3.97.98 \(\int \frac {1024 x+3584 x^2+5376 x^3+4480 x^4+2240 x^5+672 x^6+112 x^7+8 x^8+e^2 (1024+3584 x+5376 x^2+4480 x^3+2240 x^4+672 x^5+112 x^6+8 x^7)+(e^4 (3584+10752 x+13440 x^2+8960 x^3+3360 x^4+672 x^5+56 x^6)+e^2 (3584 x+10752 x^2+13440 x^3+8960 x^4+3360 x^5+672 x^6+56 x^7)) \log (2 x)+(e^6 (5376+13440 x+13440 x^2+6720 x^3+1680 x^4+168 x^5)+e^4 (5376 x+13440 x^2+13440 x^3+6720 x^4+1680 x^5+168 x^6)) \log ^2(2 x)+(e^8 (4480+8960 x+6720 x^2+2240 x^3+280 x^4)+e^6 (4480 x+8960 x^2+6720 x^3+2240 x^4+280 x^5)) \log ^3(2 x)+(e^{10} (2240+3360 x+1680 x^2+280 x^3)+e^8 (2240 x+3360 x^2+1680 x^3+280 x^4)) \log ^4(2 x)+(e^{12} (672+672 x+168 x^2)+e^{10} (672 x+672 x^2+168 x^3)) \log ^5(2 x)+(e^{14} (112+56 x)+e^{12} (112 x+56 x^2)) \log ^6(2 x)+(8 e^{16}+8 e^{14} x) \log ^7(2 x)}{x} \, dx\) [9698]

Optimal. Leaf size=15 \[ -1+\left (2+x+e^2 \log (2 x)\right )^8 \]

[Out]

(2+exp(2)*ln(2*x)+x)^8-1

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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(1914\) vs. \(2(15)=30\).
time = 1.90, antiderivative size = 1914, normalized size of antiderivative = 127.60, number of steps used = 115, number of rules used = 12, integrand size = 429, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {14, 81, 45, 2404, 2332, 2338, 2341, 2333, 2339, 30, 2342, 2388} \begin {gather*} (x+2)^8+e^{16} \log ^8(2 x)+8 e^{14} x \log ^7(2 x)+16 e^{14} \log ^7(2 x)-\frac {14}{9} e^2 \left (12+e^2\right ) x^6+\frac {14 e^4 x^6}{9}+\frac {56 e^2 x^6}{3}+28 e^{12} x^2 \log ^6(2 x)+56 e^{12} \left (2+e^2\right ) x \log ^6(2 x)-56 e^{14} x \log ^6(2 x)+112 e^{12} \log ^6(2 x)+\frac {336}{125} e^4 \left (10+e^2\right ) x^5-\frac {672}{25} e^2 \left (5+e^2\right ) x^5-\frac {336 e^6 x^5}{125}+\frac {672 e^2 x^5}{5}+56 e^{10} x^3 \log ^5(2 x)+84 e^{10} \left (4+e^2\right ) x^2 \log ^5(2 x)-84 e^{12} x^2 \log ^5(2 x)-336 e^{12} \left (2+e^2\right ) x \log ^5(2 x)+672 e^{10} \left (1+e^2\right ) x \log ^5(2 x)+336 e^{14} x \log ^5(2 x)+448 e^{10} \log ^5(2 x)-70 e^2 \left (8+3 e^2\right ) x^4-\frac {105}{16} e^6 \left (8+e^2\right ) x^4+\frac {105}{2} e^4 \left (4+e^2\right ) x^4+\frac {105 e^8 x^4}{16}+560 e^2 x^4+70 e^8 x^4 \log ^4(2 x)+\frac {280}{3} e^8 \left (6+e^2\right ) x^3 \log ^4(2 x)-\frac {280}{3} e^{10} x^3 \log ^4(2 x)-210 e^{10} \left (4+e^2\right ) x^2 \log ^4(2 x)+840 e^8 \left (2+e^2\right ) x^2 \log ^4(2 x)+210 e^{12} x^2 \log ^4(2 x)+1120 e^8 \left (2+3 e^2\right ) x \log ^4(2 x)+1680 e^{12} \left (2+e^2\right ) x \log ^4(2 x)-3360 e^{10} \left (1+e^2\right ) x \log ^4(2 x)-1680 e^{14} x \log ^4(2 x)+1120 e^8 \log ^4(2 x)-\frac {4480}{9} e^2 \left (3+2 e^2\right ) x^3+\frac {2240}{81} e^8 \left (6+e^2\right ) x^3-\frac {4480}{27} e^6 \left (3+e^2\right ) x^3+\frac {4480}{9} e^4 \left (2+e^2\right ) x^3-\frac {2240 e^{10} x^3}{81}+\frac {4480 e^2 x^3}{3}+56 e^6 x^5 \log ^3(2 x)+70 e^6 \left (8+e^2\right ) x^4 \log ^3(2 x)-70 e^8 x^4 \log ^3(2 x)-\frac {1120}{9} e^8 \left (6+e^2\right ) x^3 \log ^3(2 x)+\frac {2240}{3} e^6 \left (3+e^2\right ) x^3 \log ^3(2 x)+\frac {1120}{9} e^{10} x^3 \log ^3(2 x)+1120 e^6 \left (4+3 e^2\right ) x^2 \log ^3(2 x)+420 e^{10} \left (4+e^2\right ) x^2 \log ^3(2 x)-1680 e^8 \left (2+e^2\right ) x^2 \log ^3(2 x)-420 e^{12} x^2 \log ^3(2 x)-4480 e^8 \left (2+3 e^2\right ) x \log ^3(2 x)+4480 e^6 \left (1+2 e^2\right ) x \log ^3(2 x)-6720 e^{12} \left (2+e^2\right ) x \log ^3(2 x)+13440 e^{10} \left (1+e^2\right ) x \log ^3(2 x)+6720 e^{14} x \log ^3(2 x)+1792 e^6 \log ^3(2 x)-672 e^2 \left (4+5 e^2\right ) x^2-840 e^6 \left (4+3 e^2\right ) x^2-315 e^{10} \left (4+e^2\right ) x^2+1260 e^8 \left (2+e^2\right ) x^2+3360 e^4 \left (1+e^2\right ) x^2+315 e^{12} x^2+2688 e^2 x^2+28 e^4 x^6 \log ^2(2 x)+\frac {168}{5} e^4 \left (10+e^2\right ) x^5 \log ^2(2 x)-\frac {168}{5} e^6 x^5 \log ^2(2 x)-\frac {105}{2} e^6 \left (8+e^2\right ) x^4 \log ^2(2 x)+420 e^4 \left (4+e^2\right ) x^4 \log ^2(2 x)+\frac {105}{2} e^8 x^4 \log ^2(2 x)+\frac {1120}{9} e^8 \left (6+e^2\right ) x^3 \log ^2(2 x)-\frac {2240}{3} e^6 \left (3+e^2\right ) x^3 \log ^2(2 x)+2240 e^4 \left (2+e^2\right ) x^3 \log ^2(2 x)-\frac {1120}{9} e^{10} x^3 \log ^2(2 x)-1680 e^6 \left (4+3 e^2\right ) x^2 \log ^2(2 x)-630 e^{10} \left (4+e^2\right ) x^2 \log ^2(2 x)+2520 e^8 \left (2+e^2\right ) x^2 \log ^2(2 x)+6720 e^4 \left (1+e^2\right ) x^2 \log ^2(2 x)+630 e^{12} x^2 \log ^2(2 x)+2688 e^4 \left (2+5 e^2\right ) x \log ^2(2 x)+13440 e^8 \left (2+3 e^2\right ) x \log ^2(2 x)-13440 e^6 \left (1+2 e^2\right ) x \log ^2(2 x)+20160 e^{12} \left (2+e^2\right ) x \log ^2(2 x)-40320 e^{10} \left (1+e^2\right ) x \log ^2(2 x)-20160 e^{14} x \log ^2(2 x)+1792 e^4 \log ^2(2 x)+5376 e^4 \left (2+5 e^2\right ) x+26880 e^8 \left (2+3 e^2\right ) x-3584 e^2 \left (1+3 e^2\right ) x-26880 e^6 \left (1+2 e^2\right ) x+40320 e^{12} \left (2+e^2\right ) x-80640 e^{10} \left (1+e^2\right ) x-40320 e^{14} x+3584 e^2 x+1024 e^2 \log (x)+8 e^2 x^7 \log (2 x)+\frac {28}{3} e^2 \left (12+e^2\right ) x^6 \log (2 x)-\frac {28}{3} e^4 x^6 \log (2 x)-\frac {336}{25} e^4 \left (10+e^2\right ) x^5 \log (2 x)+\frac {672}{5} e^2 \left (5+e^2\right ) x^5 \log (2 x)+\frac {336}{25} e^6 x^5 \log (2 x)+280 e^2 \left (8+3 e^2\right ) x^4 \log (2 x)+\frac {105}{4} e^6 \left (8+e^2\right ) x^4 \log (2 x)-210 e^4 \left (4+e^2\right ) x^4 \log (2 x)-\frac {105}{4} e^8 x^4 \log (2 x)+\frac {4480}{3} e^2 \left (3+2 e^2\right ) x^3 \log (2 x)-\frac {2240}{27} e^8 \left (6+e^2\right ) x^3 \log (2 x)+\frac {4480}{9} e^6 \left (3+e^2\right ) x^3 \log (2 x)-\frac {4480}{3} e^4 \left (2+e^2\right ) x^3 \log (2 x)+\frac {2240}{27} e^{10} x^3 \log (2 x)+1344 e^2 \left (4+5 e^2\right ) x^2 \log (2 x)+1680 e^6 \left (4+3 e^2\right ) x^2 \log (2 x)+630 e^{10} \left (4+e^2\right ) x^2 \log (2 x)-2520 e^8 \left (2+e^2\right ) x^2 \log (2 x)-6720 e^4 \left (1+e^2\right ) x^2 \log (2 x)-630 e^{12} x^2 \log (2 x)-5376 e^4 \left (2+5 e^2\right ) x \log (2 x)-26880 e^8 \left (2+3 e^2\right ) x \log (2 x)+3584 e^2 \left (1+3 e^2\right ) x \log (2 x)+26880 e^6 \left (1+2 e^2\right ) x \log (2 x)-40320 e^{12} \left (2+e^2\right ) x \log (2 x)+80640 e^{10} \left (1+e^2\right ) x \log (2 x)+40320 e^{14} x \log (2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1024*x + 3584*x^2 + 5376*x^3 + 4480*x^4 + 2240*x^5 + 672*x^6 + 112*x^7 + 8*x^8 + E^2*(1024 + 3584*x + 537
6*x^2 + 4480*x^3 + 2240*x^4 + 672*x^5 + 112*x^6 + 8*x^7) + (E^4*(3584 + 10752*x + 13440*x^2 + 8960*x^3 + 3360*
x^4 + 672*x^5 + 56*x^6) + E^2*(3584*x + 10752*x^2 + 13440*x^3 + 8960*x^4 + 3360*x^5 + 672*x^6 + 56*x^7))*Log[2
*x] + (E^6*(5376 + 13440*x + 13440*x^2 + 6720*x^3 + 1680*x^4 + 168*x^5) + E^4*(5376*x + 13440*x^2 + 13440*x^3
+ 6720*x^4 + 1680*x^5 + 168*x^6))*Log[2*x]^2 + (E^8*(4480 + 8960*x + 6720*x^2 + 2240*x^3 + 280*x^4) + E^6*(448
0*x + 8960*x^2 + 6720*x^3 + 2240*x^4 + 280*x^5))*Log[2*x]^3 + (E^10*(2240 + 3360*x + 1680*x^2 + 280*x^3) + E^8
*(2240*x + 3360*x^2 + 1680*x^3 + 280*x^4))*Log[2*x]^4 + (E^12*(672 + 672*x + 168*x^2) + E^10*(672*x + 672*x^2
+ 168*x^3))*Log[2*x]^5 + (E^14*(112 + 56*x) + E^12*(112*x + 56*x^2))*Log[2*x]^6 + (8*E^16 + 8*E^14*x)*Log[2*x]
^7)/x,x]

