\(\int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} (10917504 x^7+6718464 x^8+839808 x^9) \log (13+8 x+x^2)+e^{12 x^8} (279936+69984 x) \log ^4(13+8 x+x^2)+e^{12 x^8} (-3639168 x^7-2239488 x^8-279936 x^9) \log ^5(13+8 x+x^2)+e^{8 x^8} (-31104-7776 x) \log ^8(13+8 x+x^2)+e^{8 x^8} (404352 x^7+248832 x^8+31104 x^9) \log ^9(13+8 x+x^2)+e^{4 x^8} (1152+288 x) \log ^{12}(13+8 x+x^2)+e^{4 x^8} (-14976 x^7-9216 x^8-1152 x^9) \log ^{13}(13+8 x+x^2)}{(13+8 x+x^2) \log ^{17}(13+8 x+x^2)} \, dx\) [2306]

Optimal result

Integrand size = 246, antiderivative size = 23 \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=\left (-1+\frac {9 e^{4 x^8}}{\log ^4\left (-3+(4+x)^2\right )}\right )^4 \] Output:

(9*exp(x^8)^4/ln((4+x)^2-3)^4-1)^4
                                                                                    
                                                                                    
 

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(83\) vs. \(2(23)=46\).

Time = 0.05 (sec) , antiderivative size = 83, normalized size of antiderivative = 3.61 \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=\frac {9 e^{4 x^8} \left (729 e^{12 x^8}-324 e^{8 x^8} \log ^4\left (13+8 x+x^2\right )+54 e^{4 x^8} \log ^8\left (13+8 x+x^2\right )-4 \log ^{12}\left (13+8 x+x^2\right )\right )}{\log ^{16}\left (13+8 x+x^2\right )} \] Input:

Integrate[(E^(16*x^8)*(-839808 - 209952*x) + E^(16*x^8)*(10917504*x^7 + 67 
18464*x^8 + 839808*x^9)*Log[13 + 8*x + x^2] + E^(12*x^8)*(279936 + 69984*x 
)*Log[13 + 8*x + x^2]^4 + E^(12*x^8)*(-3639168*x^7 - 2239488*x^8 - 279936* 
x^9)*Log[13 + 8*x + x^2]^5 + E^(8*x^8)*(-31104 - 7776*x)*Log[13 + 8*x + x^ 
2]^8 + E^(8*x^8)*(404352*x^7 + 248832*x^8 + 31104*x^9)*Log[13 + 8*x + x^2] 
^9 + E^(4*x^8)*(1152 + 288*x)*Log[13 + 8*x + x^2]^12 + E^(4*x^8)*(-14976*x 
^7 - 9216*x^8 - 1152*x^9)*Log[13 + 8*x + x^2]^13)/((13 + 8*x + x^2)*Log[13 
 + 8*x + x^2]^17),x]
 

Output:

(9*E^(4*x^8)*(729*E^(12*x^8) - 324*E^(8*x^8)*Log[13 + 8*x + x^2]^4 + 54*E^ 
(4*x^8)*Log[13 + 8*x + x^2]^8 - 4*Log[13 + 8*x + x^2]^12))/Log[13 + 8*x + 
x^2]^16
 

Rubi [A] (verified)

Time = 1.82 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04, number of steps used = 6, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {7239, 27, 25, 7263, 17}

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.

