3.14.50 $\int \frac{-1215000+1761750x^2-972000x^4+256320x^6-32256x^8+1536x^{10}+e^{4x}(-120x^4-96x^5-18x^6+24x^7)+(-1296000+1814400x^2-977400x^4+254112x^6-31872x^8+1536x^{10})\log (2)+(-518400+699840x^2-367920x^4+94356x^6-11808x^8+576x^{10}){\log }^2(2)+(-92160+119808x^2-61440x^4+15552x^6-1944x^8+96x^{10}){\log }^3(2)+(-6144+7680x^2-3840x^4+960x^6-120x^8+6x^{10}){\log }^4(2)+e^{3x}(5760x^3+4320x^4-864x^5-2232x^6-192x^7+288x^8+(1536x^3+1152x^4-192x^5-576x^6-48x^7+72x^8)\log (2))+e^{2x}(-97200x^2-64800x^3+45900x^4+50760x^5-3168x^6-13248x^7-576x^8+1152x^9+(-51840x^2-34560x^3+23040x^4+26496x^5-1368x^6-6768x^7-288x^8+576x^9)\log (2)+(-6912x^2-4608x^3+2880x^4+3456x^5-144x^6-864x^7-36x^8+72x^9){\log }^2(2))+e^x(648000x+324000x^2-550800x^3-340200x^4+155520x^5+133920x^6-14592x^7-23424x^8+1536x^{10}+(518400x+259200x^2-423360x^3-267840x^4+114912x^5+103752x^6-10368x^7-17856x^8+1152x^{10})\log (2)+(138240x+69120x^2-108288x^3-70272x^4+28224x^5+26784x^6-2448x^7-4536x^8+288x^{10}){\log }^2(2)+(12288x+6144x^2-9216x^3-6144x^4+2304x^5+2304x^6-192x^7-384x^8+24x^{10}){\log }^3(2))}{-1024+1280x^2-640x^4+160x^6-20x^8+x^{10}}dx$

Optimal. Leaf size=27 $$6x{(-4-\frac{1+e^{x}x}{-4+x^2}-\log (2))}^4$$

________________________________________________________________________________________

Rubi [B]  time = 6.02, antiderivative size = 1088, normalized size of antiderivative = 40.30, number of steps used = 39, number of rules used = 8, integrand size = 609, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.013, Rules used = {6688, 12, 6742, 2288, 288, 321, 207, 199}

result too large to display

Antiderivative was successfully verified.

[In]

Int[(-1215000 + 1761750*x^2 - 972000*x^4 + 256320*x^6 - 32256*x^8 + 1536*x^10 + E^(4*x)*(-120*x^4 - 96*x^5 - 1
8*x^6 + 24*x^7) + (-1296000 + 1814400*x^2 - 977400*x^4 + 254112*x^6 - 31872*x^8 + 1536*x^10)*Log[2] + (-518400
+ 699840*x^2 - 367920*x^4 + 94356*x^6 - 11808*x^8 + 576*x^10)*Log[2]^2 + (-92160 + 119808*x^2 - 61440*x^4 + 1
5552*x^6 - 1944*x^8 + 96*x^10)*Log[2]^3 + (-6144 + 7680*x^2 - 3840*x^4 + 960*x^6 - 120*x^8 + 6*x^10)*Log[2]^4
+ E^(3*x)*(5760*x^3 + 4320*x^4 - 864*x^5 - 2232*x^6 - 192*x^7 + 288*x^8 + (1536*x^3 + 1152*x^4 - 192*x^5 - 576
*x^6 - 48*x^7 + 72*x^8)*Log[2]) + E^(2*x)*(-97200*x^2 - 64800*x^3 + 45900*x^4 + 50760*x^5 - 3168*x^6 - 13248*x
^7 - 576*x^8 + 1152*x^9 + (-51840*x^2 - 34560*x^3 + 23040*x^4 + 26496*x^5 - 1368*x^6 - 6768*x^7 - 288*x^8 + 57
6*x^9)*Log[2] + (-6912*x^2 - 4608*x^3 + 2880*x^4 + 3456*x^5 - 144*x^6 - 864*x^7 - 36*x^8 + 72*x^9)*Log[2]^2) +
E^x*(648000*x + 324000*x^2 - 550800*x^3 - 340200*x^4 + 155520*x^5 + 133920*x^6 - 14592*x^7 - 23424*x^8 + 1536
*x^10 + (518400*x + 259200*x^2 - 423360*x^3 - 267840*x^4 + 114912*x^5 + 103752*x^6 - 10368*x^7 - 17856*x^8 + 1
152*x^10)*Log[2] + (138240*x + 69120*x^2 - 108288*x^3 - 70272*x^4 + 28224*x^5 + 26784*x^6 - 2448*x^7 - 4536*x^
8 + 288*x^10)*Log[2]^2 + (12288*x + 6144*x^2 - 9216*x^3 - 6144*x^4 + 2304*x^5 + 2304*x^6 - 192*x^7 - 384*x^8 +
24*x^10)*Log[2]^3))/(-1024 + 1280*x^2 - 640*x^4 + 160*x^6 - 20*x^8 + x^10),x]

[Out]

(6*E^(4*x)*x^4*(4*x - x^3))/(4 - x^2)^5 + (945*x*(4 + Log[2])^4)/64 - (3*x^9*(4 + Log[2])^4)/(4*(4 - x^2)^4) +
(9*x^7*(4 + Log[2])^4)/(8*(4 - x^2)^3) - (63*x^5*(4 + Log[2])^4)/(32*(4 - x^2)^2) + (315*x^3*(4 + Log[2])^4)/
(64*(4 - x^2)) - (945*ArcTanh[x/2]*(4 + Log[2])^4)/32 + (3*x*(15 + Log[16])^4)/(4*(4 - x^2)^4) + (7*x*(15 + Lo
g[16])^4)/(32*(4 - x^2)^3) + (35*x*(15 + Log[16])^4)/(512*(4 - x^2)^2) + (105*x*(15 + Log[16])^4)/(4096*(4 - x
^2)) + (105*ArcTanh[x/2]*(15 + Log[16])^4)/8192 - (24*E^(3*x)*x^3*(x^5*(4 + Log[2]) + 4*x*(15 + Log[16]) - x^3
*(31 + Log[256])))/(4 - x^2)^5 + (36*E^(2*x)*x^2*(15 - x^2*(4 + Log[2]) + Log[16])*(x^5*(4 + Log[2]) + 4*x*(15
+ Log[16]) - x^3*(31 + Log[256])))/(4 - x^2)^5 - (24*E^x*x*(15 - x^2*(4 + Log[2]) + Log[16])^2*(x^5*(4 + Log[
2]) + 4*x*(15 + Log[16]) - x^3*(31 + Log[256])))/(4 - x^2)^5 + (3*x^3*(4 + Log[2])*(15 + Log[16])^2*(180 + Log
[16] + 3*Log[256] + Log[4096]))/(4*(4 - x^2)^4) - (3*x*(4 + Log[2])*(15 + Log[16])^2*(180 + Log[16] + 3*Log[25
6] + Log[4096]))/(8*(4 - x^2)^3) + (3*x*(4 + Log[2])*(15 + Log[16])^2*(180 + Log[16] + 3*Log[256] + Log[4096])
)/(128*(4 - x^2)^2) + (9*x*(4 + Log[2])*(15 + Log[16])^2*(180 + Log[16] + 3*Log[256] + Log[4096]))/(1024*(4 -
x^2)) + (9*ArcTanh[x/2]*(4 + Log[2])*(15 + Log[16])^2*(180 + Log[16] + 3*Log[256] + Log[4096]))/2048 - (3*x^5*
(4 + Log[2])^3*(15 + Log[16])*(1 + (3*(54 + Log[4096]))/(16 + Log[16])))/(4 - x^2)^4 + (5*x^3*(4 + Log[2])^3*(
15 + Log[16])*(1 + (3*(54 + Log[4096]))/(16 + Log[16])))/(2*(4 - x^2)^3) - (15*x*(4 + Log[2])^3*(15 + Log[16])
*(1 + (3*(54 + Log[4096]))/(16 + Log[16])))/(8*(4 - x^2)^2) + (15*x*(4 + Log[2])^3*(15 + Log[16])*(1 + (3*(54
+ Log[4096]))/(16 + Log[16])))/(64*(4 - x^2)) + (15*ArcTanh[x/2]*(4 + Log[2])^3*(15 + Log[16])*(1 + (3*(54 + L
og[4096]))/(16 + Log[16])))/128 + (9*x^7*(4 + Log[2])^3*(15 + Log[16])*(84 + Log[1048576]))/(4*(4 - x^2)^4*(45
+ Log[4096])) - (21*x^5*(4 + Log[2])^3*(15 + Log[16])*(84 + Log[1048576]))/(8*(4 - x^2)^3*(45 + Log[4096])) +
(105*x^3*(4 + Log[2])^3*(15 + Log[16])*(84 + Log[1048576]))/(32*(4 - x^2)^2*(45 + Log[4096])) - (315*x*(4 + L
og[2])^3*(15 + Log[16])*(84 + Log[1048576]))/(64*(4 - x^2)*(45 + Log[4096])) + (315*ArcTanh[x/2]*(4 + Log[2])^
3*(15 + Log[16])*(84 + Log[1048576]))/(128*(45 + Log[4096])) - (9*x*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[10
48576]))/((4 - x^2)^4*(48 + Log[4096])) + (3*x*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[1048576]))/(8*(4 - x^2)
^3*(48 + Log[4096])) + (15*x*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[1048576]))/(128*(4 - x^2)^2*(48 + Log[409
6])) + (45*x*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[1048576]))/(1024*(4 - x^2)*(48 + Log[4096])) + (45*ArcTan
h[x/2]*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[1048576]))/(2048*(48 + Log[4096]))

