Integrand size = 147, antiderivative size = 24 \[ \int \frac {x^6 \left (e^{4 x} \left (8 x+4 x^2\right )+\frac {16 e^{6+3 x} \left (24 x+40 x^2+12 x^3\right )}{x^2}+\frac {256 e^{12+2 x} \left (24 x+72 x^2+60 x^3+12 x^4\right )}{x^4}+\frac {65536 e^{24} \left (1+4 x^2+12 x^3+12 x^4+4 x^5\right )}{x^8}+\frac {4096 e^{18+x} \left (8 x+40 x^2+60 x^3+32 x^4+4 x^5\right )}{x^6}\right )}{65536 e^{24}} \, dx=3-\frac {1}{x}+\left (1+x+\frac {1}{16} e^{-6+x} x^2\right )^4 \]
Leaf count is larger than twice the leaf count of optimal. \(89\) vs. \(2(24)=48\).
Time = 0.92 (sec) , antiderivative size = 89, normalized size of antiderivative = 3.71 \[ \int \frac {x^6 \left (e^{4 x} \left (8 x+4 x^2\right )+\frac {16 e^{6+3 x} \left (24 x+40 x^2+12 x^3\right )}{x^2}+\frac {256 e^{12+2 x} \left (24 x+72 x^2+60 x^3+12 x^4\right )}{x^4}+\frac {65536 e^{24} \left (1+4 x^2+12 x^3+12 x^4+4 x^5\right )}{x^8}+\frac {4096 e^{18+x} \left (8 x+40 x^2+60 x^3+32 x^4+4 x^5\right )}{x^6}\right )}{65536 e^{24}} \, dx=-\frac {1}{x}+4 x+6 x^2+4 x^3+x^4+\frac {e^{4 (-6+x)} x^8}{65536}+\frac {e^{3 (-6+x)} x^6 (1+x)}{1024}+\frac {3}{128} e^{2 (-6+x)} x^4 (1+x)^2+\frac {1}{4} e^{-6+x} x^2 (1+x)^3 \]
Integrate[(x^6*(E^(4*x)*(8*x + 4*x^2) + (16*E^(6 + 3*x)*(24*x + 40*x^2 + 1 2*x^3))/x^2 + (256*E^(12 + 2*x)*(24*x + 72*x^2 + 60*x^3 + 12*x^4))/x^4 + ( 65536*E^24*(1 + 4*x^2 + 12*x^3 + 12*x^4 + 4*x^5))/x^8 + (4096*E^(18 + x)*( 8*x + 40*x^2 + 60*x^3 + 32*x^4 + 4*x^5))/x^6))/(65536*E^24),x]
-x^(-1) + 4*x + 6*x^2 + 4*x^3 + x^4 + (E^(4*(-6 + x))*x^8)/65536 + (E^(3*( -6 + x))*x^6*(1 + x))/1024 + (3*E^(2*(-6 + x))*x^4*(1 + x)^2)/128 + (E^(-6 + x)*x^2*(1 + x)^3)/4
Leaf count is larger than twice the leaf count of optimal. \(158\) vs. \(2(24)=48\).
Time = 1.24 (sec) , antiderivative size = 158, normalized size of antiderivative = 6.58, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {27, 27, 2010, 2009}
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.