[Out]

3584*E^2*x - 40320*E^14*x - 80640*E^10*(1 + E^2)*x + 40320*E^12*(2 + E^2)*x - 26880*E^6*(1 + 2*E^2)*x - 3584*E
^2*(1 + 3*E^2)*x + 26880*E^8*(2 + 3*E^2)*x + 5376*E^4*(2 + 5*E^2)*x + 2688*E^2*x^2 + 315*E^12*x^2 + 3360*E^4*(
1 + E^2)*x^2 + 1260*E^8*(2 + E^2)*x^2 - 315*E^10*(4 + E^2)*x^2 - 840*E^6*(4 + 3*E^2)*x^2 - 672*E^2*(4 + 5*E^2)
*x^2 + (4480*E^2*x^3)/3 - (2240*E^10*x^3)/81 + (4480*E^4*(2 + E^2)*x^3)/9 - (4480*E^6*(3 + E^2)*x^3)/27 + (224
0*E^8*(6 + E^2)*x^3)/81 - (4480*E^2*(3 + 2*E^2)*x^3)/9 + 560*E^2*x^4 + (105*E^8*x^4)/16 + (105*E^4*(4 + E^2)*x
^4)/2 - (105*E^6*(8 + E^2)*x^4)/16 - 70*E^2*(8 + 3*E^2)*x^4 + (672*E^2*x^5)/5 - (336*E^6*x^5)/125 - (672*E^2*(
5 + E^2)*x^5)/25 + (336*E^4*(10 + E^2)*x^5)/125 + (56*E^2*x^6)/3 + (14*E^4*x^6)/9 - (14*E^2*(12 + E^2)*x^6)/9
+ (2 + x)^8 + 1024*E^2*Log[x] + 40320*E^14*x*Log[2*x] + 80640*E^10*(1 + E^2)*x*Log[2*x] - 40320*E^12*(2 + E^2)
*x*Log[2*x] + 26880*E^6*(1 + 2*E^2)*x*Log[2*x] + 3584*E^2*(1 + 3*E^2)*x*Log[2*x] - 26880*E^8*(2 + 3*E^2)*x*Log
[2*x] - 5376*E^4*(2 + 5*E^2)*x*Log[2*x] - 630*E^12*x^2*Log[2*x] - 6720*E^4*(1 + E^2)*x^2*Log[2*x] - 2520*E^8*(
2 + E^2)*x^2*Log[2*x] + 630*E^10*(4 + E^2)*x^2*Log[2*x] + 1680*E^6*(4 + 3*E^2)*x^2*Log[2*x] + 1344*E^2*(4 + 5*
E^2)*x^2*Log[2*x] + (2240*E^10*x^3*Log[2*x])/27 - (4480*E^4*(2 + E^2)*x^3*Log[2*x])/3 + (4480*E^6*(3 + E^2)*x^
3*Log[2*x])/9 - (2240*E^8*(6 + E^2)*x^3*Log[2*x])/27 + (4480*E^2*(3 + 2*E^2)*x^3*Log[2*x])/3 - (105*E^8*x^4*Lo
g[2*x])/4 - 210*E^4*(4 + E^2)*x^4*Log[2*x] + (105*E^6*(8 + E^2)*x^4*Log[2*x])/4 + 280*E^2*(8 + 3*E^2)*x^4*Log[
2*x] + (336*E^6*x^5*Log[2*x])/25 + (672*E^2*(5 + E^2)*x^5*Log[2*x])/5 - (336*E^4*(10 + E^2)*x^5*Log[2*x])/25 -
(28*E^4*x^6*Log[2*x])/3 + (28*E^2*(12 + E^2)*x^6*Log[2*x])/3 + 8*E^2*x^7*Log[2*x] + 1792*E^4*Log[2*x]^2 - 201
60*E^14*x*Log[2*x]^2 - 40320*E^10*(1 + E^2)*x*Log[2*x]^2 + 20160*E^12*(2 + E^2)*x*Log[2*x]^2 - 13440*E^6*(1 +
2*E^2)*x*Log[2*x]^2 + 13440*E^8*(2 + 3*E^2)*x*Log[2*x]^2 + 2688*E^4*(2 + 5*E^2)*x*Log[2*x]^2 + 630*E^12*x^2*Lo
g[2*x]^2 + 6720*E^4*(1 + E^2)*x^2*Log[2*x]^2 + 2520*E^8*(2 + E^2)*x^2*Log[2*x]^2 - 630*E^10*(4 + E^2)*x^2*Log[
2*x]^2 - 1680*E^6*(4 + 3*E^2)*x^2*Log[2*x]^2 - (1120*E^10*x^3*Log[2*x]^2)/9 + 2240*E^4*(2 + E^2)*x^3*Log[2*x]^
2 - (2240*E^6*(3 + E^2)*x^3*Log[2*x]^2)/3 + (1120*E^8*(6 + E^2)*x^3*Log[2*x]^2)/9 + (105*E^8*x^4*Log[2*x]^2)/2
+ 420*E^4*(4 + E^2)*x^4*Log[2*x]^2 - (105*E^6*(8 + E^2)*x^4*Log[2*x]^2)/2 - (168*E^6*x^5*Log[2*x]^2)/5 + (168
*E^4*(10 + E^2)*x^5*Log[2*x]^2)/5 + 28*E^4*x^6*Log[2*x]^2 + 1792*E^6*Log[2*x]^3 + 6720*E^14*x*Log[2*x]^3 + 134
40*E^10*(1 + E^2)*x*Log[2*x]^3 - 6720*E^12*(2 + E^2)*x*Log[2*x]^3 + 4480*E^6*(1 + 2*E^2)*x*Log[2*x]^3 - 4480*E
^8*(2 + 3*E^2)*x*Log[2*x]^3 - 420*E^12*x^2*Log[2*x]^3 - 1680*E^8*(2 + E^2)*x^2*Log[2*x]^3 + 420*E^10*(4 + E^2)
*x^2*Log[2*x]^3 + 1120*E^6*(4 + 3*E^2)*x^2*Log[2*x]^3 + (1120*E^10*x^3*Log[2*x]^3)/9 + (2240*E^6*(3 + E^2)*x^3
*Log[2*x]^3)/3 - (1120*E^8*(6 + E^2)*x^3*Log[2*x]^3)/9 - 70*E^8*x^4*Log[2*x]^3 + 70*E^6*(8 + E^2)*x^4*Log[2*x]
^3 + 56*E^6*x^5*Log[2*x]^3 + 1120*E^8*Log[2*x]^4 - 1680*E^14*x*Log[2*x]^4 - 3360*E^10*(1 + E^2)*x*Log[2*x]^4 +
1680*E^12*(2 + E^2)*x*Log[2*x]^4 + 1120*E^8*(2 + 3*E^2)*x*Log[2*x]^4 + 210*E^12*x^2*Log[2*x]^4 + 840*E^8*(2 +
E^2)*x^2*Log[2*x]^4 - 210*E^10*(4 + E^2)*x^2*Log[2*x]^4 - (280*E^10*x^3*Log[2*x]^4)/3 + (280*E^8*(6 + E^2)*x^
3*Log[2*x]^4)/3 + 70*E^8*x^4*Log[2*x]^4 + 448*E^10*Log[2*x]^5 + 336*E^14*x*Log[2*x]^5 + 672*E^10*(1 + E^2)*x*L
og[2*x]^5 - 336*E^12*(2 + E^2)*x*Log[2*x]^5 - 84*E^12*x^2*Log[2*x]^5 + 84*E^10*(4 + E^2)*x^2*Log[2*x]^5 + 56*E
^10*x^3*Log[2*x]^5 + 112*E^12*Log[2*x]^6 - 56*E^14*x*Log[2*x]^6 + 56*E^12*(2 + E^2)*x*Log[2*x]^6 + 28*E^12*x^2
*Log[2*x]^6 + 16*E^14*Log[2*x]^7 + 8*E^14*x*Log[2*x]^7 + E^16*Log[2*x]^8

