\(\int \frac {e^{\frac {x^3}{8 e^3 x^2+e^5 x^3+e^x (8 e^3+e^5 x)}} (128 e^6 x^4+16 e^3 x^5+32 e^8 x^5+2 e^{10} x^6+e^{2 x} (128 e^6+32 e^8 x+2 e^{10} x^2)+e^x (256 e^6 x^2+4 e^{10} x^4+e^3 (48 x^3-16 x^4)+e^5 (64 e^3 x^3+4 x^4-2 x^5)))}{64 e^6 x^4+16 e^8 x^5+e^{10} x^6+e^{2 x} (64 e^6+16 e^8 x+e^{10} x^2)+e^x (128 e^6 x^2+32 e^8 x^3+2 e^{10} x^4)} \, dx\) [74]

Optimal result

Integrand size = 238, antiderivative size = 32 \[ \int \frac {e^{\frac {x^3}{8 e^3 x^2+e^5 x^3+e^x \left (8 e^3+e^5 x\right )}} \left (128 e^6 x^4+16 e^3 x^5+32 e^8 x^5+2 e^{10} x^6+e^{2 x} \left (128 e^6+32 e^8 x+2 e^{10} x^2\right )+e^x \left (256 e^6 x^2+4 e^{10} x^4+e^3 \left (48 x^3-16 x^4\right )+e^5 \left (64 e^3 x^3+4 x^4-2 x^5\right )\right )\right )}{64 e^6 x^4+16 e^8 x^5+e^{10} x^6+e^{2 x} \left (64 e^6+16 e^8 x+e^{10} x^2\right )+e^x \left (128 e^6 x^2+32 e^8 x^3+2 e^{10} x^4\right )} \, dx=2 e^{\frac {x^2}{\left (e^5+\frac {8 e^3}{x}\right ) \left (e^x+x^2\right )}} x \] Output:

2*exp(x^2/(exp(5)+8*exp(3)/x)/(x^2+exp(x)))*x
 

Mathematica [A] (verified)

Time = 0.13 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.94 \[ \int \frac {e^{\frac {x^3}{8 e^3 x^2+e^5 x^3+e^x \left (8 e^3+e^5 x\right )}} \left (128 e^6 x^4+16 e^3 x^5+32 e^8 x^5+2 e^{10} x^6+e^{2 x} \left (128 e^6+32 e^8 x+2 e^{10} x^2\right )+e^x \left (256 e^6 x^2+4 e^{10} x^4+e^3 \left (48 x^3-16 x^4\right )+e^5 \left (64 e^3 x^3+4 x^4-2 x^5\right )\right )\right )}{64 e^6 x^4+16 e^8 x^5+e^{10} x^6+e^{2 x} \left (64 e^6+16 e^8 x+e^{10} x^2\right )+e^x \left (128 e^6 x^2+32 e^8 x^3+2 e^{10} x^4\right )} \, dx=2 e^{\frac {x^3}{e^3 \left (8+e^2 x\right ) \left (e^x+x^2\right )}} x \] Input:

Integrate[(E^(x^3/(8*E^3*x^2 + E^5*x^3 + E^x*(8*E^3 + E^5*x)))*(128*E^6*x^ 
4 + 16*E^3*x^5 + 32*E^8*x^5 + 2*E^10*x^6 + E^(2*x)*(128*E^6 + 32*E^8*x + 2 
*E^10*x^2) + E^x*(256*E^6*x^2 + 4*E^10*x^4 + E^3*(48*x^3 - 16*x^4) + E^5*( 
64*E^3*x^3 + 4*x^4 - 2*x^5))))/(64*E^6*x^4 + 16*E^8*x^5 + E^10*x^6 + E^(2* 
x)*(64*E^6 + 16*E^8*x + E^10*x^2) + E^x*(128*E^6*x^2 + 32*E^8*x^3 + 2*E^10 
*x^4)),x]
 

Output:

2*E^(x^3/(E^3*(8 + E^2*x)*(E^x + x^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.