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 199

Int[((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> -Simp[(x*(a + b*x^n)^(p + 1))/(a*n*(p + 1)), x] + Dist[(n*(p +
1) + 1)/(a*n*(p + 1)), Int[(a + b*x^n)^(p + 1), x], x] /; FreeQ[{a, b}, x] && IGtQ[n, 0] && LtQ[p, -1] && (In
tegerQ[2*p] || (n == 2 && IntegerQ[4*p]) || (n == 2 && IntegerQ[3*p]) || Denominator[p + 1/n] < Denominator[p]
)

Rule 207

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> -Simp[ArcTanh[(Rt[b, 2]*x)/Rt[-a, 2]]/(Rt[-a, 2]*Rt[b, 2]), x] /;
FreeQ[{a, b}, x] && NegQ[a/b] && (LtQ[a, 0] || GtQ[b, 0])

Rule 288

Int[((c_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(c^(n - 1)*(c*x)^(m - n + 1)*(a + b*x^
n)^(p + 1))/(b*n*(p + 1)), x] - Dist[(c^n*(m - n + 1))/(b*n*(p + 1)), Int[(c*x)^(m - n)*(a + b*x^n)^(p + 1), x
], x] /; FreeQ[{a, b, c}, x] && IGtQ[n, 0] && LtQ[p, -1] && GtQ[m + 1, n] &&  !ILtQ[(m + n*(p + 1) + 1)/n, 0]
&& IntBinomialQ[a, b, c, n, m, p, x]

Rule 321

Int[((c_.)*(x_))^(m_)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(c^(n - 1)*(c*x)^(m - n + 1)*(a + b*x^n
)^(p + 1))/(b*(m + n*p + 1)), x] - Dist[(a*c^n*(m - n + 1))/(b*(m + n*p + 1)), Int[(c*x)^(m - n)*(a + b*x^n)^p
, x], x] /; FreeQ[{a, b, c, p}, x] && IGtQ[n, 0] && GtQ[m, n - 1] && NeQ[m + n*p + 1, 0] && IntBinomialQ[a, b,
c, n, m, p, x]

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rule 6688

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

Rule 6742

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{6{(e^{x}x-15(1+\frac{4\log (2)}{15})+x^2(4+\log (2)))}^3(-e^{x}x(-20-16x-3x^2+4x^3)-60(1+\frac{4\log (2)}{15})-x^4(4+\log (2))+x^2(39+\log (256)))}{{(4-x^2)}^5}dx\\ & =6\int \frac{{(e^{x}x-15(1+\frac{4\log (2)}{15})+x^2(4+\log (2)))}^3(-e^{x}x(-20-16x-3x^2+4x^3)-60(1+\frac{4\log (2)}{15})-x^4(4+\log (2))+x^2(39+\log (256)))}{{(4-x^2)}^5}dx\\ & =6\int (\frac{e^{4x}{x}^4(-20-16x-3x^2+4x^3)}{{(-4+x^2)}^5}+\frac{e^{3x}{x}^3(144x^2(1+\frac{2\log (2)}{9})+32x^4(1+\frac{\log (2)}{4})-48x^5(1+\frac{\log (2)}{4})+372x^3(1+\frac{8\log (2)}{31})-960(1+\frac{4\log (2)}{15})-720x(1+\frac{4\log (2)}{15}))}{{(4-x^2)}^5}+\frac{x^{10}(4+\log (2){)}^4}{{(-4+x^2)}^5}+\frac{3e^{2x}{x}^2(74x^2(1+\frac{8\log (2)}{37})+8x^4(1+\frac{\log (2)}{4})-16x^5(1+\frac{\log (2)}{4})+124x^3(1+\frac{8\log (2)}{31})-360(1+\frac{4\log (2)}{15})-240x(1+\frac{4\log (2)}{15}))(-15-4\log (2)+x^2(4+\log (2)))}{{(4-x^2)}^5}-\frac{4(15+\log (16){)}^4}{{(-4+x^2)}^5}+\frac{4e^{x}x(38x^2(1+\frac{4\log (2)}{19})-4x^5(1+\frac{\log (2)}{4})+31x^3(1+\frac{8\log (2)}{31})-120(1+\frac{4\log (2)}{15})-60x(1+\frac{4\log (2)}{15})){(15-x^2(4+\log (2))+\log (16))}^2}{{(4-x^2)}^5}-\frac{12x^4(4+\log (2){)}^2(15+\log (16){)}^2(1+\frac{\log (16)+3(44+\log (256))}{12(4+\log (2))})}{{(-4+x^2)}^5}-\frac{3x^8(4+\log (2){)}^3(15+\log (16))(1+\frac{39+\log (256)}{45+\log (4096)})}{{(-4+x^2)}^5}+\frac{12x^2(4+\log (2))(15+\log (16){)}^3(1+\frac{39+\log (256)}{48+\log (4096)})}{{(-4+x^2)}^5}+\frac{4x^6(4+\log (2){)}^3(15+\log (16))(1+\frac{3(54+\log (4096))}{16+\log (16)})}{{(-4+x^2)}^5})dx\\ & =6\int \frac{e^{4x}{x}^4(-20-16x-3x^2+4x^3)}{{(-4+x^2)}^5}dx+6\int \frac{e^{3x}{x}^3(144x^2(1+\frac{2\log (2)}{9})+32x^4(1+\frac{\log (2)}{4})-48x^5(1+\frac{\log (2)}{4})+372x^3(1+\frac{8\log (2)}{31})-960(1+\frac{4\log (2)}{15})-720x(1+\frac{4\log (2)}{15}))}{{(4-x^2)}^5}dx+18\int \frac{e^{2x}{x}^2(74x^2(1+\frac{8\log (2)}{37})+8x^4(1+\frac{\log (2)}{4})-16x^5(1+\frac{\log (2)}{4})+124x^3(1+\frac{8\log (2)}{31})-360(1+\frac{4\log (2)}{15})-240x(1+\frac{4\log (2)}{15}))(-15-4\log (2)+x^2(4+\log (2)))}{{(4-x^2)}^5}dx+24\int \frac{e^{x}x(38x^2(1+\frac{4\log (2)}{19})-4x^5(1+\frac{\log (2)}{4})+31x^3(1+\frac{8\log (2)}{31})-120(1+\frac{4\log (2)}{15})-60x(1+\frac{4\log (2)}{15})){(15-x^2(4+\log (2))+\log (16))}^2}{{(4-x^2)}^5}dx+(6(4+\log (2){)}^4)\int \frac{x^{10}}{{(-4+x^2)}^5}dx-(24(15+\log (16){)}^4)\int \frac{1}{{(-4+x^2)}^5}dx-(6(4+\log (2))(15+\log (16){)}^2(180+\log (16)+3\log (256)+\log (4096)))\int \frac{x^4}{{(-4+x^2)}^5}dx-(18(4+\log (2){)}^3(15+\log (16))(1+\frac{39+\log (256)}{45+\log (4096)}))\int \frac{x^8}{{(-4+x^2)}^5}dx+(72(4+\log (2))(15+\log (16){)}^3(1+\frac{39+\log (256)}{48+\log (4096)}))\int \frac{x^2}{{(-4+x^2)}^5}dx+(24(4+\log (2){)}^3(15+\log (16))(1+\frac{3(54+\log (4096))}{16+\log (16)}))\int \frac{x^6}{{(-4+x^2)}^5}dx\\ & =\frac{6e^{4x}{x}^4(4x-x^3)}{{(4-x^2)}^5}-\frac{3x^9(4+\log (2){)}^4}{4{(4-x^2)}^4}+\frac{3x(15+\log (16){)}^4}{4{(4-x^2)}^4}-\frac{24e^{3x}{x}^3(x^5(4+\log (2))+4x(15+\log (16))-x^3(31+\log (256)))}{{(4-x^2)}^5}+\frac{36e^{2x}{x}^2(15-x^2(4+\log (2))+\log (16))(x^5(4+\log (2))+4x(15+\log (16))-x^3(31+\log (256)))}{{(4-x^2)}^5}-\frac{24e^{x}x{(15-x^2(4+\log (2))+\log (16))}^2(x^5(4+\log (2))+4x(15+\log (16))-x^3(31+\log (256)))}{{(4-x^2)}^5}+\frac{9x^7(4+\log (2){)}^3(15+\log (16))(84+\log (256)+\log (4096))}{4{(4-x^2)}^4(45+\log (4096))}-\frac{9x(4+\log (2))(15+\log (16){)}^3(87+\log (256)+\log (4096))}{{(4-x^2)}^4(48+\log (4096))}+\frac{3x^3(4+\log (2))(15+\log (16){)}^2(180+\log (16)+3\log (256)+\log (4096))}{4{(4-x^2)}^4}-\frac{3x^5(4+\log (2){)}^3(15+\log (16))(1+\frac{3(54+\log (4096))}{16+\log (16)})}{{(4-x^2)}^4}+\frac{1}{4}(27(4+\log (2){)}^4)\int \frac{x^8}{{(-4+x^2)}^4}dx+\frac{1}{4}(21(15+\log (16){)}^4)\int \frac{1}{{(-4+x^2)}^4}dx-\frac{1}{4}(9(4+\log (2))(15+\log (16){)}^2(180+\log (16)+3\log (256)+\log (4096)))\int \frac{x^2}{{(-4+x^2)}^4}dx-\frac{1}{4}(63(4+\log (2){)}^3(15+\log (16))(1+\frac{39+\log (256)}{45+\log (4096)}))\int \frac{x^6}{{(-4+x^2)}^4}dx+(9(4+\log (2))(15+\log (16){)}^3(1+\frac{39+\log (256)}{48+\log (4096)}))\int \frac{1}{{(-4+x^2)}^4}dx+(15(4+\log (2){)}^3(15+\log (16))(1+\frac{3(54+\log (4096))}{16+\log (16)}))\int \frac{x^4}{{(-4+x^2)}^4}dx\\ & =\text{Rest of rules removed due to large latex content}\end{array}\end{array}$$

