lst:=[[x^3*LambertW(a*x),x,6,-1/16*x^4-3/512*x^4/LambertW(a*x)^4+3/128*x^4/LambertW(a*x)^3-3/64*x^4/LambertW(a*x)^2+1/16*x^4/LambertW(a*x)+1/4*x^4*LambertW(a*x),1],
[x^2*LambertW(a*x),x,5,-1/9*x^3+2/81*x^3/LambertW(a*x)^3-2/27*x^3/LambertW(a*x)^2+1/9*x^3/LambertW(a*x)+1/3*x^3*LambertW(a*x),1],
[x*LambertW(a*x),x,4,-1/4*x^2-1/8*x^2/LambertW(a*x)^2+1/4*x^2/LambertW(a*x)+1/2*x^2*LambertW(a*x),1],
[LambertW(a*x),x,3,-x+x/LambertW(a*x)+x*LambertW(a*x),1],
[LambertW(a*x)/x,x,2,LambertW(a*x)+1/2*LambertW(a*x)^2,1],
[LambertW(a*x)/x^2,x,2,a*Ei(-LambertW(a*x))-LambertW(a*x)/x,1],
[LambertW(a*x)/x^3,x,2,-a^2*Ei(-2*LambertW(a*x))-LambertW(a*x)/x^2,1],
[LambertW(a*x)/x^4,x,3,3/2*a^3*Ei(-3*LambertW(a*x))-1/2*LambertW(a*x)/x^3+1/2*LambertW(a*x)^2/x^3,1],
[LambertW(a*x)/x^5,x,4,-8/3*a^4*Ei(-4*LambertW(a*x))-1/3*LambertW(a*x)/x^4+1/6*LambertW(a*x)^2/x^4-2/3*LambertW(a*x)^3/x^4,1],
[LambertW(a*x)/x^6,x,5,125/24*a^5*Ei(-5*LambertW(a*x))-1/4*LambertW(a*x)/x^5+1/12*LambertW(a*x)^2/x^5-5/24*LambertW(a*x)^3/x^5+25/24*LambertW(a*x)^4/x^5,1],
[x^2*LambertW(a*x)^2,x,6,8/27*x^3-16/243*x^3/LambertW(a*x)^3+16/81*x^3/LambertW(a*x)^2-8/27*x^3/LambertW(a*x)-2/9*x^3*LambertW(a*x)+1/3*x^3*LambertW(a*x)^2,1],
[x*LambertW(a*x)^2,x,5,3/4*x^2+3/8*x^2/LambertW(a*x)^2-3/4*x^2/LambertW(a*x)-1/2*x^2*LambertW(a*x)+1/2*x^2*LambertW(a*x)^2,1],
[LambertW(a*x)^2,x,4,4*x-4*x/LambertW(a*x)-2*x*LambertW(a*x)+x*LambertW(a*x)^2,1],
[LambertW(a*x)^2/x,x,2,1/2*LambertW(a*x)^2+1/3*LambertW(a*x)^3,1],
[LambertW(a*x)^2/x^2,x,2,-2*LambertW(a*x)/x-LambertW(a*x)^2/x,1],
[LambertW(a*x)^2/x^3,x,2,a^2*Ei(-2*LambertW(a*x))-1/2*LambertW(a*x)^2/x^2,1],
[LambertW(a*x)^2/x^4,x,2,-2*a^3*Ei(-3*LambertW(a*x))-LambertW(a*x)^2/x^3,1],
[LambertW(a*x)^2/x^5,x,3,4*a^4*Ei(-4*LambertW(a*x))-1/2*LambertW(a*x)^2/x^4+LambertW(a*x)^3/x^4,1],
[LambertW(a*x)^2/x^6,x,4,-25/3*a^5*Ei(-5*LambertW(a*x))-1/3*LambertW(a*x)^2/x^5+1/3*LambertW(a*x)^3/x^5-5/3*LambertW(a*x)^4/x^5,1],
[LambertW(a*x)^2/x^7,x,5,18*a^6*Ei(-6*LambertW(a*x))-1/4*LambertW(a*x)^2/x^6+1/6*LambertW(a*x)^3/x^6-1/2*LambertW(a*x)^4/x^6+3*LambertW(a*x)^5/x^6,1],
[x^2*LambertW(a*x)^3,x,7,-20/27*x^3+40/243*x^3/LambertW(a*x)^3-40/81*x^3/LambertW(a*x)^2+20/27*x^3/LambertW(a*x)+5/9*x^3*LambertW(a*x)-1/3*x^3*LambertW(a*x)^2+1/3*x^3*LambertW(a*x)^3,1],
[x*LambertW(a*x)^3,x,6,-9/4*x^2-9/8*x^2/LambertW(a*x)^2+9/4*x^2/LambertW(a*x)+3/2*x^2*LambertW(a*x)-3/4*x^2*LambertW(a*x)^2+1/2*x^2*LambertW(a*x)^3,1],
[LambertW(a*x)^3,x,5,-18*x+18*x/LambertW(a*x)+9*x*LambertW(a*x)-3*x*LambertW(a*x)^2+x*LambertW(a*x)^3,1],
[LambertW(a*x)^3/x,x,2,1/3*LambertW(a*x)^3+1/4*LambertW(a*x)^4,1],
[LambertW(a*x)^3/x^2,x,3,-3*LambertW(a*x)/x-3*LambertW(a*x)^2/x-LambertW(a*x)^3/x,1],
[LambertW(a*x)^3/x^3,x,2,-3/4*LambertW(a*x)^2/x^2-1/2*LambertW(a*x)^3/x^2,1],
[LambertW(a*x)^3/x^4,x,2,a^3*Ei(-3*LambertW(a*x))-1/3*LambertW(a*x)^3/x^3,1],
[LambertW(a*x)^3/x^5,x,2,-3*a^4*Ei(-4*LambertW(a*x))-LambertW(a*x)^3/x^4,1],
[LambertW(a*x)^3/x^6,x,3,15/2*a^5*Ei(-5*LambertW(a*x))-1/2*LambertW(a*x)^3/x^5+3/2*LambertW(a*x)^4/x^5,1],
[LambertW(a*x)^3/x^7,x,4,-18*a^6*Ei(-6*LambertW(a*x))-1/3*LambertW(a*x)^3/x^6+1/2*LambertW(a*x)^4/x^6-3*LambertW(a*x)^5/x^6,1],
[LambertW(a*x)^3/x^8,x,5,343/8*a^7*Ei(-7*LambertW(a*x))-1/4*LambertW(a*x)^3/x^7+1/4*LambertW(a*x)^4/x^7-7/8*LambertW(a*x)^5/x^7+49/8*LambertW(a*x)^6/x^7,1],
[x^4/LambertW(a*x),x,5,-6/3125*x^5/LambertW(a*x)^5+6/625*x^5/LambertW(a*x)^4-3/125*x^5/LambertW(a*x)^3+1/25*x^5/LambertW(a*x)^2+1/5*x^5/LambertW(a*x),1],
[x^3/LambertW(a*x),x,4,1/128*x^4/LambertW(a*x)^4-1/32*x^4/LambertW(a*x)^3+1/16*x^4/LambertW(a*x)^2+1/4*x^4/LambertW(a*x),1],
[x^2/LambertW(a*x),x,3,-1/27*x^3/LambertW(a*x)^3+1/9*x^3/LambertW(a*x)^2+1/3*x^3/LambertW(a*x),1],
