\(\int e^{5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} (-9 x^4+18 x^5-9 x^6)+e^{2 x} (36 x^3-66 x^4+24 x^5+6 x^6)} (-72 x+180 x^2-52 x^3-50 x^4-6 x^5+e^{4 x} (-36 x^3+54 x^4+18 x^5-36 x^6)+e^{2 x} (108 x^2-192 x^3-12 x^4+84 x^5+12 x^6)) \, dx\) [781]

Optimal result

Integrand size = 162, antiderivative size = 31 \[ \int e^{5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )} \left (-72 x+180 x^2-52 x^3-50 x^4-6 x^5+e^{4 x} \left (-36 x^3+54 x^4+18 x^5-36 x^6\right )+e^{2 x} \left (108 x^2-192 x^3-12 x^4+84 x^5+12 x^6\right )\right ) \, dx=e^{5-\left (x-x^2\right )^2 \left (x+3 \left (2-e^{2 x} x\right )\right )^2} \] Output:

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

Mathematica [A] (verified)

Time = 0.10 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.00 \[ \int e^{5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )} \left (-72 x+180 x^2-52 x^3-50 x^4-6 x^5+e^{4 x} \left (-36 x^3+54 x^4+18 x^5-36 x^6\right )+e^{2 x} \left (108 x^2-192 x^3-12 x^4+84 x^5+12 x^6\right )\right ) \, dx=e^{5-36 x^2+60 x^3-13 x^4-9 e^{4 x} (-1+x)^2 x^4-10 x^5-x^6+6 e^{2 x} (-1+x)^2 x^3 (6+x)} \] Input:

Integrate[E^(5 - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 
 + 18*x^5 - 9*x^6) + E^(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6))*(-72*x + 
180*x^2 - 52*x^3 - 50*x^4 - 6*x^5 + E^(4*x)*(-36*x^3 + 54*x^4 + 18*x^5 - 3 
6*x^6) + E^(2*x)*(108*x^2 - 192*x^3 - 12*x^4 + 84*x^5 + 12*x^6)),x]
 

Output:

E^(5 - 36*x^2 + 60*x^3 - 13*x^4 - 9*E^(4*x)*(-1 + x)^2*x^4 - 10*x^5 - x^6 
+ 6*E^(2*x)*(-1 + x)^2*x^3*(6 + 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.

\(\displaystyle \int \left (-6 x^5-50 x^4-52 x^3+180 x^2+e^{4 x} \left (-36 x^6+18 x^5+54 x^4-36 x^3\right )+e^{2 x} \left (12 x^6+84 x^5-12 x^4-192 x^3+108 x^2\right )-72 x\right ) \exp \left (-x^6-10 x^5-13 x^4+60 x^3-36 x^2+e^{4 x} \left (-9 x^6+18 x^5-9 x^4\right )+e^{2 x} \left (6 x^6+24 x^5-66 x^4+36 x^3\right )+5\right ) \, dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-6 x^5 \exp \left (-x^6-10 x^5-13 x^4+60 x^3-36 x^2+e^{4 x} \left (-9 x^6+18 x^5-9 x^4\right )+e^{2 x} \left (6 x^6+24 x^5-66 x^4+36 x^3\right )+5\right )-50 x^4 \exp \left (-x^6-10 x^5-13 x^4+60 x^3-36 x^2+e^{4 x} \left (-9 x^6+18 x^5-9 x^4\right )+e^{2 x} \left (6 x^6+24 x^5-66 x^4+36 x^3\right )+5\right )-52 x^3 \exp \left (-x^6-10 x^5-13 x^4+60 x^3-36 x^2+e^{4 x} \left (-9 x^6+18 x^5-9 x^4\right )+e^{2 x} \left (6 x^6+24 x^5-66 x^4+36 x^3\right )+5\right )-18 \left (2 x^3-x^2-3 x+2\right ) x^3 \exp \left (-x^6-10 x^5-13 x^4+60 x^3-36 x^2+e^{4 x} \left (-9 x^6+18 x^5-9 x^4\right )+e^{2 x} \left (6 x^6+24 x^5-66 x^4+36 x^3\right )+4 x+5\right )+180 x^2 \exp \left (-x^6-10 x^5-13 x^4+60 x^3-36 x^2+e^{4 x} \left (-9 x^6+18 x^5-9 x^4\right )+e^{2 x} \left (6 x^6+24 x^5-66 x^4+36 x^3\right )+5\right )+12 \left (x^4+7 x^3-x^2-16 x+9\right ) x^2 \exp \left (-x^6-10 x^5-13 x^4+60 x^3-36 x^2+e^{4 x} \left (-9 x^6+18 x^5-9 x^4\right )+e^{2 x} \left (6 x^6+24 x^5-66 x^4+36 x^3\right )+2 x+5\right )-72 x \exp \left (-x^6-10 x^5-13 x^4+60 x^3-36 x^2+e^{4 x} \left (-9 x^6+18 x^5-9 x^4\right )+e^{2 x} \left (6 x^6+24 x^5-66 x^4+36 x^3\right )+5\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 2 (1-x) x \left (6 e^{2 x} \left (3 e^{2 x}-1\right ) x^4+\left (-48 e^{2 x}+9 e^{4 x}+3\right ) x^3-2 \left (21 e^{2 x}+9 e^{4 x}-14\right ) x^2+54 \left (e^{2 x}+1\right ) x-36\right ) \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right )dx\)

