\(\int \frac {e^{e^{\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} x+\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} (10+x-x^2+40 x^3+2 x^4-2 x^5+x^7-x^8)}{x+2 x^4+x^7} \, dx\) [2466]

Optimal result

Integrand size = 107, antiderivative size = 24 \[ \int \frac {e^{e^{\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} x+\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} \left (10+x-x^2+40 x^3+2 x^4-2 x^5+x^7-x^8\right )}{x+2 x^4+x^7} \, dx=e^{e^{2-x+2 \left (1-\frac {5}{x+x^4}\right )} x} \] Output:

exp(exp(-x+4-10/(x^4+x))*x)
 

Mathematica [A] (verified)

Time = 0.14 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.17 \[ \int \frac {e^{e^{\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} x+\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} \left (10+x-x^2+40 x^3+2 x^4-2 x^5+x^7-x^8\right )}{x+2 x^4+x^7} \, dx=e^{e^{4-\frac {10}{x}-x+\frac {10 x^2}{1+x^3}} x} \] Input:

Integrate[(E^(E^((-10 + 4*x - x^2 + 4*x^4 - x^5)/(x + x^4))*x + (-10 + 4*x 
 - x^2 + 4*x^4 - x^5)/(x + x^4))*(10 + x - x^2 + 40*x^3 + 2*x^4 - 2*x^5 + 
x^7 - x^8))/(x + 2*x^4 + x^7),x]
 

Output:

E^(E^(4 - 10/x - x + (10*x^2)/(1 + x^3))*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.

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (e^{\frac {-x^5+4 x^4-x^2+4 x-10}{x^4+x}} x+\frac {-x^5+4 x^4-x^2+4 x-10}{x^4+x}\right )}{x^7+2 x^4+x} \, dx\)

\(\Big \downarrow \) 2026

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (e^{\frac {-x^5+4 x^4-x^2+4 x-10}{x^4+x}} x+\frac {-x^5+4 x^4-x^2+4 x-10}{x^4+x}\right )}{x \left (x^6+2 x^3+1\right )}dx\)

\(\Big \downarrow \) 1380

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )\right )-\frac {20 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{\left (x^2-x+1\right )^2}+\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )-\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)^2}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )\right )-\frac {20 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{\left (x^2-x+1\right )^2}+\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )-\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)^2}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )\right )-\frac {20 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{\left (x^2-x+1\right )^2}+\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )-\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)^2}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )\right )-\frac {20 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{\left (x^2-x+1\right )^2}+\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )-\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)^2}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )\right )-\frac {20 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{\left (x^2-x+1\right )^2}+\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )-\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)^2}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )\right )-\frac {20 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{\left (x^2-x+1\right )^2}+\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )-\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)^2}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )\right )-\frac {20 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{\left (x^2-x+1\right )^2}+\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )-\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)^2}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )\right )-\frac {20 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{\left (x^2-x+1\right )^2}+\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )-\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)^2}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )\right )-\frac {20 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{\left (x^2-x+1\right )^2}+\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )-\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)^2}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )\right )-\frac {20 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{\left (x^2-x+1\right )^2}+\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )-\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)^2}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )\right )-\frac {20 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{\left (x^2-x+1\right )^2}+\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )-\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)^2}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )\right )-\frac {20 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{\left (x^2-x+1\right )^2}+\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )-\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)^2}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )\right )-\frac {20 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{\left (x^2-x+1\right )^2}+\exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )-\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{3 (x+1)^2}+\frac {10 \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x \left (x^3+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (x \left (-\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )\right )-\frac {20 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 \left (x^2-x+1\right )}+\frac {10 x \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{\left (x^2-x+1\right )^2}+\exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )-\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{3 (x+1)^2}+\frac {10 \exp \left (-\frac {x^5-4 x^4+x^2-e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} \left (x^5+x^2\right )-4 x+10}{x \left (x^3+1\right )}\right )}{x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-x^8+x^7-2 x^5+2 x^4+40 x^3-x^2+x+10\right ) \exp \left (e^{-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}} x-\frac {x^5-4 x^4+x^2-4 x+10}{x^4+x}\right )}{x \left (x^3+1\right )^2}dx\)