[x/LambertW(a*x),x,2,1/4*x^2/LambertW(a*x)^2+1/2*x^2/LambertW(a*x),1],
[1/LambertW(a*x),x,2,Ei(LambertW(a*x))/a+x/LambertW(a*x),1],
[1/x/LambertW(a*x),x,2,ln(LambertW(a*x))-1/LambertW(a*x),1],
[1/x^2/LambertW(a*x),x,3,-1/2/x-1/2*a*Ei(-LambertW(a*x))-1/2/x/LambertW(a*x),1],
[1/x^3/LambertW(a*x),x,4,-1/6/x^2+2/3*a^2*Ei(-2*LambertW(a*x))-1/3/x^2/LambertW(a*x)+1/3*LambertW(a*x)/x^2,1],
[1/x^4/LambertW(a*x),x,5,-1/12/x^3-9/8*a^3*Ei(-3*LambertW(a*x))-1/4/x^3/LambertW(a*x)+1/8*LambertW(a*x)/x^3-3/8*LambertW(a*x)^2/x^3,1],
[x^5/LambertW(a*x)^2,x,5,-1/648*x^6/LambertW(a*x)^6+1/108*x^6/LambertW(a*x)^5-1/36*x^6/LambertW(a*x)^4+1/18*x^6/LambertW(a*x)^3+1/6*x^6/LambertW(a*x)^2,1],
[x^4/LambertW(a*x)^2,x,4,4/625*x^5/LambertW(a*x)^5-4/125*x^5/LambertW(a*x)^4+2/25*x^5/LambertW(a*x)^3+1/5*x^5/LambertW(a*x)^2,1],
[x^3/LambertW(a*x)^2,x,3,-1/32*x^4/LambertW(a*x)^4+1/8*x^4/LambertW(a*x)^3+1/4*x^4/LambertW(a*x)^2,1],
[x^2/LambertW(a*x)^2,x,2,2/9*x^3/LambertW(a*x)^3+1/3*x^3/LambertW(a*x)^2,1],
[x/LambertW(a*x)^2,x,2,Ei(2*LambertW(a*x))/a^2+1/2*x^2/LambertW(a*x)^2,1],
[1/LambertW(a*x)^2,x,2,2*Ei(LambertW(a*x))/a-x/LambertW(a*x)^2,1],
[1/x/LambertW(a*x)^2,x,2,-1/2/LambertW(a*x)^2-1/LambertW(a*x),1],
[1/x^2/LambertW(a*x)^2,x,4,1/3/x+1/3*a*Ei(-LambertW(a*x))-1/3/x/LambertW(a*x)^2-1/3/x/LambertW(a*x),1],
[1/x^3/LambertW(a*x)^2,x,5,1/6/x^2-2/3*a^2*Ei(-2*LambertW(a*x))-1/4/x^2/LambertW(a*x)^2-1/6/x^2/LambertW(a*x)-1/3*LambertW(a*x)/x^2,1],
[x^6/LambertW(a*x)^3,x,5,-18/16807*x^7/LambertW(a*x)^7+18/2401*x^7/LambertW(a*x)^6-9/343*x^7/LambertW(a*x)^5+3/49*x^7/LambertW(a*x)^4+1/7*x^7/LambertW(a*x)^3,1],
[x^5/LambertW(a*x)^3,x,4,1/216*x^6/LambertW(a*x)^6-1/36*x^6/LambertW(a*x)^5+1/12*x^6/LambertW(a*x)^4+1/6*x^6/LambertW(a*x)^3,1],
[x^4/LambertW(a*x)^3,x,3,-3/125*x^5/LambertW(a*x)^5+3/25*x^5/LambertW(a*x)^4+1/5*x^5/LambertW(a*x)^3,1],
[x^3/LambertW(a*x)^3,x,2,3/16*x^4/LambertW(a*x)^4+1/4*x^4/LambertW(a*x)^3,1],
[x^2/LambertW(a*x)^3,x,2,Ei(3*LambertW(a*x))/a^3+1/3*x^3/LambertW(a*x)^3,1],
[x/LambertW(a*x)^3,x,2,3*Ei(2*LambertW(a*x))/a^2-x^2/LambertW(a*x)^3,1],
[1/LambertW(a*x)^3,x,3,3/2*Ei(LambertW(a*x))/a-1/2*x/LambertW(a*x)^3-3/2*x/LambertW(a*x)^2,1],
[1/x/LambertW(a*x)^3,x,2,-1/3/LambertW(a*x)^3-1/2/LambertW(a*x)^2,1],
[1/x^2/LambertW(a*x)^3,x,5,-1/8/x-1/8*a*Ei(-LambertW(a*x))-1/4/x/LambertW(a*x)^3-1/4/x/LambertW(a*x)^2+1/8/x/LambertW(a*x),1],
[1/x^3/LambertW(a*x)^3,x,6,-1/10/x^2+2/5*a^2*Ei(-2*LambertW(a*x))-1/5/x^2/LambertW(a*x)^3-3/20/x^2/LambertW(a*x)^2+1/10/x^2/LambertW(a*x)+1/5*LambertW(a*x)/x^2,1],
[x^3*sqrt(c*LambertW(a*x)),x,6,-105/65536*sqrt(c)*sqrt(Pi)*erfi(2*sqrt(c*LambertW(a*x))/sqrt(c))/a^4+105/16384*c^4*x^4/(c*LambertW(a*x))^(7/2)-35/2048*c^3*x^4/(c*LambertW(a*x))^(5/2)+7/256*c^2*x^4/(c*LambertW(a*x))^(3/2)-1/32*c*x^4/sqrt(c*LambertW(a*x))+1/4*x^4*sqrt(c*LambertW(a*x)),1],
[x^2*sqrt(c*LambertW(a*x)),x,5,5/432*sqrt(c)*sqrt(1/3*Pi)*erfi(sqrt(3)*sqrt(c*LambertW(a*x))/sqrt(c))/a^3-5/216*c^3*x^3/(c*LambertW(a*x))^(5/2)+5/108*c^2*x^3/(c*LambertW(a*x))^(3/2)-1/18*c*x^3/sqrt(c*LambertW(a*x))+1/3*x^3*sqrt(c*LambertW(a*x)),1],
[x*sqrt(c*LambertW(a*x)),x,4,-3/64*sqrt(c)*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(a*x))/sqrt(c))/a^2+3/32*c^2*x^2/(c*LambertW(a*x))^(3/2)-1/8*c*x^2/sqrt(c*LambertW(a*x))+1/2*x^2*sqrt(c*LambertW(a*x)),1],
[sqrt(c*LambertW(a*x)),x,3,1/4*sqrt(c)*sqrt(Pi)*erfi(sqrt(c*LambertW(a*x))/sqrt(c))/a-1/2*c*x/sqrt(c*LambertW(a*x))+x*sqrt(c*LambertW(a*x)),1],
[sqrt(c*LambertW(a*x))/x,x,2,2*sqrt(c*LambertW(a*x))+2/3*(c*LambertW(a*x))^(3/2)/c,1],
[sqrt(c*LambertW(a*x))/x^2,x,2,-a*sqrt(c)*sqrt(Pi)*erf(sqrt(c*LambertW(a*x))/sqrt(c))-2*sqrt(c*LambertW(a*x))/x,1],