\(\Big \downarrow \) 27

\(\displaystyle 2 \int -\exp \left (-x^6-10 x^5-9 e^{4 x} (1-x)^2 x^4-13 x^4+6 e^{2 x} (1-x)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (6 e^{2 x} \left (1-3 e^{2 x}\right ) x^4-3 \left (1-16 e^{2 x}+3 e^{4 x}\right ) x^3-2 \left (14-21 e^{2 x}-9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 25

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (1-x)^2 x^4-13 x^4+6 e^{2 x} (1-x)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (6 e^{2 x} \left (1-3 e^{2 x}\right ) x^4-3 \left (1-16 e^{2 x}+3 e^{4 x}\right ) x^3-2 \left (14-21 e^{2 x}-9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (9 \exp \left (-x^6-10 x^5-9 e^{4 x} (1-x)^2 x^4-13 x^4+6 e^{2 x} (1-x)^2 (x+6) x^3+60 x^3-36 x^2+4 x+5\right ) \left (2 x^3-x^2-3 x+2\right ) x^3-6 \exp \left (-x^6-10 x^5-9 e^{4 x} (1-x)^2 x^4-13 x^4+6 e^{2 x} (1-x)^2 (x+6) x^3+60 x^3-36 x^2+2 x+5\right ) \left (x^4+7 x^3-x^2-16 x+9\right ) x^2+\exp \left (-x^6-10 x^5-9 e^{4 x} (1-x)^2 x^4-13 x^4+6 e^{2 x} (1-x)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) \left (3 x^4+25 x^3+26 x^2-90 x+36\right ) x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (-6 e^{2 x} \left (-1+3 e^{2 x}\right ) x^4-\left (3-48 e^{2 x}+9 e^{4 x}\right ) x^3+2 \left (-14+21 e^{2 x}+9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (9 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+4 x+5\right ) \left (2 x^3-x^2-3 x+2\right ) x^3-6 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+2 x+5\right ) \left (x^4+7 x^3-x^2-16 x+9\right ) x^2+\exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) \left (3 x^4+25 x^3+26 x^2-90 x+36\right ) x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (-6 e^{2 x} \left (-1+3 e^{2 x}\right ) x^4-\left (3-48 e^{2 x}+9 e^{4 x}\right ) x^3+2 \left (-14+21 e^{2 x}+9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (9 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+4 x+5\right ) \left (2 x^3-x^2-3 x+2\right ) x^3-6 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+2 x+5\right ) \left (x^4+7 x^3-x^2-16 x+9\right ) x^2+\exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) \left (3 x^4+25 x^3+26 x^2-90 x+36\right ) x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (-6 e^{2 x} \left (-1+3 e^{2 x}\right ) x^4-\left (3-48 e^{2 x}+9 e^{4 x}\right ) x^3+2 \left (-14+21 e^{2 x}+9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (9 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+4 x+5\right ) \left (2 x^3-x^2-3 x+2\right ) x^3-6 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+2 x+5\right ) \left (x^4+7 x^3-x^2-16 x+9\right ) x^2+\exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) \left (3 x^4+25 x^3+26 x^2-90 x+36\right ) x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (-6 e^{2 x} \left (-1+3 e^{2 x}\right ) x^4-\left (3-48 e^{2 x}+9 e^{4 x}\right ) x^3+2 \left (-14+21 e^{2 x}+9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (9 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+4 x+5\right ) \left (2 x^3-x^2-3 x+2\right ) x^3-6 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+2 x+5\right ) \left (x^4+7 x^3-x^2-16 x+9\right ) x^2+\exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) \left (3 x^4+25 x^3+26 x^2-90 x+36\right ) x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (-6 e^{2 x} \left (-1+3 e^{2 x}\right ) x^4-\left (3-48 e^{2 x}+9 e^{4 x}\right ) x^3+2 \left (-14+21 e^{2 x}+9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (9 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+4 x+5\right ) \left (2 x^3-x^2-3 x+2\right ) x^3-6 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+2 x+5\right ) \left (x^4+7 x^3-x^2-16 x+9\right ) x^2+\exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) \left (3 x^4+25 x^3+26 x^2-90 x+36\right ) x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (-6 e^{2 x} \left (-1+3 e^{2 x}\right ) x^4-\left (3-48 e^{2 x}+9 e^{4 x}\right ) x^3+2 \left (-14+21 e^{2 