| \(\displaystyle \int \frac {x^6 \left (e^{4 x} \left (4 x^2+8 x\right )+\frac {16 e^{3 x+6} \left (12 x^3+40 x^2+24 x\right )}{x^2}+\frac {256 e^{2 x+12} \left (12 x^4+60 x^3+72 x^2+24 x\right )}{x^4}+\frac {65536 e^{24} \left (4 x^5+12 x^4+12 x^3+4 x^2+1\right )}{x^8}+\frac {4096 e^{x+18} \left (4 x^5+32 x^4+60 x^3+40 x^2+8 x\right )}{x^6}\right )}{65536 e^{24}} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int 4 x^6 \left (e^{4 x} \left (x^2+2 x\right )+\frac {16 e^{3 x+6} \left (3 x^3+10 x^2+6 x\right )}{x^2}+\frac {768 e^{2 x+12} \left (x^4+5 x^3+6 x^2+2 x\right )}{x^4}+\frac {4096 e^{x+18} \left (x^5+8 x^4+15 x^3+10 x^2+2 x\right )}{x^6}+\frac {16384 e^{24} \left (4 x^5+12 x^4+12 x^3+4 x^2+1\right )}{x^8}\right )dx}{65536 e^{24}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int x^6 \left (e^{4 x} \left (x^2+2 x\right )+\frac {16 e^{3 x+6} \left (3 x^3+10 x^2+6 x\right )}{x^2}+\frac {768 e^{2 x+12} \left (x^4+5 x^3+6 x^2+2 x\right )}{x^4}+\frac {4096 e^{x+18} \left (x^5+8 x^4+15 x^3+10 x^2+2 x\right )}{x^6}+\frac {16384 e^{24} \left (4 x^5+12 x^4+12 x^3+4 x^2+1\right )}{x^8}\right )dx}{16384 e^{24}}\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle \frac {\int \left (e^{4 x} (x+2) x^7+16 e^{3 x+6} \left (3 x^2+10 x+6\right ) x^5+768 e^{2 x+12} (x+1) \left (x^2+4 x+2\right ) x^3+4096 e^{x+18} (x+1)^2 \left (x^2+6 x+2\right ) x+\frac {16384 e^{24} \left (4 x^5+12 x^4+12 x^3+4 x^2+1\right )}{x^2}\right )dx}{16384 e^{24}}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {\frac {1}{4} e^{4 x} x^8+16 e^{3 x+6} x^7+384 e^{2 x+12} x^6+16 e^{3 x+6} x^6+4096 e^{x+18} x^5+768 e^{2 x+12} x^5+12288 e^{x+18} x^4+384 e^{2 x+12} x^4+16384 e^{24} x^4+12288 e^{x+18} x^3+65536 e^{24} x^3+4096 e^{x+18} x^2+98304 e^{24} x^2+65536 e^{24} x-\frac {16384 e^{24}}{x}}{16384 e^{24}}\) |
Int[(x^6*(E^(4*x)*(8*x + 4*x^2) + (16*E^(6 + 3*x)*(24*x + 40*x^2 + 12*x^3) )/x^2 + (256*E^(12 + 2*x)*(24*x + 72*x^2 + 60*x^3 + 12*x^4))/x^4 + (65536* E^24*(1 + 4*x^2 + 12*x^3 + 12*x^4 + 4*x^5))/x^8 + (4096*E^(18 + x)*(8*x + 40*x^2 + 60*x^3 + 32*x^4 + 4*x^5))/x^6))/(65536*E^24),x]
((-16384*E^24)/x + 65536*E^24*x + 98304*E^24*x^2 + 4096*E^(18 + x)*x^2 + 6 5536*E^24*x^3 + 12288*E^(18 + x)*x^3 + 16384*E^24*x^4 + 12288*E^(18 + x)*x ^4 + 384*E^(12 + 2*x)*x^4 + 4096*E^(18 + x)*x^5 + 768*E^(12 + 2*x)*x^5 + 3 84*E^(12 + 2*x)*x^6 + 16*E^(6 + 3*x)*x^6 + 16*E^(6 + 3*x)*x^7 + (E^(4*x)*x ^8)/4)/(16384*E^24)
3.17.88.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
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]]
Leaf count of result is larger than twice the leaf count of optimal. \(77\) vs. \(2(26)=52\).
