Integrand size = 291, antiderivative size = 23 \[ \int \frac {e^{-16-16 x} \left (-32 e^{2+2 x} x^{21}+3 x^{24}-2 x^{25}+\left (7168 e^{4+4 x} x^{18}+e^{2+2 x} \left (-672 x^{21}+448 x^{22}\right )\right ) \log (x)+\left (-688128 e^{6+6 x} x^{15}+e^{4+4 x} \left (64512 x^{18}-43008 x^{19}\right )\right ) \log ^2(x)+\left (36700160 e^{8+8 x} x^{12}+e^{6+6 x} \left (-3440640 x^{15}+2293760 x^{16}\right )\right ) \log ^3(x)+\left (-1174405120 e^{10+10 x} x^9+e^{8+8 x} \left (110100480 x^{12}-73400320 x^{13}\right )\right ) \log ^4(x)+\left (22548578304 e^{12+12 x} x^6+e^{10+10 x} \left (-2113929216 x^9+1409286144 x^{10}\right )\right ) \log ^5(x)+\left (-240518168576 e^{14+14 x} x^3+e^{12+12 x} \left (22548578304 x^6-15032385536 x^7\right )\right ) \log ^6(x)+\left (1099511627776 e^{16+16 x}+e^{14+14 x} \left (-103079215104 x^3+68719476736 x^4\right )\right ) \log ^7(x)\right )}{2097152 x} \, dx=256 \left (-\frac {1}{16} e^{-2-2 x} x^3+2 \log (x)\right )^8 \] Output:
256*(2*ln(x)-1/16*x^3/exp(1+x)^2)^8
Time = 0.46 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.22 \[ \int \frac {e^{-16-16 x} \left (-32 e^{2+2 x} x^{21}+3 x^{24}-2 x^{25}+\left (7168 e^{4+4 x} x^{18}+e^{2+2 x} \left (-672 x^{21}+448 x^{22}\right )\right ) \log (x)+\left (-688128 e^{6+6 x} x^{15}+e^{4+4 x} \left (64512 x^{18}-43008 x^{19}\right )\right ) \log ^2(x)+\left (36700160 e^{8+8 x} x^{12}+e^{6+6 x} \left (-3440640 x^{15}+2293760 x^{16}\right )\right ) \log ^3(x)+\left (-1174405120 e^{10+10 x} x^9+e^{8+8 x} \left (110100480 x^{12}-73400320 x^{13}\right )\right ) \log ^4(x)+\left (22548578304 e^{12+12 x} x^6+e^{10+10 x} \left (-2113929216 x^9+1409286144 x^{10}\right )\right ) \log ^5(x)+\left (-240518168576 e^{14+14 x} x^3+e^{12+12 x} \left (22548578304 x^6-15032385536 x^7\right )\right ) \log ^6(x)+\left (1099511627776 e^{16+16 x}+e^{14+14 x} \left (-103079215104 x^3+68719476736 x^4\right )\right ) \log ^7(x)\right )}{2097152 x} \, dx=\frac {e^{-16 (1+x)} \left (x^3-32 e^{2+2 x} \log (x)\right )^8}{16777216} \] Input:
Integrate[(E^(-16 - 16*x)*(-32*E^(2 + 2*x)*x^21 + 3*x^24 - 2*x^25 + (7168* E^(4 + 4*x)*x^18 + E^(2 + 2*x)*(-672*x^21 + 448*x^22))*Log[x] + (-688128*E ^(6 + 6*x)*x^15 + E^(4 + 4*x)*(64512*x^18 - 43008*x^19))*Log[x]^2 + (36700 160*E^(8 + 8*x)*x^12 + E^(6 + 6*x)*(-3440640*x^15 + 2293760*x^16))*Log[x]^ 3 + (-1174405120*E^(10 + 10*x)*x^9 + E^(8 + 8*x)*(110100480*x^12 - 7340032 0*x^13))*Log[x]^4 + (22548578304*E^(12 + 12*x)*x^6 + E^(10 + 10*x)*(-21139 29216*x^9 + 1409286144*x^10))*Log[x]^5 + (-240518168576*E^(14 + 14*x)*x^3 + E^(12 + 12*x)*(22548578304*x^6 - 15032385536*x^7))*Log[x]^6 + (109951162 7776*E^(16 + 16*x) + E^(14 + 14*x)*(-103079215104*x^3 + 68719476736*x^4))* Log[x]^7))/(2097152*x),x]
Output:
(x^3 - 32*E^(2 + 2*x)*Log[x])^8/(16777216*E^(16*(1 + x)))
Leaf count is larger than twice the leaf count of optimal. \(135\) vs. \(2(23)=46\).