________________________________________________________________________________________

Mathematica [B]  time = 4.68, size = 699, normalized size = 25.89 $$\begin{array}{c}6(\frac{e^{4x}{x}^5}{{(-4+x^2)}^4}+\frac{x^9(4+\log (2){)}^4}{{(-4+x^2)}^4}-\frac{3(2x(-6720+6160x^2-2044x^4+279x^6)+105{(-4+x^2)}^4{\tanh }^{-1}\left(\frac{x}{2}\right))(4+\log (2){)}^4}{64{(-4+x^2)}^4}+\frac{4e^{3x}{x}^4(-15-4\log (2)+x^2(4+\log (2)))}{{(-4+x^2)}^4}+\frac{x(15+\log (16){)}^4}{8{(-4+x^2)}^4}+\frac{7(-2x(528-160x^2+15x^4)+15{(-4+x^2)}^3{\tanh }^{-1}\left(\frac{x}{2}\right))(15+\log (16){)}^4}{49152{(-4+x^2)}^3}+\frac{6e^{2x}{x}^3(-15-4\log (2)+x^2(4+\log (2)))(x^4(4+\log (2))+4(15+\log (16))-x^2(31+\log (256)))}{{(-4+x^2)}^5}+\frac{4e^x{x}^2{(15-x^2(4+\log (2))+\log (16))}^2(x^4(4+\log (2))+4(15+\log (16))-x^2(31+\log (256)))}{{(-4+x^2)}^5}+\frac{x^3(4+\log (2))(15+\log (16){)}^2(180+\log (16)+3\log (256)+\log (4096))}{5{(-4+x^2)}^4}+\frac{(-2x(960+1168x^2-220x^4+15x^6)+15{(-4+x^2)}^4{\tanh }^{-1}\left(\frac{x}{2}\right))(4+\log (2))(15+\log (16){)}^2(180+\log (16)+3\log (256)+\log (4096))}{20480{(-4+x^2)}^4}-\frac{4x^5(4+\log (2){)}^3(15+\log (16))(178+\log (16)+3\log (4096))}{3{(-4+x^2)}^4(16+\log (16))}+\frac{5(-384x+352x^3+88x^5-6x^7+3{(-4+x^2)}^4{\tanh }^{-1}\left(\frac{x}{2}\right))(4+\log (2){)}^3(15+\log (16))(178+\log (16)+3\log (4096))}{768{(-4+x^2)}^4(16+\log (16))}+\frac{3x^7(4+\log (2){)}^3(15+\log (16))(84+\log (1048576))}{{(-4+x^2)}^4(45+\log (4096))}+\frac{7(-2x(960-880x^2+292x^4+15x^6)+15{(-4+x^2)}^4{\tanh }^{-1}\left(\frac{x}{2}\right))(4+\log (2){)}^3(15+\log (16))(84+\log (1048576))}{256{(-4+x^2)}^4(45+\log (4096))}-\frac{12x(4+\log (2))(15+\log (16){)}^3(87+\log (1048576))}{7{(-4+x^2)}^4(48+\log (4096))}+\frac{(35712x-16352x^3+3080x^5-210x^7+105{(-4+x^2)}^4{\tanh }^{-1}\left(\frac{x}{2}\right))(4+\log (2))(15+\log (16){)}^3(87+\log (1048576))}{28672{(-4+x^2)}^4(48+\log (4096))})\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-1215000 + 1761750*x^2 - 972000*x^4 + 256320*x^6 - 32256*x^8 + 1536*x^10 + E^(4*x)*(-120*x^4 - 96*x
^5 - 18*x^6 + 24*x^7) + (-1296000 + 1814400*x^2 - 977400*x^4 + 254112*x^6 - 31872*x^8 + 1536*x^10)*Log[2] + (-
518400 + 699840*x^2 - 367920*x^4 + 94356*x^6 - 11808*x^8 + 576*x^10)*Log[2]^2 + (-92160 + 119808*x^2 - 61440*x
^4 + 15552*x^6 - 1944*x^8 + 96*x^10)*Log[2]^3 + (-6144 + 7680*x^2 - 3840*x^4 + 960*x^6 - 120*x^8 + 6*x^10)*Log
[2]^4 + E^(3*x)*(5760*x^3 + 4320*x^4 - 864*x^5 - 2232*x^6 - 192*x^7 + 288*x^8 + (1536*x^3 + 1152*x^4 - 192*x^5
- 576*x^6 - 48*x^7 + 72*x^8)*Log[2]) + E^(2*x)*(-97200*x^2 - 64800*x^3 + 45900*x^4 + 50760*x^5 - 3168*x^6 - 1
3248*x^7 - 576*x^8 + 1152*x^9 + (-51840*x^2 - 34560*x^3 + 23040*x^4 + 26496*x^5 - 1368*x^6 - 6768*x^7 - 288*x^
8 + 576*x^9)*Log[2] + (-6912*x^2 - 4608*x^3 + 2880*x^4 + 3456*x^5 - 144*x^6 - 864*x^7 - 36*x^8 + 72*x^9)*Log[2
]^2) + E^x*(648000*x + 324000*x^2 - 550800*x^3 - 340200*x^4 + 155520*x^5 + 133920*x^6 - 14592*x^7 - 23424*x^8
+ 1536*x^10 + (518400*x + 259200*x^2 - 423360*x^3 - 267840*x^4 + 114912*x^5 + 103752*x^6 - 10368*x^7 - 17856*x
^8 + 1152*x^10)*Log[2] + (138240*x + 69120*x^2 - 108288*x^3 - 70272*x^4 + 28224*x^5 + 26784*x^6 - 2448*x^7 - 4
536*x^8 + 288*x^10)*Log[2]^2 + (12288*x + 6144*x^2 - 9216*x^3 - 6144*x^4 + 2304*x^5 + 2304*x^6 - 192*x^7 - 384
*x^8 + 24*x^10)*Log[2]^3))/(-1024 + 1280*x^2 - 640*x^4 + 160*x^6 - 20*x^8 + x^10),x]

[Out]

6*((E^(4*x)*x^5)/(-4 + x^2)^4 + (x^9*(4 + Log[2])^4)/(-4 + x^2)^4 - (3*(2*x*(-6720 + 6160*x^2 - 2044*x^4 + 279
*x^6) + 105*(-4 + x^2)^4*ArcTanh[x/2])*(4 + Log[2])^4)/(64*(-4 + x^2)^4) + (4*E^(3*x)*x^4*(-15 - 4*Log[2] + x^
2*(4 + Log[2])))/(-4 + x^2)^4 + (x*(15 + Log[16])^4)/(8*(-4 + x^2)^4) + (7*(-2*x*(528 - 160*x^2 + 15*x^4) + 15
*(-4 + x^2)^3*ArcTanh[x/2])*(15 + Log[16])^4)/(49152*(-4 + x^2)^3) + (6*E^(2*x)*x^3*(-15 - 4*Log[2] + x^2*(4 +
Log[2]))*(x^4*(4 + Log[2]) + 4*(15 + Log[16]) - x^2*(31 + Log[256])))/(-4 + x^2)^5 + (4*E^x*x^2*(15 - x^2*(4
+ Log[2]) + Log[16])^2*(x^4*(4 + Log[2]) + 4*(15 + Log[16]) - x^2*(31 + Log[256])))/(-4 + x^2)^5 + (x^3*(4 + L
og[2])*(15 + Log[16])^2*(180 + Log[16] + 3*Log[256] + Log[4096]))/(5*(-4 + x^2)^4) + ((-2*x*(960 + 1168*x^2 -
220*x^4 + 15*x^6) + 15*(-4 + x^2)^4*ArcTanh[x/2])*(4 + Log[2])*(15 + Log[16])^2*(180 + Log[16] + 3*Log[256] +
Log[4096]))/(20480*(-4 + x^2)^4) - (4*x^5*(4 + Log[2])^3*(15 + Log[16])*(178 + Log[16] + 3*Log[4096]))/(3*(-4
+ x^2)^4*(16 + Log[16])) + (5*(-384*x + 352*x^3 + 88*x^5 - 6*x^7 + 3*(-4 + x^2)^4*ArcTanh[x/2])*(4 + Log[2])^3
*(15 + Log[16])*(178 + Log[16] + 3*Log[4096]))/(768*(-4 + x^2)^4*(16 + Log[16])) + (3*x^7*(4 + Log[2])^3*(15 +
Log[16])*(84 + Log[1048576]))/((-4 + x^2)^4*(45 + Log[4096])) + (7*(-2*x*(960 - 880*x^2 + 292*x^4 + 15*x^6) +
15*(-4 + x^2)^4*ArcTanh[x/2])*(4 + Log[2])^3*(15 + Log[16])*(84 + Log[1048576]))/(256*(-4 + x^2)^4*(45 + Log[
4096])) - (12*x*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[1048576]))/(7*(-4 + x^2)^4*(48 + Log[4096])) + ((35712
*x - 16352*x^3 + 3080*x^5 - 210*x^7 + 105*(-4 + x^2)^4*ArcTanh[x/2])*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[1
048576]))/(28672*(-4 + x^2)^4*(48 + Log[4096])))