Time = 2.10 (sec) , antiderivative size = 78, normalized size of antiderivative = 3.25
| method | result | size |
| risch | \(\left (1+x \right )^{4}-\frac {1}{x}+\frac {x^{2} \left (x^{3}+3 x^{2}+3 x +1\right ) {\mathrm e}^{-6+x}}{4}+\frac {3 x^{4} \left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x -12}}{128}+\frac {x^{6} \left (1+x \right ) {\mathrm e}^{3 x -18}}{1024}+\frac {x^{8} {\mathrm e}^{4 x -24}}{65536}\) | \(78\) |
| parallelrisch | \(\frac {\left (x^{3} {\mathrm e}^{4 x}+16384 \,{\mathrm e}^{x} {\mathrm e}^{18}+\frac {49152 \,{\mathrm e}^{x} {\mathrm e}^{18}}{x}+1536 \,{\mathrm e}^{2 x} x \,{\mathrm e}^{12}+\frac {49152 \,{\mathrm e}^{x} {\mathrm e}^{18}}{x^{2}}+3072 \,{\mathrm e}^{2 x} {\mathrm e}^{12}+\frac {16384 \,{\mathrm e}^{x} {\mathrm e}^{18}}{x^{3}}+64 \,{\mathrm e}^{3 x} x^{2} {\mathrm e}^{6}+\frac {1536 \,{\mathrm e}^{2 x} {\mathrm e}^{12}}{x}+64 \,{\mathrm e}^{3 x} x \,{\mathrm e}^{6}+\frac {393216 \,{\mathrm e}^{24}}{x^{3}}+\frac {262144 \,{\mathrm e}^{24}}{x^{4}}-\frac {65536 \,{\mathrm e}^{24}}{x^{6}}+\frac {262144 \,{\mathrm e}^{24}}{x^{2}}+\frac {65536 \,{\mathrm e}^{24}}{x}\right ) x^{5} {\mathrm e}^{-24}}{65536}\) | \(276\) |
| default | \(\text {Expression too large to display}\) | \(11630\) |
| parts | \(\text {Expression too large to display}\) | \(11630\) |
int(((4*x^5+12*x^4+12*x^3+4*x^2+1)*exp(ln(4/x)+3)^8+(4*x^5+32*x^4+60*x^3+4 0*x^2+8*x)*exp(x)*exp(ln(4/x)+3)^6+(12*x^4+60*x^3+72*x^2+24*x)*exp(x)^2*ex p(ln(4/x)+3)^4+(12*x^3+40*x^2+24*x)*exp(x)^3*exp(ln(4/x)+3)^2+(4*x^2+8*x)* exp(x)^4)/x^2/exp(ln(4/x)+3)^8,x,method=_RETURNVERBOSE)
(1+x)^4-1/x+1/4*x^2*(x^3+3*x^2+3*x+1)*exp(-6+x)+3/128*x^4*(x^2+2*x+1)*exp( 2*x-12)+1/1024*x^6*(1+x)*exp(3*x-18)+1/65536*x^8*exp(4*x-24)
Leaf count of result is larger than twice the leaf count of optimal. 132 vs. \(2 (24) = 48\).
Time = 0.26 (sec) , antiderivative size = 132, normalized size of antiderivative = 5.50 \[ \int \frac {x^6 \left (e^{4 x} \left (8 x+4 x^2\right )+\frac {16 e^{6+3 x} \left (24 x+40 x^2+12 x^3\right )}{x^2}+\frac {256 e^{12+2 x} \left (24 x+72 x^2+60 x^3+12 x^4\right )}{x^4}+\frac {65536 e^{24} \left (1+4 x^2+12 x^3+12 x^4+4 x^5\right )}{x^8}+\frac {4096 e^{18+x} \left (8 x+40 x^2+60 x^3+32 x^4+4 x^5\right )}{x^6}\right )}{65536 e^{24}} \, dx=\frac {{\left (x^{33} e^{\left (4 \, x + 24 \, \log \left (\frac {4}{x}\right ) + 72\right )} + 18446744073709551616 \, {\left (x^{5} + 4 \, x^{4} + 6 \, x^{3} + 4 \, x^{2} - 1\right )} e^{96} + 262144 \, {\left (x^{26} + x^{25}\right )} e^{\left (3 \, x + 18 \, \log \left (\frac {4}{x}\right ) + 78\right )} + 25769803776 \, {\left (x^{19} + 2 \, x^{18} + x^{17}\right )} e^{\left (2 \, x + 12 \, \log \left (\frac {4}{x}\right ) + 84\right )} + 1125899906842624 \, {\left (x^{12} + 3 \, x^{11} + 3 \, x^{10} + x^{9}\right )} e^{\left (x + 6 \, \log \left (\frac {4}{x}\right ) + 90\right )}\right )} e^{\left (-96\right )}}{18446744073709551616 \, x} \]
integrate(((4*x^5+12*x^4+12*x^3+4*x^2+1)*exp(log(4/x)+3)^8+(4*x^5+32*x^4+6 0*x^3+40*x^2+8*x)*exp(x)*exp(log(4/x)+3)^6+(12*x^4+60*x^3+72*x^2+24*x)*exp (x)^2*exp(log(4/x)+3)^4+(12*x^3+40*x^2+24*x)*exp(x)^3*exp(log(4/x)+3)^2+(4 *x^2+8*x)*exp(x)^4)/x^2/exp(log(4/x)+3)^8,x, algorithm=\
1/18446744073709551616*(x^33*e^(4*x + 24*log(4/x) + 72) + 1844674407370955 1616*(x^5 + 4*x^4 + 6*x^3 + 4*x^2 - 1)*e^96 + 262144*(x^26 + x^25)*e^(3*x + 18*log(4/x) + 78) + 25769803776*(x^19 + 2*x^18 + x^17)*e^(2*x + 12*log(4 /x) + 84) + 1125899906842624*(x^12 + 3*x^11 + 3*x^10 + x^9)*e^(x + 6*log(4 /x) + 90))*e^(-96)/x
Leaf count of result is larger than twice the leaf count of optimal. 128 vs. \(2 (20) = 40\).