x}+9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (9 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+4 x+5\right ) \left (2 x^3-x^2-3 x+2\right ) x^3-6 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+2 x+5\right ) \left (x^4+7 x^3-x^2-16 x+9\right ) x^2+\exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) \left (3 x^4+25 x^3+26 x^2-90 x+36\right ) x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (-6 e^{2 x} \left (-1+3 e^{2 x}\right ) x^4-\left (3-48 e^{2 x}+9 e^{4 x}\right ) x^3+2 \left (-14+21 e^{2 x}+9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (9 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+4 x+5\right ) \left (2 x^3-x^2-3 x+2\right ) x^3-6 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+2 x+5\right ) \left (x^4+7 x^3-x^2-16 x+9\right ) x^2+\exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) \left (3 x^4+25 x^3+26 x^2-90 x+36\right ) x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (-6 e^{2 x} \left (-1+3 e^{2 x}\right ) x^4-\left (3-48 e^{2 x}+9 e^{4 x}\right ) x^3+2 \left (-14+21 e^{2 x}+9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (9 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+4 x+5\right ) \left (2 x^3-x^2-3 x+2\right ) x^3-6 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+2 x+5\right ) \left (x^4+7 x^3-x^2-16 x+9\right ) x^2+\exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) \left (3 x^4+25 x^3+26 x^2-90 x+36\right ) x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (-6 e^{2 x} \left (-1+3 e^{2 x}\right ) x^4-\left (3-48 e^{2 x}+9 e^{4 x}\right ) x^3+2 \left (-14+21 e^{2 x}+9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (9 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+4 x+5\right ) \left (2 x^3-x^2-3 x+2\right ) x^3-6 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+2 x+5\right ) \left (x^4+7 x^3-x^2-16 x+9\right ) x^2+\exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) \left (3 x^4+25 x^3+26 x^2-90 x+36\right ) x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (-6 e^{2 x} \left (-1+3 e^{2 x}\right ) x^4-\left (3-48 e^{2 x}+9 e^{4 x}\right ) x^3+2 \left (-14+21 e^{2 x}+9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (9 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+4 x+5\right ) \left (2 x^3-x^2-3 x+2\right ) x^3-6 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+2 x+5\right ) \left (x^4+7 x^3-x^2-16 x+9\right ) x^2+\exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) \left (3 x^4+25 x^3+26 x^2-90 x+36\right ) x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (-6 e^{2 x} \left (-1+3 e^{2 x}\right ) x^4-\left (3-48 e^{2 x}+9 e^{4 x}\right ) x^3+2 \left (-14+21 e^{2 x}+9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (9 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+4 x+5\right ) \left (2 x^3-x^2-3 x+2\right ) x^3-6 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+2 x+5\right ) \left (x^4+7 x^3-x^2-16 x+9\right ) x^2+\exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) \left (3 x^4+25 x^3+26 x^2-90 x+36\right ) x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (-6 e^{2 x} \left (-1+3 e^{2 x}\right ) x^4-\left (3-48 e^{2 x}+9 e^{4 x}\right ) x^3+2 \left (-14+21 e^{2 x}+9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (9 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+4 x+5\right ) \left (2 x^3-x^2-3 x+2\right ) x^3-6 \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+2 x+5\right ) \left (x^4+7 x^3-x^2-16 x+9\right ) x^2+\exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) \left (3 x^4+25 x^3+26 x^2-90 x+36\right ) x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -2 \int \exp \left (-x^6-10 x^5-9 e^{4 x} (x-1)^2 x^4-13 x^4+6 e^{2 x} (x-1)^2 (x+6) x^3+60 x^3-36 x^2+5\right ) (1-x) x \left (-6 e^{2 x} \left (-1+3 e^{2 x}\right ) x^4-\left (3-48 e^{2 x}+9 e^{4 x}\right ) x^3+2 \left (-14+21 e^{2 x}+9 e^{4 x}\right ) x^2-54 \left (1+e^{2 x}\right ) x+36\right )dx\)