\(\displaystyle \int \frac {\left (2 e^{10} x^6+32 e^8 x^5+16 e^3 x^5+128 e^6 x^4+e^{2 x} \left (2 e^{10} x^2+32 e^8 x+128 e^6\right )+e^x \left (4 e^{10} x^4+256 e^6 x^2+e^3 \left (48 x^3-16 x^4\right )+e^5 \left (-2 x^5+4 x^4+64 e^3 x^3\right )\right )\right ) \exp \left (\frac {x^3}{e^5 x^3+8 e^3 x^2+e^x \left (e^5 x+8 e^3\right )}\right )}{e^{10} x^6+16 e^8 x^5+64 e^6 x^4+e^{2 x} \left (e^{10} x^2+16 e^8 x+64 e^6\right )+e^x \left (2 e^{10} x^4+32 e^8 x^3+128 e^6 x^2\right )} \, dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {\left (2 e^{10} x^6+\left (16 e^3+32 e^8\right ) x^5+128 e^6 x^4+e^{2 x} \left (2 e^{10} x^2+32 e^8 x+128 e^6\right )+e^x \left (4 e^{10} x^4+256 e^6 x^2+e^3 \left (48 x^3-16 x^4\right )+e^5 \left (-2 x^5+4 x^4+64 e^3 x^3\right )\right )\right ) \exp \left (\frac {x^3}{e^5 x^3+8 e^3 x^2+e^x \left (e^5 x+8 e^3\right )}\right )}{e^{10} x^6+16 e^8 x^5+64 e^6 x^4+e^{2 x} \left (e^{10} x^2+16 e^8 x+64 e^6\right )+e^x \left (2 e^{10} x^4+32 e^8 x^3+128 e^6 x^2\right )}dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {e^{\frac {x^3}{e^3 \left (e^2 x+8\right ) \left (x^2+e^x\right )}-6} \left (2 e^{10} x^6+\left (16 e^3+32 e^8\right ) x^5+128 e^6 x^4+e^{2 x} \left (2 e^{10} x^2+32 e^8 x+128 e^6\right )+e^x \left (4 e^{10} x^4+256 e^6 x^2+e^3 \left (48 x^3-16 x^4\right )+e^5 \left (-2 x^5+4 x^4+64 e^3 x^3\right )\right )\right )}{\left (e^2 x+8\right )^2 \left (x^2+e^x\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {2 e^{\frac {x^3}{e^3 \left (e^2 x+8\right ) \left (x^2+e^x\right )}-3} \left (-e^2 x^2-2 \left (4-e^2\right ) x+24\right ) x^3}{\left (e^2 x+8\right )^2 \left (x^2+e^x\right )}+2 e^{\frac {x^3}{e^3 \left (e^2 x+8\right ) \left (x^2+e^x\right )}}+\frac {2 e^{\frac {x^3}{e^3 \left (e^2 x+8\right ) \left (x^2+e^x\right )}-3} (x-2) x^5}{\left (e^2 x+8\right ) \left (x^2+e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7299

\(\displaystyle \int \left (\frac {2 e^{\frac {x^3}{e^3 \left (e^2 x+8\right ) \left (x^2+e^x\right )}-3} \left (-e^2 x^2-2 \left (4-e^2\right ) x+24\right ) x^3}{\left (e^2 x+8\right )^2 \left (x^2+e^x\right )}+2 e^{\frac {x^3}{e^3 \left (e^2 x+8\right ) \left (x^2+e^x\right )}}+\frac {2 e^{\frac {x^3}{e^3 \left (e^2 x+8\right ) \left (x^2+e^x\right )}-3} (x-2) x^5}{\left (e^2 x+8\right ) \left (x^2+e^x\right )^2}\right )dx\)

Input:

Int[(E^(x^3/(8*E^3*x^2 + E^5*x^3 + E^x*(8*E^3 + E^5*x)))*(128*E^6*x^4 + 16 
*E^3*x^5 + 32*E^8*x^5 + 2*E^10*x^6 + E^(2*x)*(128*E^6 + 32*E^8*x + 2*E^10* 
x^2) + E^x*(256*E^6*x^2 + 4*E^10*x^4 + E^3*(48*x^3 - 16*x^4) + E^5*(64*E^3 
*x^3 + 4*x^4 - 2*x^5))))/(64*E^6*x^4 + 16*E^8*x^5 + E^10*x^6 + E^(2*x)*(64 
*E^6 + 16*E^8*x + E^10*x^2) + E^x*(128*E^6*x^2 + 32*E^8*x^3 + 2*E^10*x^4)) 
,x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 23.14 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.16

method	result	size
risch	\(2 x \,{\mathrm e}^{\frac {x^{3}}{x^{3} {\mathrm e}^{5}+x \,{\mathrm e}^{5+x}+8 x^{2} {\mathrm e}^{3}+8 \,{\mathrm e}^{3+x}}}\)	\(37\)
parallelrisch	\(2 x \,{\mathrm e}^{\frac {x^{3}}{x^{3} {\mathrm e}^{5}+x \,{\mathrm e}^{5} {\mathrm e}^{x}+8 x^{2} {\mathrm e}^{3}+8 \,{\mathrm e}^{x} {\mathrm e}^{3}}}\)	\(37\)

Input:

int(((2*x^2*exp(5)^2+32*x*exp(3)*exp(5)+128*exp(3)^2)*exp(x)^2+(4*x^4*exp( 
5)^2+(64*x^3*exp(3)-2*x^5+4*x^4)*exp(5)+256*x^2*exp(3)^2+(-16*x^4+48*x^3)* 
exp(3))*exp(x)+2*x^6*exp(5)^2+32*x^5*exp(3)*exp(5)+128*x^4*exp(3)^2+16*x^5 
*exp(3))*exp(x^3/((x*exp(5)+8*exp(3))*exp(x)+x^3*exp(5)+8*x^2*exp(3)))/((x 
^2*exp(5)^2+16*x*exp(3)*exp(5)+64*exp(3)^2)*exp(x)^2+(2*x^4*exp(5)^2+32*x^ 
3*exp(3)*exp(5)+128*x^2*exp(3)^2)*exp(x)+x^6*exp(5)^2+16*x^5*exp(3)*exp(5) 
+64*x^4*exp(3)^2),x,method=_RETURNVERBOSE)
 

Output:

2*x*exp(x^3/(x^3*exp(5)+x*exp(5+x)+8*x^2*exp(3)+8*exp(3+x)))
 

Fricas [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.12 \[ \int \frac {e^{\frac {x^3}{8 e^3 x^2+e^5 x^3+e^x \left (8 e^3+e^5 x\right )}} \left (128 e^6 x^4+16 e^3 x^5+32 e^8 x^5+2 e^{10} x^6+e^{2 x} \left (128 e^6+32 e^8 x+2 e^{10} x^2\right )+e^x \left (256 e^6 x^2+4 e^{10} x^4+e^3 \left (48 x^3-16 x^4\right )+e^5 \left (64 e^3 x^3+4 x^4-2 x^5\right )\right )\right )}{64 e^6 x^4+16 e^8 x^5+e^{10} x^6+e^{2 x} \left (64 e^6+16 e^8 x+e^{10} x^2\right )+e^x \left (128 e^6 x^2+32 e^8 x^3+2 e^{10} x^4\right )} \, dx=2 \, x e^{\left (\frac {x^{3}}{x^{3} e^{5} + 8 \, x^{2} e^{3} + {\left (x e^{5} + 8 \, e^{3}\right )} e^{x}}\right )} \] Input:

integrate(((2*x^2*exp(5)^2+32*x*exp(3)*exp(5)+128*exp(3)^2)*exp(x)^2+(4*x^ 
4*exp(5)^2+(64*x^3*exp(3)-2*x^5+4*x^4)*exp(5)+256*x^2*exp(3)^2+(-16*x^4+48 
*x^3)*exp(3))*exp(x)+2*x^6*exp(5)^2+32*x^5*exp(3)*exp(5)+128*x^4*exp(3)^2+ 
16*x^5*exp(3))*exp(x^3/((x*exp(5)+8*exp(3))*exp(x)+x^3*exp(5)+8*x^2*exp(3) 
))/((x^2*exp(5)^2+16*x*exp(3)*exp(5)+64*exp(3)^2)*exp(x)^2+(2*x^4*exp(5)^2 
+32*x^3*exp(3)*exp(5)+128*x^2*exp(3)^2)*exp(x)+x^6*exp(5)^2+16*x^5*exp(3)* 
exp(5)+64*x^4*exp(3)^2),x, algorithm="fricas")
 