[sqrt(c*LambertW(a*x))/x^3,x,3,2/3*a^2*sqrt(c)*sqrt(2*Pi)*erf(sqrt(2)*sqrt(c*LambertW(a*x))/sqrt(c))-2/3*sqrt(c*LambertW(a*x))/x^2+2/3*(c*LambertW(a*x))^(3/2)/c/x^2,1],
[sqrt(c*LambertW(a*x))/x^4,x,4,-4/5*a^3*sqrt(c)*sqrt(3*Pi)*erf(sqrt(3)*sqrt(c*LambertW(a*x))/sqrt(c))-2/5*sqrt(c*LambertW(a*x))/x^3+2/15*(c*LambertW(a*x))^(3/2)/c/x^3-4/5*(c*LambertW(a*x))^(5/2)/c^2/x^3,1],
[sqrt(c*LambertW(a*x))/x^5,x,5,256/105*a^4*sqrt(c)*sqrt(Pi)*erf(2*sqrt(c*LambertW(a*x))/sqrt(c))-2/7*sqrt(c*LambertW(a*x))/x^4+2/35*(c*LambertW(a*x))^(3/2)/c/x^4-16/105*(c*LambertW(a*x))^(5/2)/c^2/x^4+128/105*(c*LambertW(a*x))^(7/2)/c^3/x^4,1],
[sqrt(c*LambertW(a*x))/x^6,x,6,-400/189*a^5*sqrt(c)*sqrt(5*Pi)*erf(sqrt(5)*sqrt(c*LambertW(a*x))/sqrt(c))-2/9*sqrt(c*LambertW(a*x))/x^5+2/63*(c*LambertW(a*x))^(3/2)/c/x^5-4/63*(c*LambertW(a*x))^(5/2)/c^2/x^5+40/189*(c*LambertW(a*x))^(7/2)/c^3/x^5-400/189*(c*LambertW(a*x))^(9/2)/c^4/x^5,1],
[x^4/sqrt(c*LambertW(a*x)),x,6,21/20000*sqrt(1/5*Pi)*erfi(sqrt(5)*sqrt(c*LambertW(a*x))/sqrt(c))/a^5/sqrt(c)-21/10000*c^4*x^5/(c*LambertW(a*x))^(9/2)+7/1000*c^3*x^5/(c*LambertW(a*x))^(7/2)-7/500*c^2*x^5/(c*LambertW(a*x))^(5/2)+1/50*c*x^5/(c*LambertW(a*x))^(3/2)+1/5*x^5/sqrt(c*LambertW(a*x)),1],
[x^3/sqrt(c*LambertW(a*x)),x,5,-15/8192*sqrt(Pi)*erfi(2*sqrt(c*LambertW(a*x))/sqrt(c))/a^4/sqrt(c)+15/2048*c^3*x^4/(c*LambertW(a*x))^(7/2)-5/256*c^2*x^4/(c*LambertW(a*x))^(5/2)+1/32*c*x^4/(c*LambertW(a*x))^(3/2)+1/4*x^4/sqrt(c*LambertW(a*x)),1],
[x^2/sqrt(c*LambertW(a*x)),x,4,1/72*sqrt(1/3*Pi)*erfi(sqrt(3)*sqrt(c*LambertW(a*x))/sqrt(c))/a^3/sqrt(c)-1/36*c^2*x^3/(c*LambertW(a*x))^(5/2)+1/18*c*x^3/(c*LambertW(a*x))^(3/2)+1/3*x^3/sqrt(c*LambertW(a*x)),1],
[x/sqrt(c*LambertW(a*x)),x,3,-1/16*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(a*x))/sqrt(c))/a^2/sqrt(c)+1/8*c*x^2/(c*LambertW(a*x))^(3/2)+1/2*x^2/sqrt(c*LambertW(a*x)),1],
[1/sqrt(c*LambertW(a*x)),x,2,1/2*sqrt(Pi)*erfi(sqrt(c*LambertW(a*x))/sqrt(c))/a/sqrt(c)+x/sqrt(c*LambertW(a*x)),1],
[1/x/sqrt(c*LambertW(a*x)),x,2,-2/sqrt(c*LambertW(a*x))+2*sqrt(c*LambertW(a*x))/c,1],
[1/x^2/sqrt(c*LambertW(a*x)),x,3,-2/3*a*sqrt(Pi)*erf(sqrt(c*LambertW(a*x))/sqrt(c))/sqrt(c)-2/3/x/sqrt(c*LambertW(a*x))-2/3*sqrt(c*LambertW(a*x))/c/x,1],
[1/x^3/sqrt(c*LambertW(a*x)),x,4,8/15*a^2*sqrt(2*Pi)*erf(sqrt(2)*sqrt(c*LambertW(a*x))/sqrt(c))/sqrt(c)-2/5/x^2/sqrt(c*LambertW(a*x))-2/15*sqrt(c*LambertW(a*x))/c/x^2+8/15*(c*LambertW(a*x))^(3/2)/c^2/x^2,1],
[1/x^4/sqrt(c*LambertW(a*x)),x,5,-24/35*a^3*sqrt(3*Pi)*erf(sqrt(3)*sqrt(c*LambertW(a*x))/sqrt(c))/sqrt(c)-2/7/x^3/sqrt(c*LambertW(a*x))-2/35*sqrt(c*LambertW(a*x))/c/x^3+4/35*(c*LambertW(a*x))^(3/2)/c^2/x^3-24/35*(c*LambertW(a*x))^(5/2)/c^3/x^3,1],
[1/x^5/sqrt(c*LambertW(a*x)),x,6,2048/945*a^4*sqrt(Pi)*erf(2*sqrt(c*LambertW(a*x))/sqrt(c))/sqrt(c)-2/9/x^4/sqrt(c*LambertW(a*x))-2/63*sqrt(c*LambertW(a*x))/c/x^4+16/315*(c*LambertW(a*x))^(3/2)/c^2/x^4-128/945*(c*LambertW(a*x))^(5/2)/c^3/x^4+1024/945*(c*LambertW(a*x))^(7/2)/c^4/x^4,1],
[x^m*LambertW(a*x),x,3,x^m*GAMMA(3+m,(-1-m)*LambertW(a*x))*LambertW(a*x)^2*((-1-m)*LambertW(a*x))^(-2-m)/a/exp(m*LambertW(a*x))/(1+m)+x^m*GAMMA(2+m,(-1-m)*LambertW(a*x))*LambertW(a*x)*((-1-m)*LambertW(a*x))^(-1-m)/a/exp(m*LambertW(a*x))/(1+m),1],
[x^m*LambertW(a*x)^2,x,3,x^m*GAMMA(4+m,(-1-m)*LambertW(a*x))*LambertW(a*x)^3*((-1-m)*LambertW(a*x))^(-3-m)/a/exp(m*LambertW(a*x))/(1+m)+x^m*GAMMA(3+m,(-1-m)*LambertW(a*x))*LambertW(a*x)^2*((-1-m)*LambertW(a*x))^(-2-m)/a/exp(m*LambertW(a*x))/(1+m),1],
[x^m/LambertW(a*x),x,3,x^m*GAMMA(m,(-1-m)*LambertW(a*x))*((-1-m)*LambertW(a*x))^(1-m)/a/exp(m*LambertW(a*x))/(1+m)/LambertW(a*x)+x^m*GAMMA(1+m,(-1-m)*LambertW(a*x))/a/exp(m*LambertW(a*x))/(1+m)/(((-1-m)*LambertW(a*x))^m),1],