________________________________________________________________________________________

fricas [B]  time = 0.88, size = 362, normalized size = 13.41 $$\begin{array}{c}\frac{6(256x^9-3840x^7+x^5{e}^{\left(4x\right)}+21600x^5+(x^9-16x^7+96x^5-256x^3+256x)\log (2{)}^4+4(4x^9-63x^7+372x^5-976x^3+960x)\log (2{)}^3-54000x^3+6(16x^9-248x^7+1441x^5-3720x^3+3600x)\log (2{)}^2+4(4x^6-15x^4+(x^6-4x^4)\log (2))e^{\left(3x\right)}+6(16x^7-120x^5+225x^3+(x^7-8x^5+16x^3)\log (2{)}^2+2(4x^7-31x^5+60x^3)\log (2))e^{\left(2x\right)}+4(64x^8-720x^6+2700x^4+(x^8-12x^6+48x^4-64x^2)\log (2{)}^3+3(4x^8-47x^6+184x^4-240x^2)\log (2{)}^2-3375x^2+3(16x^8-184x^6+705x^4-900x^2)\log (2))e^x+4(64x^9-976x^7+5580x^5-14175x^3+13500x)\log (2)+50625x)}{x^8-16x^6+96x^4-256x^2+256}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x^7-18*x^6-96*x^5-120*x^4)*exp(x)^4+((72*x^8-48*x^7-576*x^6-192*x^5+1152*x^4+1536*x^3)*log(2)+2
88*x^8-192*x^7-2232*x^6-864*x^5+4320*x^4+5760*x^3)*exp(x)^3+((72*x^9-36*x^8-864*x^7-144*x^6+3456*x^5+2880*x^4-
4608*x^3-6912*x^2)*log(2)^2+(576*x^9-288*x^8-6768*x^7-1368*x^6+26496*x^5+23040*x^4-34560*x^3-51840*x^2)*log(2)
+1152*x^9-576*x^8-13248*x^7-3168*x^6+50760*x^5+45900*x^4-64800*x^3-97200*x^2)*exp(x)^2+((24*x^10-384*x^8-192*x
^7+2304*x^6+2304*x^5-6144*x^4-9216*x^3+6144*x^2+12288*x)*log(2)^3+(288*x^10-4536*x^8-2448*x^7+26784*x^6+28224*
x^5-70272*x^4-108288*x^3+69120*x^2+138240*x)*log(2)^2+(1152*x^10-17856*x^8-10368*x^7+103752*x^6+114912*x^5-267
840*x^4-423360*x^3+259200*x^2+518400*x)*log(2)+1536*x^10-23424*x^8-14592*x^7+133920*x^6+155520*x^5-340200*x^4-
550800*x^3+324000*x^2+648000*x)*exp(x)+(6*x^10-120*x^8+960*x^6-3840*x^4+7680*x^2-6144)*log(2)^4+(96*x^10-1944*
x^8+15552*x^6-61440*x^4+119808*x^2-92160)*log(2)^3+(576*x^10-11808*x^8+94356*x^6-367920*x^4+699840*x^2-518400)
*log(2)^2+(1536*x^10-31872*x^8+254112*x^6-977400*x^4+1814400*x^2-1296000)*log(2)+1536*x^10-32256*x^8+256320*x^
6-972000*x^4+1761750*x^2-1215000)/(x^10-20*x^8+160*x^6-640*x^4+1280*x^2-1024),x, algorithm="fricas")

[Out]

6*(256*x^9 - 3840*x^7 + x^5*e^(4*x) + 21600*x^5 + (x^9 - 16*x^7 + 96*x^5 - 256*x^3 + 256*x)*log(2)^4 + 4*(4*x^
9 - 63*x^7 + 372*x^5 - 976*x^3 + 960*x)*log(2)^3 - 54000*x^3 + 6*(16*x^9 - 248*x^7 + 1441*x^5 - 3720*x^3 + 360
0*x)*log(2)^2 + 4*(4*x^6 - 15*x^4 + (x^6 - 4*x^4)*log(2))*e^(3*x) + 6*(16*x^7 - 120*x^5 + 225*x^3 + (x^7 - 8*x
^5 + 16*x^3)*log(2)^2 + 2*(4*x^7 - 31*x^5 + 60*x^3)*log(2))*e^(2*x) + 4*(64*x^8 - 720*x^6 + 2700*x^4 + (x^8 -
12*x^6 + 48*x^4 - 64*x^2)*log(2)^3 + 3*(4*x^8 - 47*x^6 + 184*x^4 - 240*x^2)*log(2)^2 - 3375*x^2 + 3*(16*x^8 -
184*x^6 + 705*x^4 - 900*x^2)*log(2))*e^x + 4*(64*x^9 - 976*x^7 + 5580*x^5 - 14175*x^3 + 13500*x)*log(2) + 5062
5*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256)

________________________________________________________________________________________

giac [B]  time = 0.63, size = 508, normalized size = 18.81 $$\begin{array}{c}\frac{6(x^9\log (2{)}^4+16x^9\log (2{)}^3+4x^8{e}^x\log (2{)}^3+96x^9\log (2{)}^2+48x^8{e}^x\log (2{)}^2-16x^7\log (2{)}^4+256x^9\log (2)+192x^8{e}^x\log (2)+6x^7{e}^{\left(2x\right)}\log (2{)}^2-252x^7\log (2{)}^3-48x^6{e}^x\log (2{)}^3+256x^9+256x^8{e}^x+48x^7{e}^{\left(2x\right)}\log (2)-1488x^7\log (2{)}^2-564x^6{e}^x\log (2{)}^2+96x^5\log (2{)}^4+96x^7{e}^{\left(2x\right)}-3904x^7\log (2)+4x^6{e}^{\left(3x\right)}\log (2)-2208x^6{e}^x\log (2)-48x^5{e}^{\left(2x\right)}\log (2{)}^2+1488x^5\log (2{)}^3+192x^4{e}^x\log (2{)}^3-3840x^7+16x^6{e}^{\left(3x\right)}-2880x^6{e}^x-372x^5{e}^{\left(2x\right)}\log (2)+8646x^5\log (2{)}^2+2208x^4{e}^x\log (2{)}^2-256x^3\log (2{)}^4+x^5{e}^{\left(4x\right)}-720x^5{e}^{\left(2x\right)}+22320x^5\log (2)-16x^4{e}^{\left(3x\right)}\log (2)+8460x^4{e}^x\log (2)+96x^3{e}^{\left(2x\right)}\log (2{)}^2-3904x^3\log (2{)}^3-256x^2{e}^x\log (2{)}^3+21600x^5-60x^4{e}^{\left(3x\right)}+10800x^4{e}^x+720x^3{e}^{\left(2x\right)}\log (2)-22320x^3\log (2{)}^2-2880x^2{e}^x\log (2{)}^2+256x\log (2{)}^4+1350x^3{e}^{\left(2x\right)}-56700x^3\log (2)-10800x^2{e}^x\log (2)+3840x\log (2{)}^3-54000x^3-13500x^2{e}^x+21600x\log (2{)}^2+54000x\log (2)+50625x)}{x^8-16x^6+96x^4-256x^2+256}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x^7-18*x^6-96*x^5-120*x^4)*exp(x)^4+((72*x^8-48*x^7-576*x^6-192*x^5+1152*x^4+1536*x^3)*log(2)+2
88*x^8-192*x^7-2232*x^6-864*x^5+4320*x^4+5760*x^3)*exp(x)^3+((72*x^9-36*x^8-864*x^7-144*x^6+3456*x^5+2880*x^4-
4608*x^3-6912*x^2)*log(2)^2+(576*x^9-288*x^8-6768*x^7-1368*x^6+26496*x^5+23040*x^4-34560*x^3-51840*x^2)*log(2)
+1152*x^9-576*x^8-13248*x^7-3168*x^6+50760*x^5+45900*x^4-64800*x^3-97200*x^2)*exp(x)^2+((24*x^10-384*x^8-192*x
^7+2304*x^6+2304*x^5-6144*x^4-9216*x^3+6144*x^2+12288*x)*log(2)^3+(288*x^10-4536*x^8-2448*x^7+26784*x^6+28224*
x^5-70272*x^4-108288*x^3+69120*x^2+138240*x)*log(2)^2+(1152*x^10-17856*x^8-10368*x^7+103752*x^6+114912*x^5-267
840*x^4-423360*x^3+259200*x^2+518400*x)*log(2)+1536*x^10-23424*x^8-14592*x^7+133920*x^6+155520*x^5-340200*x^4-
550800*x^3+324000*x^2+648000*x)*exp(x)+(6*x^10-120*x^8+960*x^6-3840*x^4+7680*x^2-6144)*log(2)^4+(96*x^10-1944*
x^8+15552*x^6-61440*x^4+119808*x^2-92160)*log(2)^3+(576*x^10-11808*x^8+94356*x^6-367920*x^4+699840*x^2-518400)
*log(2)^2+(1536*x^10-31872*x^8+254112*x^6-977400*x^4+1814400*x^2-1296000)*log(2)+1536*x^10-32256*x^8+256320*x^
6-972000*x^4+1761750*x^2-1215000)/(x^10-20*x^8+160*x^6-640*x^4+1280*x^2-1024),x, algorithm="giac")