Output:

2*x*e^(x^3/(x^3*e^5 + 8*x^2*e^3 + (x*e^5 + 8*e^3)*e^x))
 

Sympy [A] (verification not implemented)

Time = 2.90 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.12 \[ \int \frac {e^{\frac {x^3}{8 e^3 x^2+e^5 x^3+e^x \left (8 e^3+e^5 x\right )}} \left (128 e^6 x^4+16 e^3 x^5+32 e^8 x^5+2 e^{10} x^6+e^{2 x} \left (128 e^6+32 e^8 x+2 e^{10} x^2\right )+e^x \left (256 e^6 x^2+4 e^{10} x^4+e^3 \left (48 x^3-16 x^4\right )+e^5 \left (64 e^3 x^3+4 x^4-2 x^5\right )\right )\right )}{64 e^6 x^4+16 e^8 x^5+e^{10} x^6+e^{2 x} \left (64 e^6+16 e^8 x+e^{10} x^2\right )+e^x \left (128 e^6 x^2+32 e^8 x^3+2 e^{10} x^4\right )} \, dx=2 x e^{\frac {x^{3}}{x^{3} e^{5} + 8 x^{2} e^{3} + \left (x e^{5} + 8 e^{3}\right ) e^{x}}} \] Input:

integrate(((2*x**2*exp(5)**2+32*x*exp(3)*exp(5)+128*exp(3)**2)*exp(x)**2+( 
4*x**4*exp(5)**2+(64*x**3*exp(3)-2*x**5+4*x**4)*exp(5)+256*x**2*exp(3)**2+ 
(-16*x**4+48*x**3)*exp(3))*exp(x)+2*x**6*exp(5)**2+32*x**5*exp(3)*exp(5)+1 
28*x**4*exp(3)**2+16*x**5*exp(3))*exp(x**3/((x*exp(5)+8*exp(3))*exp(x)+x** 
3*exp(5)+8*x**2*exp(3)))/((x**2*exp(5)**2+16*x*exp(3)*exp(5)+64*exp(3)**2) 
*exp(x)**2+(2*x**4*exp(5)**2+32*x**3*exp(3)*exp(5)+128*x**2*exp(3)**2)*exp 
(x)+x**6*exp(5)**2+16*x**5*exp(3)*exp(5)+64*x**4*exp(3)**2),x)
 

Output:

2*x*exp(x**3/(x**3*exp(5) + 8*x**2*exp(3) + (x*exp(5) + 8*exp(3))*exp(x)))
 

Maxima [F]

\[ \int \frac {e^{\frac {x^3}{8 e^3 x^2+e^5 x^3+e^x \left (8 e^3+e^5 x\right )}} \left (128 e^6 x^4+16 e^3 x^5+32 e^8 x^5+2 e^{10} x^6+e^{2 x} \left (128 e^6+32 e^8 x+2 e^{10} x^2\right )+e^x \left (256 e^6 x^2+4 e^{10} x^4+e^3 \left (48 x^3-16 x^4\right )+e^5 \left (64 e^3 x^3+4 x^4-2 x^5\right )\right )\right )}{64 e^6 x^4+16 e^8 x^5+e^{10} x^6+e^{2 x} \left (64 e^6+16 e^8 x+e^{10} x^2\right )+e^x \left (128 e^6 x^2+32 e^8 x^3+2 e^{10} x^4\right )} \, dx=\int { \frac {2 \, {\left (x^{6} e^{10} + 16 \, x^{5} e^{8} + 8 \, x^{5} e^{3} + 64 \, x^{4} e^{6} + {\left (x^{2} e^{10} + 16 \, x e^{8} + 64 \, e^{6}\right )} e^{\left (2 \, x\right )} + {\left (2 \, x^{4} e^{10} + 128 \, x^{2} e^{6} - {\left (x^{5} - 2 \, x^{4} - 32 \, x^{3} e^{3}\right )} e^{5} - 8 \, {\left (x^{4} - 3 \, x^{3}\right )} e^{3}\right )} e^{x}\right )} e^{\left (\frac {x^{3}}{x^{3} e^{5} + 8 \, x^{2} e^{3} + {\left (x e^{5} + 8 \, e^{3}\right )} e^{x}}\right )}}{x^{6} e^{10} + 16 \, x^{5} e^{8} + 64 \, x^{4} e^{6} + {\left (x^{2} e^{10} + 16 \, x e^{8} + 64 \, e^{6}\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{4} e^{10} + 16 \, x^{3} e^{8} + 64 \, x^{2} e^{6}\right )} e^{x}} \,d x } \] Input:

integrate(((2*x^2*exp(5)^2+32*x*exp(3)*exp(5)+128*exp(3)^2)*exp(x)^2+(4*x^ 
4*exp(5)^2+(64*x^3*exp(3)-2*x^5+4*x^4)*exp(5)+256*x^2*exp(3)^2+(-16*x^4+48 
*x^3)*exp(3))*exp(x)+2*x^6*exp(5)^2+32*x^5*exp(3)*exp(5)+128*x^4*exp(3)^2+ 
16*x^5*exp(3))*exp(x^3/((x*exp(5)+8*exp(3))*exp(x)+x^3*exp(5)+8*x^2*exp(3) 
))/((x^2*exp(5)^2+16*x*exp(3)*exp(5)+64*exp(3)^2)*exp(x)^2+(2*x^4*exp(5)^2 
+32*x^3*exp(3)*exp(5)+128*x^2*exp(3)^2)*exp(x)+x^6*exp(5)^2+16*x^5*exp(3)* 
exp(5)+64*x^4*exp(3)^2),x, algorithm="maxima")
 

Output:

2*integrate((x^6*e^10 + 16*x^5*e^8 + 8*x^5*e^3 + 64*x^4*e^6 + (x^2*e^10 + 
16*x*e^8 + 64*e^6)*e^(2*x) + (2*x^4*e^10 + 128*x^2*e^6 - (x^5 - 2*x^4 - 32 
*x^3*e^3)*e^5 - 8*(x^4 - 3*x^3)*e^3)*e^x)*e^(x^3/(x^3*e^5 + 8*x^2*e^3 + (x 
*e^5 + 8*e^3)*e^x))/(x^6*e^10 + 16*x^5*e^8 + 64*x^4*e^6 + (x^2*e^10 + 16*x 
*e^8 + 64*e^6)*e^(2*x) + 2*(x^4*e^10 + 16*x^3*e^8 + 64*x^2*e^6)*e^x), x)
 

Giac [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {x^3}{8 e^3 x^2+e^5 x^3+e^x \left (8 e^3+e^5 x\right )}} \left (128 e^6 x^4+16 e^3 x^5+32 e^8 x^5+2 e^{10} x^6+e^{2 x} \left (128 e^6+32 e^8 x+2 e^{10} x^2\right )+e^x \left (256 e^6 x^2+4 e^{10} x^4+e^3 \left (48 x^3-16 x^4\right )+e^5 \left (64 e^3 x^3+4 x^4-2 x^5\right )\right )\right )}{64 e^6 x^4+16 e^8 x^5+e^{10} x^6+e^{2 x} \left (64 e^6+16 e^8 x+e^{10} x^2\right )+e^x \left (128 e^6 x^2+32 e^8 x^3+2 e^{10} x^4\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(((2*x^2*exp(5)^2+32*x*exp(3)*exp(5)+128*exp(3)^2)*exp(x)^2+(4*x^ 
4*exp(5)^2+(64*x^3*exp(3)-2*x^5+4*x^4)*exp(5)+256*x^2*exp(3)^2+(-16*x^4+48 
*x^3)*exp(3))*exp(x)+2*x^6*exp(5)^2+32*x^5*exp(3)*exp(5)+128*x^4*exp(3)^2+ 
16*x^5*exp(3))*exp(x^3/((x*exp(5)+8*exp(3))*exp(x)+x^3*exp(5)+8*x^2*exp(3) 
))/((x^2*exp(5)^2+16*x*exp(3)*exp(5)+64*exp(3)^2)*exp(x)^2+(2*x^4*exp(5)^2 
+32*x^3*exp(3)*exp(5)+128*x^2*exp(3)^2)*exp(x)+x^6*exp(5)^2+16*x^5*exp(3)* 
exp(5)+64*x^4*exp(3)^2),x, algorithm="giac")
 