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rule 45

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rule 81

Int[((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[b*(c + d*x)^
(n + 1)*((e + f*x)^(p + 1)/(d*f*(n + p + 2))), x] + Dist[(a*d*f*(n + p + 2) - b*(d*e*(n + 1) + c*f*(p + 1)))/(
d*f*(n + p + 2)), Int[(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n, p}, x] && NeQ[n + p + 2,
0]

Rule 2332

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rule 2333

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.), x_Symbol] :> Simp[x*(a + b*Log[c*x^n])^p, x] - Dist[b*n*p, In
t[(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{a, b, c, n}, x] && GtQ[p, 0] && IntegerQ[2*p]

Rule 2338

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))/(x_), x_Symbol] :> Simp[(a + b*Log[c*x^n])^2/(2*b*n), x] /; FreeQ[{a
, b, c, n}, x]

Rule 2339

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/(x_), x_Symbol] :> Dist[1/(b*n), Subst[Int[x^p, x], x, a + b*L
og[c*x^n]], x] /; FreeQ[{a, b, c, n, p}, x]

Rule 2341

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(d*x)^(m + 1)*((a + b*Log[c*x^
n])/(d*(m + 1))), x] - Simp[b*n*((d*x)^(m + 1)/(d*(m + 1)^2)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rule 2342

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

Rule 2388

Int[(((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_) + (e_.)*(x_))^(q_.))/(x_), x_Symbol] :> Dist[d, Int[(d
+ e*x)^(q - 1)*((a + b*Log[c*x^n])^p/x), x], x] + Dist[e, Int[(d + e*x)^(q - 1)*(a + b*Log[c*x^n])^p, x], x] /
; FreeQ[{a, b, c, d, e, n}, x] && IGtQ[p, 0] && GtQ[q, 0] && IntegerQ[2*q]

Rule 2404

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(RFx_), x_Symbol] :> With[{u = ExpandIntegrand[(a + b*Log[c*x^
n])^p, RFx, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, n}, x] && RationalFunctionQ[RFx, x] && IGtQ[p, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {8 (2+x)^7 \left (e^2+x\right )}{x}+\frac {56 e^2 (2+x)^6 \left (e^2+x\right ) \log (2 x)}{x}+\frac {168 e^4 (2+x)^5 \left (e^2+x\right ) \log ^2(2 x)}{x}+\frac {280 e^6 (2+x)^4 \left (e^2+x\right ) \log ^3(2 x)}{x}+\frac {280 e^8 (2+x)^3 \left (e^2+x\right ) \log ^4(2 x)}{x}+\frac {168 e^{10} (2+x)^2 \left (e^2+x\right ) \log ^5(2 x)}{x}+\frac {56 e^{12} (2+x) \left (e^2+x\right ) \log ^6(2 x)}{x}+\frac {8 e^{14} \left (e^2+x\right ) \log ^7(2 x)}{x}\right ) \, dx\\ &=8 \int \frac {(2+x)^7 \left (e^2+x\right )}{x} \, dx+\left (56 e^2\right ) \int \frac {(2+x)^6 \left (e^2+x\right ) \log (2 x)}{x} \, dx+\left (168 e^4\right ) \int \frac {(2+x)^5 \left (e^2+x\right ) \log ^2(2 x)}{x} \, dx+\left (280 e^6\right ) \int \frac {(2+x)^4 \left (e^2+x\right ) \log ^3(2 x)}{x} \, dx+\left (280 e^8\right ) \int \frac {(2+x)^3 \left (e^2+x\right ) \log ^4(2 x)}{x} \, dx+\left (168 e^{10}\right ) \int \frac {(2+x)^2 \left (e^2+x\right ) \log ^5(2 x)}{x} \, dx+\left (56 e^{12}\right ) \int \frac {(2+x) \left (e^2+x\right ) \log ^6(2 x)}{x} \, dx+\left (8 e^{14}\right ) \int \frac {\left (e^2+x\right ) \log ^7(2 x)}{x} \, dx\\ &=(2+x)^8+\left (8 e^2\right ) \int \frac {(2+x)^7}{x} \, dx+\left (56 e^2\right ) \int \left (64 \left (1+3 e^2\right ) \log (2 x)+\frac {64 e^2 \log (2 x)}{x}+48 \left (4+5 e^2\right ) x \log (2 x)+80 \left (3+2 e^2\right ) x^2 \log (2 x)+20 \left (8+3 e^2\right ) x^3 \log (2 x)+12 \left (5+e^2\right ) x^4 \log (2 x)+\left (12+e^2\right ) x^5 \log (2 x)+x^6 \log (2 x)\right ) \, dx+\left (168 e^4\right ) \int \left (16 \left (2+5 e^2\right ) \log ^2(2 x)+\frac {32 e^2 \log ^2(2 x)}{x}+80 \left (1+e^2\right ) x \log ^2(2 x)+40 \left (2+e^2\right ) x^2 \log ^2(2 x)+10 \left (4+e^2\right ) x^3 \log ^2(2 x)+\left (10+e^2\right ) x^4 \log ^2(2 x)+x^5 \log ^2(2 x)\right ) \, dx+\left (280 e^6\right ) \int \left (16 \left (1+2 e^2\right ) \log ^3(2 x)+\frac {16 e^2 \log ^3(2 x)}{x}+8 \left (4+3 e^2\right ) x \log ^3(2 x)+8 \left (3+e^2\right ) x^2 \log ^3(2 x)+\left (8+e^2\right ) x^3 \log ^3(2 x)+x^4 \log ^3(2 x)\right ) \, dx+\left (280 e^8\right ) \int \left (4 \left (2+3 e^2\right ) \log ^4(2 x)+\frac {8 e^2 \log ^4(2 x)}{x}+6 \left (2+e^2\right ) x \log ^4(2 x)+\left (6+e^2\right ) x^2 \log ^4(2 x)+x^3 \log ^4(2 x)\right ) \, dx+\left (168 e^{10}\right ) \int \left (4 \left (1+e^2\right ) \log ^5(2 x)+\frac {4 e^2 \log ^5(2 x)}{x}+\left (4+e^2\right ) x \log ^5(2 x)+x^2 \log ^5(2 x)\right ) \, dx+\left (56 e^{12}\right ) \int \left (\left (2+e^2\right ) \log ^6(2 x)+\frac {2 e^2 \log ^6(2 x)}{x}+x \log ^6(2 x)\right ) \, dx+\left (8 e^{14}\right ) \int \log ^7(2 x) \, dx+\left (8 e^{16}\right ) \int \frac {\log ^7(2 x)}{x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.07, size = 13, normalized size = 0.87 \begin {gather*} \left (2+x+e^2 \log (2 x)\right )^8 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1024*x + 3584*x^2 + 5376*x^3 + 4480*x^4 + 2240*x^5 + 672*x^6 + 112*x^7 + 8*x^8 + E^2*(1024 + 3584*x
+ 5376*x^2 + 4480*x^3 + 2240*x^4 + 672*x^5 + 112*x^6 + 8*x^7) + (E^4*(3584 + 10752*x + 13440*x^2 + 8960*x^3 +
3360*x^4 + 672*x^5 + 56*x^6) + E^2*(3584*x + 10752*x^2 + 13440*x^3 + 8960*x^4 + 3360*x^5 + 672*x^6 + 56*x^7))
*Log[2*x] + (E^6*(5376 + 13440*x + 13440*x^2 + 6720*x^3 + 1680*x^4 + 168*x^5) + E^4*(5376*x + 13440*x^2 + 1344
0*x^3 + 6720*x^4 + 1680*x^5 + 168*x^6))*Log[2*x]^2 + (E^8*(4480 + 8960*x + 6720*x^2 + 2240*x^3 + 280*x^4) + E^
6*(4480*x + 8960*x^2 + 6720*x^3 + 2240*x^4 + 280*x^5))*Log[2*x]^3 + (E^10*(2240 + 3360*x + 1680*x^2 + 280*x^3)
+ E^8*(2240*x + 3360*x^2 + 1680*x^3 + 280*x^4))*Log[2*x]^4 + (E^12*(672 + 672*x + 168*x^2) + E^10*(672*x + 67
2*x^2 + 168*x^3))*Log[2*x]^5 + (E^14*(112 + 56*x) + E^12*(112*x + 56*x^2))*Log[2*x]^6 + (8*E^16 + 8*E^14*x)*Lo
g[2*x]^7)/x,x]

