\(\int \frac {e^x (1280-288 x-144 x^2+32 x^3+16 x^4+e^{20} (-32 x+16 x^2)+e^{10} (192 x-32 x^3)-256 \log (2))}{6400+1440 x^2+960 x^3+241 x^4+e^{40} x^4+108 x^5+54 x^6+12 x^7+x^8+e^{30} (-12 x^4-4 x^5)+e^{20} (160 x^2+54 x^4+36 x^5+6 x^6)+e^{10} (-960 x^2-320 x^3-108 x^4-108 x^5-36 x^6-4 x^7)+(-2560-288 x^2-32 e^{20} x^2-192 x^3-32 x^4+e^{10} (192 x^2+64 x^3)) \log (2)+256 \log ^2(2)} \, dx\) [2026]

Optimal result

Integrand size = 222, antiderivative size = 29 \[ \int \frac {e^x \left (1280-288 x-144 x^2+32 x^3+16 x^4+e^{20} \left (-32 x+16 x^2\right )+e^{10} \left (192 x-32 x^3\right )-256 \log (2)\right )}{6400+1440 x^2+960 x^3+241 x^4+e^{40} x^4+108 x^5+54 x^6+12 x^7+x^8+e^{30} \left (-12 x^4-4 x^5\right )+e^{20} \left (160 x^2+54 x^4+36 x^5+6 x^6\right )+e^{10} \left (-960 x^2-320 x^3-108 x^4-108 x^5-36 x^6-4 x^7\right )+\left (-2560-288 x^2-32 e^{20} x^2-192 x^3-32 x^4+e^{10} \left (192 x^2+64 x^3\right )\right ) \log (2)+256 \log ^2(2)} \, dx=\frac {e^x}{5+\frac {1}{16} x^2 \left (3-e^{10}+x\right )^2-\log (2)} \] Output:

exp(x)/(1/16*x^2*(x-exp(10)+3)^2+5-ln(2))
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 3.80 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.31 \[ \int \frac {e^x \left (1280-288 x-144 x^2+32 x^3+16 x^4+e^{20} \left (-32 x+16 x^2\right )+e^{10} \left (192 x-32 x^3\right )-256 \log (2)\right )}{6400+1440 x^2+960 x^3+241 x^4+e^{40} x^4+108 x^5+54 x^6+12 x^7+x^8+e^{30} \left (-12 x^4-4 x^5\right )+e^{20} \left (160 x^2+54 x^4+36 x^5+6 x^6\right )+e^{10} \left (-960 x^2-320 x^3-108 x^4-108 x^5-36 x^6-4 x^7\right )+\left (-2560-288 x^2-32 e^{20} x^2-192 x^3-32 x^4+e^{10} \left (192 x^2+64 x^3\right )\right ) \log (2)+256 \log ^2(2)} \, dx=\frac {16 e^x}{\left (-3+e^{10}\right )^2 x^2-2 \left (-3+e^{10}\right ) x^3+x^4-16 (-5+\log (2))} \] Input:

Integrate[(E^x*(1280 - 288*x - 144*x^2 + 32*x^3 + 16*x^4 + E^20*(-32*x + 1 
6*x^2) + E^10*(192*x - 32*x^3) - 256*Log[2]))/(6400 + 1440*x^2 + 960*x^3 + 
 241*x^4 + E^40*x^4 + 108*x^5 + 54*x^6 + 12*x^7 + x^8 + E^30*(-12*x^4 - 4* 
x^5) + E^20*(160*x^2 + 54*x^4 + 36*x^5 + 6*x^6) + E^10*(-960*x^2 - 320*x^3 
 - 108*x^4 - 108*x^5 - 36*x^6 - 4*x^7) + (-2560 - 288*x^2 - 32*E^20*x^2 - 
192*x^3 - 32*x^4 + E^10*(192*x^2 + 64*x^3))*Log[2] + 256*Log[2]^2),x]
 

Output:

(16*E^x)/((-3 + E^10)^2*x^2 - 2*(-3 + E^10)*x^3 + x^4 - 16*(-5 + Log[2]))
 

Rubi [A] (verified)

Time = 1.21 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.52, number of steps used = 6, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {6, 2463, 6, 6, 6, 2727}

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.