Output:

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro 
unding error%%%{64,[0,8,42,46]%%%}+%%%{-768,[0,8,41,46]%%%}+%%%{7168,[0,8, 
41,44]%%%
 

Mupad [B] (verification not implemented)

Time = 0.99 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.12 \[ \int \frac {e^{\frac {x^3}{8 e^3 x^2+e^5 x^3+e^x \left (8 e^3+e^5 x\right )}} \left (128 e^6 x^4+16 e^3 x^5+32 e^8 x^5+2 e^{10} x^6+e^{2 x} \left (128 e^6+32 e^8 x+2 e^{10} x^2\right )+e^x \left (256 e^6 x^2+4 e^{10} x^4+e^3 \left (48 x^3-16 x^4\right )+e^5 \left (64 e^3 x^3+4 x^4-2 x^5\right )\right )\right )}{64 e^6 x^4+16 e^8 x^5+e^{10} x^6+e^{2 x} \left (64 e^6+16 e^8 x+e^{10} x^2\right )+e^x \left (128 e^6 x^2+32 e^8 x^3+2 e^{10} x^4\right )} \, dx=2\,x\,{\mathrm {e}}^{\frac {x^3}{8\,x^2\,{\mathrm {e}}^3+x^3\,{\mathrm {e}}^5+8\,{\mathrm {e}}^3\,{\mathrm {e}}^x+x\,{\mathrm {e}}^5\,{\mathrm {e}}^x}} \] Input:

int((exp(x^3/(8*x^2*exp(3) + x^3*exp(5) + exp(x)*(8*exp(3) + x*exp(5))))*( 
exp(x)*(exp(5)*(64*x^3*exp(3) + 4*x^4 - 2*x^5) + exp(3)*(48*x^3 - 16*x^4) 
+ 256*x^2*exp(6) + 4*x^4*exp(10)) + exp(2*x)*(128*exp(6) + 32*x*exp(8) + 2 
*x^2*exp(10)) + 16*x^5*exp(3) + 128*x^4*exp(6) + 32*x^5*exp(8) + 2*x^6*exp 
(10)))/(exp(x)*(128*x^2*exp(6) + 32*x^3*exp(8) + 2*x^4*exp(10)) + exp(2*x) 
*(64*exp(6) + 16*x*exp(8) + x^2*exp(10)) + 64*x^4*exp(6) + 16*x^5*exp(8) + 
 x^6*exp(10)),x)
 

Output:

2*x*exp(x^3/(8*x^2*exp(3) + x^3*exp(5) + 8*exp(3)*exp(x) + x*exp(5)*exp(x) 
))
 

Reduce [F]