Time = 0.20 (sec) , antiderivative size = 128, normalized size of antiderivative = 5.33 \[ \int \frac {x^6 \left (e^{4 x} \left (8 x+4 x^2\right )+\frac {16 e^{6+3 x} \left (24 x+40 x^2+12 x^3\right )}{x^2}+\frac {256 e^{12+2 x} \left (24 x+72 x^2+60 x^3+12 x^4\right )}{x^4}+\frac {65536 e^{24} \left (1+4 x^2+12 x^3+12 x^4+4 x^5\right )}{x^8}+\frac {4096 e^{18+x} \left (8 x+40 x^2+60 x^3+32 x^4+4 x^5\right )}{x^6}\right )}{65536 e^{24}} \, dx=x^{4} + 4 x^{3} + 6 x^{2} + 4 x + \frac {524288 x^{8} e^{36} e^{4 x} + \left (33554432 x^{7} e^{42} + 33554432 x^{6} e^{42}\right ) e^{3 x} + \left (805306368 x^{6} e^{48} + 1610612736 x^{5} e^{48} + 805306368 x^{4} e^{48}\right ) e^{2 x} + \left (8589934592 x^{5} e^{54} + 25769803776 x^{4} e^{54} + 25769803776 x^{3} e^{54} + 8589934592 x^{2} e^{54}\right ) e^{x}}{34359738368 e^{60}} - \frac {1}{x} \]
integrate(((4*x**5+12*x**4+12*x**3+4*x**2+1)*exp(ln(4/x)+3)**8+(4*x**5+32* x**4+60*x**3+40*x**2+8*x)*exp(x)*exp(ln(4/x)+3)**6+(12*x**4+60*x**3+72*x** 2+24*x)*exp(x)**2*exp(ln(4/x)+3)**4+(12*x**3+40*x**2+24*x)*exp(x)**3*exp(l n(4/x)+3)**2+(4*x**2+8*x)*exp(x)**4)/x**2/exp(ln(4/x)+3)**8,x)
x**4 + 4*x**3 + 6*x**2 + 4*x + (524288*x**8*exp(36)*exp(4*x) + (33554432*x **7*exp(42) + 33554432*x**6*exp(42))*exp(3*x) + (805306368*x**6*exp(48) + 1610612736*x**5*exp(48) + 805306368*x**4*exp(48))*exp(2*x) + (8589934592*x **5*exp(54) + 25769803776*x**4*exp(54) + 25769803776*x**3*exp(54) + 858993 4592*x**2*exp(54))*exp(x))*exp(-60)/34359738368 - 1/x
Leaf count of result is larger than twice the leaf count of optimal. 575 vs. \(2 (24) = 48\).