\(\displaystyle \int \frac {e^x \left (16 x^4+32 x^3+e^{10} \left (192 x-32 x^3\right )-144 x^2+e^{20} \left (16 x^2-32 x\right )-288 x+1280-256 \log (2)\right )}{x^8+12 x^7+54 x^6+108 x^5+e^{40} x^4+241 x^4+960 x^3+1440 x^2+e^{30} \left (-4 x^5-12 x^4\right )+\left (-32 x^4-192 x^3-32 e^{20} x^2-288 x^2+e^{10} \left (64 x^3+192 x^2\right )-2560\right ) \log (2)+e^{20} \left (6 x^6+36 x^5+54 x^4+160 x^2\right )+e^{10} \left (-4 x^7-36 x^6-108 x^5-108 x^4-320 x^3-960 x^2\right )+6400+256 \log ^2(2)} \, dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {e^x \left (16 x^4+32 x^3+e^{10} \left (192 x-32 x^3\right )-144 x^2+e^{20} \left (16 x^2-32 x\right )-288 x+1280-256 \log (2)\right )}{x^8+12 x^7+54 x^6+108 x^5+\left (241+e^{40}\right ) x^4+960 x^3+1440 x^2+e^{30} \left (-4 x^5-12 x^4\right )+\left (-32 x^4-192 x^3-32 e^{20} x^2-288 x^2+e^{10} \left (64 x^3+192 x^2\right )-2560\right ) \log (2)+e^{20} \left (6 x^6+36 x^5+54 x^4+160 x^2\right )+e^{10} \left (-4 x^7-36 x^6-108 x^5-108 x^4-320 x^3-960 x^2\right )+6400+256 \log ^2(2)}dx\)

\(\Big \downarrow \) 2463

\(\displaystyle \int \frac {e^x \left (16 x^4+32 x^3+e^{10} \left (192 x-32 x^3\right )-144 x^2+e^{20} \left (16 x^2-32 x\right )-288 x+1280-256 \log (2)\right )}{\left (x^4-2 e^{10} x^3+6 x^3+e^{20} x^2-6 e^{10} x^2+9 x^2+80-16 \log (2)\right )^2}dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {e^x \left (16 x^4+32 x^3+e^{10} \left (192 x-32 x^3\right )-144 x^2+e^{20} \left (16 x^2-32 x\right )-288 x+1280-256 \log (2)\right )}{\left (x^4-2 e^{10} x^3+6 x^3+\left (9-6 e^{10}\right ) x^2+e^{20} x^2+80-16 \log (2)\right )^2}dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {e^x \left (16 x^4+32 x^3+e^{10} \left (192 x-32 x^3\right )-144 x^2+e^{20} \left (16 x^2-32 x\right )-288 x+1280-256 \log (2)\right )}{\left (x^4-2 e^{10} x^3+6 x^3+\left (9-6 e^{10}+e^{20}\right ) x^2+80-16 \log (2)\right )^2}dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {e^x \left (16 x^4+32 x^3+e^{10} \left (192 x-32 x^3\right )-144 x^2+e^{20} \left (16 x^2-32 x\right )-288 x+1280-256 \log (2)\right )}{\left (x^4+\left (6-2 e^{10}\right ) x^3+\left (9-6 e^{10}+e^{20}\right ) x^2+80-16 \log (2)\right )^2}dx\)

\(\Big \downarrow \) 2727

\(\displaystyle \frac {16 e^x}{x^4+2 \left (3-e^{10}\right ) x^3+\left (3-e^{10}\right )^2 x^2+16 (5-\log (2))}\)

Input:

Int[(E^x*(1280 - 288*x - 144*x^2 + 32*x^3 + 16*x^4 + E^20*(-32*x + 16*x^2) 
 + E^10*(192*x - 32*x^3) - 256*Log[2]))/(6400 + 1440*x^2 + 960*x^3 + 241*x 
^4 + E^40*x^4 + 108*x^5 + 54*x^6 + 12*x^7 + x^8 + E^30*(-12*x^4 - 4*x^5) + 
 E^20*(160*x^2 + 54*x^4 + 36*x^5 + 6*x^6) + E^10*(-960*x^2 - 320*x^3 - 108 
*x^4 - 108*x^5 - 36*x^6 - 4*x^7) + (-2560 - 288*x^2 - 32*E^20*x^2 - 192*x^ 
3 - 32*x^4 + E^10*(192*x^2 + 64*x^3))*Log[2] + 256*Log[2]^2),x]
 