Time = 13.28 (sec) , antiderivative size = 135, normalized size of antiderivative = 5.87, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {27, 25, 7239, 7293, 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.
| \(\displaystyle \int \frac {e^{-16 x-16} \left (-2 x^{25}+3 x^{24}-32 e^{2 x+2} x^{21}+\left (e^{14 x+14} \left (68719476736 x^4-103079215104 x^3\right )+1099511627776 e^{16 x+16}\right ) \log ^7(x)+\left (7168 e^{4 x+4} x^{18}+e^{2 x+2} \left (448 x^{22}-672 x^{21}\right )\right ) \log (x)+\left (e^{4 x+4} \left (64512 x^{18}-43008 x^{19}\right )-688128 e^{6 x+6} x^{15}\right ) \log ^2(x)+\left (36700160 e^{8 x+8} x^{12}+e^{6 x+6} \left (2293760 x^{16}-3440640 x^{15}\right )\right ) \log ^3(x)+\left (e^{8 x+8} \left (110100480 x^{12}-73400320 x^{13}\right )-1174405120 e^{10 x+10} x^9\right ) \log ^4(x)+\left (22548578304 e^{12 x+12} x^6+e^{10 x+10} \left (1409286144 x^{10}-2113929216 x^9\right )\right ) \log ^5(x)+\left (e^{12 x+12} \left (22548578304 x^6-15032385536 x^7\right )-240518168576 e^{14 x+14} x^3\right ) \log ^6(x)\right )}{2097152 x} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int -\frac {e^{-16 x-16} \left (2 x^{25}-3 x^{24}+32 e^{2 x+2} x^{21}-34359738368 \left (32 e^{16 x+16}-e^{14 x+14} \left (3 x^3-2 x^4\right )\right ) \log ^7(x)+7516192768 \left (32 e^{14 x+14} x^3-e^{12 x+12} \left (3 x^6-2 x^7\right )\right ) \log ^6(x)-704643072 \left (32 e^{12 x+12} x^6-e^{10 x+10} \left (3 x^9-2 x^{10}\right )\right ) \log ^5(x)+36700160 \left (32 e^{10 x+10} x^9-e^{8 x+8} \left (3 x^{12}-2 x^{13}\right )\right ) \log ^4(x)-1146880 \left (32 e^{8 x+8} x^{12}-e^{6 x+6} \left (3 x^{15}-2 x^{16}\right )\right ) \log ^3(x)+21504 \left (32 e^{6 x+6} x^{15}-e^{4 x+4} \left (3 x^{18}-2 x^{19}\right )\right ) \log ^2(x)-224 \left (32 e^{4 x+4} x^{18}-e^{2 x+2} \left (3 x^{21}-2 x^{22}\right )\right ) \log (x)\right )}{x}dx}{2097152}\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {\int \frac {e^{-16 x-16} \left (2 x^{25}-3 x^{24}+32 e^{2 x+2} x^{21}-34359738368 \left (32 e^{16 x+16}-e^{14 x+14} \left (3 x^3-2 x^4\right )\right ) \log ^7(x)+7516192768 \left (32 e^{14 x+14} x^3-e^{12 x+12} \left (3 x^6-2 x^7\right )\right ) \log ^6(x)-704643072 \left (32 e^{12 x+12} x^6-e^{10 x+10} \left (3 x^9-2 x^{10}\right )\right ) \log ^5(x)+36700160 \left (32 e^{10 x+10} x^9-e^{8 x+8} \left (3 x^{12}-2 x^{13}\right )\right ) \log ^4(x)-1146880 \left (32 e^{8 x+8} x^{12}-e^{6 x+6} \left (3 x^{15}-2 x^{16}\right )\right ) \log ^3(x)+21504 \left (32 e^{6 x+6} x^{15}-e^{4 x+4} \left (3 x^{18}-2 x^{19}\right )\right ) \log ^2(x)-224 \left (32 e^{4 x+4} x^{18}-e^{2 x+2} \left (3 x^{21}-2 x^{22}\right )\right ) \log (x)\right )}{x}dx}{2097152}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {e^{-16 x-16} \left ((2 x-3) x^3+32 e^{2 x+2}\right ) \left (x^3-32 e^{2 x+2} \log (x)\right )^7}{x}dx}{2097152}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (e^{-16 x-16} (2 x-3) x^{23}-32 e^{-14 x-14} (14 x \log (x)-21 \log (x)-1) x^{20}+7168 e^{-12 x-12} \log (x) (6 x \log (x)-9 \log (x)-1) x^{17}-229376 e^{-10 x-10} \log ^2(x) (10 x \log (x)-15 \log (x)-3) x^{14}+36700160 e^{-8 x-8} \log ^3(x) (2 x \log (x)-3 \log (x)-1) x^{11}-234881024 e^{-6 x-6} \log ^4(x) (6 x \log (x)-9 \log (x)-5) x^8+7516192768 