right ) x^3+3360 x^3+1645 x^2-450 x+25\right ) \left (108 x^5+1140 x^4+3968 x^3+5040 x^2+1645 x-225\right )\right )dx\)

Input:

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]
 

Output:

$Aborted
 

Maple [B] (verified)

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

Time = 0.85 (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	\({\mathrm e}^{\left (36 x^{7} {\mathrm e}^{x}+9 x^{8}+36 x^{6} {\mathrm e}^{2 x}+408 x^{6} {\mathrm e}^{x}+90 x^{7}+456 x^{5} {\mathrm e}^{2 x}+1410 x^{5} {\mathrm e}^{x}+225 x^{6}+1984 \,{\mathrm e}^{2 x} x^{4}+1320 \,{\mathrm e}^{x} x^{4}+3360 \,{\mathrm e}^{2 x} x^{3}-150 \,{\mathrm e}^{x} x^{3}+1645 \,{\mathrm e}^{2 x} x^{2}-450 x \,{\mathrm e}^{2 x}+25 \,{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x}}\)	\(116\)

Input:

int(((216*x^5+2280*x^4+7936*x^3+10080*x^2+3290*x-450)*exp(x)^2+(-36*x^7-15 
6*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+13 
50*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)/e 
xp(x)^2)/exp(x)^2,x,method=_RETURNVERBOSE)
 

Output:

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 = 0.10 (sec) , antiderivative size = 91, normalized size of antiderivative = 2.94 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{\left ({\left (9 \, x^{8} + 90 \, x^{7} + 225 \, x^{6} + {\left (36 \, x^{6} + 456 \, x^{5} + 1984 \, x^{4} + 3360 \, x^{3} + 1645 \, x^{2} - 452 \, x + 25\right )} e^{\left (2 \, x\right )} + 6 \, {\left (6 \, x^{7} + 68 \, x^{6} + 235 \, x^{5} + 220 \, x^{4} - 25 \, x^{3}\right )} e^{x}\right )} e^{\left (-2 \, x\right )} + 2 \, x\right )} \] Input:

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)*ex 
p(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, algorithm="fricas")
 

Output:

e^((9*x^8 + 90*x^7 + 225*x^6 + (36*x^6 + 456*x^5 + 1984*x^4 + 3360*x^3 + 1 
645*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 = 0.56 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.74 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{\left (9 x^{8} + 90 x^{7} + 225 x^{6} + \left (36 x^{7} + 408 x^{6} + 1410 x^{5} + 1320 x^{4} - 150 x^{3}\right ) e^{x} + \left (36 x^{6} + 456 x^{5} + 1984 x^{4} + 3360 x^{3} + 1645 x^{2} - 450 x + 25\right ) e^{2 x}\right ) e^{- 2 x}} \] Input:

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+16 
45*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)
 

Output:

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 + 16 
45*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 = 1.15 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.32 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{\left (9 \, x^{8} e^{\left (-2 \, x\right )} + 36 \, x^{7} e^{\left (-x\right )} + 90 \, x^{7} e^{\left (-2 \, x\right )} + 408 \, x^{6} e^{\left (-x\right )} + 225 \, x^{6} e^{\left (-2 \, x\right )} + 36 \, x^{6} + 1410 \, x^{5} e^{\left (-x\right )} + 456 \, x^{5} + 1320 \, x^{4} e^{\left (-x\right )} + 1984 \, x^{4} - 150 \, x^{3} e^{\left (-x\right )} + 3360 \, x^{3} + 1645 \, x^{2} - 450 \, x + 25\right )} \] Input:

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)*ex 
p(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, algorithm="maxima")
 

Output:

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) + 198 
4*x^4 - 150*x^3*e^(-x) + 3360*x^3 + 1645*x^2 - 450*x + 25)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 115 vs. \(2 (29) = 58\).

Time = 0.59 (sec) , antiderivative size = 115, normalized size of antiderivative = 3.71 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{\left ({\left (9 \, x^{8} + 36 \, x^{7} e^{x} + 90 \, x^{7} + 36 \, x^{6} e^{\left (2 \, x\right )} + 408 \, x^{6} e^{x} + 225 \, x^{6} + 456 \, x^{5} e^{\left (2 \, x\right )} + 1410 \, x^{5} e^{x} + 1984 \, x^{4} e^{\left (2 \, x\right )} + 1320 \, x^{4} e^{x} + 3360 \, x^{3} e^{\left (2 \, x\right )} - 150 \, x^{3} e^{x} + 1645 \, x^{2} e^{\left (2 \, x\right )} - 450 \, x e^{\left (2 \, x\right )} + 25 \, e^{\left (2 \, x\right )}\right )} e^{\left (-2 \, x\right )}\right )} \] Input:

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)*ex 
p(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, algorithm="giac")
 

Output:

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

Mupad [B] (verification not implemented)

Time = 3.23 (sec) , antiderivative size = 117, normalized size of antiderivative = 3.77 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx={\mathrm {e}}^{-450\,x}\,{\mathrm {e}}^{25}\,{\mathrm {e}}^{36\,x^6}\,{\mathrm {e}}^{456\,x^5}\,{\mathrm {e}}^{1645\,x^2}\,{\mathrm {e}}^{1984\,x^4}\,{\mathrm {e}}^{3360\,x^3}\,{\mathrm {e}}^{9\,x^8\,{\mathrm {e}}^{-2\,x}}\,{\mathrm {e}}^{36\,x^7\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{90\,x^7\,{\mathrm {e}}^{-2\,x}}\,{\mathrm {e}}^{-150\,x^3\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{225\,x^6\,{\mathrm {e}}^{-2\,x}}\,{\mathrm {e}}^{408\,x^6\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{1320\,x^4\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{1410\,x^5\,{\mathrm {e}}^{-x}} \] Input:

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 + 336 
0*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)
 

Output:

exp(-450*x)*exp(25)*exp(36*x^6)*exp(456*x^5)*exp(1645*x^2)*exp(1984*x^4)*e 
xp(3360*x^3)*exp(9*x^8*exp(-2*x))*exp(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(13 
20*x^4*exp(-x))*exp(1410*x^5*exp(-x))
 

Reduce [F]

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

int(((216*x^5+2280*x^4+7936*x^3+10080*x^2+3290*x-450)*exp(x)^2+(-36*x^7-15 
6*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+13 
50*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)/e 
xp(x)^2)/exp(x)^2,x)
 

Output:

int(((216*x^5+2280*x^4+7936*x^3+10080*x^2+3290*x-450)*exp(x)^2+(-36*x^7-15 
6*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+13 
50*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)/e 
xp(x)^2)/exp(x)^2,x)