Output:

(16*E^x)/((3 - E^10)^2*x^2 + 2*(3 - E^10)*x^3 + x^4 + 16*(5 - Log[2]))
 

Defintions of rubi rules used

rule 6

Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v 
+ (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] &&  !FreeQ[Fx, x]
 

rule 2463

Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr 
and[u, Qx^p, x], x] /;  !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt 
Q[Expon[Px, x], 2] &&  !BinomialQ[Px, x] &&  !TrinomialQ[Px, x] && ILtQ[p, 
0]
 

rule 2727

Int[(F_)^(u_)*(v_)^(n_.)*(w_), x_Symbol] :> With[{z = Log[F]*v*D[u, x] + (n 
 + 1)*D[v, x]}, Simp[(Coefficient[w, x, Exponent[w, x]]/Coefficient[z, x, E 
xponent[z, x]])*F^u*v^(n + 1), x] /; EqQ[Exponent[w, x], Exponent[z, x]] && 
 EqQ[w*Coefficient[z, x, Exponent[z, x]], z*Coefficient[w, x, Exponent[w, x 
]]]] /; FreeQ[{F, n}, x] && PolynomialQ[u, x] && PolynomialQ[v, x] && Polyn 
omialQ[w, x]
 

Maple [A] (verified)

Time = 1.52 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59

method	result	size
risch	\(\frac {16 \,{\mathrm e}^{x}}{{\mathrm e}^{20} x^{2}-2 x^{3} {\mathrm e}^{10}+x^{4}-6 x^{2} {\mathrm e}^{10}+6 x^{3}+9 x^{2}-16 \ln \left (2\right )+80}\)	\(46\)
gosper	\(\frac {16 \,{\mathrm e}^{x}}{{\mathrm e}^{20} x^{2}-2 x^{3} {\mathrm e}^{10}+x^{4}-6 x^{2} {\mathrm e}^{10}+6 x^{3}+9 x^{2}-16 \ln \left (2\right )+80}\)	\(48\)
norman	\(\frac {16 \,{\mathrm e}^{x}}{{\mathrm e}^{20} x^{2}-2 x^{3} {\mathrm e}^{10}+x^{4}-6 x^{2} {\mathrm e}^{10}+6 x^{3}+9 x^{2}-16 \ln \left (2\right )+80}\)	\(48\)
parallelrisch	\(\frac {16 \,{\mathrm e}^{x}}{{\mathrm e}^{20} x^{2}-2 x^{3} {\mathrm e}^{10}+x^{4}-6 x^{2} {\mathrm e}^{10}+6 x^{3}+9 x^{2}-16 \ln \left (2\right )+80}\)	\(48\)
default	\(\text {Expression too large to display}\)	\(5381\)

Input:

int((-256*ln(2)+(16*x^2-32*x)*exp(10)^2+(-32*x^3+192*x)*exp(10)+16*x^4+32* 
x^3-144*x^2-288*x+1280)*exp(x)/(256*ln(2)^2+(-32*x^2*exp(10)^2+(64*x^3+192 
*x^2)*exp(10)-32*x^4-192*x^3-288*x^2-2560)*ln(2)+x^4*exp(10)^4+(-4*x^5-12* 
x^4)*exp(10)^3+(6*x^6+36*x^5+54*x^4+160*x^2)*exp(10)^2+(-4*x^7-36*x^6-108* 
x^5-108*x^4-320*x^3-960*x^2)*exp(10)+x^8+12*x^7+54*x^6+108*x^5+241*x^4+960 
*x^3+1440*x^2+6400),x,method=_RETURNVERBOSE)
 

Output:

16*exp(x)/(exp(20)*x^2-2*x^3*exp(10)+x^4-6*x^2*exp(10)+6*x^3+9*x^2-16*ln(2 
)+80)
 