[Out]

(2 + x + E^2*Log[2*x])^8

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(2063\) vs. \(2(14)=28\).
time = 0.06, size = 2064, normalized size = 137.60

method	result	size
risch	\({\mathrm e}^{16} \ln \left (2 x \right )^{8}+\left (8 x \,{\mathrm e}^{14}+16 \,{\mathrm e}^{14}\right ) \ln \left (2 x \right )^{7}+\left (28 x^{2} {\mathrm e}^{12}+112 x \,{\mathrm e}^{12}+112 \,{\mathrm e}^{12}\right ) \ln \left (2 x \right )^{6}+56 \,{\mathrm e}^{10} \left (2+x \right )^{3} \ln \left (2 x \right )^{5}+70 \,{\mathrm e}^{8} \left (2+x \right )^{4} \ln \left (2 x \right )^{4}+56 \,{\mathrm e}^{6} \left (2+x \right )^{5} \ln \left (2 x \right )^{3}+28 \,{\mathrm e}^{4} \left (2+x \right )^{6} \ln \left (2 x \right )^{2}+8 \,{\mathrm e}^{2} \left (2+x \right )^{7} \ln \left (2 x \right )+\left (2+x \right )^{8}\)	\(130\)
derivativedivides	\(\text {Expression too large to display}\)	\(2064\)
default	\(\text {Expression too large to display}\)	\(2064\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((8*exp(2)^8+8*x*exp(2)^7)*ln(2*x)^7+((56*x+112)*exp(2)^7+(56*x^2+112*x)*exp(2)^6)*ln(2*x)^6+((168*x^2+672
*x+672)*exp(2)^6+(168*x^3+672*x^2+672*x)*exp(2)^5)*ln(2*x)^5+((280*x^3+1680*x^2+3360*x+2240)*exp(2)^5+(280*x^4
+1680*x^3+3360*x^2+2240*x)*exp(2)^4)*ln(2*x)^4+((280*x^4+2240*x^3+6720*x^2+8960*x+4480)*exp(2)^4+(280*x^5+2240
*x^4+6720*x^3+8960*x^2+4480*x)*exp(2)^3)*ln(2*x)^3+((168*x^5+1680*x^4+6720*x^3+13440*x^2+13440*x+5376)*exp(2)^
3+(168*x^6+1680*x^5+6720*x^4+13440*x^3+13440*x^2+5376*x)*exp(2)^2)*ln(2*x)^2+((56*x^6+672*x^5+3360*x^4+8960*x^
3+13440*x^2+10752*x+3584)*exp(2)^2+(56*x^7+672*x^6+3360*x^5+8960*x^4+13440*x^3+10752*x^2+3584*x)*exp(2))*ln(2*
x)+(8*x^7+112*x^6+672*x^5+2240*x^4+4480*x^3+5376*x^2+3584*x+1024)*exp(2)+8*x^8+112*x^7+672*x^6+2240*x^5+4480*x
^4+5376*x^3+3584*x^2+1024*x)/x,x,method=_RETURNVERBOSE)

[Out]

1024*x+16*x^7+x^8+1120*x^4+1792*x^3+1792*x^2+112*x^6+448*x^5+56/3*x^6*exp(2)+4480/3*x^3*exp(2)+2688*x^2*exp(2)
+560*x^4*exp(2)+1024*exp(2)*ln(2*x)+14*exp(2)^6*(2*x^2*ln(2*x)^6-6*x^2*ln(2*x)^5+15*x^2*ln(2*x)^4-30*x^2*ln(2*
x)^3+45*x^2*ln(2*x)^2-45*x^2*ln(2*x)+45/2*x^2)+8/7*exp(2)*x^7+112*exp(2)^6*ln(2*x)^6+448*exp(2)^5*ln(2*x)^5+11
20*ln(2*x)^4*exp(2)^4+1792*ln(2*x)^3*exp(2)^3+1792*ln(2*x)^2*exp(2)^2+840*exp(2)^3*(8/3*x^3*ln(2*x)^3-8/3*x^3*
ln(2*x)^2+16/9*x^3*ln(2*x)-16/27*x^3)+21/4*exp(2)^3*(32/5*x^5*ln(2*x)^2-64/25*x^5*ln(2*x)+64/125*x^5)+21/8*exp
(2)^2*(32/3*x^6*ln(2*x)^2-32/9*x^6*ln(2*x)+16/27*x^6)+280*exp(2)^4*(8/3*x^3*ln(2*x)^3-8/3*x^3*ln(2*x)^2+16/9*x
^3*ln(2*x)-16/27*x^3)+140*exp(2)^3*(4*x^4*ln(2*x)^3-3*x^4*ln(2*x)^2+3/2*x^4*ln(2*x)-3/8*x^4)+35/4*exp(2)^3*(32
/5*x^5*ln(2*x)^3-96/25*x^5*ln(2*x)^2+192/125*x^5*ln(2*x)-192/625*x^5)+840*exp(2)^4*(2*x^2*ln(2*x)^4-4*x^2*ln(2
*x)^3+6*x^2*ln(2*x)^2-6*x^2*ln(2*x)+3*x^2)+210*exp(2)^4*(8/3*x^3*ln(2*x)^4-32/9*x^3*ln(2*x)^3+32/9*x^3*ln(2*x)
^2-64/27*x^3*ln(2*x)+64/81*x^3)+35/2*exp(2)^4*(4*x^4*ln(2*x)^3-3*x^4*ln(2*x)^2+3/2*x^4*ln(2*x)-3/8*x^4)+420*ex
p(2)^5*(2*x^2*ln(2*x)^4-4*x^2*ln(2*x)^3+6*x^2*ln(2*x)^2-6*x^2*ln(2*x)+3*x^2)+35/2*exp(2)^4*(4*x^4*ln(2*x)^4-4*
x^4*ln(2*x)^3+3*x^4*ln(2*x)^2-3/2*x^4*ln(2*x)+3/8*x^4)+168*exp(2)^5*(2*x^2*ln(2*x)^5-5*x^2*ln(2*x)^4+10*x^2*ln
(2*x)^3-15*x^2*ln(2*x)^2+15*x^2*ln(2*x)-15/2*x^2)+35*exp(2)^5*(8/3*x^3*ln(2*x)^4-32/9*x^3*ln(2*x)^3+32/9*x^3*l
n(2*x)^2-64/27*x^3*ln(2*x)+64/81*x^3)+21*exp(2)^5*(8/3*x^3*ln(2*x)^5-40/9*x^3*ln(2*x)^4+160/27*x^3*ln(2*x)^3-1
60/27*x^3*ln(2*x)^2+320/81*x^3*ln(2*x)-320/243*x^3)+42*exp(2)^6*(2*x^2*ln(2*x)^5-5*x^2*ln(2*x)^4+10*x^2*ln(2*x
)^3-15*x^2*ln(2*x)^2+15*x^2*ln(2*x)-15/2*x^2)+105*exp(2)*(32/5*x^5*ln(2*x)-32/25*x^5)+21/2*exp(2)*(32/3*x^6*ln
(2*x)-16/9*x^6)+3360*exp(2)^3*(2*x^2*ln(2*x)^2-2*x^2*ln(2*x)+x^2)+840*exp(2)^3*(8/3*x^3*ln(2*x)^2-16/9*x^3*ln(
2*x)+16/27*x^3)+420*exp(2)^2*(4*x^4*ln(2*x)^2-2*x^4*ln(2*x)+1/2*x^4)+21*exp(2)^2*(32/5*x^5*ln(2*x)-32/25*x^5)+
7/8*exp(2)^2*(32/3*x^6*ln(2*x)-16/9*x^6)+7/16*exp(2)*(128/7*x^7*ln(2*x)-128/49*x^7)+2240*exp(2)^3*(2*x^2*ln(2*
x)^3-3*x^2*ln(2*x)^2+3*x^2*ln(2*x)-3/2*x^2)+105*exp(2)^3*(4*x^4*ln(2*x)^2-2*x^4*ln(2*x)+1/2*x^4)+105/2*exp(2)^
2*(32/5*x^5*ln(2*x)^2-64/25*x^5*ln(2*x)+64/125*x^5)+1680*exp(2)^4*(2*x^2*ln(2*x)^3-3*x^2*ln(2*x)^2+3*x^2*ln(2*
x)-3/2*x^2)+56*exp(2)^6*(2*x*ln(2*x)^6-12*x*ln(2*x)^5+60*x*ln(2*x)^4-240*x*ln(2*x)^3+720*x*ln(2*x)^2-1440*x*ln
(2*x)+1440*x)+4*exp(2)^7*(2*x*ln(2*x)^7-14*x*ln(2*x)^6+84*x*ln(2*x)^5-420*x*ln(2*x)^4+1680*x*ln(2*x)^3-5040*x*
ln(2*x)^2+10080*x*ln(2*x)-10080*x)+5376*exp(2)^2*(2*x*ln(2*x)-2*x)+6720*exp(2)^3*(2*x*ln(2*x)^2-4*x*ln(2*x)+4*
x)+4480*exp(2)^4*(2*x*ln(2*x)^3-6*x*ln(2*x)^2+12*x*ln(2*x)-12*x)+336*exp(2)^6*(2*x*ln(2*x)^5-10*x*ln(2*x)^4+40
*x*ln(2*x)^3-120*x*ln(2*x)^2+240*x*ln(2*x)-240*x)+1680*exp(2)^5*(2*x*ln(2*x)^4-8*x*ln(2*x)^3+24*x*ln(2*x)^2-48
*x*ln(2*x)+48*x)+2688*exp(2)*(2*x^2*ln(2*x)-x^2)+28*exp(2)^7*(2*x*ln(2*x)^6-12*x*ln(2*x)^5+60*x*ln(2*x)^4-240*
x*ln(2*x)^3+720*x*ln(2*x)^2-1440*x*ln(2*x)+1440*x)+560*exp(2)*(4*x^4*ln(2*x)-x^4)+3360*exp(2)^2*(2*x^2*ln(2*x)
-x^2)+1680*exp(2)*(8/3*x^3*ln(2*x)-8/9*x^3)+3360*exp(2)^2*(2*x^2*ln(2*x)^2-2*x^2*ln(2*x)+x^2)+1120*exp(2)^2*(8
/3*x^3*ln(2*x)-8/9*x^3)+1680*exp(2)^2*(8/3*x^3*ln(2*x)^2-16/9*x^3*ln(2*x)+16/27*x^3)+210*exp(2)^2*(4*x^4*ln(2*
x)-x^4)+2688*exp(2)^2*(2*x*ln(2*x)^2-4*x*ln(2*x)+4*x)+1792*exp(2)*(2*x*ln(2*x)-2*x)+exp(2)^8*ln(2*x)^8+336*exp
(2)^5*(2*x*ln(2*x)^5-10*x*ln(2*x)^4+40*x*ln(2*x)^3-120*x*ln(2*x)^2+240*x*ln(2*x)-240*x)+1120*exp(2)^4*(2*x*ln(
2*x)^4-8*x*ln(2*x)^3+24*x*ln(2*x)^2-48*x*ln(2*x)+48*x)+2240*exp(2)^3*(2*x*ln(2*x)^3-6*x*ln(2*x)^2+12*x*ln(2*x)
-12*x)+16*exp(2)^7*ln(2*x)^7+672/5*exp(2)*x^5+3584*exp(2)*x