[x^m/LambertW(a*x)^2,x,3,x^m*GAMMA(m,(-1-m)*LambertW(a*x))*((-1-m)*LambertW(a*x))^(1-m)/a/exp(m*LambertW(a*x))/(1+m)/LambertW(a*x)+x^m*GAMMA(-1+m,(-1-m)*LambertW(a*x))*((-1-m)*LambertW(a*x))^(2-m)/a/exp(m*LambertW(a*x))/(1+m)/LambertW(a*x)^2,1],
[x^m*sqrt(c*LambertW(a*x)),x,3,x^m*GAMMA(5/2+m,(-1-m)*LambertW(a*x))*(c*LambertW(a*x))^(3/2)*((-1-m)*LambertW(a*x))^(-3/2-m)/a/c/exp(m*LambertW(a*x))/(1+m)+x^m*GAMMA(3/2+m,(-1-m)*LambertW(a*x))*sqrt(c*LambertW(a*x))*((-1-m)*LambertW(a*x))^(-1/2-m)/a/exp(m*LambertW(a*x))/(1+m),1],
[x^m/sqrt(c*LambertW(a*x)),x,3,x^m*GAMMA(3/2+m,(-1-m)*LambertW(a*x))*sqrt(c*LambertW(a*x))*((-1-m)*LambertW(a*x))^(-1/2-m)/a/c/exp(m*LambertW(a*x))/(1+m)+x^m*GAMMA(1/2+m,(-1-m)*LambertW(a*x))*((-1-m)*LambertW(a*x))^(1/2-m)/a/exp(m*LambertW(a*x))/(1+m)/sqrt(c*LambertW(a*x)),1],
[x^2*(c*LambertW(a*x))^p,x,3,3^(-3-p)*x^2*GAMMA(3+p,-3*LambertW(a*x))*(-LambertW(a*x))^(-2-p)*(c*LambertW(a*x))^p/a/exp(2*LambertW(a*x))+3^(-4-p)*x^2*GAMMA(4+p,-3*LambertW(a*x))*(-LambertW(a*x))^(-3-p)*(c*LambertW(a*x))^(p+1)/a/c/exp(2*LambertW(a*x)),1],
[x*(c*LambertW(a*x))^p,x,3,2^(-2-p)*x*GAMMA(2+p,-2*LambertW(a*x))*(-LambertW(a*x))^(-1-p)*(c*LambertW(a*x))^p/a/exp(LambertW(a*x))+2^(-3-p)*x*GAMMA(3+p,-2*LambertW(a*x))*(-LambertW(a*x))^(-2-p)*(c*LambertW(a*x))^(p+1)/a/c/exp(LambertW(a*x)),1],
[(c*LambertW(a*x))^p/x,x,2,(c*LambertW(a*x))^p/p+(c*LambertW(a*x))^(p+1)/c/(p+1),1],
[(c*LambertW(a*x))^p/x^2,x,3,-exp(2*LambertW(a*x))*GAMMA(-1+p,LambertW(a*x))*LambertW(a*x)^(2-p)*(c*LambertW(a*x))^p/a/x^2-exp(2*LambertW(a*x))*GAMMA(p,LambertW(a*x))*LambertW(a*x)^(1-p)*(c*LambertW(a*x))^(p+1)/a/c/x^2,1],
[(c*LambertW(a*x))^p/x^3,x,3,-2^(2-p)*exp(3*LambertW(a*x))*GAMMA(-2+p,2*LambertW(a*x))*LambertW(a*x)^(3-p)*(c*LambertW(a*x))^p/a/x^3-2^(1-p)*exp(3*LambertW(a*x))*GAMMA(-1+p,2*LambertW(a*x))*LambertW(a*x)^(2-p)*(c*LambertW(a*x))^(p+1)/a/c/x^3,1],
[x^m*(c*LambertW(a*x))^p,x,3,x^m*GAMMA(2+m+p,(-1-m)*LambertW(a*x))*(c*LambertW(a*x))^(p+1)*((-1-m)*LambertW(a*x))^(-1-m-p)/a/c/exp(m*LambertW(a*x))/(1+m)+x^m*GAMMA(1+m+p,(-1-m)*LambertW(a*x))*(c*LambertW(a*x))^p*((-1-m)*LambertW(a*x))^(-m-p)/a/exp(m*LambertW(a*x))/(1+m),1],
[x^5*LambertW(a*x^2),x,6,-1/18*x^6+1/81*x^6/LambertW(a*x^2)^3-1/27*x^6/LambertW(a*x^2)^2+1/18*x^6/LambertW(a*x^2)+1/6*x^6*LambertW(a*x^2),1],
[x^3*LambertW(a*x^2),x,5,-1/8*x^4-1/16*x^4/LambertW(a*x^2)^2+1/8*x^4/LambertW(a*x^2)+1/4*x^4*LambertW(a*x^2),1],
[x*LambertW(a*x^2),x,4,-1/2*x^2+1/2*x^2/LambertW(a*x^2)+1/2*x^2*LambertW(a*x^2),1],
[LambertW(a*x^2)/x,x,3,1/2*LambertW(a*x^2)+1/4*LambertW(a*x^2)^2,1],
[LambertW(a*x^2)/x^3,x,3,1/2*a*Ei(-LambertW(a*x^2))-1/2*LambertW(a*x^2)/x^2,1],
[LambertW(a*x^2)/x^5,x,3,-1/2*a^2*Ei(-2*LambertW(a*x^2))-1/2*LambertW(a*x^2)/x^4,1],
[LambertW(a*x^2)/x^7,x,4,3/4*a^3*Ei(-3*LambertW(a*x^2))-1/4*LambertW(a*x^2)/x^6+1/4*LambertW(a*x^2)^2/x^6,1],
[x^4*LambertW(a*x^2),x,11,-2/25*x^5-6/125*x^5/LambertW(a*x^2)^2+3/125*sqrt(2/5)*x^3*GAMMA(1/2,-5/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/exp(3/2*LambertW(a*x^2))/LambertW(a*x^2)^2+2/25*x^5/LambertW(a*x^2)+1/5*x^5*LambertW(a*x^2),1],
[x^2*LambertW(a*x^2),x,9,-2/9*x^3+2/9*x^3/LambertW(a*x^2)-1/9*sqrt(2/3)*x*GAMMA(1/2,-3/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/exp(1/2*LambertW(a*x^2))/LambertW(a*x^2)+1/3*x^3*LambertW(a*x^2),1],
[LambertW(a*x^2),x,7,-2*x+sqrt(2)*exp(1/2*LambertW(a*x^2))*GAMMA(1/2,-1/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/x+x*LambertW(a*x^2),1],
[LambertW(a*x^2)/x^2,x,5,-LambertW(a*x^2)/x-sqrt(2)*exp(3/2*LambertW(a*x^2))*GAMMA(1/2,1/2*LambertW(a*x^2))*LambertW(a*x^2)^(3/2)/a/x^3,1],
[LambertW(a*x^2)/x^4,x,5,-LambertW(a*x^2)/x^3+sqrt(3/2)*exp(5/2*LambertW(a*x^2))*GAMMA(1/2,3/2*LambertW(a*x^2))*LambertW(a*x^2)^(5/2)/a/x^5-exp(5/2*LambertW(a*x^2))*GAMMA(1/2,3/2*LambertW(a*x^2))*LambertW(a*x^2)^(5/2)/sqrt(6)/a/x^5,1],