Input:

Int[E^(5 - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18* 
x^5 - 9*x^6) + E^(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6))*(-72*x + 180*x^ 
2 - 52*x^3 - 50*x^4 - 6*x^5 + E^(4*x)*(-36*x^3 + 54*x^4 + 18*x^5 - 36*x^6) 
 + E^(2*x)*(108*x^2 - 192*x^3 - 12*x^4 + 84*x^5 + 12*x^6)),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(77\) vs. \(2(26)=52\).

Time = 0.70 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.52

method	result	size
parallelrisch	\({\mathrm e}^{\left (-9 x^{6}+18 x^{5}-9 x^{4}\right ) {\mathrm e}^{4 x}+\left (6 x^{6}+24 x^{5}-66 x^{4}+36 x^{3}\right ) {\mathrm e}^{2 x}-x^{6}-10 x^{5}-13 x^{4}+60 x^{3}-36 x^{2}+5}\)	\(78\)
risch	\({\mathrm e}^{6 \,{\mathrm e}^{2 x} x^{6}-9 \,{\mathrm e}^{4 x} x^{6}+24 x^{5} {\mathrm e}^{2 x}+18 \,{\mathrm e}^{4 x} x^{5}-x^{6}-66 \,{\mathrm e}^{2 x} x^{4}-9 \,{\mathrm e}^{4 x} x^{4}-10 x^{5}+36 \,{\mathrm e}^{2 x} x^{3}-13 x^{4}+60 x^{3}-36 x^{2}+5}\)	\(92\)

Input:

int(((-36*x^6+18*x^5+54*x^4-36*x^3)*exp(2*x)^2+(12*x^6+84*x^5-12*x^4-192*x 
^3+108*x^2)*exp(2*x)-6*x^5-50*x^4-52*x^3+180*x^2-72*x)*exp((-9*x^6+18*x^5- 
9*x^4)*exp(2*x)^2+(6*x^6+24*x^5-66*x^4+36*x^3)*exp(2*x)-x^6-10*x^5-13*x^4+ 
60*x^3-36*x^2+5),x,method=_RETURNVERBOSE)
 

Output:

exp((-9*x^6+18*x^5-9*x^4)*exp(2*x)^2+(6*x^6+24*x^5-66*x^4+36*x^3)*exp(2*x) 
-x^6-10*x^5-13*x^4+60*x^3-36*x^2+5)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (28) = 56\).