Fricas [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.52 \[ \int \frac {e^x \left (1280-288 x-144 x^2+32 x^3+16 x^4+e^{20} \left (-32 x+16 x^2\right )+e^{10} \left (192 x-32 x^3\right )-256 \log (2)\right )}{6400+1440 x^2+960 x^3+241 x^4+e^{40} x^4+108 x^5+54 x^6+12 x^7+x^8+e^{30} \left (-12 x^4-4 x^5\right )+e^{20} \left (160 x^2+54 x^4+36 x^5+6 x^6\right )+e^{10} \left (-960 x^2-320 x^3-108 x^4-108 x^5-36 x^6-4 x^7\right )+\left (-2560-288 x^2-32 e^{20} x^2-192 x^3-32 x^4+e^{10} \left (192 x^2+64 x^3\right )\right ) \log (2)+256 \log ^2(2)} \, dx=\frac {16 \, e^{x}}{x^{4} + 6 \, x^{3} + x^{2} e^{20} + 9 \, x^{2} - 2 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{10} - 16 \, \log \left (2\right ) + 80} \] Input:

integrate((-256*log(2)+(16*x^2-32*x)*exp(10)^2+(-32*x^3+192*x)*exp(10)+16* 
x^4+32*x^3-144*x^2-288*x+1280)*exp(x)/(256*log(2)^2+(-32*x^2*exp(10)^2+(64 
*x^3+192*x^2)*exp(10)-32*x^4-192*x^3-288*x^2-2560)*log(2)+x^4*exp(10)^4+(- 
4*x^5-12*x^4)*exp(10)^3+(6*x^6+36*x^5+54*x^4+160*x^2)*exp(10)^2+(-4*x^7-36 
*x^6-108*x^5-108*x^4-320*x^3-960*x^2)*exp(10)+x^8+12*x^7+54*x^6+108*x^5+24 
1*x^4+960*x^3+1440*x^2+6400),x, algorithm="fricas")
 

Output:

16*e^x/(x^4 + 6*x^3 + x^2*e^20 + 9*x^2 - 2*(x^3 + 3*x^2)*e^10 - 16*log(2) 
+ 80)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (20) = 40\).

Time = 0.20 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.66 \[ \int \frac {e^x \left (1280-288 x-144 x^2+32 x^3+16 x^4+e^{20} \left (-32 x+16 x^2\right )+e^{10} \left (192 x-32 x^3\right )-256 \log (2)\right )}{6400+1440 x^2+960 x^3+241 x^4+e^{40} x^4+108 x^5+54 x^6+12 x^7+x^8+e^{30} \left (-12 x^4-4 x^5\right )+e^{20} \left (160 x^2+54 x^4+36 x^5+6 x^6\right )+e^{10} \left (-960 x^2-320 x^3-108 x^4-108 x^5-36 x^6-4 x^7\right )+\left (-2560-288 x^2-32 e^{20} x^2-192 x^3-32 x^4+e^{10} \left (192 x^2+64 x^3\right )\right ) \log (2)+256 \log ^2(2)} \, dx=\frac {16 e^{x}}{x^{4} - 2 x^{3} e^{10} + 6 x^{3} - 6 x^{2} e^{10} + 9 x^{2} + x^{2} e^{20} - 16 \log {\left (2 \right )} + 80} \] Input:

integrate((-256*ln(2)+(16*x**2-32*x)*exp(10)**2+(-32*x**3+192*x)*exp(10)+1 
6*x**4+32*x**3-144*x**2-288*x+1280)*exp(x)/(256*ln(2)**2+(-32*x**2*exp(10) 
**2+(64*x**3+192*x**2)*exp(10)-32*x**4-192*x**3-288*x**2-2560)*ln(2)+x**4* 
exp(10)**4+(-4*x**5-12*x**4)*exp(10)**3+(6*x**6+36*x**5+54*x**4+160*x**2)* 
exp(10)**2+(-4*x**7-36*x**6-108*x**5-108*x**4-320*x**3-960*x**2)*exp(10)+x 
**8+12*x**7+54*x**6+108*x**5+241*x**4+960*x**3+1440*x**2+6400),x)
 

Output:

16*exp(x)/(x**4 - 2*x**3*exp(10) + 6*x**3 - 6*x**2*exp(10) + 9*x**2 + x**2 
*exp(20) - 16*log(2) + 80)
 

Maxima [A] (verification not implemented)