Input:

Int[(E^(E^((-10 + 4*x - x^2 + 4*x^4 - x^5)/(x + x^4))*x + (-10 + 4*x - x^2 
 + 4*x^4 - x^5)/(x + x^4))*(10 + x - x^2 + 40*x^3 + 2*x^4 - 2*x^5 + x^7 - 
x^8))/(x + 2*x^4 + x^7),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 26.87 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.38

method	result	size
parallelrisch	\({\mathrm e}^{x \,{\mathrm e}^{-\frac {x^{5}-4 x^{4}+x^{2}-4 x +10}{x \left (x^{3}+1\right )}}}\)	\(33\)
risch	\({\mathrm e}^{x \,{\mathrm e}^{-\frac {x^{5}-4 x^{4}+x^{2}-4 x +10}{x \left (1+x \right ) \left (x^{2}-x +1\right )}}}\)	\(41\)

Input:

int((-x^8+x^7-2*x^5+2*x^4+40*x^3-x^2+x+10)*exp((-x^5+4*x^4-x^2+4*x-10)/(x^ 
4+x))*exp(x*exp((-x^5+4*x^4-x^2+4*x-10)/(x^4+x)))/(x^7+2*x^4+x),x,method=_ 
RETURNVERBOSE)
 

Output:

exp(x*exp(-(x^5-4*x^4+x^2-4*x+10)/x/(x^3+1)))
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 86 vs. \(2 (18) = 36\).

Time = 0.07 (sec) , antiderivative size = 86, normalized size of antiderivative = 3.58 \[ \int \frac {e^{e^{\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} x+\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} \left (10+x-x^2+40 x^3+2 x^4-2 x^5+x^7-x^8\right )}{x+2 x^4+x^7} \, dx=e^{\left (-\frac {x^{5} - 4 \, x^{4} + x^{2} - {\left (x^{5} + x^{2}\right )} e^{\left (-\frac {x^{5} - 4 \, x^{4} + x^{2} - 4 \, x + 10}{x^{4} + x}\right )} - 4 \, x + 10}{x^{4} + x} + \frac {x^{5} - 4 \, x^{4} + x^{2} - 4 \, x + 10}{x^{4} + x}\right )} \] Input:

integrate((-x^8+x^7-2*x^5+2*x^4+40*x^3-x^2+x+10)*exp((-x^5+4*x^4-x^2+4*x-1 
0)/(x^4+x))*exp(x*exp((-x^5+4*x^4-x^2+4*x-10)/(x^4+x)))/(x^7+2*x^4+x),x, a 
lgorithm="fricas")
 

Output:

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

Sympy [A] (verification not implemented)

Time = 0.38 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {e^{e^{\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} x+\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} \left (10+x-x^2+40 x^3+2 x^4-2 x^5+x^7-x^8\right )}{x+2 x^4+x^7} \, dx=e^{x e^{\frac {- x^{5} + 4 x^{4} - x^{2} + 4 x - 10}{x^{4} + x}}} \] Input:

integrate((-x**8+x**7-2*x**5+2*x**4+40*x**3-x**2+x+10)*exp((-x**5+4*x**4-x 
**2+4*x-10)/(x**4+x))*exp(x*exp((-x**5+4*x**4-x**2+4*x-10)/(x**4+x)))/(x** 
7+2*x**4+x),x)
 

Output:

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

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (18) = 36\).