\[ \int \frac {e^{\frac {x^3}{8 e^3 x^2+e^5 x^3+e^x \left (8 e^3+e^5 x\right )}} \left (128 e^6 x^4+16 e^3 x^5+32 e^8 x^5+2 e^{10} x^6+e^{2 x} \left (128 e^6+32 e^8 x+2 e^{10} x^2\right )+e^x \left (256 e^6 x^2+4 e^{10} x^4+e^3 \left (48 x^3-16 x^4\right )+e^5 \left (64 e^3 x^3+4 x^4-2 x^5\right )\right )\right )}{64 e^6 x^4+16 e^8 x^5+e^{10} x^6+e^{2 x} \left (64 e^6+16 e^8 x+e^{10} x^2\right )+e^x \left (128 e^6 x^2+32 e^8 x^3+2 e^{10} x^4\right )} \, dx=\int \frac {\left (\left (2 x^{2} \left ({\mathrm e}^{5}\right )^{2}+32 x \,{\mathrm e}^{3} {\mathrm e}^{5}+128 \left ({\mathrm e}^{3}\right )^{2}\right ) \left ({\mathrm e}^{x}\right )^{2}+\left (4 x^{4} \left ({\mathrm e}^{5}\right )^{2}+\left (64 x^{3} {\mathrm e}^{3}-2 x^{5}+4 x^{4}\right ) {\mathrm e}^{5}+256 x^{2} \left ({\mathrm e}^{3}\right )^{2}+\left (-16 x^{4}+48 x^{3}\right ) {\mathrm e}^{3}\right ) {\mathrm e}^{x}+2 x^{6} \left ({\mathrm e}^{5}\right )^{2}+32 x^{5} {\mathrm e}^{3} {\mathrm e}^{5}+128 x^{4} \left ({\mathrm e}^{3}\right )^{2}+16 x^{5} {\mathrm e}^{3}\right ) {\mathrm e}^{\frac {x^{3}}{\left (x \,{\mathrm e}^{5}+8 \,{\mathrm e}^{3}\right ) {\mathrm e}^{x}+x^{3} {\mathrm e}^{5}+8 x^{2} {\mathrm e}^{3}}}}{\left (x^{2} \left ({\mathrm e}^{5}\right )^{2}+16 x \,{\mathrm e}^{3} {\mathrm e}^{5}+64 \left ({\mathrm e}^{3}\right )^{2}\right ) \left ({\mathrm e}^{x}\right )^{2}+\left (2 x^{4} \left ({\mathrm e}^{5}\right )^{2}+32 x^{3} {\mathrm e}^{3} {\mathrm e}^{5}+128 x^{2} \left ({\mathrm e}^{3}\right )^{2}\right ) {\mathrm e}^{x}+x^{6} \left ({\mathrm e}^{5}\right )^{2}+16 x^{5} {\mathrm e}^{3} {\mathrm e}^{5}+64 x^{4} \left ({\mathrm e}^{3}\right )^{2}}d x \] Input:

int(((2*x^2*exp(5)^2+32*x*exp(3)*exp(5)+128*exp(3)^2)*exp(x)^2+(4*x^4*exp( 
5)^2+(64*x^3*exp(3)-2*x^5+4*x^4)*exp(5)+256*x^2*exp(3)^2+(-16*x^4+48*x^3)* 
exp(3))*exp(x)+2*x^6*exp(5)^2+32*x^5*exp(3)*exp(5)+128*x^4*exp(3)^2+16*x^5 
*exp(3))*exp(x^3/((x*exp(5)+8*exp(3))*exp(x)+x^3*exp(5)+8*x^2*exp(3)))/((x 
^2*exp(5)^2+16*x*exp(3)*exp(5)+64*exp(3)^2)*exp(x)^2+(2*x^4*exp(5)^2+32*x^ 
3*exp(3)*exp(5)+128*x^2*exp(3)^2)*exp(x)+x^6*exp(5)^2+16*x^5*exp(3)*exp(5) 
+64*x^4*exp(3)^2),x)
 

Output:

int(((2*x^2*exp(5)^2+32*x*exp(3)*exp(5)+128*exp(3)^2)*exp(x)^2+(4*x^4*exp( 
5)^2+(64*x^3*exp(3)-2*x^5+4*x^4)*exp(5)+256*x^2*exp(3)^2+(-16*x^4+48*x^3)* 
exp(3))*exp(x)+2*x^6*exp(5)^2+32*x^5*exp(3)*exp(5)+128*x^4*exp(3)^2+16*x^5 
*exp(3))*exp(x^3/((x*exp(5)+8*exp(3))*exp(x)+x^3*exp(5)+8*x^2*exp(3)))/((x 
^2*exp(5)^2+16*x*exp(3)*exp(5)+64*exp(3)^2)*exp(x)^2+(2*x^4*exp(5)^2+32*x^ 
3*exp(3)*exp(5)+128*x^2*exp(3)^2)*exp(x)+x^6*exp(5)^2+16*x^5*exp(3)*exp(5) 
+64*x^4*exp(3)^2),x)