Time = 0.18 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.24 \[ \int \frac {e^x \left (1280-288 x-144 x^2+32 x^3+16 x^4+e^{20} \left (-32 x+16 x^2\right )+e^{10} \left (192 x-32 x^3\right )-256 \log (2)\right )}{6400+1440 x^2+960 x^3+241 x^4+e^{40} x^4+108 x^5+54 x^6+12 x^7+x^8+e^{30} \left (-12 x^4-4 x^5\right )+e^{20} \left (160 x^2+54 x^4+36 x^5+6 x^6\right )+e^{10} \left (-960 x^2-320 x^3-108 x^4-108 x^5-36 x^6-4 x^7\right )+\left (-2560-288 x^2-32 e^{20} x^2-192 x^3-32 x^4+e^{10} \left (192 x^2+64 x^3\right )\right ) \log (2)+256 \log ^2(2)} \, dx=\frac {16 \, e^{x}}{x^{4} - 2 \, x^{3} {\left (e^{10} - 3\right )} + x^{2} {\left (e^{20} - 6 \, e^{10} + 9\right )} - 16 \, \log \left (2\right ) + 80} \] Input:

integrate((-256*log(2)+(16*x^2-32*x)*exp(10)^2+(-32*x^3+192*x)*exp(10)+16* 
x^4+32*x^3-144*x^2-288*x+1280)*exp(x)/(256*log(2)^2+(-32*x^2*exp(10)^2+(64 
*x^3+192*x^2)*exp(10)-32*x^4-192*x^3-288*x^2-2560)*log(2)+x^4*exp(10)^4+(- 
4*x^5-12*x^4)*exp(10)^3+(6*x^6+36*x^5+54*x^4+160*x^2)*exp(10)^2+(-4*x^7-36 
*x^6-108*x^5-108*x^4-320*x^3-960*x^2)*exp(10)+x^8+12*x^7+54*x^6+108*x^5+24 
1*x^4+960*x^3+1440*x^2+6400),x, algorithm="maxima")
 

Output:

16*e^x/(x^4 - 2*x^3*(e^10 - 3) + x^2*(e^20 - 6*e^10 + 9) - 16*log(2) + 80)
 

Giac [A] (verification not implemented)

Time = 0.96 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.55 \[ \int \frac {e^x \left (1280-288 x-144 x^2+32 x^3+16 x^4+e^{20} \left (-32 x+16 x^2\right )+e^{10} \left (192 x-32 x^3\right )-256 \log (2)\right )}{6400+1440 x^2+960 x^3+241 x^4+e^{40} x^4+108 x^5+54 x^6+12 x^7+x^8+e^{30} \left (-12 x^4-4 x^5\right )+e^{20} \left (160 x^2+54 x^4+36 x^5+6 x^6\right )+e^{10} \left (-960 x^2-320 x^3-108 x^4-108 x^5-36 x^6-4 x^7\right )+\left (-2560-288 x^2-32 e^{20} x^2-192 x^3-32 x^4+e^{10} \left (192 x^2+64 x^3\right )\right ) \log (2)+256 \log ^2(2)} \, dx=\frac {32 \, e^{x}}{x^{4} - 2 \, x^{3} e^{10} + 6 \, x^{3} + x^{2} e^{20} - 6 \, x^{2} e^{10} + 9 \, x^{2} - 16 \, \log \left (2\right ) + 80} \] Input:

integrate((-256*log(2)+(16*x^2-32*x)*exp(10)^2+(-32*x^3+192*x)*exp(10)+16* 
x^4+32*x^3-144*x^2-288*x+1280)*exp(x)/(256*log(2)^2+(-32*x^2*exp(10)^2+(64 
*x^3+192*x^2)*exp(10)-32*x^4-192*x^3-288*x^2-2560)*log(2)+x^4*exp(10)^4+(- 
4*x^5-12*x^4)*exp(10)^3+(6*x^6+36*x^5+54*x^4+160*x^2)*exp(10)^2+(-4*x^7-36 
*x^6-108*x^5-108*x^4-320*x^3-960*x^2)*exp(10)+x^8+12*x^7+54*x^6+108*x^5+24 
1*x^4+960*x^3+1440*x^2+6400),x, algorithm="giac")
 

Output:

32*e^x/(x^4 - 2*x^3*e^10 + 6*x^3 + x^2*e^20 - 6*x^2*e^10 + 9*x^2 - 16*log( 
2) + 80)
 

Mupad [B] (verification not implemented)