Time = 0.08 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.29 \[ \int e^{5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )} \left (-72 x+180 x^2-52 x^3-50 x^4-6 x^5+e^{4 x} \left (-36 x^3+54 x^4+18 x^5-36 x^6\right )+e^{2 x} \left (108 x^2-192 x^3-12 x^4+84 x^5+12 x^6\right )\right ) \, dx=e^{\left (-x^{6} - 10 \, x^{5} - 13 \, x^{4} + 60 \, x^{3} - 36 \, x^{2} - 9 \, {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} e^{\left (4 \, x\right )} + 6 \, {\left (x^{6} + 4 \, x^{5} - 11 \, x^{4} + 6 \, x^{3}\right )} e^{\left (2 \, x\right )} + 5\right )} \] Input:

integrate(((-36*x^6+18*x^5+54*x^4-36*x^3)*exp(2*x)^2+(12*x^6+84*x^5-12*x^4 
-192*x^3+108*x^2)*exp(2*x)-6*x^5-50*x^4-52*x^3+180*x^2-72*x)*exp((-9*x^6+1 
8*x^5-9*x^4)*exp(2*x)^2+(6*x^6+24*x^5-66*x^4+36*x^3)*exp(2*x)-x^6-10*x^5-1 
3*x^4+60*x^3-36*x^2+5),x, algorithm="fricas")
 

Output:

e^(-x^6 - 10*x^5 - 13*x^4 + 60*x^3 - 36*x^2 - 9*(x^6 - 2*x^5 + x^4)*e^(4*x 
) + 6*(x^6 + 4*x^5 - 11*x^4 + 6*x^3)*e^(2*x) + 5)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (22) = 44\).

Time = 0.25 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.29 \[ \int e^{5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )} \left (-72 x+180 x^2-52 x^3-50 x^4-6 x^5+e^{4 x} \left (-36 x^3+54 x^4+18 x^5-36 x^6\right )+e^{2 x} \left (108 x^2-192 x^3-12 x^4+84 x^5+12 x^6\right )\right ) \, dx=e^{- x^{6} - 10 x^{5} - 13 x^{4} + 60 x^{3} - 36 x^{2} + \left (- 9 x^{6} + 18 x^{5} - 9 x^{4}\right ) e^{4 x} + \left (6 x^{6} + 24 x^{5} - 66 x^{4} + 36 x^{3}\right ) e^{2 x} + 5} \] Input:

integrate(((-36*x**6+18*x**5+54*x**4-36*x**3)*exp(2*x)**2+(12*x**6+84*x**5 
-12*x**4-192*x**3+108*x**2)*exp(2*x)-6*x**5-50*x**4-52*x**3+180*x**2-72*x) 
*exp((-9*x**6+18*x**5-9*x**4)*exp(2*x)**2+(6*x**6+24*x**5-66*x**4+36*x**3) 
*exp(2*x)-x**6-10*x**5-13*x**4+60*x**3-36*x**2+5),x)
 

Output:

exp(-x**6 - 10*x**5 - 13*x**4 + 60*x**3 - 36*x**2 + (-9*x**6 + 18*x**5 - 9 
*x**4)*exp(4*x) + (6*x**6 + 24*x**5 - 66*x**4 + 36*x**3)*exp(2*x) + 5)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 91 vs. \(2 (28) = 56\).