[Out]

6*(x^9*log(2)^4 + 16*x^9*log(2)^3 + 4*x^8*e^x*log(2)^3 + 96*x^9*log(2)^2 + 48*x^8*e^x*log(2)^2 - 16*x^7*log(2)
^4 + 256*x^9*log(2) + 192*x^8*e^x*log(2) + 6*x^7*e^(2*x)*log(2)^2 - 252*x^7*log(2)^3 - 48*x^6*e^x*log(2)^3 + 2
56*x^9 + 256*x^8*e^x + 48*x^7*e^(2*x)*log(2) - 1488*x^7*log(2)^2 - 564*x^6*e^x*log(2)^2 + 96*x^5*log(2)^4 + 96
*x^7*e^(2*x) - 3904*x^7*log(2) + 4*x^6*e^(3*x)*log(2) - 2208*x^6*e^x*log(2) - 48*x^5*e^(2*x)*log(2)^2 + 1488*x
^5*log(2)^3 + 192*x^4*e^x*log(2)^3 - 3840*x^7 + 16*x^6*e^(3*x) - 2880*x^6*e^x - 372*x^5*e^(2*x)*log(2) + 8646*
x^5*log(2)^2 + 2208*x^4*e^x*log(2)^2 - 256*x^3*log(2)^4 + x^5*e^(4*x) - 720*x^5*e^(2*x) + 22320*x^5*log(2) - 1
6*x^4*e^(3*x)*log(2) + 8460*x^4*e^x*log(2) + 96*x^3*e^(2*x)*log(2)^2 - 3904*x^3*log(2)^3 - 256*x^2*e^x*log(2)^
3 + 21600*x^5 - 60*x^4*e^(3*x) + 10800*x^4*e^x + 720*x^3*e^(2*x)*log(2) - 22320*x^3*log(2)^2 - 2880*x^2*e^x*lo
g(2)^2 + 256*x*log(2)^4 + 1350*x^3*e^(2*x) - 56700*x^3*log(2) - 10800*x^2*e^x*log(2) + 3840*x*log(2)^3 - 54000
*x^3 - 13500*x^2*e^x + 21600*x*log(2)^2 + 54000*x*log(2) + 50625*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256)

________________________________________________________________________________________

maple [B]  time = 0.33, size = 380, normalized size = 14.07

method	result	size
risch	$6x\ln (2{)}^4+96x\ln (2{)}^3+576x\ln (2{)}^2+1536x\ln (2)+1536x+\frac{(24\ln (2{)}^3+288\ln (2{)}^2+1152\ln (2)+1536)x^7+(-288\ln (2{)}^3-3420\ln (2{)}^2-13536\ln (2)-17856)x^5+(1152\ln (2{)}^3+13536\ln (2{)}^2+53016\ln (2)+69216)x^3+(-1536\ln (2{)}^3-17856\ln (2{)}^2-69216\ln (2)-89466)x}{x^8-16x^6+96x^4-256x^2+256}+\frac{6x^5{\mathrm{e}}^{4x}}{{(x^2-4)}^4}+\frac{24x^4(x^2\ln (2)+4x^2-4\ln (2)-15){\mathrm{e}}^{3x}}{{(x^2-4)}^4}+\frac{36x^3(x^4\ln (2{)}^2+8x^4\ln (2)-8x^2\ln (2{)}^2+16x^4-62x^2\ln (2)+16\ln (2{)}^2-120x^2+120\ln (2)+225){\mathrm{e}}^{2x}}{{(x^2-4)}^4}+\frac{24x^2(x^6\ln (2{)}^3+12x^6\ln (2{)}^2-12x^4\ln (2{)}^3+48x^6\ln (2)-141x^4\ln (2{)}^2+64x^6+48x^2\ln (2{)}^3-552x^4\ln (2)+552x^2\ln (2{)}^2-720x^4-64\ln (2{)}^3+2115x^2\ln (2)-720\ln (2{)}^2+2700x^2-2700\ln (2)-3375){\mathrm{e}}^x}{{(x^2-4)}^4}$	$380$
default	$1536x-\frac{9\ln (2{)}^2}{2{(2+x)}^2}+1536{\mathrm{e}}^x+24\ln (2{)}^3{\mathrm{e}}^x+288\ln (2{)}^2{\mathrm{e}}^x+96x\ln (2{)}^3+\frac{3}{64{(x-2)}^4}+1152{\mathrm{e}}^x\ln (2)+\frac{768}{2+x}+6x\ln (2{)}^4+576x\ln (2{)}^2+1536x\ln (2)+\frac{768}{x-2}+\frac{3{\mathrm{e}}^x}{8{(2+x)}^4}+\frac{18717{\mathrm{e}}^x}{64{(2+x)}^2}-\frac{18{\mathrm{e}}^x}{{(2+x)}^3}-\frac{214755{\mathrm{e}}^x}{128(2+x)}+\frac{18{\mathrm{e}}^x}{{(x-2)}^3}+\frac{214755{\mathrm{e}}^x}{128(x-2)}+\frac{18717{\mathrm{e}}^x}{64{(x-2)}^2}+\frac{3{\mathrm{e}}^x}{8{(x-2)}^4}+\frac{12\ln (2{)}^3}{x-2}+\frac{12\ln (2{)}^3}{2+x}+\frac{144\ln (2{)}^2}{2+x}+\frac{9\ln (2{)}^2}{2{(x-2)}^2}+\frac{144\ln (2{)}^2}{x-2}+\frac{3\ln (2)}{4{(x-2)}^3}+\frac{573\ln (2)}{16{(x-2)}^2}+\frac{576\ln (2)}{x-2}+\frac{3\ln (2)}{4{(2+x)}^3}-\frac{573\ln (2)}{16{(2+x)}^2}+\frac{576\ln (2)}{2+x}-\frac{36483}{512{(2+x)}^2}+\frac{36483}{512{(x-2)}^2}-\frac{3}{64{(2+x)}^4}-\frac{24\ln (2{)}^3{\mathrm{e}}^x}{2+x}+\frac{24\ln (2{)}^3{\mathrm{e}}^x}{x-2}+\frac{18\ln (2{)}^2{\mathrm{e}}^x}{{(2+x)}^2}-\frac{297\ln (2{)}^2{\mathrm{e}}^x}{2+x}+\frac{297\ln (2{)}^2{\mathrm{e}}^x}{x-2}+\frac{18\ln (2{)}^2{\mathrm{e}}^x}{{(x-2)}^2}+\frac{381}{128{(x-2)}^3}+\frac{381}{128{(2+x)}^3}+\frac{9\ln (2){\mathrm{e}}^{2x}}{{(x-2)}^3}-\frac{603\ln (2){\mathrm{e}}^{2x}}{4{(2+x)}^2}+\frac{9\ln (2){\mathrm{e}}^{2x}}{{(2+x)}^3}+\frac{144\ln (2){\mathrm{e}}^{2x}}{x-2}+\frac{603\ln (2){\mathrm{e}}^{2x}}{4{(x-2)}^2}+\frac{144\ln (2){\mathrm{e}}^{2x}}{2+x}+\frac{6\ln (2){\mathrm{e}}^{3x}}{{(x-2)}^3}+\frac{15\ln (2){\mathrm{e}}^{3x}}{2{(2+x)}^2}-\frac{6\ln (2){\mathrm{e}}^{3x}}{{(2+x)}^3}+\frac{9\ln (2){\mathrm{e}}^{3x}}{4(x-2)}+\frac{15\ln (2){\mathrm{e}}^{3x}}{2{(x-2)}^2}-\frac{9\ln (2){\mathrm{e}}^{3x}}{4(2+x)}-\frac{18\ln (2{)}^2{\mathrm{e}}^{2x}}{{(2+x)}^2}+\frac{18\ln (2{)}^2{\mathrm{e}}^{2x}}{x-2}+\frac{18\ln (2{)}^2{\mathrm{e}}^{2x}}{{(x-2)}^2}+\frac{18\ln (2{)}^2{\mathrm{e}}^{2x}}{2+x}-\frac{9{\mathrm{e}}^{2x}}{8{(2+x)}^4}+\frac{585{\mathrm{e}}^{2x}}{16{(x-2)}^3}-\frac{20151{\mathrm{e}}^{2x}}{64{(2+x)}^2}+\frac{585{\mathrm{e}}^{2x}}{16{(2+x)}^3}+\frac{288{\mathrm{e}}^{2x}}{x-2}+\frac{20151{\mathrm{e}}^{2x}}{64{(x-2)}^2}+\frac{288{\mathrm{e}}^{2x}}{2+x}+\frac{9{\mathrm{e}}^{2x}}{8{(x-2)}^4}-\frac{15{\mathrm{e}}^{4x}}{32{(2+x)}^2}+\frac{9{\mathrm{e}}^{4x}}{8{(2+x)}^3}+\frac{9{\mathrm{e}}^{4x}}{8{(x-2)}^3}+\frac{15{\mathrm{e}}^{4x}}{32{(x-2)}^2}-\frac{3{\mathrm{e}}^{4x}}{4{(2+x)}^4}+\frac{3{\mathrm{e}}^{4x}}{4{(x-2)}^4}+\frac{3{\mathrm{e}}^{3x}}{2{(2+x)}^4}+\frac{51{\mathrm{e}}^{3x}}{2{(x-2)}^3}+\frac{483{\mathrm{e}}^{3x}}{16{(2+x)}^2}-\frac{51{\mathrm{e}}^{3x}}{2{(2+x)}^3}+\frac{285{\mathrm{e}}^{3x}}{32(x-2)}+\frac{483{\mathrm{e}}^{3x}}{16{(x-2)}^2}-\frac{285{\mathrm{e}}^{3x}}{32(2+x)}+\frac{3{\mathrm{e}}^{3x}}{2{(x-2)}^4}+\frac{1161\ln (2){\mathrm{e}}^x}{8{(2+x)}^2}-\frac{9\ln (2){\mathrm{e}}^x}{2{(2+x)}^3}-\frac{19575\ln (2){\mathrm{e}}^x}{16(2+x)}+\frac{9\ln (2){\mathrm{e}}^x}{2{(x-2)}^3}+\frac{19575\ln (2){\mathrm{e}}^x}{16(x-2)}+\frac{1161\ln (2){\mathrm{e}}^x}{8{(x-2)}^2}$	$907$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((24*x^7-18*x^6-96*x^5-120*x^4)*exp(x)^4+((72*x^8-48*x^7-576*x^6-192*x^5+1152*x^4+1536*x^3)*ln(2)+288*x^8-
192*x^7-2232*x^6-864*x^5+4320*x^4+5760*x^3)*exp(x)^3+((72*x^9-36*x^8-864*x^7-144*x^6+3456*x^5+2880*x^4-4608*x^
3-6912*x^2)*ln(2)^2+(576*x^9-288*x^8-6768*x^7-1368*x^6+26496*x^5+23040*x^4-34560*x^3-51840*x^2)*ln(2)+1152*x^9
-576*x^8-13248*x^7-3168*x^6+50760*x^5+45900*x^4-64800*x^3-97200*x^2)*exp(x)^2+((24*x^10-384*x^8-192*x^7+2304*x
^6+2304*x^5-6144*x^4-9216*x^3+6144*x^2+12288*x)*ln(2)^3+(288*x^10-4536*x^8-2448*x^7+26784*x^6+28224*x^5-70272*
x^4-108288*x^3+69120*x^2+138240*x)*ln(2)^2+(1152*x^10-17856*x^8-10368*x^7+103752*x^6+114912*x^5-267840*x^4-423
360*x^3+259200*x^2+518400*x)*ln(2)+1536*x^10-23424*x^8-14592*x^7+133920*x^6+155520*x^5-340200*x^4-550800*x^3+3
24000*x^2+648000*x)*exp(x)+(6*x^10-120*x^8+960*x^6-3840*x^4+7680*x^2-6144)*ln(2)^4+(96*x^10-1944*x^8+15552*x^6
-61440*x^4+119808*x^2-92160)*ln(2)^3+(576*x^10-11808*x^8+94356*x^6-367920*x^4+699840*x^2-518400)*ln(2)^2+(1536
*x^10-31872*x^8+254112*x^6-977400*x^4+1814400*x^2-1296000)*ln(2)+1536*x^10-32256*x^8+256320*x^6-972000*x^4+176
1750*x^2-1215000)/(x^10-20*x^8+160*x^6-640*x^4+1280*x^2-1024),x,method=_RETURNVERBOSE)