Time = 3.66 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.24 \[ \int \frac {e^x \left (1280-288 x-144 x^2+32 x^3+16 x^4+e^{20} \left (-32 x+16 x^2\right )+e^{10} \left (192 x-32 x^3\right )-256 \log (2)\right )}{6400+1440 x^2+960 x^3+241 x^4+e^{40} x^4+108 x^5+54 x^6+12 x^7+x^8+e^{30} \left (-12 x^4-4 x^5\right )+e^{20} \left (160 x^2+54 x^4+36 x^5+6 x^6\right )+e^{10} \left (-960 x^2-320 x^3-108 x^4-108 x^5-36 x^6-4 x^7\right )+\left (-2560-288 x^2-32 e^{20} x^2-192 x^3-32 x^4+e^{10} \left (192 x^2+64 x^3\right )\right ) \log (2)+256 \log ^2(2)} \, dx=\frac {16\,{\mathrm {e}}^x}{x^4+\left (6-2\,{\mathrm {e}}^{10}\right )\,x^3+{\left ({\mathrm {e}}^{10}-3\right )}^2\,x^2-16\,\ln \left (2\right )+80} \] Input:

int(-(exp(x)*(288*x + 256*log(2) + exp(20)*(32*x - 16*x^2) - exp(10)*(192* 
x - 32*x^3) + 144*x^2 - 32*x^3 - 16*x^4 - 1280))/(x^4*exp(40) - exp(30)*(1 
2*x^4 + 4*x^5) - exp(10)*(960*x^2 + 320*x^3 + 108*x^4 + 108*x^5 + 36*x^6 + 
 4*x^7) + 256*log(2)^2 + 1440*x^2 + 960*x^3 + 241*x^4 + 108*x^5 + 54*x^6 + 
 12*x^7 + x^8 - log(2)*(32*x^2*exp(20) - exp(10)*(192*x^2 + 64*x^3) + 288* 
x^2 + 192*x^3 + 32*x^4 + 2560) + exp(20)*(160*x^2 + 54*x^4 + 36*x^5 + 6*x^ 
6) + 6400),x)
 

Output:

(16*exp(x))/(x^2*(exp(10) - 3)^2 - x^3*(2*exp(10) - 6) - 16*log(2) + x^4 + 
 80)
 

Reduce [B] (verification not implemented)

Time = 0.20 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.79 \[ \int \frac {e^x \left (1280-288 x-144 x^2+32 x^3+16 x^4+e^{20} \left (-32 x+16 x^2\right )+e^{10} \left (192 x-32 x^3\right )-256 \log (2)\right )}{6400+1440 x^2+960 x^3+241 x^4+e^{40} x^4+108 x^5+54 x^6+12 x^7+x^8+e^{30} \left (-12 x^4-4 x^5\right )+e^{20} \left (160 x^2+54 x^4+36 x^5+6 x^6\right )+e^{10} \left (-960 x^2-320 x^3-108 x^4-108 x^5-36 x^6-4 x^7\right )+\left (-2560-288 x^2-32 e^{20} x^2-192 x^3-32 x^4+e^{10} \left (192 x^2+64 x^3\right )\right ) \log (2)+256 \log ^2(2)} \, dx=-\frac {16 e^{x}}{16 \,\mathrm {log}\left (2\right )-e^{20} x^{2}+2 e^{10} x^{3}+6 e^{10} x^{2}-x^{4}-6 x^{3}-9 x^{2}-80} \] Input:

int((-256*log(2)+(16*x^2-32*x)*exp(10)^2+(-32*x^3+192*x)*exp(10)+16*x^4+32 
*x^3-144*x^2-288*x+1280)*exp(x)/(256*log(2)^2+(-32*x^2*exp(10)^2+(64*x^3+1 
92*x^2)*exp(10)-32*x^4-192*x^3-288*x^2-2560)*log(2)+x^4*exp(10)^4+(-4*x^5- 
12*x^4)*exp(10)^3+(6*x^6+36*x^5+54*x^4+160*x^2)*exp(10)^2+(-4*x^7-36*x^6-1 
08*x^5-108*x^4-320*x^3-960*x^2)*exp(10)+x^8+12*x^7+54*x^6+108*x^5+241*x^4+ 
960*x^3+1440*x^2+6400),x)
 

Output:

( - 16*e**x)/(16*log(2) - e**20*x**2 + 2*e**10*x**3 + 6*e**10*x**2 - x**4 
- 6*x**3 - 9*x**2 - 80)