[x^3*LambertW(a*x^2)^2,x,6,3/8*x^4+3/16*x^4/LambertW(a*x^2)^2-3/8*x^4/LambertW(a*x^2)-1/4*x^4*LambertW(a*x^2)+1/4*x^4*LambertW(a*x^2)^2,1],
[x*LambertW(a*x^2)^2,x,5,2*x^2-2*x^2/LambertW(a*x^2)-x^2*LambertW(a*x^2)+1/2*x^2*LambertW(a*x^2)^2,1],
[LambertW(a*x^2)^2/x,x,3,1/4*LambertW(a*x^2)^2+1/6*LambertW(a*x^2)^3,1],
[LambertW(a*x^2)^2/x^3,x,3,-LambertW(a*x^2)/x^2-1/2*LambertW(a*x^2)^2/x^2,1],
[LambertW(a*x^2)^2/x^5,x,3,1/2*a^2*Ei(-2*LambertW(a*x^2))-1/4*LambertW(a*x^2)^2/x^4,1],
[LambertW(a*x^2)^2/x^7,x,3,-a^3*Ei(-3*LambertW(a*x^2))-1/2*LambertW(a*x^2)^2/x^6,1],
[LambertW(a*x^2)^2/x^9,x,4,2*a^4*Ei(-4*LambertW(a*x^2))-1/4*LambertW(a*x^2)^2/x^8+1/2*LambertW(a*x^2)^3/x^8,1],
[x^2*LambertW(a*x^2)^2,x,11,20/27*x^3-20/27*x^3/LambertW(a*x^2)+10/27*sqrt(2/3)*x*GAMMA(1/2,-3/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/exp(1/2*LambertW(a*x^2))/LambertW(a*x^2)-4/9*x^3*LambertW(a*x^2)+1/3*x^3*LambertW(a*x^2)^2,1],
[LambertW(a*x^2)^2,x,9,12*x-6*sqrt(2)*exp(1/2*LambertW(a*x^2))*GAMMA(1/2,-1/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/x-4*x*LambertW(a*x^2)+x*LambertW(a*x^2)^2,1],
[LambertW(a*x^2)^2/x^2,x,7,-4*LambertW(a*x^2)/x-2*sqrt(2)*exp(3/2*LambertW(a*x^2))*GAMMA(1/2,1/2*LambertW(a*x^2))*LambertW(a*x^2)^(3/2)/a/x^3-LambertW(a*x^2)^2/x,1],
[LambertW(a*x^2)^2/x^4,x,5,-1/3*LambertW(a*x^2)^2/x^3-2/3*sqrt(2/3)*exp(5/2*LambertW(a*x^2))*GAMMA(1/2,3/2*LambertW(a*x^2))*LambertW(a*x^2)^(5/2)/a/x^5,1],
[LambertW(a*x^2)^2/x^6,x,5,-LambertW(a*x^2)^2/x^5+sqrt(5/2)*exp(7/2*LambertW(a*x^2))*GAMMA(1/2,5/2*LambertW(a*x^2))*LambertW(a*x^2)^(7/2)/a/x^7-exp(7/2*LambertW(a*x^2))*GAMMA(1/2,5/2*LambertW(a*x^2))*LambertW(a*x^2)^(7/2)/sqrt(10)/a/x^7,1],
[LambertW(a*x^2)^2/x^8,x,7,-1/3*LambertW(a*x^2)^2/x^7+4/3*LambertW(a*x^2)^3/x^7-2/3*sqrt(14)*exp(9/2*LambertW(a*x^2))*GAMMA(1/2,7/2*LambertW(a*x^2))*LambertW(a*x^2)^(9/2)/a/x^9,1],
[x*LambertW(a*x^2)^3,x,6,-9*x^2+9*x^2/LambertW(a*x^2)+9/2*x^2*LambertW(a*x^2)-3/2*x^2*LambertW(a*x^2)^2+1/2*x^2*LambertW(a*x^2)^3,1],
[LambertW(a*x^2)^3/x,x,3,1/6*LambertW(a*x^2)^3+1/8*LambertW(a*x^2)^4,1],
[LambertW(a*x^2)^3/x^3,x,4,-3/2*LambertW(a*x^2)/x^2-3/2*LambertW(a*x^2)^2/x^2-1/2*LambertW(a*x^2)^3/x^2,1],
[LambertW(a*x^2)^3/x^5,x,3,-3/8*LambertW(a*x^2)^2/x^4-1/4*LambertW(a*x^2)^3/x^4,1],
[LambertW(a*x^2)^3/x^7,x,3,1/2*a^3*Ei(-3*LambertW(a*x^2))-1/6*LambertW(a*x^2)^3/x^6,1],
[LambertW(a*x^2)^3/x^9,x,3,-3/2*a^4*Ei(-4*LambertW(a*x^2))-1/2*LambertW(a*x^2)^3/x^8,1],
[LambertW(a*x^2)^3/x^11,x,4,15/4*a^5*Ei(-5*LambertW(a*x^2))-1/4*LambertW(a*x^2)^3/x^10+3/4*LambertW(a*x^2)^4/x^10,1],
[x^2*LambertW(a*x^2)^3,x,13,-70/27*x^3+70/27*x^3/LambertW(a*x^2)-35/27*sqrt(2/3)*x*GAMMA(1/2,-3/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/exp(1/2*LambertW(a*x^2))/LambertW(a*x^2)+14/9*x^3*LambertW(a*x^2)-2/3*x^3*LambertW(a*x^2)^2+1/3*x^3*LambertW(a*x^2)^3,1],
[LambertW(a*x^2)^3,x,11,-90*x+45*sqrt(2)*exp(1/2*LambertW(a*x^2))*GAMMA(1/2,-1/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/x+30*x*LambertW(a*x^2)-6*x*LambertW(a*x^2)^2+x*LambertW(a*x^2)^3,1],
[LambertW(a*x^2)^3/x^2,x,9,-18*LambertW(a*x^2)/x-9*sqrt(2)*exp(3/2*LambertW(a*x^2))*GAMMA(1/2,1/2*LambertW(a*x^2))*LambertW(a*x^2)^(3/2)/a/x^3-6*LambertW(a*x^2)^2/x-LambertW(a*x^2)^3/x,1],
[LambertW(a*x^2)^3/x^4,x,7,-2/3*LambertW(a*x^2)^2/x^3-1/3*sqrt(2/3)*exp(5/2*LambertW(a*x^2))*GAMMA(1/2,3/2*LambertW(a*x^2))*LambertW(a*x^2)^(5/2)/a/x^5-1/3*LambertW(a*x^2)^3/x^3,1],
[LambertW(a*x^2)^3/x^6,x,5,-1/5*LambertW(a*x^2)^3/x^5-3/5*sqrt(2/5)*exp(7/2*LambertW(a*x^2))*GAMMA(1/2,5/2*LambertW(a*x^2))*LambertW(a*x^2)^(7/2)/a/x^7,1],