[Out]

6*x*ln(2)^4+96*x*ln(2)^3+576*x*ln(2)^2+1536*x*ln(2)+1536*x+((24*ln(2)^3+288*ln(2)^2+1152*ln(2)+1536)*x^7+(-288
*ln(2)^3-3420*ln(2)^2-13536*ln(2)-17856)*x^5+(1152*ln(2)^3+13536*ln(2)^2+53016*ln(2)+69216)*x^3+(-1536*ln(2)^3
-17856*ln(2)^2-69216*ln(2)-89466)*x)/(x^8-16*x^6+96*x^4-256*x^2+256)+6*x^5/(x^2-4)^4*exp(4*x)+24*x^4*(x^2*ln(2
)+4*x^2-4*ln(2)-15)/(x^2-4)^4*exp(3*x)+36*x^3*(x^4*ln(2)^2+8*x^4*ln(2)-8*x^2*ln(2)^2+16*x^4-62*x^2*ln(2)+16*ln
(2)^2-120*x^2+120*ln(2)+225)/(x^2-4)^4*exp(2*x)+24*x^2*(x^6*ln(2)^3+12*x^6*ln(2)^2-12*x^4*ln(2)^3+48*x^6*ln(2)
-141*x^4*ln(2)^2+64*x^6+48*x^2*ln(2)^3-552*x^4*ln(2)+552*x^2*ln(2)^2-720*x^4-64*ln(2)^3+2115*x^2*ln(2)-720*ln(
2)^2+2700*x^2-2700*ln(2)-3375)/(x^2-4)^4*exp(x)

________________________________________________________________________________________

maxima [B]  time = 0.84, size = 1957, normalized size = 72.48 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x^7-18*x^6-96*x^5-120*x^4)*exp(x)^4+((72*x^8-48*x^7-576*x^6-192*x^5+1152*x^4+1536*x^3)*log(2)+2
88*x^8-192*x^7-2232*x^6-864*x^5+4320*x^4+5760*x^3)*exp(x)^3+((72*x^9-36*x^8-864*x^7-144*x^6+3456*x^5+2880*x^4-
4608*x^3-6912*x^2)*log(2)^2+(576*x^9-288*x^8-6768*x^7-1368*x^6+26496*x^5+23040*x^4-34560*x^3-51840*x^2)*log(2)
+1152*x^9-576*x^8-13248*x^7-3168*x^6+50760*x^5+45900*x^4-64800*x^3-97200*x^2)*exp(x)^2+((24*x^10-384*x^8-192*x
^7+2304*x^6+2304*x^5-6144*x^4-9216*x^3+6144*x^2+12288*x)*log(2)^3+(288*x^10-4536*x^8-2448*x^7+26784*x^6+28224*
x^5-70272*x^4-108288*x^3+69120*x^2+138240*x)*log(2)^2+(1152*x^10-17856*x^8-10368*x^7+103752*x^6+114912*x^5-267
840*x^4-423360*x^3+259200*x^2+518400*x)*log(2)+1536*x^10-23424*x^8-14592*x^7+133920*x^6+155520*x^5-340200*x^4-
550800*x^3+324000*x^2+648000*x)*exp(x)+(6*x^10-120*x^8+960*x^6-3840*x^4+7680*x^2-6144)*log(2)^4+(96*x^10-1944*
x^8+15552*x^6-61440*x^4+119808*x^2-92160)*log(2)^3+(576*x^10-11808*x^8+94356*x^6-367920*x^4+699840*x^2-518400)
*log(2)^2+(1536*x^10-31872*x^8+254112*x^6-977400*x^4+1814400*x^2-1296000)*log(2)+1536*x^10-32256*x^8+256320*x^
6-972000*x^4+1761750*x^2-1215000)/(x^10-20*x^8+160*x^6-640*x^4+1280*x^2-1024),x, algorithm="maxima")

[Out]