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 1620 vs. \(2 (14) = 28\).
time = 0.30, size = 1620, normalized size = 108.00 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*exp(2)^8+8*x*exp(2)^7)*log(2*x)^7+((56*x+112)*exp(2)^7+(56*x^2+112*x)*exp(2)^6)*log(2*x)^6+((168
*x^2+672*x+672)*exp(2)^6+(168*x^3+672*x^2+672*x)*exp(2)^5)*log(2*x)^5+((280*x^3+1680*x^2+3360*x+2240)*exp(2)^5
+(280*x^4+1680*x^3+3360*x^2+2240*x)*exp(2)^4)*log(2*x)^4+((280*x^4+2240*x^3+6720*x^2+8960*x+4480)*exp(2)^4+(28
0*x^5+2240*x^4+6720*x^3+8960*x^2+4480*x)*exp(2)^3)*log(2*x)^3+((168*x^5+1680*x^4+6720*x^3+13440*x^2+13440*x+53
76)*exp(2)^3+(168*x^6+1680*x^5+6720*x^4+13440*x^3+13440*x^2+5376*x)*exp(2)^2)*log(2*x)^2+((56*x^6+672*x^5+3360
*x^4+8960*x^3+13440*x^2+10752*x+3584)*exp(2)^2+(56*x^7+672*x^6+3360*x^5+8960*x^4+13440*x^3+10752*x^2+3584*x)*e
xp(2))*log(2*x)+(8*x^7+112*x^6+672*x^5+2240*x^4+4480*x^3+5376*x^2+3584*x+1024)*exp(2)+8*x^8+112*x^7+672*x^6+22
40*x^5+4480*x^4+5376*x^3+3584*x^2+1024*x)/x,x, algorithm="maxima")

[Out]