[LambertW(a*x^2)^3/x^8,x,5,-LambertW(a*x^2)^3/x^7+sqrt(7/2)*exp(9/2*LambertW(a*x^2))*GAMMA(1/2,7/2*LambertW(a*x^2))*LambertW(a*x^2)^(9/2)/a/x^9-exp(9/2*LambertW(a*x^2))*GAMMA(1/2,7/2*LambertW(a*x^2))*LambertW(a*x^2)^(9/2)/sqrt(14)/a/x^9,1],
[x^7/LambertW(a*x^2),x,5,1/256*x^8/LambertW(a*x^2)^4-1/64*x^8/LambertW(a*x^2)^3+1/32*x^8/LambertW(a*x^2)^2+1/8*x^8/LambertW(a*x^2),1],
[x^5/LambertW(a*x^2),x,4,-1/54*x^6/LambertW(a*x^2)^3+1/18*x^6/LambertW(a*x^2)^2+1/6*x^6/LambertW(a*x^2),1],
[x^3/LambertW(a*x^2),x,3,1/8*x^4/LambertW(a*x^2)^2+1/4*x^4/LambertW(a*x^2),1],
[x/LambertW(a*x^2),x,3,1/2*Ei(LambertW(a*x^2))/a+1/2*x^2/LambertW(a*x^2),1],
[1/x/LambertW(a*x^2),x,3,1/2*ln(LambertW(a*x^2))-1/2/LambertW(a*x^2),1],
[1/x^3/LambertW(a*x^2),x,4,-1/4/x^2-1/4*a*Ei(-LambertW(a*x^2))-1/4/x^2/LambertW(a*x^2),1],
[1/x^5/LambertW(a*x^2),x,5,-1/12/x^4+1/3*a^2*Ei(-2*LambertW(a*x^2))-1/6/x^4/LambertW(a*x^2)+1/6*LambertW(a*x^2)/x^4,1],
[x^4/LambertW(a*x^2),x,7,2/25*x^5/LambertW(a*x^2)^2-1/25*sqrt(2/5)*x^3*GAMMA(1/2,-5/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/exp(3/2*LambertW(a*x^2))/LambertW(a*x^2)^2+1/5*x^5/LambertW(a*x^2),1],
[x^2/LambertW(a*x^2),x,5,1/3*x^3/LambertW(a*x^2)+1/3*sqrt(2/3)*x*GAMMA(1/2,-3/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/exp(1/2*LambertW(a*x^2))/LambertW(a*x^2),1],
[1/LambertW(a*x^2),x,5,sqrt(2)*exp(1/2*LambertW(a*x^2))*GAMMA(1/2,-1/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/x-x/LambertW(a*x^2),1],
[1/x^2/LambertW(a*x^2),x,7,-2/3/x-1/3/x/LambertW(a*x^2)+1/3*sqrt(2)*exp(3/2*LambertW(a*x^2))*GAMMA(1/2,1/2*LambertW(a*x^2))*LambertW(a*x^2)^(3/2)/a/x^3,1],
[1/x^4/LambertW(a*x^2),x,9,-2/15/x^3-1/5/x^3/LambertW(a*x^2)+2/5*LambertW(a*x^2)/x^3-1/5*sqrt(6)*exp(5/2*LambertW(a*x^2))*GAMMA(1/2,3/2*LambertW(a*x^2))*LambertW(a*x^2)^(5/2)/a/x^5,1],
[x^7/LambertW(a*x^2)^2,x,4,-1/64*x^8/LambertW(a*x^2)^4+1/16*x^8/LambertW(a*x^2)^3+1/8*x^8/LambertW(a*x^2)^2,1],
[x^5/LambertW(a*x^2)^2,x,3,1/9*x^6/LambertW(a*x^2)^3+1/6*x^6/LambertW(a*x^2)^2,1],
[x^3/LambertW(a*x^2)^2,x,3,1/2*Ei(2*LambertW(a*x^2))/a^2+1/4*x^4/LambertW(a*x^2)^2,1],
[x/LambertW(a*x^2)^2,x,3,Ei(LambertW(a*x^2))/a-1/2*x^2/LambertW(a*x^2)^2,1],
[1/x/LambertW(a*x^2)^2,x,3,-1/4/LambertW(a*x^2)^2-1/2/LambertW(a*x^2),1],
[1/x^3/LambertW(a*x^2)^2,x,5,1/6/x^2+1/6*a*Ei(-LambertW(a*x^2))-1/6/x^2/LambertW(a*x^2)^2-1/6/x^2/LambertW(a*x^2),1],
[x^6/LambertW(a*x^2)^2,x,7,4/49*x^7/LambertW(a*x^2)^3-2/49*sqrt(2/7)*x^5*GAMMA(1/2,-7/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/exp(5/2*LambertW(a*x^2))/LambertW(a*x^2)^3+1/7*x^7/LambertW(a*x^2)^2,1],
[x^4/LambertW(a*x^2)^2,x,5,1/5*x^5/LambertW(a*x^2)^2+2/5*sqrt(2/5)*x^3*GAMMA(1/2,-5/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/exp(3/2*LambertW(a*x^2))/LambertW(a*x^2)^2,1],
[x^2/LambertW(a*x^2)^2,x,5,-x^3/LambertW(a*x^2)^2+sqrt(3/2)*x*GAMMA(1/2,-3/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/exp(1/2*LambertW(a*x^2))/LambertW(a*x^2)+x*GAMMA(1/2,-3/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/sqrt(6)/a/exp(1/2*LambertW(a*x^2))/LambertW(a*x^2),1],
[1/LambertW(a*x^2)^2,x,7,2/3*sqrt(2)*exp(1/2*LambertW(a*x^2))*GAMMA(1/2,-1/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/a/x-1/3*x/LambertW(a*x^2)^2-4/3*x/LambertW(a*x^2),1],
[1/x^2/LambertW(a*x^2)^2,x,9,4/15/x-1/5/x/LambertW(a*x^2)^2-4/15/x/LambertW(a*x^2)-2/15*sqrt(2)*exp(3/2*LambertW(a*x^2))*GAMMA(1/2,1/2*LambertW(a*x^2))*LambertW(a*x^2)^(3/2)/a/x^3,1],
[1/x^4/LambertW(a*x^2)^2,x,11,4/35/x^3-1/7/x^3/LambertW(a*x^2)^2-4/35/x^3/LambertW(a*x^2)-12/35*LambertW(a*x^2)/x^3+6/35*sqrt(6)*exp(5/2*LambertW(a*x^2))*GAMMA(1/2,3/2*LambertW(a*x^2))*LambertW(a*x^2)^(5/2)/a/x^5,1],
[x^5*sqrt(c*LambertW(a*x^2)),x,6,5/864*sqrt(c)*sqrt(1/3*Pi)*erfi(sqrt(3)*sqrt(c*LambertW(a*x^2))/sqrt(c))/a^3-5/432*c^3*x^6/(c*LambertW(a*x^2))^(5/2)+5/216*c^2*x^6/(c*LambertW(a*x^2))^(3/2)-1/36*c*x^6/sqrt(c*LambertW(a*x^2))+1/6*x^6*sqrt(c*LambertW(a*x^2)),1],