e^{-4 x-4} \log ^5(x) (2 x \log (x)-3 \log (x)-3) x^5-34359738368 e^{-2 x-2} \log ^6(x) (2 x \log (x)-3 \log (x)-7) x^2-\frac {1099511627776 \log ^7(x)}{x}\right )dx}{2097152}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {\frac {1}{8} e^{-16 x-16} x^{24}-32 e^{-14 x-14} x^{21} \log (x)+3584 e^{-12 x-12} x^{18} \log ^2(x)-229376 e^{-10 x-10} x^{15} \log ^3(x)+9175040 e^{-8 x-8} x^{12} \log ^4(x)-234881024 e^{-6 x-6} x^9 \log ^5(x)+3758096384 e^{-4 x-4} x^6 \log ^6(x)-34359738368 e^{-2 x-2} x^3 \log ^7(x)+137438953472 \log ^8(x)}{2097152}\) |
Input:
Int[(E^(-16 - 16*x)*(-32*E^(2 + 2*x)*x^21 + 3*x^24 - 2*x^25 + (7168*E^(4 + 4*x)*x^18 + E^(2 + 2*x)*(-672*x^21 + 448*x^22))*Log[x] + (-688128*E^(6 + 6*x)*x^15 + E^(4 + 4*x)*(64512*x^18 - 43008*x^19))*Log[x]^2 + (36700160*E^ (8 + 8*x)*x^12 + E^(6 + 6*x)*(-3440640*x^15 + 2293760*x^16))*Log[x]^3 + (- 1174405120*E^(10 + 10*x)*x^9 + E^(8 + 8*x)*(110100480*x^12 - 73400320*x^13 ))*Log[x]^4 + (22548578304*E^(12 + 12*x)*x^6 + E^(10 + 10*x)*(-2113929216* x^9 + 1409286144*x^10))*Log[x]^5 + (-240518168576*E^(14 + 14*x)*x^3 + E^(1 2 + 12*x)*(22548578304*x^6 - 15032385536*x^7))*Log[x]^6 + (1099511627776*E ^(16 + 16*x) + E^(14 + 14*x)*(-103079215104*x^3 + 68719476736*x^4))*Log[x] ^7))/(2097152*x),x]
Output:
((E^(-16 - 16*x)*x^24)/8 - 32*E^(-14 - 14*x)*x^21*Log[x] + 3584*E^(-12 - 1 2*x)*x^18*Log[x]^2 - 229376*E^(-10 - 10*x)*x^15*Log[x]^3 + 9175040*E^(-8 - 8*x)*x^12*Log[x]^4 - 234881024*E^(-6 - 6*x)*x^9*Log[x]^5 + 3758096384*E^( -4 - 4*x)*x^6*Log[x]^6 - 34359738368*E^(-2 - 2*x)*x^3*Log[x]^7 + 137438953 472*Log[x]^8)/2097152
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(121\) vs. \(2(20)=40\).
Time = 0.04 (sec) , antiderivative size = 122, normalized size of antiderivative = 5.30
\[65536 \ln \left (x \right )^{8}-16384 x^{3} {\mathrm e}^{-2-2 x} \ln \left (x \right )^{7}+1792 x^{6} {\mathrm e}^{-4-4 x} \ln \left (x \right )^{6}-112 x^{9} {\mathrm e}^{-6 x -6} \ln \left (x \right )^{5}+\frac {35 x^{12} {\mathrm e}^{-8 x -8} \ln \left (x \right )^{4}}{8}-\frac {7 x^{15} {\mathrm e}^{-10 x -10} \ln \left (x \right )^{3}}{64}+\frac {7 x^{18} {\mathrm e}^{-12 x -12} \ln \left (x \right )^{2}}{4096}-\frac {x^{21} {\mathrm e}^{-14-14 x} \ln \left (x \right )}{65536}+\frac {x^{24} {\mathrm e}^{-16 x -16}}{16777216}\]
Input:
int(1/2097152*((1099511627776*exp(1+x)^16+(68719476736*x^4-103079215104*x^ 3)*exp(1+x)^14)*ln(x)^7+(-240518168576*x^3*exp(1+x)^14+(-15032385536*x^7+2 2548578304*x^6)*exp(1+x)^12)*ln(x)^6+(22548578304*x^6*exp(1+x)^12+(1409286 144*x^10-2113929216*x^9)*exp(1+x)^10)*ln(x)^5+(-1174405120*x^9*exp(1+x)^10 +(-73400320*x^13+110100480*x^12)*exp(1+x)^8)*ln(x)^4+(36700160*x^12*exp(1+ x)^8+(2293760*x^16-3440640*x^15)*exp(1+x)^6)*ln(x)^3+(-688128*x^15*exp(1+x )^6+(-43008*x^19+64512*x^18)*exp(1+x)^4)*ln(x)^2+(7168*x^18*exp(1+x)^4+(44 8*x^22-672*x^21)*exp(1+x)^2)*ln(x)-32*x^21*exp(1+x)^2-2*x^25+3*x^24)/x/exp (1+x)^16,x)
Output:
65536*ln(x)^8-16384*x^3*exp(-2-2*x)*ln(x)^7+1792*x^6*exp(-4-4*x)*ln(x)^6-1 12*x^9*exp(-6*x-6)*ln(x)^5+35/8*x^12*exp(-8*x-8)*ln(x)^4-7/64*x^15*exp(-10 *x-10)*ln(x)^3+7/4096*x^18*exp(-12*x-12)*ln(x)^2-1/65536*x^21*exp(-14-14*x )*ln(x)+1/16777216*x^24*exp(-16*x-16)
Leaf count of result is larger than twice the leaf count of optimal. 127 vs. \(2 (19) = 38\).