Time = 0.22 (sec) , antiderivative size = 575, normalized size of antiderivative = 23.96 \[ \int \frac {x^6 \left (e^{4 x} \left (8 x+4 x^2\right )+\frac {16 e^{6+3 x} \left (24 x+40 x^2+12 x^3\right )}{x^2}+\frac {256 e^{12+2 x} \left (24 x+72 x^2+60 x^3+12 x^4\right )}{x^4}+\frac {65536 e^{24} \left (1+4 x^2+12 x^3+12 x^4+4 x^5\right )}{x^8}+\frac {4096 e^{18+x} \left (8 x+40 x^2+60 x^3+32 x^4+4 x^5\right )}{x^6}\right )}{65536 e^{24}} \, dx =\text {Too large to display} \]
integrate(((4*x^5+12*x^4+12*x^3+4*x^2+1)*exp(log(4/x)+3)^8+(4*x^5+32*x^4+6 0*x^3+40*x^2+8*x)*exp(x)*exp(log(4/x)+3)^6+(12*x^4+60*x^3+72*x^2+24*x)*exp (x)^2*exp(log(4/x)+3)^4+(12*x^3+40*x^2+24*x)*exp(x)^3*exp(log(4/x)+3)^2+(4 *x^2+8*x)*exp(x)^4)/x^2/exp(log(4/x)+3)^8,x, algorithm=\
1/8153726976*(8153726976*x^4*e^24 + 32614907904*x^3*e^24 + 48922361856*x^2 *e^24 + 32614907904*x*e^24 + 243*(512*x^8 - 1024*x^7 + 1792*x^6 - 2688*x^5 + 3360*x^4 - 3360*x^3 + 2520*x^2 - 1260*x + 315)*e^(4*x) + 243*(1024*x^7 - 1792*x^6 + 2688*x^5 - 3360*x^4 + 3360*x^3 - 2520*x^2 + 1260*x - 315)*e^( 4*x) + 32768*(243*x^7*e^6 - 567*x^6*e^6 + 1134*x^5*e^6 - 1890*x^4*e^6 + 25 20*x^3*e^6 - 2520*x^2*e^6 + 1680*x*e^6 - 560*e^6)*e^(3*x) + 327680*(81*x^6 *e^6 - 162*x^5*e^6 + 270*x^4*e^6 - 360*x^3*e^6 + 360*x^2*e^6 - 240*x*e^6 + 80*e^6)*e^(3*x) + 196608*(81*x^5*e^6 - 135*x^4*e^6 + 180*x^3*e^6 - 180*x^ 2*e^6 + 120*x*e^6 - 40*e^6)*e^(3*x) + 47775744*(4*x^6*e^12 - 12*x^5*e^12 + 30*x^4*e^12 - 60*x^3*e^12 + 90*x^2*e^12 - 90*x*e^12 + 45*e^12)*e^(2*x) + 238878720*(4*x^5*e^12 - 10*x^4*e^12 + 20*x^3*e^12 - 30*x^2*e^12 + 30*x*e^1 2 - 15*e^12)*e^(2*x) + 573308928*(2*x^4*e^12 - 4*x^3*e^12 + 6*x^2*e^12 - 6 *x*e^12 + 3*e^12)*e^(2*x) + 95551488*(4*x^3*e^12 - 6*x^2*e^12 + 6*x*e^12 - 3*e^12)*e^(2*x) + 2038431744*(x^5*e^18 - 5*x^4*e^18 + 20*x^3*e^18 - 60*x^ 2*e^18 + 120*x*e^18 - 120*e^18)*e^x + 16307453952*(x^4*e^18 - 4*x^3*e^18 + 12*x^2*e^18 - 24*x*e^18 + 24*e^18)*e^x + 30576476160*(x^3*e^18 - 3*x^2*e^ 18 + 6*x*e^18 - 6*e^18)*e^x + 20384317440*(x^2*e^18 - 2*x*e^18 + 2*e^18)*e ^x + 4076863488*(x*e^18 - e^18)*e^x - 8153726976*e^24/x)*e^(-24)
Leaf count of result is larger than twice the leaf count of optimal. 141 vs. \(2 (24) = 48\).