Time = 0.77 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.92 \[ \int \frac {e^{e^{\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} x+\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} \left (10+x-x^2+40 x^3+2 x^4-2 x^5+x^7-x^8\right )}{x+2 x^4+x^7} \, dx=e^{\left (x e^{\left (-x + \frac {20 \, x}{3 \, {\left (x^{2} - x + 1\right )}} - \frac {10}{3 \, {\left (x^{2} - x + 1\right )}} + \frac {10}{3 \, {\left (x + 1\right )}} - \frac {10}{x} + 4\right )}\right )} \] Input:

integrate((-x^8+x^7-2*x^5+2*x^4+40*x^3-x^2+x+10)*exp((-x^5+4*x^4-x^2+4*x-1 
0)/(x^4+x))*exp(x*exp((-x^5+4*x^4-x^2+4*x-10)/(x^4+x)))/(x^7+2*x^4+x),x, a 
lgorithm="maxima")
 

Output:

e^(x*e^(-x + 20/3*x/(x^2 - x + 1) - 10/3/(x^2 - x + 1) + 10/3/(x + 1) - 10 
/x + 4))
 

Giac [F]

\[ \int \frac {e^{e^{\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} x+\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} \left (10+x-x^2+40 x^3+2 x^4-2 x^5+x^7-x^8\right )}{x+2 x^4+x^7} \, dx=\int { -\frac {{\left (x^{8} - x^{7} + 2 \, x^{5} - 2 \, x^{4} - 40 \, x^{3} + x^{2} - x - 10\right )} e^{\left (x e^{\left (-\frac {x^{5} - 4 \, x^{4} + x^{2} - 4 \, x + 10}{x^{4} + x}\right )} - \frac {x^{5} - 4 \, x^{4} + x^{2} - 4 \, x + 10}{x^{4} + x}\right )}}{x^{7} + 2 \, x^{4} + x} \,d x } \] Input:

integrate((-x^8+x^7-2*x^5+2*x^4+40*x^3-x^2+x+10)*exp((-x^5+4*x^4-x^2+4*x-1 
0)/(x^4+x))*exp(x*exp((-x^5+4*x^4-x^2+4*x-10)/(x^4+x)))/(x^7+2*x^4+x),x, a 
lgorithm="giac")
 

Output:

integrate(-(x^8 - x^7 + 2*x^5 - 2*x^4 - 40*x^3 + x^2 - x - 10)*e^(x*e^(-(x 
^5 - 4*x^4 + x^2 - 4*x + 10)/(x^4 + x)) - (x^5 - 4*x^4 + x^2 - 4*x + 10)/( 
x^4 + x))/(x^7 + 2*x^4 + x), x)
 

Mupad [B] (verification not implemented)

Time = 2.03 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.50 \[ \int \frac {e^{e^{\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} x+\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} \left (10+x-x^2+40 x^3+2 x^4-2 x^5+x^7-x^8\right )}{x+2 x^4+x^7} \, dx={\mathrm {e}}^{x\,{\mathrm {e}}^{-\frac {x^4}{x^3+1}}\,{\mathrm {e}}^{\frac {4\,x^3}{x^3+1}}\,{\mathrm {e}}^{\frac {4}{x^3+1}}\,{\mathrm {e}}^{-\frac {x}{x^3+1}}\,{\mathrm {e}}^{-\frac {10}{x^4+x}}} \] Input:

int((exp(x*exp(-(x^2 - 4*x - 4*x^4 + x^5 + 10)/(x + x^4)))*exp(-(x^2 - 4*x 
 - 4*x^4 + x^5 + 10)/(x + x^4))*(x - x^2 + 40*x^3 + 2*x^4 - 2*x^5 + x^7 - 
x^8 + 10))/(x + 2*x^4 + x^7),x)
 

Output:

exp(x*exp(-x^4/(x^3 + 1))*exp((4*x^3)/(x^3 + 1))*exp(4/(x^3 + 1))*exp(-x/( 
x^3 + 1))*exp(-10/(x + x^4)))
 

Reduce [F]