Time = 0.34 (sec) , antiderivative size = 91, normalized size of antiderivative = 2.94 \[ \int e^{5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )} \left (-72 x+180 x^2-52 x^3-50 x^4-6 x^5+e^{4 x} \left (-36 x^3+54 x^4+18 x^5-36 x^6\right )+e^{2 x} \left (108 x^2-192 x^3-12 x^4+84 x^5+12 x^6\right )\right ) \, dx=e^{\left (-9 \, x^{6} e^{\left (4 \, x\right )} + 6 \, x^{6} e^{\left (2 \, x\right )} - x^{6} + 18 \, x^{5} e^{\left (4 \, x\right )} + 24 \, x^{5} e^{\left (2 \, x\right )} - 10 \, x^{5} - 9 \, x^{4} e^{\left (4 \, x\right )} - 66 \, x^{4} e^{\left (2 \, x\right )} - 13 \, x^{4} + 36 \, x^{3} e^{\left (2 \, x\right )} + 60 \, x^{3} - 36 \, x^{2} + 5\right )} \] Input:

integrate(((-36*x^6+18*x^5+54*x^4-36*x^3)*exp(2*x)^2+(12*x^6+84*x^5-12*x^4 
-192*x^3+108*x^2)*exp(2*x)-6*x^5-50*x^4-52*x^3+180*x^2-72*x)*exp((-9*x^6+1 
8*x^5-9*x^4)*exp(2*x)^2+(6*x^6+24*x^5-66*x^4+36*x^3)*exp(2*x)-x^6-10*x^5-1 
3*x^4+60*x^3-36*x^2+5),x, algorithm="maxima")
 

Output:

e^(-9*x^6*e^(4*x) + 6*x^6*e^(2*x) - x^6 + 18*x^5*e^(4*x) + 24*x^5*e^(2*x) 
- 10*x^5 - 9*x^4*e^(4*x) - 66*x^4*e^(2*x) - 13*x^4 + 36*x^3*e^(2*x) + 60*x 
^3 - 36*x^2 + 5)
 

Giac [F]

\[ \int e^{5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )} \left (-72 x+180 x^2-52 x^3-50 x^4-6 x^5+e^{4 x} \left (-36 x^3+54 x^4+18 x^5-36 x^6\right )+e^{2 x} \left (108 x^2-192 x^3-12 x^4+84 x^5+12 x^6\right )\right ) \, dx=\int { -2 \, {\left (3 \, x^{5} + 25 \, x^{4} + 26 \, x^{3} - 90 \, x^{2} + 9 \, {\left (2 \, x^{6} - x^{5} - 3 \, x^{4} + 2 \, x^{3}\right )} e^{\left (4 \, x\right )} - 6 \, {\left (x^{6} + 7 \, x^{5} - x^{4} - 16 \, x^{3} + 9 \, x^{2}\right )} e^{\left (2 \, x\right )} + 36 \, x\right )} e^{\left (-x^{6} - 10 \, x^{5} - 13 \, x^{4} + 60 \, x^{3} - 36 \, x^{2} - 9 \, {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} e^{\left (4 \, x\right )} + 6 \, {\left (x^{6} + 4 \, x^{5} - 11 \, x^{4} + 6 \, x^{3}\right )} e^{\left (2 \, x\right )} + 5\right )} \,d x } \] Input:

integrate(((-36*x^6+18*x^5+54*x^4-36*x^3)*exp(2*x)^2+(12*x^6+84*x^5-12*x^4 
-192*x^3+108*x^2)*exp(2*x)-6*x^5-50*x^4-52*x^3+180*x^2-72*x)*exp((-9*x^6+1 
8*x^5-9*x^4)*exp(2*x)^2+(6*x^6+24*x^5-66*x^4+36*x^3)*exp(2*x)-x^6-10*x^5-1 
3*x^4+60*x^3-36*x^2+5),x, algorithm="giac")
 

Output:

integrate(-2*(3*x^5 + 25*x^4 + 26*x^3 - 90*x^2 + 9*(2*x^6 - x^5 - 3*x^4 + 
2*x^3)*e^(4*x) - 6*(x^6 + 7*x^5 - x^4 - 16*x^3 + 9*x^2)*e^(2*x) + 36*x)*e^ 
(-x^6 - 10*x^5 - 13*x^4 + 60*x^3 - 36*x^2 - 9*(x^6 - 2*x^5 + x^4)*e^(4*x) 
+ 6*(x^6 + 4*x^5 - 11*x^4 + 6*x^3)*e^(2*x) + 5), x)
 