Time = 0.10 (sec) , antiderivative size = 127, normalized size of antiderivative = 5.52 \[ \int \frac {e^{-16-16 x} \left (-32 e^{2+2 x} x^{21}+3 x^{24}-2 x^{25}+\left (7168 e^{4+4 x} x^{18}+e^{2+2 x} \left (-672 x^{21}+448 x^{22}\right )\right ) \log (x)+\left (-688128 e^{6+6 x} x^{15}+e^{4+4 x} \left (64512 x^{18}-43008 x^{19}\right )\right ) \log ^2(x)+\left (36700160 e^{8+8 x} x^{12}+e^{6+6 x} \left (-3440640 x^{15}+2293760 x^{16}\right )\right ) \log ^3(x)+\left (-1174405120 e^{10+10 x} x^9+e^{8+8 x} \left (110100480 x^{12}-73400320 x^{13}\right )\right ) \log ^4(x)+\left (22548578304 e^{12+12 x} x^6+e^{10+10 x} \left (-2113929216 x^9+1409286144 x^{10}\right )\right ) \log ^5(x)+\left (-240518168576 e^{14+14 x} x^3+e^{12+12 x} \left (22548578304 x^6-15032385536 x^7\right )\right ) \log ^6(x)+\left (1099511627776 e^{16+16 x}+e^{14+14 x} \left (-103079215104 x^3+68719476736 x^4\right )\right ) \log ^7(x)\right )}{2097152 x} \, dx=\frac {1}{16777216} \, {\left (x^{24} - 256 \, x^{21} e^{\left (2 \, x + 2\right )} \log \left (x\right ) + 28672 \, x^{18} e^{\left (4 \, x + 4\right )} \log \left (x\right )^{2} - 1835008 \, x^{15} e^{\left (6 \, x + 6\right )} \log \left (x\right )^{3} + 73400320 \, x^{12} e^{\left (8 \, x + 8\right )} \log \left (x\right )^{4} - 1879048192 \, x^{9} e^{\left (10 \, x + 10\right )} \log \left (x\right )^{5} + 30064771072 \, x^{6} e^{\left (12 \, x + 12\right )} \log \left (x\right )^{6} - 274877906944 \, x^{3} e^{\left (14 \, x + 14\right )} \log \left (x\right )^{7} + 1099511627776 \, e^{\left (16 \, x + 16\right )} \log \left (x\right )^{8}\right )} e^{\left (-16 \, x - 16\right )} \] Input:
integrate(1/2097152*((1099511627776*exp(1+x)^16+(68719476736*x^4-103079215 104*x^3)*exp(1+x)^14)*log(x)^7+(-240518168576*x^3*exp(1+x)^14+(-1503238553 6*x^7+22548578304*x^6)*exp(1+x)^12)*log(x)^6+(22548578304*x^6*exp(1+x)^12+ (1409286144*x^10-2113929216*x^9)*exp(1+x)^10)*log(x)^5+(-1174405120*x^9*ex p(1+x)^10+(-73400320*x^13+110100480*x^12)*exp(1+x)^8)*log(x)^4+(36700160*x ^12*exp(1+x)^8+(2293760*x^16-3440640*x^15)*exp(1+x)^6)*log(x)^3+(-688128*x ^15*exp(1+x)^6+(-43008*x^19+64512*x^18)*exp(1+x)^4)*log(x)^2+(7168*x^18*ex p(1+x)^4+(448*x^22-672*x^21)*exp(1+x)^2)*log(x)-32*x^21*exp(1+x)^2-2*x^25+ 3*x^24)/x/exp(1+x)^16,x, algorithm="fricas")
Output:
1/16777216*(x^24 - 256*x^21*e^(2*x + 2)*log(x) + 28672*x^18*e^(4*x + 4)*lo g(x)^2 - 1835008*x^15*e^(6*x + 6)*log(x)^3 + 73400320*x^12*e^(8*x + 8)*log (x)^4 - 1879048192*x^9*e^(10*x + 10)*log(x)^5 + 30064771072*x^6*e^(12*x + 12)*log(x)^6 - 274877906944*x^3*e^(14*x + 14)*log(x)^7 + 1099511627776*e^( 16*x + 16)*log(x)^8)*e^(-16*x - 16)
Leaf count of result is larger than twice the leaf count of optimal. 153 vs. \(2 (20) = 40\).
Time = 0.64 (sec) , antiderivative size = 153, normalized size of antiderivative = 6.65 \[ \int \frac {e^{-16-16 x} \left (-32 e^{2+2 x} x^{21}+3 x^{24}-2 x^{25}+\left (7168 e^{4+4 x} x^{18}+e^{2+2 x} \left (-672 x^{21}+448 x^{22}\right )\right ) \log (x)+\left (-688128 e^{6+6 x} x^{15}+e^{4+4 x} \left (64512 x^{18}-43008 x^{19}\right )\right ) \log ^2(x)+\left (36700160 e^{8+8 x} x^{12}+e^{6+6 x} \left (-3440640 x^{15}+2293760 x^{16}\right )\right ) \log ^3(x)+\left (-1174405120 e^{10+10 x} x^9+e^{8+8 x} \left (110100480 x^{12}-73400320 x^{13}\right )\right ) \log ^4(x)+\left (22548578304 e^{12+12 x} x^6+e^{10+10 x} \left (-2113929216 x^9+1409286144 x^{10}\right )\right ) \log ^5(x)+\left (-240518168576 e^{14+14 x} x^3+e^{12+12 x} \left (22548578304 x^6-15032385536 x^7\right )\right ) \log ^6(x)+\left (1099511627776 e^{16+16 x}+e^{14+14 x} \left (-103079215104 x^3+68719476736 x^4\right )\right ) \log ^7(x)\right )}{2097152 x} \, dx=\frac {x^{24} e^{- 16 x - 16}}{16777216} - \frac {x^{21} e^{- 14 x - 14} \log {\left (x \right )}}{65536} + \frac {7 x^{18} e^{- 12 x - 12} \log {\left (x \right )}^{2}}{4096} - \frac {7 x^{15} e^{- 10 x - 10} \log {\left (x \right )}^{3}}{64} + \frac {35 x^{12} e^{- 8 x - 8} \log {\left (x \right )}^{4}}{8} - 112 x^{9} e^{- 6 x - 6} \log {\left (x \right )}^{5} + 1792 x^{6} e^{- 4 x - 4} \log {\left (x \right )}^{6} - 16384 x^{3} e^{- 2 x - 2} \log {\left (x \right )}^{7} + 65536 \log {\left (x \right )}^{8} \] Input:
integrate(1/2097152*((1099511627776*exp(1+x)**16+(68719476736*x**4-1030792 15104*x**3)*exp(1+x)**14)*ln(x)**7+(-240518168576*x**3*exp(1+x)**14+(-1503 2385536*x**7+22548578304*x**6)*exp(1+x)**12)*ln(x)**6+(22548578304*x**6*ex p(1+x)**12+(1409286144*x**10-2113929216*x**9)*exp(1+x)**10)*ln(x)**5+(-117 4405120*x**9*exp(1+x)**10+(-73400320*x**13+110100480*x**12)*exp(1+x)**8)*l n(x)**4+(36700160*x**12*exp(1+x)**8+(2293760*x**16-3440640*x**15)*exp(1+x) **6)*ln(x)**3+(-688128*x**15*exp(1+x)**6+(-43008*x**19+64512*x**18)*exp(1+ x)**4)*ln(x)**2+(7168*x**18*exp(1+x)**4+(448*x**22-672*x**21)*exp(1+x)**2) *ln(x)-32*x**21*exp(1+x)**2-2*x**25+3*x**24)/x/exp(1+x)**16,x)
Output:
x**24*exp(-16*x - 16)/16777216 - x**21*exp(-14*x - 14)*log(x)/65536 + 7*x* *18*exp(-12*x - 12)*log(x)**2/4096 - 7*x**15*exp(-10*x - 10)*log(x)**3/64 + 35*x**12*exp(-8*x - 8)*log(x)**4/8 - 112*x**9*exp(-6*x - 6)*log(x)**5 + 1792*x**6*exp(-4*x - 4)*log(x)**6 - 16384*x**3*exp(-2*x - 2)*log(x)**7 + 6 5536*log(x)**8
Leaf count of result is larger than twice the leaf count of optimal. 576 vs. \(2 (19) = 38\).
Time = 0.21 (sec) , antiderivative size = 576, normalized size of antiderivative = 25.04 \[ \int \frac {e^{-16-16 x} \left (-32 e^{2+2 x} x^{21}+3 x^{24}-2 x^{25}+\left (7168 e^{4+4 x} x^{18}+e^{2+2 x} \left (-672 x^{21}+448 x^{22}\right )\right ) \log (x)+\left (-688128 e^{6+6 x} x^{15}+e^{4+4 x} \left (64512 x^{18}-43008 x^{19}\right )\right ) \log ^2(x)+\left (36700160 e^{8+8 x} x^{12}+e^{6+6 x} \left (-3440640 x^{15}+2293760 x^{16}\right )\right ) \log ^3(x)+\left (-1174405120 e^{10+10 x} x^9+e^{8+8 x} \left (110100480 x^{12}-73400320 x^{13}\right )\right ) \log ^4(x)+\left (22548578304 e^{12+12 x} x^6+e^{10+10 x} \left (-2113929216 x^9+1409286144 x^{10}\right )\right ) \log ^5(x)+\left (-240518168576 e^{14+14 x} x^3+e^{12+12 x} \left (22548578304 x^6-15032385536 x^7\right )\right ) \log ^6(x)+\left (1099511627776 e^{16+16 x}+e^{14+14 x} \left (-103079215104 x^3+68719476736 x^4\right )\right ) \log ^7(x)\right )}{2097152 x} \, dx=\text {Too large to display} \] Input:
integrate(1/2097152*((1099511627776*exp(1+x)^16+(68719476736*x^4-103079215 104*x^3)*exp(1+x)^14)*log(x)^7+(-240518168576*x^3*exp(1+x)^14+(-1503238553 6*x^7+22548578304*x^6)*exp(1+x)^12)*log(x)^6+(22548578304*x^6*exp(1+x)^12+ (1409286144*x^10-2113929216*x^9)*exp(1+x)^10)*log(x)^5+(-1174405120*x^9*ex p(1+x)^10+(-73400320*x^13+110100480*x^12)*exp(1+x)^8)*log(x)^4+(36700160*x ^12*exp(1+x)^8+(2293760*x^16-3440640*x^15)*exp(1+x)^6)*log(x)^3+(-688128*x ^15*exp(1+x)^6+(-43008*x^19+64512*x^18)*exp(1+x)^4)*log(x)^2+(7168*x^18*ex p(1+x)^4+(448*x^22-672*x^21)*exp(1+x)^2)*log(x)-32*x^21*exp(1+x)^2-2*x^25+ 3*x^24)/x/exp(1+x)^16,x, algorithm="maxima")
Output:
1/5976303958948914397184*(10213410086094336128*x^18*e^(-12*x + 2)*log(x)^2 - 653658245510037512192*x^15*e^(-10*x + 4)*log(x)^3 + 2614632982040150048 7680*x^12*e^(-8*x + 6)*log(x)^4 - 669346043402278412484608*x^9*e^(-6*x + 8 )*log(x)^5 + 10709536694436454599753728*x^6*e^(-4*x + 10)*log(x)^6 - 97915 764063419013483462656*x^3*e^(-2*x + 12)*log(x)^7 + 39166305625367605393385 0624*e^14*log(x)^8 - (91191161482985144*x^21*log(x) + 6513654391641796*x^2 0 + 9305220559488280*x^19 + 12628513616448380*x^18 + 16236660364005060*x^1 7 + 19715944727720430*x^16 + 22532508260251920*x^15 + 24141973135984200*x^ 14 + 24141973135984200*x^13 + 22417546483413900*x^12 + 19215039842926200*x ^11 + 15097531305156300*x^10 + 10783950932254500*x^9 + 6932539885020750*x^ 8 + 3961451362869000*x^7 + 1980725681434500*x^6 + 848882434900500*x^5 + 30 3172298178750*x^4 + 86620656622500*x^3 + 18561569276250*x^2 + 265165275375 0*x + 189403768125)*e^(-14*x))*e^(-14) + 1/5976303958948914397184*(6513654 391641796*x^20 + 9305220559488280*x^19 + 12628513616448380*x^18 + 16236660 364005060*x^17 + 19715944727720430*x^16 + 22532508260251920*x^15 + 2414197 3135984200*x^14 + 24141973135984200*x^13 + 22417546483413900*x^12 + 192150 39842926200*x^11 + 15097531305156300*x^10 + 10783950932254500*x^9 + 693253 9885020750*x^8 + 3961451362869000*x^7 + 1980725681434500*x^6 + 84888243490 0500*x^5 + 303172298178750*x^4 + 86620656622500*x^3 + 18561569276250*x^2 + 2651652753750*x + 189403768125)*e^(-14*x - 14) + 1/3169126500570573503...