\(\displaystyle \int \frac {e^{16 x^8} (-209952 x-839808)+e^{4 x^8} (288 x+1152) \log ^{12}\left (x^2+8 x+13\right )+e^{8 x^8} (-7776 x-31104) \log ^8\left (x^2+8 x+13\right )+e^{12 x^8} (69984 x+279936) \log ^4\left (x^2+8 x+13\right )+e^{4 x^8} \left (-1152 x^9-9216 x^8-14976 x^7\right ) \log ^{13}\left (x^2+8 x+13\right )+e^{8 x^8} \left (31104 x^9+248832 x^8+404352 x^7\right ) \log ^9\left (x^2+8 x+13\right )+e^{12 x^8} \left (-279936 x^9-2239488 x^8-3639168 x^7\right ) \log ^5\left (x^2+8 x+13\right )+e^{16 x^8} \left (839808 x^9+6718464 x^8+10917504 x^7\right ) \log \left (x^2+8 x+13\right )}{\left (x^2+8 x+13\right ) \log ^{17}\left (x^2+8 x+13\right )} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {288 e^{4 x^8} \left (4 \left (x^2+8 x+13\right ) x^7 \log \left (x^2+8 x+13\right )-x-4\right ) \left (9 e^{4 x^8}-\log ^4\left (x^2+8 x+13\right )\right )^3}{\left (x^2+8 x+13\right ) \log ^{17}\left (x^2+8 x+13\right )}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 288 \int -\frac {e^{4 x^8} \left (-4 \left (x^2+8 x+13\right ) \log \left (x^2+8 x+13\right ) x^7+x+4\right ) \left (9 e^{4 x^8}-\log ^4\left (x^2+8 x+13\right )\right )^3}{\left (x^2+8 x+13\right ) \log ^{17}\left (x^2+8 x+13\right )}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -288 \int \frac {e^{4 x^8} \left (-4 \left (x^2+8 x+13\right ) \log \left (x^2+8 x+13\right ) x^7+x+4\right ) \left (9 e^{4 x^8}-\log ^4\left (x^2+8 x+13\right )\right )^3}{\left (x^2+8 x+13\right ) \log ^{17}\left (x^2+8 x+13\right )}dx\)

\(\Big \downarrow \) 7263

\(\displaystyle 36 \int \left (\frac {9 e^{4 x^8}}{\log ^4\left (x^2+8 x+13\right )}-1\right )^3d\frac {e^{4 x^8}}{\log ^4\left (x^2+8 x+13\right )}\)

\(\Big \downarrow \) 17

\(\displaystyle \left (1-\frac {9 e^{4 x^8}}{\log ^4\left (x^2+8 x+13\right )}\right )^4\)

Input:

Int[(E^(16*x^8)*(-839808 - 209952*x) + E^(16*x^8)*(10917504*x^7 + 6718464* 
x^8 + 839808*x^9)*Log[13 + 8*x + x^2] + E^(12*x^8)*(279936 + 69984*x)*Log[ 
13 + 8*x + x^2]^4 + E^(12*x^8)*(-3639168*x^7 - 2239488*x^8 - 279936*x^9)*L 
og[13 + 8*x + x^2]^5 + E^(8*x^8)*(-31104 - 7776*x)*Log[13 + 8*x + x^2]^8 + 
 E^(8*x^8)*(404352*x^7 + 248832*x^8 + 31104*x^9)*Log[13 + 8*x + x^2]^9 + E 
^(4*x^8)*(1152 + 288*x)*Log[13 + 8*x + x^2]^12 + E^(4*x^8)*(-14976*x^7 - 9 
216*x^8 - 1152*x^9)*Log[13 + 8*x + x^2]^13)/((13 + 8*x + x^2)*Log[13 + 8*x 
 + x^2]^17),x]
 

Output:

(1 - (9*E^(4*x^8))/Log[13 + 8*x + x^2]^4)^4
 

Defintions of rubi rules used

rule 17

Int[(c_.)*((a_.) + (b_.)*(x_))^(m_.), x_Symbol] :> Simp[c*((a + b*x)^(m + 1 
)/(b*(m + 1))), x] /; FreeQ[{a, b, c, m}, x] && NeQ[m, -1]
 

rule 25

Int[-(Fx_), x_Symbol] :> Simp[Identity[-1]   Int[Fx, x], x]
 

rule 27

Int[(a_)*(Fx_), x_Symbol] :> Simp[a   Int[Fx, x], x] /; FreeQ[a, x] &&  !Ma 
tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
 

rule 7239

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl 
erIntegrandQ[v, u, x]]
 

rule 7263

Int[(u_)*(v_)^(r_.)*((a_.)*(v_)^(p_.) + (b_.)*(w_)^(q_.))^(m_.), x_Symbol] 
:> With[{c = Simplify[u/(p*w*D[v, x] - q*v*D[w, x])]}, Simp[(-c)*q   Subst[ 
Int[(a + b*x^q)^m, x], x, v^(m*p + r + 1)*w], x] /; FreeQ[c, x]] /; FreeQ[{ 
a, b, m, p, q, r}, x] && EqQ[p + q*(m*p + r + 1), 0] && IntegerQ[q] && Inte 
gerQ[m]
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(79\) vs. \(2(22)=44\).