\[ \int \frac {e^{e^{\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} x+\frac {-10+4 x-x^2+4 x^4-x^5}{x+x^4}} \left (10+x-x^2+40 x^3+2 x^4-2 x^5+x^7-x^8\right )}{x+2 x^4+x^7} \, dx=e^{4} \left (10 \left (\int \frac {e^{\frac {e^{4} x}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}}}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{7}+2 e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{4}+e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x}d x \right )+\int \frac {e^{\frac {e^{4} x}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}}}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{6}+2 e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{3}+e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}d x -\left (\int \frac {e^{\frac {e^{4} x}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}} x^{7}}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{6}+2 e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{3}+e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}d x \right )+\int \frac {e^{\frac {e^{4} x}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}} x^{6}}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{6}+2 e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{3}+e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}d x -2 \left (\int \frac {e^{\frac {e^{4} x}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}} x^{4}}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{6}+2 e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{3}+e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}d x \right )+2 \left (\int \frac {e^{\frac {e^{4} x}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}} x^{3}}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{6}+2 e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{3}+e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}d x \right )+40 \left (\int \frac {e^{\frac {e^{4} x}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}} x^{2}}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{6}+2 e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{3}+e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}d x \right )-\left (\int \frac {e^{\frac {e^{4} x}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}} x}{e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{6}+2 e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}} x^{3}+e^{\frac {x^{5}+x^{2}+10}{x^{4}+x}}}d x \right )\right ) \] Input:

int((-x^8+x^7-2*x^5+2*x^4+40*x^3-x^2+x+10)*exp((-x^5+4*x^4-x^2+4*x-10)/(x^ 
4+x))*exp(x*exp((-x^5+4*x^4-x^2+4*x-10)/(x^4+x)))/(x^7+2*x^4+x),x)
 

Output:

e**4*(10*int(e**((e**4*x)/e**((x**5 + x**2 + 10)/(x**4 + x)))/(e**((x**5 + 
 x**2 + 10)/(x**4 + x))*x**7 + 2*e**((x**5 + x**2 + 10)/(x**4 + x))*x**4 + 
 e**((x**5 + x**2 + 10)/(x**4 + x))*x),x) + int(e**((e**4*x)/e**((x**5 + x 
**2 + 10)/(x**4 + x)))/(e**((x**5 + x**2 + 10)/(x**4 + x))*x**6 + 2*e**((x 
**5 + x**2 + 10)/(x**4 + x))*x**3 + e**((x**5 + x**2 + 10)/(x**4 + x))),x) 
 - int((e**((e**4*x)/e**((x**5 + x**2 + 10)/(x**4 + x)))*x**7)/(e**((x**5 
+ x**2 + 10)/(x**4 + x))*x**6 + 2*e**((x**5 + x**2 + 10)/(x**4 + x))*x**3 
+ e**((x**5 + x**2 + 10)/(x**4 + x))),x) + int((e**((e**4*x)/e**((x**5 + x 
**2 + 10)/(x**4 + x)))*x**6)/(e**((x**5 + x**2 + 10)/(x**4 + x))*x**6 + 2* 
e**((x**5 + x**2 + 10)/(x**4 + x))*x**3 + e**((x**5 + x**2 + 10)/(x**4 + x 
))),x) - 2*int((e**((e**4*x)/e**((x**5 + x**2 + 10)/(x**4 + x)))*x**4)/(e* 
*((x**5 + x**2 + 10)/(x**4 + x))*x**6 + 2*e**((x**5 + x**2 + 10)/(x**4 + x 
))*x**3 + e**((x**5 + x**2 + 10)/(x**4 + x))),x) + 2*int((e**((e**4*x)/e** 
((x**5 + x**2 + 10)/(x**4 + x)))*x**3)/(e**((x**5 + x**2 + 10)/(x**4 + x)) 
*x**6 + 2*e**((x**5 + x**2 + 10)/(x**4 + x))*x**3 + e**((x**5 + x**2 + 10) 
/(x**4 + x))),x) + 40*int((e**((e**4*x)/e**((x**5 + x**2 + 10)/(x**4 + x)) 
)*x**2)/(e**((x**5 + x**2 + 10)/(x**4 + x))*x**6 + 2*e**((x**5 + x**2 + 10 
)/(x**4 + x))*x**3 + e**((x**5 + x**2 + 10)/(x**4 + x))),x) - int((e**((e* 
*4*x)/e**((x**5 + x**2 + 10)/(x**4 + x)))*x)/(e**((x**5 + x**2 + 10)/(x**4 
 + x))*x**6 + 2*e**((x**5 + x**2 + 10)/(x**4 + x))*x**3 + e**((x**5 + x...