Leaf count of result is larger than twice the leaf count of optimal. 124 vs. \(2 (19) = 38\).
Time = 0.14 (sec) , antiderivative size = 124, normalized size of antiderivative = 5.39 \[ \int \frac {e^{-16-16 x} \left (-32 e^{2+2 x} x^{21}+3 x^{24}-2 x^{25}+\left (7168 e^{4+4 x} x^{18}+e^{2+2 x} \left (-672 x^{21}+448 x^{22}\right )\right ) \log (x)+\left (-688128 e^{6+6 x} x^{15}+e^{4+4 x} \left (64512 x^{18}-43008 x^{19}\right )\right ) \log ^2(x)+\left (36700160 e^{8+8 x} x^{12}+e^{6+6 x} \left (-3440640 x^{15}+2293760 x^{16}\right )\right ) \log ^3(x)+\left (-1174405120 e^{10+10 x} x^9+e^{8+8 x} \left (110100480 x^{12}-73400320 x^{13}\right )\right ) \log ^4(x)+\left (22548578304 e^{12+12 x} x^6+e^{10+10 x} \left (-2113929216 x^9+1409286144 x^{10}\right )\right ) \log ^5(x)+\left (-240518168576 e^{14+14 x} x^3+e^{12+12 x} \left (22548578304 x^6-15032385536 x^7\right )\right ) \log ^6(x)+\left (1099511627776 e^{16+16 x}+e^{14+14 x} \left (-103079215104 x^3+68719476736 x^4\right )\right ) \log ^7(x)\right )}{2097152 x} \, dx=\frac {1}{16777216} \, {\left (x^{24} e^{\left (-16 \, x\right )} - 256 \, x^{21} e^{\left (-14 \, x + 2\right )} \log \left (x\right ) + 28672 \, x^{18} e^{\left (-12 \, x + 4\right )} \log \left (x\right )^{2} - 1835008 \, x^{15} e^{\left (-10 \, x + 6\right )} \log \left (x\right )^{3} + 73400320 \, x^{12} e^{\left (-8 \, x + 8\right )} \log \left (x\right )^{4} - 1879048192 \, x^{9} e^{\left (-6 \, x + 10\right )} \log \left (x\right )^{5} + 30064771072 \, x^{6} e^{\left (-4 \, x + 12\right )} \log \left (x\right )^{6} - 274877906944 \, x^{3} e^{\left (-2 \, x + 14\right )} \log \left (x\right )^{7} + 1099511627776 \, e^{16} \log \left (x\right )^{8}\right )} e^{\left (-16\right )} \] Input:
integrate(1/2097152*((1099511627776*exp(1+x)^16+(68719476736*x^4-103079215 104*x^3)*exp(1+x)^14)*log(x)^7+(-240518168576*x^3*exp(1+x)^14+(-1503238553 6*x^7+22548578304*x^6)*exp(1+x)^12)*log(x)^6+(22548578304*x^6*exp(1+x)^12+ (1409286144*x^10-2113929216*x^9)*exp(1+x)^10)*log(x)^5+(-1174405120*x^9*ex p(1+x)^10+(-73400320*x^13+110100480*x^12)*exp(1+x)^8)*log(x)^4+(36700160*x ^12*exp(1+x)^8+(2293760*x^16-3440640*x^15)*exp(1+x)^6)*log(x)^3+(-688128*x ^15*exp(1+x)^6+(-43008*x^19+64512*x^18)*exp(1+x)^4)*log(x)^2+(7168*x^18*ex p(1+x)^4+(448*x^22-672*x^21)*exp(1+x)^2)*log(x)-32*x^21*exp(1+x)^2-2*x^25+ 3*x^24)/x/exp(1+x)^16,x, algorithm="giac")
Output:
1/16777216*(x^24*e^(-16*x) - 256*x^21*e^(-14*x + 2)*log(x) + 28672*x^18*e^ (-12*x + 4)*log(x)^2 - 1835008*x^15*e^(-10*x + 6)*log(x)^3 + 73400320*x^12 *e^(-8*x + 8)*log(x)^4 - 1879048192*x^9*e^(-6*x + 10)*log(x)^5 + 300647710 72*x^6*e^(-4*x + 12)*log(x)^6 - 274877906944*x^3*e^(-2*x + 14)*log(x)^7 + 1099511627776*e^16*log(x)^8)*e^(-16)