e^16*log(2*x)^8 + x^8 + 14/9*(18*log(2*x)^2 - 6*log(2*x) + 1)*x^6*e^4 + 8/7*x^7*e^2 + 16*e^14*log(2*x)^7 + 16*
x^7 + 56/125*(125*log(2*x)^3 - 75*log(2*x)^2 + 30*log(2*x) - 6)*x^5*e^6 + 168/125*(25*log(2*x)^2 - 10*log(2*x)
+ 2)*x^5*e^6 + 336/25*(25*log(2*x)^2 - 10*log(2*x) + 2)*x^5*e^4 + 56/3*x^6*e^2 + 112*e^12*log(2*x)^6 + 112*x^
6 + 35/16*(32*log(2*x)^4 - 32*log(2*x)^3 + 24*log(2*x)^2 - 12*log(2*x) + 3)*x^4*e^8 + 35/16*(32*log(2*x)^3 - 2
4*log(2*x)^2 + 12*log(2*x) - 3)*x^4*e^8 + 35/2*(32*log(2*x)^3 - 24*log(2*x)^2 + 12*log(2*x) - 3)*x^4*e^6 + 105
/2*(8*log(2*x)^2 - 4*log(2*x) + 1)*x^4*e^6 + 210*(8*log(2*x)^2 - 4*log(2*x) + 1)*x^4*e^4 + 672/5*x^5*e^2 + 448
*e^10*log(2*x)^5 + 448*x^5 + 56/81*(81*log(2*x)^5 - 135*log(2*x)^4 + 180*log(2*x)^3 - 180*log(2*x)^2 + 120*log
(2*x) - 40)*x^3*e^10 + 280/81*(27*log(2*x)^4 - 36*log(2*x)^3 + 36*log(2*x)^2 - 24*log(2*x) + 8)*x^3*e^10 + 560
/27*(27*log(2*x)^4 - 36*log(2*x)^3 + 36*log(2*x)^2 - 24*log(2*x) + 8)*x^3*e^8 + 2240/27*(9*log(2*x)^3 - 9*log(
2*x)^2 + 6*log(2*x) - 2)*x^3*e^8 + 2240/9*(9*log(2*x)^3 - 9*log(2*x)^2 + 6*log(2*x) - 2)*x^3*e^6 + 2240/9*(9*l
og(2*x)^2 - 6*log(2*x) + 2)*x^3*e^6 + 4480/9*(9*log(2*x)^2 - 6*log(2*x) + 2)*x^3*e^4 + 560*x^4*e^2 + 1120*e^8*
log(2*x)^4 + 1120*x^4 + 7*(4*log(2*x)^6 - 12*log(2*x)^5 + 30*log(2*x)^4 - 60*log(2*x)^3 + 90*log(2*x)^2 - 90*l
og(2*x) + 45)*x^2*e^12 + 21*(4*log(2*x)^5 - 10*log(2*x)^4 + 20*log(2*x)^3 - 30*log(2*x)^2 + 30*log(2*x) - 15)*
x^2*e^12 + 84*(4*log(2*x)^5 - 10*log(2*x)^4 + 20*log(2*x)^3 - 30*log(2*x)^2 + 30*log(2*x) - 15)*x^2*e^10 + 420
*(2*log(2*x)^4 - 4*log(2*x)^3 + 6*log(2*x)^2 - 6*log(2*x) + 3)*x^2*e^10 + 840*(2*log(2*x)^4 - 4*log(2*x)^3 + 6
*log(2*x)^2 - 6*log(2*x) + 3)*x^2*e^8 + 840*(4*log(2*x)^3 - 6*log(2*x)^2 + 6*log(2*x) - 3)*x^2*e^8 + 1120*(4*l
og(2*x)^3 - 6*log(2*x)^2 + 6*log(2*x) - 3)*x^2*e^6 + 3360*(2*log(2*x)^2 - 2*log(2*x) + 1)*x^2*e^6 + 3360*(2*lo
g(2*x)^2 - 2*log(2*x) + 1)*x^2*e^4 + 4480/3*x^3*e^2 + 1792*e^6*log(2*x)^3 + 1792*x^3 + 8*(log(2*x)^7 - 7*log(2
*x)^6 + 42*log(2*x)^5 - 210*log(2*x)^4 + 840*log(2*x)^3 - 2520*log(2*x)^2 + 5040*log(2*x) - 5040)*x*e^14 + 56*
(log(2*x)^6 - 6*log(2*x)^5 + 30*log(2*x)^4 - 120*log(2*x)^3 + 360*log(2*x)^2 - 720*log(2*x) + 720)*x*e^14 + 11
2*(log(2*x)^6 - 6*log(2*x)^5 + 30*log(2*x)^4 - 120*log(2*x)^3 + 360*log(2*x)^2 - 720*log(2*x) + 720)*x*e^12 +
672*(log(2*x)^5 - 5*log(2*x)^4 + 20*log(2*x)^3 - 60*log(2*x)^2 + 120*log(2*x) - 120)*x*e^12 + 672*(log(2*x)^5
- 5*log(2*x)^4 + 20*log(2*x)^3 - 60*log(2*x)^2 + 120*log(2*x) - 120)*x*e^10 + 3360*(log(2*x)^4 - 4*log(2*x)^3
+ 12*log(2*x)^2 - 24*log(2*x) + 24)*x*e^10 + 2240*(log(2*x)^4 - 4*log(2*x)^3 + 12*log(2*x)^2 - 24*log(2*x) + 2
4)*x*e^8 + 8960*(log(2*x)^3 - 3*log(2*x)^2 + 6*log(2*x) - 6)*x*e^8 + 4480*(log(2*x)^3 - 3*log(2*x)^2 + 6*log(2
*x) - 6)*x*e^6 + 13440*(log(2*x)^2 - 2*log(2*x) + 2)*x*e^6 + 5376*(log(2*x)^2 - 2*log(2*x) + 2)*x*e^4 + 2688*x
^2*e^2 + 1792*e^4*log(2*x)^2 + 1792*x^2 + 14/9*(6*x^6*log(2*x) - x^6)*e^4 + 672/25*(5*x^5*log(2*x) - x^5)*e^4
+ 210*(4*x^4*log(2*x) - x^4)*e^4 + 8960/9*(3*x^3*log(2*x) - x^3)*e^4 + 3360*(2*x^2*log(2*x) - x^2)*e^4 + 10752
*(x*log(2*x) - x)*e^4 + 8/7*(7*x^7*log(2*x) - x^7)*e^2 + 56/3*(6*x^6*log(2*x) - x^6)*e^2 + 672/5*(5*x^5*log(2*
x) - x^5)*e^2 + 560*(4*x^4*log(2*x) - x^4)*e^2 + 4480/3*(3*x^3*log(2*x) - x^3)*e^2 + 2688*(2*x^2*log(2*x) - x^
2)*e^2 + 3584*(x*log(2*x) - x)*e^2 + 3584*x*e^2 + 1024*e^2*log(x) + 1024*x

________________________________________________________________________________________

Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 240 vs. \(2 (14) = 28\).
time = 0.40, size = 240, normalized size = 16.00 \begin {gather*} 8 \, {\left (x + 2\right )} e^{14} \log \left (2 \, x\right )^{7} + e^{16} \log \left (2 \, x\right )^{8} + x^{8} + 28 \, {\left (x^{2} + 4 \, x + 4\right )} e^{12} \log \left (2 \, x\right )^{6} + 16 \, x^{7} + 56 \, {\left (x^{3} + 6 \, x^{2} + 12 \, x + 8\right )} e^{10} \log \left (2 \, x\right )^{5} + 112 \, x^{6} + 70 \, {\left (x^{4} + 8 \, x^{3} + 24 \, x^{2} + 32 \, x + 16\right )} e^{8} \log \left (2 \, x\right )^{4} + 448 \, x^{5} + 56 \, {\left (x^{5} + 10 \, x^{4} + 40 \, x^{3} + 80 \, x^{2} + 80 \, x + 32\right )} e^{6} \log \left (2 \, x\right )^{3} + 1120 \, x^{4} + 28 \, {\left (x^{6} + 12 \, x^{5} + 60 \, x^{4} + 160 \, x^{3} + 240 \, x^{2} + 192 \, x + 64\right )} e^{4} \log \left (2 \, x\right )^{2} + 1792 \, x^{3} + 8 \, {\left (x^{7} + 14 \, x^{6} + 84 \, x^{5} + 280 \, x^{4} + 560 \, x^{3} + 672 \, x^{2} + 448 \, x + 128\right )} e^{2} \log \left (2 \, x\right ) + 1792 \, x^{2} + 1024 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*exp(2)^8+8*x*exp(2)^7)*log(2*x)^7+((56*x+112)*exp(2)^7+(56*x^2+112*x)*exp(2)^6)*log(2*x)^6+((168
*x^2+672*x+672)*exp(2)^6+(168*x^3+672*x^2+672*x)*exp(2)^5)*log(2*x)^5+((280*x^3+1680*x^2+3360*x+2240)*exp(2)^5
+(280*x^4+1680*x^3+3360*x^2+2240*x)*exp(2)^4)*log(2*x)^4+((280*x^4+2240*x^3+6720*x^2+8960*x+4480)*exp(2)^4+(28
0*x^5+2240*x^4+6720*x^3+8960*x^2+4480*x)*exp(2)^3)*log(2*x)^3+((168*x^5+1680*x^4+6720*x^3+13440*x^2+13440*x+53
76)*exp(2)^3+(168*x^6+1680*x^5+6720*x^4+13440*x^3+13440*x^2+5376*x)*exp(2)^2)*log(2*x)^2+((56*x^6+672*x^5+3360
*x^4+8960*x^3+13440*x^2+10752*x+3584)*exp(2)^2+(56*x^7+672*x^6+3360*x^5+8960*x^4+13440*x^3+10752*x^2+3584*x)*e
xp(2))*log(2*x)+(8*x^7+112*x^6+672*x^5+2240*x^4+4480*x^3+5376*x^2+3584*x+1024)*exp(2)+8*x^8+112*x^7+672*x^6+22
40*x^5+4480*x^4+5376*x^3+3584*x^2+1024*x)/x,x, algorithm="fricas")

[Out]

8*(x + 2)*e^14*log(2*x)^7 + e^16*log(2*x)^8 + x^8 + 28*(x^2 + 4*x + 4)*e^12*log(2*x)^6 + 16*x^7 + 56*(x^3 + 6*
x^2 + 12*x + 8)*e^10*log(2*x)^5 + 112*x^6 + 70*(x^4 + 8*x^3 + 24*x^2 + 32*x + 16)*e^8*log(2*x)^4 + 448*x^5 + 5
6*(x^5 + 10*x^4 + 40*x^3 + 80*x^2 + 80*x + 32)*e^6*log(2*x)^3 + 1120*x^4 + 28*(x^6 + 12*x^5 + 60*x^4 + 160*x^3
+ 240*x^2 + 192*x + 64)*e^4*log(2*x)^2 + 1792*x^3 + 8*(x^7 + 14*x^6 + 84*x^5 + 280*x^4 + 560*x^3 + 672*x^2 +
448*x + 128)*e^2*log(2*x) + 1792*x^2 + 1024*x