Time = 0.04 (sec) , antiderivative size = 80, normalized size of antiderivative = 3.48

\[\frac {9 \,{\mathrm e}^{4 x^{8}} \left (729 \,{\mathrm e}^{12 x^{8}}-324 \,{\mathrm e}^{8 x^{8}} \ln \left (x^{2}+8 x +13\right )^{4}+54 \,{\mathrm e}^{4 x^{8}} \ln \left (x^{2}+8 x +13\right )^{8}-4 \ln \left (x^{2}+8 x +13\right )^{12}\right )}{\ln \left (x^{2}+8 x +13\right )^{16}}\]

Input:

int(((-1152*x^9-9216*x^8-14976*x^7)*exp(x^8)^4*ln(x^2+8*x+13)^13+(288*x+11 
52)*exp(x^8)^4*ln(x^2+8*x+13)^12+(31104*x^9+248832*x^8+404352*x^7)*exp(x^8 
)^8*ln(x^2+8*x+13)^9+(-7776*x-31104)*exp(x^8)^8*ln(x^2+8*x+13)^8+(-279936* 
x^9-2239488*x^8-3639168*x^7)*exp(x^8)^12*ln(x^2+8*x+13)^5+(69984*x+279936) 
*exp(x^8)^12*ln(x^2+8*x+13)^4+(839808*x^9+6718464*x^8+10917504*x^7)*exp(x^ 
8)^16*ln(x^2+8*x+13)+(-209952*x-839808)*exp(x^8)^16)/(x^2+8*x+13)/ln(x^2+8 
*x+13)^17,x)
 

Output:

9*exp(4*x^8)*(729*exp(12*x^8)-324*exp(8*x^8)*ln(x^2+8*x+13)^4+54*exp(4*x^8 
)*ln(x^2+8*x+13)^8-4*ln(x^2+8*x+13)^12)/ln(x^2+8*x+13)^16
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (22) = 44\).

Time = 0.07 (sec) , antiderivative size = 79, normalized size of antiderivative = 3.43 \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=-\frac {9 \, {\left (4 \, e^{\left (4 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{12} - 54 \, e^{\left (8 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{8} + 324 \, e^{\left (12 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{4} - 729 \, e^{\left (16 \, x^{8}\right )}\right )}}{\log \left (x^{2} + 8 \, x + 13\right )^{16}} \] Input:

integrate(((-1152*x^9-9216*x^8-14976*x^7)*exp(x^8)^4*log(x^2+8*x+13)^13+(2 
88*x+1152)*exp(x^8)^4*log(x^2+8*x+13)^12+(31104*x^9+248832*x^8+404352*x^7) 
*exp(x^8)^8*log(x^2+8*x+13)^9+(-7776*x-31104)*exp(x^8)^8*log(x^2+8*x+13)^8 
+(-279936*x^9-2239488*x^8-3639168*x^7)*exp(x^8)^12*log(x^2+8*x+13)^5+(6998 
4*x+279936)*exp(x^8)^12*log(x^2+8*x+13)^4+(839808*x^9+6718464*x^8+10917504 
*x^7)*exp(x^8)^16*log(x^2+8*x+13)+(-209952*x-839808)*exp(x^8)^16)/(x^2+8*x 
+13)/log(x^2+8*x+13)^17,x, algorithm="fricas")
 

Output:

-9*(4*e^(4*x^8)*log(x^2 + 8*x + 13)^12 - 54*e^(8*x^8)*log(x^2 + 8*x + 13)^ 
8 + 324*e^(12*x^8)*log(x^2 + 8*x + 13)^4 - 729*e^(16*x^8))/log(x^2 + 8*x + 
 13)^16
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (20) = 40\).