[x^3*sqrt(c*LambertW(a*x^2)),x,5,-3/128*sqrt(c)*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(a*x^2))/sqrt(c))/a^2+3/64*c^2*x^4/(c*LambertW(a*x^2))^(3/2)-1/16*c*x^4/sqrt(c*LambertW(a*x^2))+1/4*x^4*sqrt(c*LambertW(a*x^2)),1],
[x*sqrt(c*LambertW(a*x^2)),x,4,1/8*sqrt(c)*sqrt(Pi)*erfi(sqrt(c*LambertW(a*x^2))/sqrt(c))/a-1/4*c*x^2/sqrt(c*LambertW(a*x^2))+1/2*x^2*sqrt(c*LambertW(a*x^2)),1],
[sqrt(c*LambertW(a*x^2))/x,x,3,sqrt(c*LambertW(a*x^2))+1/3*(c*LambertW(a*x^2))^(3/2)/c,1],
[sqrt(c*LambertW(a*x^2))/x^3,x,3,-1/2*a*sqrt(c)*sqrt(Pi)*erf(sqrt(c*LambertW(a*x^2))/sqrt(c))-sqrt(c*LambertW(a*x^2))/x^2,1],
[sqrt(c*LambertW(a*x^2))/x^5,x,4,1/3*a^2*sqrt(c)*sqrt(2*Pi)*erf(sqrt(2)*sqrt(c*LambertW(a*x^2))/sqrt(c))-1/3*sqrt(c*LambertW(a*x^2))/x^4+1/3*(c*LambertW(a*x^2))^(3/2)/c/x^4,1],
[sqrt(c*LambertW(a*x^2))/x^7,x,5,-2/5*a^3*sqrt(c)*sqrt(3*Pi)*erf(sqrt(3)*sqrt(c*LambertW(a*x^2))/sqrt(c))-1/5*sqrt(c*LambertW(a*x^2))/x^6+1/15*(c*LambertW(a*x^2))^(3/2)/c/x^6-2/5*(c*LambertW(a*x^2))^(5/2)/c^2/x^6,1],
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[x^2*sqrt(c*LambertW(a*x^2)),x,4,2/27*c^2*x^3/(c*LambertW(a*x^2))^(3/2)-1/9*c*x^3/sqrt(c*LambertW(a*x^2))+1/3*x^3*sqrt(c*LambertW(a*x^2)),1],
[sqrt(c*LambertW(a*x^2)),x,3,-c*x/sqrt(c*LambertW(a*x^2))+x*sqrt(c*LambertW(a*x^2)),1],
[sqrt(c*LambertW(a*x^2))/x^2,x,4,-sqrt(c*LambertW(a*x^2))/x-1/2*exp(3/2*LambertW(a*x^2))*GAMMA(0,1/2*LambertW(a*x^2))*LambertW(a*x^2)*sqrt(c*LambertW(a*x^2))/a/x^3,1],
[sqrt(c*LambertW(a*x^2))/x^4,x,5,-1/2*sqrt(c*LambertW(a*x^2))/x^3+1/4*exp(5/2*LambertW(a*x^2))*GAMMA(0,3/2*LambertW(a*x^2))*LambertW(a*x^2)*(c*LambertW(a*x^2))^(3/2)/a/c/x^5,1],
[x^5/sqrt(c*LambertW(a*x^2)),x,5,1/144*sqrt(1/3*Pi)*erfi(sqrt(3)*sqrt(c*LambertW(a*x^2))/sqrt(c))/a^3/sqrt(c)-1/72*c^2*x^6/(c*LambertW(a*x^2))^(5/2)+1/36*c*x^6/(c*LambertW(a*x^2))^(3/2)+1/6*x^6/sqrt(c*LambertW(a*x^2)),1],
[x^3/sqrt(c*LambertW(a*x^2)),x,4,-1/32*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(a*x^2))/sqrt(c))/a^2/sqrt(c)+1/16*c*x^4/(c*LambertW(a*x^2))^(3/2)+1/4*x^4/sqrt(c*LambertW(a*x^2)),1],
[x/sqrt(c*LambertW(a*x^2)),x,3,1/4*sqrt(Pi)*erfi(sqrt(c*LambertW(a*x^2))/sqrt(c))/a/sqrt(c)+1/2*x^2/sqrt(c*LambertW(a*x^2)),1],
[1/x/sqrt(c*LambertW(a*x^2)),x,3,-1/sqrt(c*LambertW(a*x^2))+sqrt(c*LambertW(a*x^2))/c,1],
[1/x^3/sqrt(c*LambertW(a*x^2)),x,4,-1/3*a*sqrt(Pi)*erf(sqrt(c*LambertW(a*x^2))/sqrt(c))/sqrt(c)-1/3/x^2/sqrt(c*LambertW(a*x^2))-1/3*sqrt(c*LambertW(a*x^2))/c/x^2,1],
[1/x^5/sqrt(c*LambertW(a*x^2)),x,5,4/15*a^2*sqrt(2*Pi)*erf(sqrt(2)*sqrt(c*LambertW(a*x^2))/sqrt(c))/sqrt(c)-1/5/x^4/sqrt(c*LambertW(a*x^2))-1/15*sqrt(c*LambertW(a*x^2))/c/x^4+4/15*(c*LambertW(a*x^2))^(3/2)/c^2/x^4,1],
[1/x^7/sqrt(c*LambertW(a*x^2)),x,6,-12/35*a^3*sqrt(3*Pi)*erf(sqrt(3)*sqrt(c*LambertW(a*x^2))/sqrt(c))/sqrt(c)-1/7/x^6/sqrt(c*LambertW(a*x^2))-1/35*sqrt(c*LambertW(a*x^2))/c/x^6+2/35*(c*LambertW(a*x^2))^(3/2)/c^2/x^6-12/35*(c*LambertW(a*x^2))^(5/2)/c^3/x^6,1],
[x^6/sqrt(c*LambertW(a*x^2)),x,5,8/2401*c^3*x^7/(c*LambertW(a*x^2))^(7/2)-4/343*c^2*x^7/(c*LambertW(a*x^2))^(5/2)+1/49*c*x^7/(c*LambertW(a*x^2))^(3/2)+1/7*x^7/sqrt(c*LambertW(a*x^2)),1],
[x^4/sqrt(c*LambertW(a*x^2)),x,4,-2/125*c^2*x^5/(c*LambertW(a*x^2))^(5/2)+1/25*c*x^5/(c*LambertW(a*x^2))^(3/2)+1/5*x^5/sqrt(c*LambertW(a*x^2)),1],
[x^2/sqrt(c*LambertW(a*x^2)),x,3,1/9*c*x^3/(c*LambertW(a*x^2))^(3/2)+1/3*x^3/sqrt(c*LambertW(a*x^2)),1],
[1/sqrt(c*LambertW(a*x^2)),x,4,x/sqrt(c*LambertW(a*x^2))-1/2*exp(1/2*LambertW(a*x^2))*GAMMA(0,-1/2*LambertW(a*x^2))*LambertW(a*x^2)/a/x/sqrt(c*LambertW(a*x^2)),1],