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 357 vs. \(2 (14) = 28\).
time = 0.62, size = 357, normalized size = 23.80 \begin {gather*} x^{8} + 16 x^{7} + 112 x^{6} + 448 x^{5} + 1120 x^{4} + 1792 x^{3} + 1792 x^{2} + 1024 x + \left (8 x e^{14} + 16 e^{14}\right ) \log {\left (2 x \right )}^{7} + \left (28 x^{2} e^{12} + 112 x e^{12} + 112 e^{12}\right ) \log {\left (2 x \right )}^{6} + \left (56 x^{3} e^{10} + 336 x^{2} e^{10} + 672 x e^{10} + 448 e^{10}\right ) \log {\left (2 x \right )}^{5} + \left (70 x^{4} e^{8} + 560 x^{3} e^{8} + 1680 x^{2} e^{8} + 2240 x e^{8} + 1120 e^{8}\right ) \log {\left (2 x \right )}^{4} + \left (56 x^{5} e^{6} + 560 x^{4} e^{6} + 2240 x^{3} e^{6} + 4480 x^{2} e^{6} + 4480 x e^{6} + 1792 e^{6}\right ) \log {\left (2 x \right )}^{3} + \left (28 x^{6} e^{4} + 336 x^{5} e^{4} + 1680 x^{4} e^{4} + 4480 x^{3} e^{4} + 6720 x^{2} e^{4} + 5376 x e^{4} + 1792 e^{4}\right ) \log {\left (2 x \right )}^{2} + \left (8 x^{7} e^{2} + 112 x^{6} e^{2} + 672 x^{5} e^{2} + 2240 x^{4} e^{2} + 4480 x^{3} e^{2} + 5376 x^{2} e^{2} + 3584 x e^{2}\right ) \log {\left (2 x \right )} + 1024 e^{2} \log {\left (x \right )} + e^{16} \log {\left (2 x \right )}^{8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*exp(2)**8+8*x*exp(2)**7)*ln(2*x)**7+((56*x+112)*exp(2)**7+(56*x**2+112*x)*exp(2)**6)*ln(2*x)**6+
((168*x**2+672*x+672)*exp(2)**6+(168*x**3+672*x**2+672*x)*exp(2)**5)*ln(2*x)**5+((280*x**3+1680*x**2+3360*x+22
40)*exp(2)**5+(280*x**4+1680*x**3+3360*x**2+2240*x)*exp(2)**4)*ln(2*x)**4+((280*x**4+2240*x**3+6720*x**2+8960*
x+4480)*exp(2)**4+(280*x**5+2240*x**4+6720*x**3+8960*x**2+4480*x)*exp(2)**3)*ln(2*x)**3+((168*x**5+1680*x**4+6
720*x**3+13440*x**2+13440*x+5376)*exp(2)**3+(168*x**6+1680*x**5+6720*x**4+13440*x**3+13440*x**2+5376*x)*exp(2)
**2)*ln(2*x)**2+((56*x**6+672*x**5+3360*x**4+8960*x**3+13440*x**2+10752*x+3584)*exp(2)**2+(56*x**7+672*x**6+33
60*x**5+8960*x**4+13440*x**3+10752*x**2+3584*x)*exp(2))*ln(2*x)+(8*x**7+112*x**6+672*x**5+2240*x**4+4480*x**3+
5376*x**2+3584*x+1024)*exp(2)+8*x**8+112*x**7+672*x**6+2240*x**5+4480*x**4+5376*x**3+3584*x**2+1024*x)/x,x)

[Out]

x**8 + 16*x**7 + 112*x**6 + 448*x**5 + 1120*x**4 + 1792*x**3 + 1792*x**2 + 1024*x + (8*x*exp(14) + 16*exp(14))
*log(2*x)**7 + (28*x**2*exp(12) + 112*x*exp(12) + 112*exp(12))*log(2*x)**6 + (56*x**3*exp(10) + 336*x**2*exp(1
0) + 672*x*exp(10) + 448*exp(10))*log(2*x)**5 + (70*x**4*exp(8) + 560*x**3*exp(8) + 1680*x**2*exp(8) + 2240*x*
exp(8) + 1120*exp(8))*log(2*x)**4 + (56*x**5*exp(6) + 560*x**4*exp(6) + 2240*x**3*exp(6) + 4480*x**2*exp(6) +
4480*x*exp(6) + 1792*exp(6))*log(2*x)**3 + (28*x**6*exp(4) + 336*x**5*exp(4) + 1680*x**4*exp(4) + 4480*x**3*ex
p(4) + 6720*x**2*exp(4) + 5376*x*exp(4) + 1792*exp(4))*log(2*x)**2 + (8*x**7*exp(2) + 112*x**6*exp(2) + 672*x*
*5*exp(2) + 2240*x**4*exp(2) + 4480*x**3*exp(2) + 5376*x**2*exp(2) + 3584*x*exp(2))*log(2*x) + 1024*exp(2)*log
(x) + exp(16)*log(2*x)**8

________________________________________________________________________________________

Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 448 vs. \(2 (14) = 28\).
time = 0.48, size = 448, normalized size = 29.87 \begin {gather*} 8 \, x^{7} e^{2} \log \left (2 \, x\right ) + 28 \, x^{6} e^{4} \log \left (2 \, x\right )^{2} + 56 \, x^{5} e^{6} \log \left (2 \, x\right )^{3} + 70 \, x^{4} e^{8} \log \left (2 \, x\right )^{4} + 56 \, x^{3} e^{10} \log \left (2 \, x\right )^{5} + 28 \, x^{2} e^{12} \log \left (2 \, x\right )^{6} + 8 \, x e^{14} \log \left (2 \, x\right )^{7} + e^{16} \log \left (2 \, x\right )^{8} + x^{8} + 112 \, x^{6} e^{2} \log \left (2 \, x\right ) + 336 \, x^{5} e^{4} \log \left (2 \, x\right )^{2} + 560 \, x^{4} e^{6} \log \left (2 \, x\right )^{3} + 560 \, x^{3} e^{8} \log \left (2 \, x\right )^{4} + 336 \, x^{2} e^{10} \log \left (2 \, x\right )^{5} + 112 \, x e^{12} \log \left (2 \, x\right )^{6} + 16 \, e^{14} \log \left (2 \, x\right )^{7} + 16 \, x^{7} + 672 \, x^{5} e^{2} \log \left (2 \, x\right ) + 1680 \, x^{4} e^{4} \log \left (2 \, x\right )^{2} + 2240 \, x^{3} e^{6} \log \left (2 \, x\right )^{3} + 1680 \, x^{2} e^{8} \log \left (2 \, x\right )^{4} + 672 \, x e^{10} \log \left (2 \, x\right )^{5} + 112 \, e^{12} \log \left (2 \, x\right )^{6} + 112 \, x^{6} + 2240 \, x^{4} e^{2} \log \left (2 \, x\right ) + 4480 \, x^{3} e^{4} \log \left (2 \, x\right )^{2} + 4480 \, x^{2} e^{6} \log \left (2 \, x\right )^{3} + 2240 \, x e^{8} \log \left (2 \, x\right )^{4} + 448 \, e^{10} \log \left (2 \, x\right )^{5} + 448 \, x^{5} + 4480 \, x^{3} e^{2} \log \left (2 \, x\right ) + 6720 \, x^{2} e^{4} \log \left (2 \, x\right )^{2} + 4480 \, x e^{6} \log \left (2 \, x\right )^{3} + 1120 \, e^{8} \log \left (2 \, x\right )^{4} + 1120 \, x^{4} + 5376 \, x^{2} e^{2} \log \left (2 \, x\right ) + 5376 \, x e^{4} \log \left (2 \, x\right )^{2} + 1792 \, e^{6} \log \left (2 \, x\right )^{3} + 1792 \, x^{3} + 3584 \, x e^{2} \log \left (2 \, x\right ) + 1792 \, e^{4} \log \left (2 \, x\right )^{2} + 1792 \, x^{2} + 1024 \, e^{2} \log \left (x\right ) + 1024 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*exp(2)^8+8*x*exp(2)^7)*log(2*x)^7+((56*x+112)*exp(2)^7+(56*x^2+112*x)*exp(2)^6)*log(2*x)^6+((168
*x^2+672*x+672)*exp(2)^6+(168*x^3+672*x^2+672*x)*exp(2)^5)*log(2*x)^5+((280*x^3+1680*x^2+3360*x+2240)*exp(2)^5
+(280*x^4+1680*x^3+3360*x^2+2240*x)*exp(2)^4)*log(2*x)^4+((280*x^4+2240*x^3+6720*x^2+8960*x+4480)*exp(2)^4+(28
0*x^5+2240*x^4+6720*x^3+8960*x^2+4480*x)*exp(2)^3)*log(2*x)^3+((168*x^5+1680*x^4+6720*x^3+13440*x^2+13440*x+53
76)*exp(2)^3+(168*x^6+1680*x^5+6720*x^4+13440*x^3+13440*x^2+5376*x)*exp(2)^2)*log(2*x)^2+((56*x^6+672*x^5+3360
*x^4+8960*x^3+13440*x^2+10752*x+3584)*exp(2)^2+(56*x^7+672*x^6+3360*x^5+8960*x^4+13440*x^3+10752*x^2+3584*x)*e
xp(2))*log(2*x)+(8*x^7+112*x^6+672*x^5+2240*x^4+4480*x^3+5376*x^2+3584*x+1024)*exp(2)+8*x^8+112*x^7+672*x^6+22
40*x^5+4480*x^4+5376*x^3+3584*x^2+1024*x)/x,x, algorithm="giac")

[Out]