3/64*(128*x - 4*(325*x^7 - 3060*x^5 + 10288*x^3 - 11968*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 315*log(x
+ 2) + 315*log(x - 2))*log(2)^4 + 5/64*(4*(279*x^7 - 2044*x^5 + 6160*x^3 - 6720*x)/(x^8 - 16*x^6 + 96*x^4 - 2
56*x^2 + 256) + 105*log(x + 2) - 105*log(x - 2))*log(2)^4 - 1/64*(4*(105*x^7 - 1540*x^5 + 8176*x^3 - 17856*x)/
(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 105*log(x + 2) + 105*log(x - 2))*log(2)^4 - 5/32*(4*(15*x^7 + 292*x^
5 - 880*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x - 2))*log(2)^4 - 5/64*
(4*(15*x^7 - 220*x^5 + 1168*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x -
2))*log(2)^4 - 15/32*(4*(3*x^7 - 44*x^5 - 176*x^3 + 192*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 3*log(x +
2) + 3*log(x - 2))*log(2)^4 + 3/4*(128*x - 4*(325*x^7 - 3060*x^5 + 10288*x^3 - 11968*x)/(x^8 - 16*x^6 + 96*x^
4 - 256*x^2 + 256) - 315*log(x + 2) + 315*log(x - 2))*log(2)^3 + 81/64*(4*(279*x^7 - 2044*x^5 + 6160*x^3 - 672
0*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) + 105*log(x + 2) - 105*log(x - 2))*log(2)^3 - 15/64*(4*(105*x^7 -
1540*x^5 + 8176*x^3 - 17856*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 105*log(x + 2) + 105*log(x - 2))*log
(2)^3 - 81/32*(4*(15*x^7 + 292*x^5 - 880*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2)
+ 15*log(x - 2))*log(2)^3 - 39/32*(4*(15*x^7 - 220*x^5 + 1168*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 +
256) - 15*log(x + 2) + 15*log(x - 2))*log(2)^3 - 15/2*(4*(3*x^7 - 44*x^5 - 176*x^3 + 192*x)/(x^8 - 16*x^6 + 96
*x^4 - 256*x^2 + 256) - 3*log(x + 2) + 3*log(x - 2))*log(2)^3 + 9/2*(128*x - 4*(325*x^7 - 3060*x^5 + 10288*x^3
- 11968*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 315*log(x + 2) + 315*log(x - 2))*log(2)^2 + 123/16*(4*(2
79*x^7 - 2044*x^5 + 6160*x^3 - 6720*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) + 105*log(x + 2) - 105*log(x -
2))*log(2)^2 - 675/512*(4*(105*x^7 - 1540*x^5 + 8176*x^3 - 17856*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) -
105*log(x + 2) + 105*log(x - 2))*log(2)^2 - 7863/512*(4*(15*x^7 + 292*x^5 - 880*x^3 + 960*x)/(x^8 - 16*x^6 + 9
6*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x - 2))*log(2)^2 - 3645/512*(4*(15*x^7 - 220*x^5 + 1168*x^3 +
960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x - 2))*log(2)^2 - 22995/512*(4*(3*x^7
- 44*x^5 - 176*x^3 + 192*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 3*log(x + 2) + 3*log(x - 2))*log(2)^2 +
12*(128*x - 4*(325*x^7 - 3060*x^5 + 10288*x^3 - 11968*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 315*log(x
+ 2) + 315*log(x - 2))*log(2) + 83/4*(4*(279*x^7 - 2044*x^5 + 6160*x^3 - 6720*x)/(x^8 - 16*x^6 + 96*x^4 - 256*
x^2 + 256) + 105*log(x + 2) - 105*log(x - 2))*log(2) - 3375/1024*(4*(105*x^7 - 1540*x^5 + 8176*x^3 - 17856*x)/
(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 105*log(x + 2) + 105*log(x - 2))*log(2) - 2647/64*(4*(15*x^7 + 292*x
^5 - 880*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x - 2))*log(2) - 4725/2
56*(4*(15*x^7 - 220*x^5 + 1168*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x
- 2))*log(2) - 122175/1024*(4*(3*x^7 - 44*x^5 - 176*x^3 + 192*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 3*
log(x + 2) + 3*log(x - 2))*log(2) + 1536*x - 48*(325*x^7 - 3060*x^5 + 10288*x^3 - 11968*x)/(x^8 - 16*x^6 + 96*
x^4 - 256*x^2 + 256) + 84*(279*x^7 - 2044*x^5 + 6160*x^3 - 6720*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 5
0625/4096*(105*x^7 - 1540*x^5 + 8176*x^3 - 17856*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 1335/8*(15*x^7 +
292*x^5 - 880*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 293625/4096*(15*x^7 - 220*x^5 + 1168*x^3
+ 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 30375/64*(3*x^7 - 44*x^5 - 176*x^3 + 192*x)/(x^8 - 16*x^6
+ 96*x^4 - 256*x^2 + 256) + 6*(x^5*e^(4*x) + 4*(x^6*(log(2) + 4) - x^4*(4*log(2) + 15))*e^(3*x) + 6*((log(2)^2
+ 8*log(2) + 16)*x^7 - 2*(4*log(2)^2 + 31*log(2) + 60)*x^5 + (16*log(2)^2 + 120*log(2) + 225)*x^3)*e^(2*x) +
4*((log(2)^3 + 12*log(2)^2 + 48*log(2) + 64)*x^8 - 3*(4*log(2)^3 + 47*log(2)^2 + 184*log(2) + 240)*x^6 + 3*(16
*log(2)^3 + 184*log(2)^2 + 705*log(2) + 900)*x^4 - (64*log(2)^3 + 720*log(2)^2 + 2700*log(2) + 3375)*x^2)*e^x)
/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256)

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.04 $$\begin{array}{c}\int \frac{{\mathrm{e}}^x(648000x+{\ln (2)}^3(24x^{10}-384x^8-192x^7+2304x^6+2304x^5-6144x^4-9216x^3+6144x^2+12288x)+{\ln (2)}^2(288x^{10}-4536x^8-2448x^7+26784x^6+28224x^5-70272x^4-108288x^3+69120x^2+138240x)+\ln (2)(1152x^{10}-17856x^8-10368x^7+103752x^6+114912x^5-267840x^4-423360x^3+259200x^2+518400x)+324000x^2-550800x^3-340200x^4+155520x^5+133920x^6-14592x^7-23424x^8+1536x^{10})+\ln (2)(1536x^{10}-31872x^8+254112x^6-977400x^4+1814400x^2-1296000)+{\ln (2)}^4(6x^{10}-120x^8+960x^6-3840x^4+7680x^2-6144)+{\ln (2)}^3(96x^{10}-1944x^8+15552x^6-61440x^4+119808x^2-92160)+{\ln (2)}^2(576x^{10}-11808x^8+94356x^6-367920x^4+699840x^2-518400)+{\mathrm{e}}^{3x}(\ln (2)(72x^8-48x^7-576x^6-192x^5+1152x^4+1536x^3)+5760x^3+4320x^4-864x^5-2232x^6-192x^7+288x^8)-{\mathrm{e}}^{2x}({\ln (2)}^2(-72x^9+36x^8+864x^7+144x^6-3456x^5-2880x^4+4608x^3+6912x^2)+97200x^2+64800x^3-45900x^4-50760x^5+3168x^6+13248x^7+576x^8-1152x^9+\ln (2)(-576x^9+288x^8+6768x^7+1368x^6-26496x^5-23040x^4+34560x^3+51840x^2))-{\mathrm{e}}^{4x}(-24x^7+18x^6+96x^5+120x^4)+1761750x^2-972000x^4+256320x^6-32256x^8+1536x^{10}-1215000}{x^{10}-20x^8+160x^6-640x^4+1280x^2-1024}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x)*(648000*x + log(2)^3*(12288*x + 6144*x^2 - 9216*x^3 - 6144*x^4 + 2304*x^5 + 2304*x^6 - 192*x^7 - 3
84*x^8 + 24*x^10) + log(2)^2*(138240*x + 69120*x^2 - 108288*x^3 - 70272*x^4 + 28224*x^5 + 26784*x^6 - 2448*x^7
- 4536*x^8 + 288*x^10) + log(2)*(518400*x + 259200*x^2 - 423360*x^3 - 267840*x^4 + 114912*x^5 + 103752*x^6 -
10368*x^7 - 17856*x^8 + 1152*x^10) + 324000*x^2 - 550800*x^3 - 340200*x^4 + 155520*x^5 + 133920*x^6 - 14592*x^
7 - 23424*x^8 + 1536*x^10) + log(2)*(1814400*x^2 - 977400*x^4 + 254112*x^6 - 31872*x^8 + 1536*x^10 - 1296000)
+ log(2)^4*(7680*x^2 - 3840*x^4 + 960*x^6 - 120*x^8 + 6*x^10 - 6144) + log(2)^3*(119808*x^2 - 61440*x^4 + 1555
2*x^6 - 1944*x^8 + 96*x^10 - 92160) + log(2)^2*(699840*x^2 - 367920*x^4 + 94356*x^6 - 11808*x^8 + 576*x^10 - 5
18400) + exp(3*x)*(log(2)*(1536*x^3 + 1152*x^4 - 192*x^5 - 576*x^6 - 48*x^7 + 72*x^8) + 5760*x^3 + 4320*x^4 -
864*x^5 - 2232*x^6 - 192*x^7 + 288*x^8) - exp(2*x)*(log(2)^2*(6912*x^2 + 4608*x^3 - 2880*x^4 - 3456*x^5 + 144*
x^6 + 864*x^7 + 36*x^8 - 72*x^9) + 97200*x^2 + 64800*x^3 - 45900*x^4 - 50760*x^5 + 3168*x^6 + 13248*x^7 + 576*
x^8 - 1152*x^9 + log(2)*(51840*x^2 + 34560*x^3 - 23040*x^4 - 26496*x^5 + 1368*x^6 + 6768*x^7 + 288*x^8 - 576*x
^9)) - exp(4*x)*(120*x^4 + 96*x^5 + 18*x^6 - 24*x^7) + 1761750*x^2 - 972000*x^4 + 256320*x^6 - 32256*x^8 + 153
6*x^10 - 1215000)/(1280*x^2 - 640*x^4 + 160*x^6 - 20*x^8 + x^10 - 1024),x)

[Out]

int((exp(x)*(648000*x + log(2)^3*(12288*x + 6144*x^2 - 9216*x^3 - 6144*x^4 + 2304*x^5 + 2304*x^6 - 192*x^7 - 3
84*x^8 + 24*x^10) + log(2)^2*(138240*x + 69120*x^2 - 108288*x^3 - 70272*x^4 + 28224*x^5 + 26784*x^6 - 2448*x^7
- 4536*x^8 + 288*x^10) + log(2)*(518400*x + 259200*x^2 - 423360*x^3 - 267840*x^4 + 114912*x^5 + 103752*x^6 -
10368*x^7 - 17856*x^8 + 1152*x^10) + 324000*x^2 - 550800*x^3 - 340200*x^4 + 155520*x^5 + 133920*x^6 - 14592*x^
7 - 23424*x^8 + 1536*x^10) + log(2)*(1814400*x^2 - 977400*x^4 + 254112*x^6 - 31872*x^8 + 1536*x^10 - 1296000)
+ log(2)^4*(7680*x^2 - 3840*x^4 + 960*x^6 - 120*x^8 + 6*x^10 - 6144) + log(2)^3*(119808*x^2 - 61440*x^4 + 1555
2*x^6 - 1944*x^8 + 96*x^10 - 92160) + log(2)^2*(699840*x^2 - 367920*x^4 + 94356*x^6 - 11808*x^8 + 576*x^10 - 5
18400) + exp(3*x)*(log(2)*(1536*x^3 + 1152*x^4 - 192*x^5 - 576*x^6 - 48*x^7 + 72*x^8) + 5760*x^3 + 4320*x^4 -
864*x^5 - 2232*x^6 - 192*x^7 + 288*x^8) - exp(2*x)*(log(2)^2*(6912*x^2 + 4608*x^3 - 2880*x^4 - 3456*x^5 + 144*
x^6 + 864*x^7 + 36*x^8 - 72*x^9) + 97200*x^2 + 64800*x^3 - 45900*x^4 - 50760*x^5 + 3168*x^6 + 13248*x^7 + 576*
x^8 - 1152*x^9 + log(2)*(51840*x^2 + 34560*x^3 - 23040*x^4 - 26496*x^5 + 1368*x^6 + 6768*x^7 + 288*x^8 - 576*x
^9)) - exp(4*x)*(120*x^4 + 96*x^5 + 18*x^6 - 24*x^7) + 1761750*x^2 - 972000*x^4 + 256320*x^6 - 32256*x^8 + 153
6*x^10 - 1215000)/(1280*x^2 - 640*x^4 + 160*x^6 - 20*x^8 + x^10 - 1024), x)