Time = 0.26 (sec) , antiderivative size = 141, normalized size of antiderivative = 5.88 \[ \int \frac {x^6 \left (e^{4 x} \left (8 x+4 x^2\right )+\frac {16 e^{6+3 x} \left (24 x+40 x^2+12 x^3\right )}{x^2}+\frac {256 e^{12+2 x} \left (24 x+72 x^2+60 x^3+12 x^4\right )}{x^4}+\frac {65536 e^{24} \left (1+4 x^2+12 x^3+12 x^4+4 x^5\right )}{x^8}+\frac {4096 e^{18+x} \left (8 x+40 x^2+60 x^3+32 x^4+4 x^5\right )}{x^6}\right )}{65536 e^{24}} \, dx=\frac {{\left (x^{9} e^{\left (4 \, x + 36\right )} + 64 \, x^{8} e^{\left (3 \, x + 42\right )} + 64 \, x^{7} e^{\left (3 \, x + 42\right )} + 1536 \, x^{7} e^{\left (2 \, x + 48\right )} + 3072 \, x^{6} e^{\left (2 \, x + 48\right )} + 16384 \, x^{6} e^{\left (x + 54\right )} + 65536 \, x^{5} e^{60} + 1536 \, x^{5} e^{\left (2 \, x + 48\right )} + 49152 \, x^{5} e^{\left (x + 54\right )} + 262144 \, x^{4} e^{60} + 49152 \, x^{4} e^{\left (x + 54\right )} + 393216 \, x^{3} e^{60} + 16384 \, x^{3} e^{\left (x + 54\right )} + 262144 \, x^{2} e^{60} - 65536 \, e^{60}\right )} e^{\left (-60\right )}}{65536 \, x} \]
integrate(((4*x^5+12*x^4+12*x^3+4*x^2+1)*exp(log(4/x)+3)^8+(4*x^5+32*x^4+6 0*x^3+40*x^2+8*x)*exp(x)*exp(log(4/x)+3)^6+(12*x^4+60*x^3+72*x^2+24*x)*exp (x)^2*exp(log(4/x)+3)^4+(12*x^3+40*x^2+24*x)*exp(x)^3*exp(log(4/x)+3)^2+(4 *x^2+8*x)*exp(x)^4)/x^2/exp(log(4/x)+3)^8,x, algorithm=\
1/65536*(x^9*e^(4*x + 36) + 64*x^8*e^(3*x + 42) + 64*x^7*e^(3*x + 42) + 15 36*x^7*e^(2*x + 48) + 3072*x^6*e^(2*x + 48) + 16384*x^6*e^(x + 54) + 65536 *x^5*e^60 + 1536*x^5*e^(2*x + 48) + 49152*x^5*e^(x + 54) + 262144*x^4*e^60 + 49152*x^4*e^(x + 54) + 393216*x^3*e^60 + 16384*x^3*e^(x + 54) + 262144* x^2*e^60 - 65536*e^60)*e^(-60)/x
Time = 8.64 (sec) , antiderivative size = 124, normalized size of antiderivative = 5.17 \[ \int \frac {x^6 \left (e^{4 x} \left (8 x+4 x^2\right )+\frac {16 e^{6+3 x} \left (24 x+40 x^2+12 x^3\right )}{x^2}+\frac {256 e^{12+2 x} \left (24 x+72 x^2+60 x^3+12 x^4\right )}{x^4}+\frac {65536 e^{24} \left (1+4 x^2+12 x^3+12 x^4+4 x^5\right )}{x^8}+\frac {4096 e^{18+x} \left (8 x+40 x^2+60 x^3+32 x^4+4 x^5\right )}{x^6}\right )}{65536 e^{24}} \, dx=4\,x+\frac {x^2\,{\mathrm {e}}^{x-6}}{4}+\frac {3\,x^3\,{\mathrm {e}}^{x-6}}{4}+\frac {3\,x^4\,{\mathrm {e}}^{x-6}}{4}+\frac {x^5\,{\mathrm {e}}^{x-6}}{4}+\frac {3\,x^4\,{\mathrm {e}}^{2\,x-12}}{128}+\frac {3\,x^5\,{\mathrm {e}}^{2\,x-12}}{64}+\frac {3\,x^6\,{\mathrm {e}}^{2\,x-12}}{128}+\frac {x^6\,{\mathrm {e}}^{3\,x-18}}{1024}+\frac {x^7\,{\mathrm {e}}^{3\,x-18}}{1024}+\frac {x^8\,{\mathrm {e}}^{4\,x-24}}{65536}-\frac {1}{x}+6\,x^2+4\,x^3+x^4 \]
int((exp(- 8*log(4/x) - 24)*(exp(4*x)*(8*x + 4*x^2) + exp(8*log(4/x) + 24) *(4*x^2 + 12*x^3 + 12*x^4 + 4*x^5 + 1) + exp(3*x)*exp(2*log(4/x) + 6)*(24* x + 40*x^2 + 12*x^3) + exp(6*log(4/x) + 18)*exp(x)*(8*x + 40*x^2 + 60*x^3 + 32*x^4 + 4*x^5) + exp(2*x)*exp(4*log(4/x) + 12)*(24*x + 72*x^2 + 60*x^3 + 12*x^4)))/x^2,x)