Mupad [B] (verification not implemented)

Time = 0.77 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.32 \[ \int e^{5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )} \left (-72 x+180 x^2-52 x^3-50 x^4-6 x^5+e^{4 x} \left (-36 x^3+54 x^4+18 x^5-36 x^6\right )+e^{2 x} \left (108 x^2-192 x^3-12 x^4+84 x^5+12 x^6\right )\right ) \, dx={\mathrm {e}}^5\,{\mathrm {e}}^{-x^6}\,{\mathrm {e}}^{-10\,x^5}\,{\mathrm {e}}^{-13\,x^4}\,{\mathrm {e}}^{-36\,x^2}\,{\mathrm {e}}^{60\,x^3}\,{\mathrm {e}}^{6\,x^6\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-9\,x^4\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{-9\,x^6\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{18\,x^5\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{24\,x^5\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{36\,x^3\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-66\,x^4\,{\mathrm {e}}^{2\,x}} \] Input:

int(-exp(exp(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6) - exp(4*x)*(9*x^4 - 1 
8*x^5 + 9*x^6) - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + 5)*(72*x - exp( 
2*x)*(108*x^2 - 192*x^3 - 12*x^4 + 84*x^5 + 12*x^6) + exp(4*x)*(36*x^3 - 5 
4*x^4 - 18*x^5 + 36*x^6) - 180*x^2 + 52*x^3 + 50*x^4 + 6*x^5),x)
 

Output:

exp(5)*exp(-x^6)*exp(-10*x^5)*exp(-13*x^4)*exp(-36*x^2)*exp(60*x^3)*exp(6* 
x^6*exp(2*x))*exp(-9*x^4*exp(4*x))*exp(-9*x^6*exp(4*x))*exp(18*x^5*exp(4*x 
))*exp(24*x^5*exp(2*x))*exp(36*x^3*exp(2*x))*exp(-66*x^4*exp(2*x))
 

Reduce [B] (verification not implemented)

Time = 68.78 (sec) , antiderivative size = 105, normalized size of antiderivative = 3.39 \[ \int e^{5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )} \left (-72 x+180 x^2-52 x^3-50 x^4-6 x^5+e^{4 x} \left (-36 x^3+54 x^4+18 x^5-36 x^6\right )+e^{2 x} \left (108 x^2-192 x^3-12 x^4+84 x^5+12 x^6\right )\right ) \, dx=\frac {e^{18 e^{4 x} x^{5}+6 e^{2 x} x^{6}+24 e^{2 x} x^{5}+36 e^{2 x} x^{3}+60 x^{3}} e^{5}}{e^{9 e^{4 x} x^{6}+9 e^{4 x} x^{4}+66 e^{2 x} x^{4}+x^{6}+10 x^{5}+13 x^{4}+36 x^{2}}} \] Input:

int(((-36*x^6+18*x^5+54*x^4-36*x^3)*exp(2*x)^2+(12*x^6+84*x^5-12*x^4-192*x 
^3+108*x^2)*exp(2*x)-6*x^5-50*x^4-52*x^3+180*x^2-72*x)*exp((-9*x^6+18*x^5- 
9*x^4)*exp(2*x)^2+(6*x^6+24*x^5-66*x^4+36*x^3)*exp(2*x)-x^6-10*x^5-13*x^4+ 
60*x^3-36*x^2+5),x)
 

Output:

(e**(18*e**(4*x)*x**5 + 6*e**(2*x)*x**6 + 24*e**(2*x)*x**5 + 36*e**(2*x)*x 
**3 + 60*x**3)*e**5)/e**(9*e**(4*x)*x**6 + 9*e**(4*x)*x**4 + 66*e**(2*x)*x 
**4 + x**6 + 10*x**5 + 13*x**4 + 36*x**2)