________________________________________________________________________________________

sympy [B]  time = 5.21, size = 1402, normalized size = 51.93 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x**7-18*x**6-96*x**5-120*x**4)*exp(x)**4+((72*x**8-48*x**7-576*x**6-192*x**5+1152*x**4+1536*x**
3)*ln(2)+288*x**8-192*x**7-2232*x**6-864*x**5+4320*x**4+5760*x**3)*exp(x)**3+((72*x**9-36*x**8-864*x**7-144*x*
*6+3456*x**5+2880*x**4-4608*x**3-6912*x**2)*ln(2)**2+(576*x**9-288*x**8-6768*x**7-1368*x**6+26496*x**5+23040*x
**4-34560*x**3-51840*x**2)*ln(2)+1152*x**9-576*x**8-13248*x**7-3168*x**6+50760*x**5+45900*x**4-64800*x**3-9720
0*x**2)*exp(x)**2+((24*x**10-384*x**8-192*x**7+2304*x**6+2304*x**5-6144*x**4-9216*x**3+6144*x**2+12288*x)*ln(2
)**3+(288*x**10-4536*x**8-2448*x**7+26784*x**6+28224*x**5-70272*x**4-108288*x**3+69120*x**2+138240*x)*ln(2)**2
+(1152*x**10-17856*x**8-10368*x**7+103752*x**6+114912*x**5-267840*x**4-423360*x**3+259200*x**2+518400*x)*ln(2)
+1536*x**10-23424*x**8-14592*x**7+133920*x**6+155520*x**5-340200*x**4-550800*x**3+324000*x**2+648000*x)*exp(x)
+(6*x**10-120*x**8+960*x**6-3840*x**4+7680*x**2-6144)*ln(2)**4+(96*x**10-1944*x**8+15552*x**6-61440*x**4+11980
8*x**2-92160)*ln(2)**3+(576*x**10-11808*x**8+94356*x**6-367920*x**4+699840*x**2-518400)*ln(2)**2+(1536*x**10-3
1872*x**8+254112*x**6-977400*x**4+1814400*x**2-1296000)*ln(2)+1536*x**10-32256*x**8+256320*x**6-972000*x**4+17
61750*x**2-1215000)/(x**10-20*x**8+160*x**6-640*x**4+1280*x**2-1024),x)

[Out]

x*(6*log(2)**4 + 96*log(2)**3 + 576*log(2)**2 + 1536*log(2) + 1536) + (x**7*(24*log(2)**3 + 288*log(2)**2 + 11
52*log(2) + 1536) + x**5*(-17856 - 13536*log(2) - 3420*log(2)**2 - 288*log(2)**3) + x**3*(1152*log(2)**3 + 135
36*log(2)**2 + 53016*log(2) + 69216) + x*(-89466 - 69216*log(2) - 17856*log(2)**2 - 1536*log(2)**3))/(x**8 - 1
6*x**6 + 96*x**4 - 256*x**2 + 256) + ((6*x**29 - 288*x**27 + 6336*x**25 - 84480*x**23 + 760320*x**21 - 4866048
*x**19 + 22708224*x**17 - 77856768*x**15 + 194641920*x**13 - 346030080*x**11 + 415236096*x**9 - 301989888*x**7
+ 100663296*x**5)*exp(4*x) + (24*x**30*log(2) + 96*x**30 - 4968*x**28 - 1248*x**28*log(2) + 29952*x**26*log(2
) + 118656*x**26 - 1731840*x**24 - 439296*x**24*log(2) + 4392960*x**22*log(2) + 17233920*x**22 - 123475968*x**
20 - 31629312*x**20*log(2) + 168689664*x**18*log(2) + 655294464*x**18 - 2608201728*x**16 - 674758656*x**16*log
(2) + 2024275968*x**14*log(2) + 7785676800*x**14 - 17214996480*x**12 - 4498391040*x**12*log(2) + 7197425664*x*
*10*log(2) + 27405582336*x**10 - 29746003968*x**8 - 7851737088*x**8*log(2) + 5234491392*x**6*log(2) + 19730006
016*x**6 - 6039797760*x**4 - 1610612736*x**4*log(2))*exp(3*x) + (36*x**31*log(2)**2 + 288*x**31*log(2) + 576*x
**31 - 31968*x**29 - 16056*x**29*log(2) - 2016*x**29*log(2)**2 + 52416*x**27*log(2)**2 + 415584*x**27*log(2) +
823716*x**27 - 13060800*x**25 - 6619392*x**25*log(2) - 838656*x**25*log(2)**2 + 9225216*x**23*log(2)**2 + 724
83840*x**23*log(2) + 142369920*x**23 - 1128619008*x**21 - 577234944*x**21*log(2) - 73801728*x**21*log(2)**2 +
442810368*x**19*log(2)**2 + 3447595008*x**19*log(2) + 6709976064*x**19 - 30393335808*x**17 - 15688138752*x**17
*log(2) - 2024275968*x**17*log(2)**2 + 7084965888*x**15*log(2)**2 + 54655451136*x**15*log(2) + 105398599680*x*
*15 - 278467706880*x**13 - 145073111040*x**13*log(2) - 18893242368*x**13*log(2)**2 + 37786484736*x**11*log(2)*
*2 + 288796704768*x**11*log(2) + 551770914816*x**11 - 795101626368*x**9 - 418104999936*x**9*log(2) - 549621596
16*x**9*log(2)**2 + 54962159616*x**7*log(2)**2 + 416142065664*x**7*log(2) + 787665125376*x**7 - 480163921920*x
**5 - 254879465472*x**5*log(2) - 33822867456*x**5*log(2)**2 + 9663676416*x**3*log(2)**2 + 72477573120*x**3*log
(2) + 135895449600*x**3)*exp(2*x) + (24*x**32*log(2)**3 + 288*x**32*log(2)**2 + 1152*x**32*log(2) + 1536*x**32
- 91008*x**30 - 68544*x**30*log(2) - 17208*x**30*log(2)**2 - 1440*x**30*log(2)**3 + 40320*x**28*log(2)**3 + 4
79808*x**28*log(2)**2 + 1903176*x**28*log(2) + 2516256*x**28 - 43065960*x**26 - 32711328*x**26*log(2) - 828172
8*x**26*log(2)**2 - 698880*x**26*log(2)**3 + 8386560*x**24*log(2)**3 + 98961408*x**24*log(2)**2 + 389226240*x*
*24*log(2) + 510261120*x**24 - 4433349888*x**22 - 3396197376*x**22*log(2) - 867170304*x**22*log(2)**2 - 738017
28*x**22*log(2)**3 + 492011520*x**20*log(2)**3 + 5756534784*x**20*log(2)**2 + 22448904192*x**20*log(2) + 29179
459584*x**20 - 148148656128*x**18 - 114466480128*x**18*log(2) - 29478518784*x**18*log(2)**2 - 2530344960*x**18
*log(2)**3 + 10121379840*x**16*log(2)**3 + 117408006144*x**16*log(2)**2 + 453943885824*x**16*log(2) + 58499629
0560*x**16 - 1796566548480*x**14 - 1400124211200*x**14*log(2) - 363694915584*x**14*log(2)**2 - 31488737280*x**
14*log(2)**3 + 75572969472*x**12*log(2)**3 + 869089148928*x**12*log(2)**2 + 3331283484672*x**12*log(2) + 42560
66174976*x**12 - 7637980151808*x**10 - 6004370571264*x**10*log(2) - 1573291819008*x**10*log(2)**2 - 1374053990
40*x**10*log(2)**3 + 183207198720*x**8*log(2)**3 + 2088562065408*x**8*log(2)**2 + 7936143261696*x**8*log(2) +
10051456598016*x**8 - 9157088378880*x**6 - 7261648846848*x**6*log(2) - 1919447728128*x**6*log(2)**2 - 16911433
7280*x**6*log(2)**3 + 96636764160*x**4*log(2)**3 + 1091995435008*x**4*log(2)**2 + 4113102274560*x**4*log(2) +
5164027084800*x**4 - 1358954496000*x**2 - 1087163596800*x**2*log(2) - 289910292480*x**2*log(2)**2 - 2576980377
6*x**2*log(2)**3)*exp(x))/(x**32 - 64*x**30 + 1920*x**28 - 35840*x**26 + 465920*x**24 - 4472832*x**22 + 328007
68*x**20 - 187432960*x**18 + 843448320*x**16 - 2998927360*x**14 + 8396996608*x**12 - 18320719872*x**10 + 30534
533120*x**8 - 37580963840*x**6 + 32212254720*x**4 - 17179869184*x**2 + 4294967296)

________________________________________________________________________________________