Time = 0.33 (sec) , antiderivative size = 92, normalized size of antiderivative = 4.00 \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=\frac {6561 e^{16 x^{8}} \log {\left (x^{2} + 8 x + 13 \right )}^{24} - 2916 e^{12 x^{8}} \log {\left (x^{2} + 8 x + 13 \right )}^{28} + 486 e^{8 x^{8}} \log {\left (x^{2} + 8 x + 13 \right )}^{32} - 36 e^{4 x^{8}} \log {\left (x^{2} + 8 x + 13 \right )}^{36}}{\log {\left (x^{2} + 8 x + 13 \right )}^{40}} \] Input:

integrate(((-1152*x**9-9216*x**8-14976*x**7)*exp(x**8)**4*ln(x**2+8*x+13)* 
*13+(288*x+1152)*exp(x**8)**4*ln(x**2+8*x+13)**12+(31104*x**9+248832*x**8+ 
404352*x**7)*exp(x**8)**8*ln(x**2+8*x+13)**9+(-7776*x-31104)*exp(x**8)**8* 
ln(x**2+8*x+13)**8+(-279936*x**9-2239488*x**8-3639168*x**7)*exp(x**8)**12* 
ln(x**2+8*x+13)**5+(69984*x+279936)*exp(x**8)**12*ln(x**2+8*x+13)**4+(8398 
08*x**9+6718464*x**8+10917504*x**7)*exp(x**8)**16*ln(x**2+8*x+13)+(-209952 
*x-839808)*exp(x**8)**16)/(x**2+8*x+13)/ln(x**2+8*x+13)**17,x)
 

Output:

(6561*exp(16*x**8)*log(x**2 + 8*x + 13)**24 - 2916*exp(12*x**8)*log(x**2 + 
 8*x + 13)**28 + 486*exp(8*x**8)*log(x**2 + 8*x + 13)**32 - 36*exp(4*x**8) 
*log(x**2 + 8*x + 13)**36)/log(x**2 + 8*x + 13)**40
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (22) = 44\).

Time = 1.74 (sec) , antiderivative size = 79, normalized size of antiderivative = 3.43 \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=-\frac {9 \, {\left (4 \, e^{\left (4 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{12} - 54 \, e^{\left (8 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{8} + 324 \, e^{\left (12 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{4} - 729 \, e^{\left (16 \, x^{8}\right )}\right )}}{\log \left (x^{2} + 8 \, x + 13\right )^{16}} \] Input:

integrate(((-1152*x^9-9216*x^8-14976*x^7)*exp(x^8)^4*log(x^2+8*x+13)^13+(2 
88*x+1152)*exp(x^8)^4*log(x^2+8*x+13)^12+(31104*x^9+248832*x^8+404352*x^7) 
*exp(x^8)^8*log(x^2+8*x+13)^9+(-7776*x-31104)*exp(x^8)^8*log(x^2+8*x+13)^8 
+(-279936*x^9-2239488*x^8-3639168*x^7)*exp(x^8)^12*log(x^2+8*x+13)^5+(6998 
4*x+279936)*exp(x^8)^12*log(x^2+8*x+13)^4+(839808*x^9+6718464*x^8+10917504 
*x^7)*exp(x^8)^16*log(x^2+8*x+13)+(-209952*x-839808)*exp(x^8)^16)/(x^2+8*x 
+13)/log(x^2+8*x+13)^17,x, algorithm="maxima")
 

Output:

-9*(4*e^(4*x^8)*log(x^2 + 8*x + 13)^12 - 54*e^(8*x^8)*log(x^2 + 8*x + 13)^ 
8 + 324*e^(12*x^8)*log(x^2 + 8*x + 13)^4 - 729*e^(16*x^8))/log(x^2 + 8*x + 
 13)^16
 

Giac [F(-1)]