Timed out. \[ \int \frac {e^{-16-16 x} \left (-32 e^{2+2 x} x^{21}+3 x^{24}-2 x^{25}+\left (7168 e^{4+4 x} x^{18}+e^{2+2 x} \left (-672 x^{21}+448 x^{22}\right )\right ) \log (x)+\left (-688128 e^{6+6 x} x^{15}+e^{4+4 x} \left (64512 x^{18}-43008 x^{19}\right )\right ) \log ^2(x)+\left (36700160 e^{8+8 x} x^{12}+e^{6+6 x} \left (-3440640 x^{15}+2293760 x^{16}\right )\right ) \log ^3(x)+\left (-1174405120 e^{10+10 x} x^9+e^{8+8 x} \left (110100480 x^{12}-73400320 x^{13}\right )\right ) \log ^4(x)+\left (22548578304 e^{12+12 x} x^6+e^{10+10 x} \left (-2113929216 x^9+1409286144 x^{10}\right )\right ) \log ^5(x)+\left (-240518168576 e^{14+14 x} x^3+e^{12+12 x} \left (22548578304 x^6-15032385536 x^7\right )\right ) \log ^6(x)+\left (1099511627776 e^{16+16 x}+e^{14+14 x} \left (-103079215104 x^3+68719476736 x^4\right )\right ) \log ^7(x)\right )}{2097152 x} \, dx=\int -\frac {{\mathrm {e}}^{-16\,x-16}\,\left (\frac {\ln \left (x\right )\,\left ({\mathrm {e}}^{2\,x+2}\,\left (672\,x^{21}-448\,x^{22}\right )-7168\,x^{18}\,{\mathrm {e}}^{4\,x+4}\right )}{2097152}-\frac {{\ln \left (x\right )}^6\,\left ({\mathrm {e}}^{12\,x+12}\,\left (22548578304\,x^6-15032385536\,x^7\right )-240518168576\,x^3\,{\mathrm {e}}^{14\,x+14}\right )}{2097152}-\frac {{\ln \left (x\right )}^2\,\left ({\mathrm {e}}^{4\,x+4}\,\left (64512\,x^{18}-43008\,x^{19}\right )-688128\,x^{15}\,{\mathrm {e}}^{6\,x+6}\right )}{2097152}+\frac {{\ln \left (x\right )}^3\,\left ({\mathrm {e}}^{6\,x+6}\,\left (3440640\,x^{15}-2293760\,x^{16}\right )-36700160\,x^{12}\,{\mathrm {e}}^{8\,x+8}\right )}{2097152}+\frac {{\ln \left (x\right )}^5\,\left ({\mathrm {e}}^{10\,x+10}\,\left (2113929216\,x^9-1409286144\,x^{10}\right )-22548578304\,x^6\,{\mathrm {e}}^{12\,x+12}\right )}{2097152}-\frac {{\ln \left (x\right )}^7\,\left (1099511627776\,{\mathrm {e}}^{16\,x+16}-{\mathrm {e}}^{14\,x+14}\,\left (103079215104\,x^3-68719476736\,x^4\right )\right )}{2097152}+\frac {x^{21}\,{\mathrm {e}}^{2\,x+2}}{65536}-\frac {3\,x^{24}}{2097152}+\frac {x^{25}}{1048576}+\frac {{\ln \left (x\right )}^4\,\left (1174405120\,x^9\,{\mathrm {e}}^{10\,x+10}-{\mathrm {e}}^{8\,x+8}\,\left (110100480\,x^{12}-73400320\,x^{13}\right )\right )}{2097152}\right )}{x} \,d x \] Input:
int(-(exp(- 16*x - 16)*((log(x)*(exp(2*x + 2)*(672*x^21 - 448*x^22) - 7168 *x^18*exp(4*x + 4)))/2097152 - (log(x)^6*(exp(12*x + 12)*(22548578304*x^6 - 15032385536*x^7) - 240518168576*x^3*exp(14*x + 14)))/2097152 - (log(x)^2 *(exp(4*x + 4)*(64512*x^18 - 43008*x^19) - 688128*x^15*exp(6*x + 6)))/2097 152 + (log(x)^3*(exp(6*x + 6)*(3440640*x^15 - 2293760*x^16) - 36700160*x^1 2*exp(8*x + 8)))/2097152 + (log(x)^5*(exp(10*x + 10)*(2113929216*x^9 - 140 9286144*x^10) - 22548578304*x^6*exp(12*x + 12)))/2097152 - (log(x)^7*(1099 511627776*exp(16*x + 16) - exp(14*x + 14)*(103079215104*x^3 - 68719476736* x^4)))/2097152 + (x^21*exp(2*x + 2))/65536 - (3*x^24)/2097152 + x^25/10485 76 + (log(x)^4*(1174405120*x^9*exp(10*x + 10) - exp(8*x + 8)*(110100480*x^ 12 - 73400320*x^13)))/2097152))/x,x)
Output:
int(-(exp(- 16*x - 16)*((log(x)*(exp(2*x + 2)*(672*x^21 - 448*x^22) - 7168 *x^18*exp(4*x + 4)))/2097152 - (log(x)^6*(exp(12*x + 12)*(22548578304*x^6 - 15032385536*x^7) - 240518168576*x^3*exp(14*x + 14)))/2097152 - (log(x)^2 *(exp(4*x + 4)*(64512*x^18 - 43008*x^19) - 688128*x^15*exp(6*x + 6)))/2097 152 + (log(x)^3*(exp(6*x + 6)*(3440640*x^15 - 2293760*x^16) - 36700160*x^1 2*exp(8*x + 8)))/2097152 + (log(x)^5*(exp(10*x + 10)*(2113929216*x^9 - 140 9286144*x^10) - 22548578304*x^6*exp(12*x + 12)))/2097152 - (log(x)^7*(1099 511627776*exp(16*x + 16) - exp(14*x + 14)*(103079215104*x^3 - 68719476736* x^4)))/2097152 + (x^21*exp(2*x + 2))/65536 - (3*x^24)/2097152 + x^25/10485 76 + (log(x)^4*(1174405120*x^9*exp(10*x + 10) - exp(8*x + 8)*(110100480*x^ 12 - 73400320*x^13)))/2097152))/x, x)
Time = 0.18 (sec) , antiderivative size = 147, normalized size of antiderivative = 6.39 \[ \int \frac {e^{-16-16 x} \left (-32 e^{2+2 x} x^{21}+3 x^{24}-2 x^{25}+\left (7168 e^{4+4 x} x^{18}+e^{2+2 x} \left (-672 x^{21}+448 x^{22}\right )\right ) \log (x)+\left (-688128 e^{6+6 x} x^{15}+e^{4+4 x} \left (64512 x^{18}-43008 x^{19}\right )\right ) \log ^2(x)+\left (36700160 e^{8+8 x} x^{12}+e^{6+6 x} \left (-3440640 x^{15}+2293760 x^{16}\right )\right ) \log ^3(x)+\left (-1174405120 e^{10+10 x} x^9+e^{8+8 x} \left (110100480 x^{12}-73400320 x^{13}\right )\right ) \log ^4(x)+\left (22548578304 e^{12+12 x} x^6+e^{10+10 x} \left (-2113929216 x^9+1409286144 x^{10}\right )\right ) \log ^5(x)+\left (-240518168576 e^{14+14 x} x^3+e^{12+12 x} \left (22548578304 x^6-15032385536 x^7\right )\right ) \log ^6(x)+\left (1099511627776 e^{16+16 x}+e^{14+14 x} \left (-103079215104 x^3+68719476736 x^4\right )\right ) \log ^7(x)\right )}{2097152 x} \, dx=\frac {1099511627776 e^{16 x} \mathrm {log}\left (x \right )^{8} e^{16}-274877906944 e^{14 x} \mathrm {log}\left (x \right )^{7} e^{14} x^{3}+30064771072 e^{12 x} \mathrm {log}\left (x \right )^{6} e^{12} x^{6}-1879048192 e^{10 x} \mathrm {log}\left (x \right )^{5} e^{10} x^{9}+73400320 e^{8 x} \mathrm {log}\left (x \right )^{4} e^{8} x^{12}-1835008 e^{6 x} \mathrm {log}\left (x \right )^{3} e^{6} x^{15}+28672 e^{4 x} \mathrm {log}\left (x \right )^{2} e^{4} x^{18}-256 e^{2 x} \mathrm {log}\left (x \right ) e^{2} x^{21}+x^{24}}{16777216 e^{16 x} e^{16}} \] Input:
int(1/2097152*((1099511627776*exp(1+x)^16+(68719476736*x^4-103079215104*x^ 3)*exp(1+x)^14)*log(x)^7+(-240518168576*x^3*exp(1+x)^14+(-15032385536*x^7+ 22548578304*x^6)*exp(1+x)^12)*log(x)^6+(22548578304*x^6*exp(1+x)^12+(14092 86144*x^10-2113929216*x^9)*exp(1+x)^10)*log(x)^5+(-1174405120*x^9*exp(1+x) ^10+(-73400320*x^13+110100480*x^12)*exp(1+x)^8)*log(x)^4+(36700160*x^12*ex p(1+x)^8+(2293760*x^16-3440640*x^15)*exp(1+x)^6)*log(x)^3+(-688128*x^15*ex p(1+x)^6+(-43008*x^19+64512*x^18)*exp(1+x)^4)*log(x)^2+(7168*x^18*exp(1+x) ^4+(448*x^22-672*x^21)*exp(1+x)^2)*log(x)-32*x^21*exp(1+x)^2-2*x^25+3*x^24 )/x/exp(1+x)^16,x)
Output:
(1099511627776*e**(16*x)*log(x)**8*e**16 - 274877906944*e**(14*x)*log(x)** 7*e**14*x**3 + 30064771072*e**(12*x)*log(x)**6*e**12*x**6 - 1879048192*e** (10*x)*log(x)**5*e**10*x**9 + 73400320*e**(8*x)*log(x)**4*e**8*x**12 - 183 5008*e**(6*x)*log(x)**3*e**6*x**15 + 28672*e**(4*x)*log(x)**2*e**4*x**18 - 256*e**(2*x)*log(x)*e**2*x**21 + x**24)/(16777216*e**(16*x)*e**16)