8*x^7*e^2*log(2*x) + 28*x^6*e^4*log(2*x)^2 + 56*x^5*e^6*log(2*x)^3 + 70*x^4*e^8*log(2*x)^4 + 56*x^3*e^10*log(2
*x)^5 + 28*x^2*e^12*log(2*x)^6 + 8*x*e^14*log(2*x)^7 + e^16*log(2*x)^8 + x^8 + 112*x^6*e^2*log(2*x) + 336*x^5*
e^4*log(2*x)^2 + 560*x^4*e^6*log(2*x)^3 + 560*x^3*e^8*log(2*x)^4 + 336*x^2*e^10*log(2*x)^5 + 112*x*e^12*log(2*
x)^6 + 16*e^14*log(2*x)^7 + 16*x^7 + 672*x^5*e^2*log(2*x) + 1680*x^4*e^4*log(2*x)^2 + 2240*x^3*e^6*log(2*x)^3
+ 1680*x^2*e^8*log(2*x)^4 + 672*x*e^10*log(2*x)^5 + 112*e^12*log(2*x)^6 + 112*x^6 + 2240*x^4*e^2*log(2*x) + 44
80*x^3*e^4*log(2*x)^2 + 4480*x^2*e^6*log(2*x)^3 + 2240*x*e^8*log(2*x)^4 + 448*e^10*log(2*x)^5 + 448*x^5 + 4480
*x^3*e^2*log(2*x) + 6720*x^2*e^4*log(2*x)^2 + 4480*x*e^6*log(2*x)^3 + 1120*e^8*log(2*x)^4 + 1120*x^4 + 5376*x^
2*e^2*log(2*x) + 5376*x*e^4*log(2*x)^2 + 1792*e^6*log(2*x)^3 + 1792*x^3 + 3584*x*e^2*log(2*x) + 1792*e^4*log(2
*x)^2 + 1792*x^2 + 1024*e^2*log(x) + 1024*x

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Mupad [B]
time = 10.15, size = 448, normalized size = 29.87 \begin {gather*} 1024\,x+1792\,{\ln \left (2\,x\right )}^2\,{\mathrm {e}}^4+1792\,{\ln \left (2\,x\right )}^3\,{\mathrm {e}}^6+1120\,{\ln \left (2\,x\right )}^4\,{\mathrm {e}}^8+448\,{\ln \left (2\,x\right )}^5\,{\mathrm {e}}^{10}+112\,{\ln \left (2\,x\right )}^6\,{\mathrm {e}}^{12}+16\,{\ln \left (2\,x\right )}^7\,{\mathrm {e}}^{14}+{\ln \left (2\,x\right )}^8\,{\mathrm {e}}^{16}+1024\,{\mathrm {e}}^2\,\ln \left (x\right )+1792\,x^2+1792\,x^3+1120\,x^4+448\,x^5+112\,x^6+16\,x^7+x^8+6720\,x^2\,{\ln \left (2\,x\right )}^2\,{\mathrm {e}}^4+4480\,x^3\,{\ln \left (2\,x\right )}^2\,{\mathrm {e}}^4+1680\,x^4\,{\ln \left (2\,x\right )}^2\,{\mathrm {e}}^4+4480\,x^2\,{\ln \left (2\,x\right )}^3\,{\mathrm {e}}^6+336\,x^5\,{\ln \left (2\,x\right )}^2\,{\mathrm {e}}^4+2240\,x^3\,{\ln \left (2\,x\right )}^3\,{\mathrm {e}}^6+28\,x^6\,{\ln \left (2\,x\right )}^2\,{\mathrm {e}}^4+560\,x^4\,{\ln \left (2\,x\right )}^3\,{\mathrm {e}}^6+1680\,x^2\,{\ln \left (2\,x\right )}^4\,{\mathrm {e}}^8+56\,x^5\,{\ln \left (2\,x\right )}^3\,{\mathrm {e}}^6+560\,x^3\,{\ln \left (2\,x\right )}^4\,{\mathrm {e}}^8+70\,x^4\,{\ln \left (2\,x\right )}^4\,{\mathrm {e}}^8+336\,x^2\,{\ln \left (2\,x\right )}^5\,{\mathrm {e}}^{10}+56\,x^3\,{\ln \left (2\,x\right )}^5\,{\mathrm {e}}^{10}+28\,x^2\,{\ln \left (2\,x\right )}^6\,{\mathrm {e}}^{12}+3584\,x\,\ln \left (2\,x\right )\,{\mathrm {e}}^2+5376\,x^2\,\ln \left (2\,x\right )\,{\mathrm {e}}^2+4480\,x^3\,\ln \left (2\,x\right )\,{\mathrm {e}}^2+5376\,x\,{\ln \left (2\,x\right )}^2\,{\mathrm {e}}^4+2240\,x^4\,\ln \left (2\,x\right )\,{\mathrm {e}}^2+672\,x^5\,\ln \left (2\,x\right )\,{\mathrm {e}}^2+112\,x^6\,\ln \left (2\,x\right )\,{\mathrm {e}}^2+4480\,x\,{\ln \left (2\,x\right )}^3\,{\mathrm {e}}^6+8\,x^7\,\ln \left (2\,x\right )\,{\mathrm {e}}^2+2240\,x\,{\ln \left (2\,x\right )}^4\,{\mathrm {e}}^8+672\,x\,{\ln \left (2\,x\right )}^5\,{\mathrm {e}}^{10}+112\,x\,{\ln \left (2\,x\right )}^6\,{\mathrm {e}}^{12}+8\,x\,{\ln \left (2\,x\right )}^7\,{\mathrm {e}}^{14} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1024*x + exp(2)*(3584*x + 5376*x^2 + 4480*x^3 + 2240*x^4 + 672*x^5 + 112*x^6 + 8*x^7 + 1024) + log(2*x)^2
*(exp(4)*(5376*x + 13440*x^2 + 13440*x^3 + 6720*x^4 + 1680*x^5 + 168*x^6) + exp(6)*(13440*x + 13440*x^2 + 6720
*x^3 + 1680*x^4 + 168*x^5 + 5376)) + log(2*x)*(exp(4)*(10752*x + 13440*x^2 + 8960*x^3 + 3360*x^4 + 672*x^5 + 5
6*x^6 + 3584) + exp(2)*(3584*x + 10752*x^2 + 13440*x^3 + 8960*x^4 + 3360*x^5 + 672*x^6 + 56*x^7)) + log(2*x)^7
*(8*exp(16) + 8*x*exp(14)) + log(2*x)^4*(exp(10)*(3360*x + 1680*x^2 + 280*x^3 + 2240) + exp(8)*(2240*x + 3360*
x^2 + 1680*x^3 + 280*x^4)) + log(2*x)^6*(exp(12)*(112*x + 56*x^2) + exp(14)*(56*x + 112)) + 3584*x^2 + 5376*x^
3 + 4480*x^4 + 2240*x^5 + 672*x^6 + 112*x^7 + 8*x^8 + log(2*x)^3*(exp(8)*(8960*x + 6720*x^2 + 2240*x^3 + 280*x
^4 + 4480) + exp(6)*(4480*x + 8960*x^2 + 6720*x^3 + 2240*x^4 + 280*x^5)) + log(2*x)^5*(exp(12)*(672*x + 168*x^
2 + 672) + exp(10)*(672*x + 672*x^2 + 168*x^3)))/x,x)

[Out]

1024*x + 1792*log(2*x)^2*exp(4) + 1792*log(2*x)^3*exp(6) + 1120*log(2*x)^4*exp(8) + 448*log(2*x)^5*exp(10) + 1
12*log(2*x)^6*exp(12) + 16*log(2*x)^7*exp(14) + log(2*x)^8*exp(16) + 1024*exp(2)*log(x) + 1792*x^2 + 1792*x^3
+ 1120*x^4 + 448*x^5 + 112*x^6 + 16*x^7 + x^8 + 6720*x^2*log(2*x)^2*exp(4) + 4480*x^3*log(2*x)^2*exp(4) + 1680
*x^4*log(2*x)^2*exp(4) + 4480*x^2*log(2*x)^3*exp(6) + 336*x^5*log(2*x)^2*exp(4) + 2240*x^3*log(2*x)^3*exp(6) +
28*x^6*log(2*x)^2*exp(4) + 560*x^4*log(2*x)^3*exp(6) + 1680*x^2*log(2*x)^4*exp(8) + 56*x^5*log(2*x)^3*exp(6)
+ 560*x^3*log(2*x)^4*exp(8) + 70*x^4*log(2*x)^4*exp(8) + 336*x^2*log(2*x)^5*exp(10) + 56*x^3*log(2*x)^5*exp(10
) + 28*x^2*log(2*x)^6*exp(12) + 3584*x*log(2*x)*exp(2) + 5376*x^2*log(2*x)*exp(2) + 4480*x^3*log(2*x)*exp(2) +
5376*x*log(2*x)^2*exp(4) + 2240*x^4*log(2*x)*exp(2) + 672*x^5*log(2*x)*exp(2) + 112*x^6*log(2*x)*exp(2) + 448
0*x*log(2*x)^3*exp(6) + 8*x^7*log(2*x)*exp(2) + 2240*x*log(2*x)^4*exp(8) + 672*x*log(2*x)^5*exp(10) + 112*x*lo
g(2*x)^6*exp(12) + 8*x*log(2*x)^7*exp(14)

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