Timed out. \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=\text {Timed out} \] Input:

integrate(((-1152*x^9-9216*x^8-14976*x^7)*exp(x^8)^4*log(x^2+8*x+13)^13+(2 
88*x+1152)*exp(x^8)^4*log(x^2+8*x+13)^12+(31104*x^9+248832*x^8+404352*x^7) 
*exp(x^8)^8*log(x^2+8*x+13)^9+(-7776*x-31104)*exp(x^8)^8*log(x^2+8*x+13)^8 
+(-279936*x^9-2239488*x^8-3639168*x^7)*exp(x^8)^12*log(x^2+8*x+13)^5+(6998 
4*x+279936)*exp(x^8)^12*log(x^2+8*x+13)^4+(839808*x^9+6718464*x^8+10917504 
*x^7)*exp(x^8)^16*log(x^2+8*x+13)+(-209952*x-839808)*exp(x^8)^16)/(x^2+8*x 
+13)/log(x^2+8*x+13)^17,x, algorithm="giac")
 

Output:

Timed out
 

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=\text {Hanged} \] Input:

int(-(exp(16*x^8)*(209952*x + 839808) - exp(4*x^8)*log(8*x + x^2 + 13)^12* 
(288*x + 1152) + exp(8*x^8)*log(8*x + x^2 + 13)^8*(7776*x + 31104) - exp(1 
2*x^8)*log(8*x + x^2 + 13)^4*(69984*x + 279936) - exp(16*x^8)*log(8*x + x^ 
2 + 13)*(10917504*x^7 + 6718464*x^8 + 839808*x^9) + exp(4*x^8)*log(8*x + x 
^2 + 13)^13*(14976*x^7 + 9216*x^8 + 1152*x^9) - exp(8*x^8)*log(8*x + x^2 + 
 13)^9*(404352*x^7 + 248832*x^8 + 31104*x^9) + exp(12*x^8)*log(8*x + x^2 + 
 13)^5*(3639168*x^7 + 2239488*x^8 + 279936*x^9))/(log(8*x + x^2 + 13)^17*( 
8*x + x^2 + 13)),x)
 

Output:

\text{Hanged}
 

Reduce [B] (verification not implemented)

Time = 0.20 (sec) , antiderivative size = 83, normalized size of antiderivative = 3.61 \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=\frac {9 e^{4 x^{8}} \left (729 e^{12 x^{8}}-324 e^{8 x^{8}} \mathrm {log}\left (x^{2}+8 x +13\right )^{4}+54 e^{4 x^{8}} \mathrm {log}\left (x^{2}+8 x +13\right )^{8}-4 \mathrm {log}\left (x^{2}+8 x +13\right )^{12}\right )}{\mathrm {log}\left (x^{2}+8 x +13\right )^{16}} \] Input:

int(((-1152*x^9-9216*x^8-14976*x^7)*exp(x^8)^4*log(x^2+8*x+13)^13+(288*x+1 
152)*exp(x^8)^4*log(x^2+8*x+13)^12+(31104*x^9+248832*x^8+404352*x^7)*exp(x 
^8)^8*log(x^2+8*x+13)^9+(-7776*x-31104)*exp(x^8)^8*log(x^2+8*x+13)^8+(-279 
936*x^9-2239488*x^8-3639168*x^7)*exp(x^8)^12*log(x^2+8*x+13)^5+(69984*x+27 
9936)*exp(x^8)^12*log(x^2+8*x+13)^4+(839808*x^9+6718464*x^8+10917504*x^7)* 
exp(x^8)^16*log(x^2+8*x+13)+(-209952*x-839808)*exp(x^8)^16)/(x^2+8*x+13)/l 
og(x^2+8*x+13)^17,x)
 

Output:

(9*e**(4*x**8)*(729*e**(12*x**8) - 324*e**(8*x**8)*log(x**2 + 8*x + 13)**4 
 + 54*e**(4*x**8)*log(x**2 + 8*x + 13)**8 - 4*log(x**2 + 8*x + 13)**12))/l 
og(x**2 + 8*x + 13)**16