[1/x^2/sqrt(c*LambertW(a*x^2)),x,5,-1/2/x/sqrt(c*LambertW(a*x^2))-1/4*exp(3/2*LambertW(a*x^2))*GAMMA(0,1/2*LambertW(a*x^2))*LambertW(a*x^2)*sqrt(c*LambertW(a*x^2))/a/c/x^3,1],
[1/x^4/sqrt(c*LambertW(a*x^2)),x,7,-1/4/x^3/sqrt(c*LambertW(a*x^2))-1/8*sqrt(c*LambertW(a*x^2))/c/x^3+3/16*exp(5/2*LambertW(a*x^2))*GAMMA(0,3/2*LambertW(a*x^2))*LambertW(a*x^2)*(c*LambertW(a*x^2))^(3/2)/a/c^2/x^5,1],
[x^3*(c*LambertW(a*x^2))^p,x,4,2^(-3-p)*x^2*GAMMA(2+p,-2*LambertW(a*x^2))*(-LambertW(a*x^2))^(-1-p)*(c*LambertW(a*x^2))^p/a/exp(LambertW(a*x^2))+2^(-4-p)*x^2*GAMMA(3+p,-2*LambertW(a*x^2))*(-LambertW(a*x^2))^(-2-p)*(c*LambertW(a*x^2))^(p+1)/a/c/exp(LambertW(a*x^2)),1],
[x*(c*LambertW(a*x^2))^p,x,3,1/2*x^2*(c*LambertW(a*x^2))^p-1/2*p*GAMMA(p+1,-LambertW(a*x^2))*(c*LambertW(a*x^2))^p/a/((-LambertW(a*x^2))^p),1],
[(c*LambertW(a*x^2))^p/x,x,3,1/2*(c*LambertW(a*x^2))^p/p+1/2*(c*LambertW(a*x^2))^(p+1)/c/(p+1),1],
[(c*LambertW(a*x^2))^p/x^3,x,4,-1/2*exp(2*LambertW(a*x^2))*GAMMA(-1+p,LambertW(a*x^2))*LambertW(a*x^2)^(2-p)*(c*LambertW(a*x^2))^p/a/x^4-1/2*exp(2*LambertW(a*x^2))*GAMMA(p,LambertW(a*x^2))*LambertW(a*x^2)^(1-p)*(c*LambertW(a*x^2))^(p+1)/a/c/x^4,1],
[x^2*(c*LambertW(a*x^2))^p,x,4,2^(1/2+p)*3^(-3/2-p)*x*GAMMA(3/2+p,-3/2*LambertW(a*x^2))*(-LambertW(a*x^2))^(-1/2-p)*(c*LambertW(a*x^2))^p/a/exp(1/2*LambertW(a*x^2))+2^(3/2+p)*3^(-5/2-p)*x*GAMMA(5/2+p,-3/2*LambertW(a*x^2))*(-LambertW(a*x^2))^(-3/2-p)*(c*LambertW(a*x^2))^(p+1)/a/c/exp(1/2*LambertW(a*x^2)),1],
[(c*LambertW(a*x^2))^p/x^2,x,4,-2^(-3/2+p)*exp(3/2*LambertW(a*x^2))*GAMMA(-1/2+p,1/2*LambertW(a*x^2))*LambertW(a*x^2)^(3/2-p)*(c*LambertW(a*x^2))^p/a/x^3-2^(-1/2+p)*exp(3/2*LambertW(a*x^2))*GAMMA(1/2+p,1/2*LambertW(a*x^2))*LambertW(a*x^2)^(1/2-p)*(c*LambertW(a*x^2))^(p+1)/a/c/x^3,1],
[(c*LambertW(a*x^2))^p/x^4,x,4,-2^(-5/2+p)*3^(3/2-p)*exp(5/2*LambertW(a*x^2))*GAMMA(-3/2+p,3/2*LambertW(a*x^2))*LambertW(a*x^2)^(5/2-p)*(c*LambertW(a*x^2))^p/a/x^5-2^(-3/2+p)*3^(1/2-p)*exp(5/2*LambertW(a*x^2))*GAMMA(-1/2+p,3/2*LambertW(a*x^2))*LambertW(a*x^2)^(3/2-p)*(c*LambertW(a*x^2))^(p+1)/a/c/x^5,1],
[x^4*LambertW(a/x),x,6,-125/24*a^5*Ei(-5*LambertW(a/x))+1/4*x^5*LambertW(a/x)-1/12*x^5*LambertW(a/x)^2+5/24*x^5*LambertW(a/x)^3-25/24*x^5*LambertW(a/x)^4,1],
[x^3*LambertW(a/x),x,5,8/3*a^4*Ei(-4*LambertW(a/x))+1/3*x^4*LambertW(a/x)-1/6*x^4*LambertW(a/x)^2+2/3*x^4*LambertW(a/x)^3,1],
[x^2*LambertW(a/x),x,4,-3/2*a^3*Ei(-3*LambertW(a/x))+1/2*x^3*LambertW(a/x)-1/2*x^3*LambertW(a/x)^2,1],
[x*LambertW(a/x),x,3,a^2*Ei(-2*LambertW(a/x))+x^2*LambertW(a/x),1],
[LambertW(a/x),x,3,-a*Ei(-LambertW(a/x))+x*LambertW(a/x),1],
[LambertW(a/x)/x,x,3,-LambertW(a/x)-1/2*LambertW(a/x)^2,1],
[LambertW(a/x)/x^2,x,4,1/x-1/x/LambertW(a/x)-LambertW(a/x)/x,1],
[LambertW(a/x)/x^3,x,5,1/4/x^2+1/8/x^2/LambertW(a/x)^2-1/4/x^2/LambertW(a/x)-1/2*LambertW(a/x)/x^2,1],
[LambertW(a/x)/x^4,x,6,1/9/x^3-2/81/x^3/LambertW(a/x)^3+2/27/x^3/LambertW(a/x)^2-1/9/x^3/LambertW(a/x)-1/3*LambertW(a/x)/x^3,1],
[LambertW(a/x)/x^5,x,7,1/16/x^4+3/512/x^4/LambertW(a/x)^4-3/128/x^4/LambertW(a/x)^3+3/64/x^4/LambertW(a/x)^2-1/16/x^4/LambertW(a/x)-1/4*LambertW(a/x)/x^4,1],
[x^4*LambertW(a/x)^2,x,5,25/3*a^5*Ei(-5*LambertW(a/x))+1/3*x^5*LambertW(a/x)^2-1/3*x^5*LambertW(a/x)^3+5/3*x^5*LambertW(a/x)^4,1],
[x^3*LambertW(a/x)^2,x,4,-4*a^4*Ei(-4*LambertW(a/x))+1/2*x^4*LambertW(a/x)^2-x^4*LambertW(a/x)^3,1],
[x^2*LambertW(a/x)^2,x,3,2*a^3*Ei(-3*LambertW(a/x))+x^3*LambertW(a/x)^2,1],
[x*LambertW(a/x)^2,x,3,-a^2*Ei(-2*LambertW(a/x))+1/2*x^2*LambertW(a/x)^2,1],
[LambertW(a/x)^2,x,3,2*x*LambertW(a/x)+x*LambertW(a/x)^2,1],
[LambertW(a/x)^2/x,x,3,-1/2*LambertW(a/x)^2-1/3*LambertW(a/x)^3,1],
[LambertW(a/x)^2/x^2,x,5,-4/x+4/x/LambertW(a/x)+2*LambertW(a/x)/x-LambertW(a/x)^2/x,1],
[LambertW(a/x)^2/x^3,x,6,-3/4/x^2-3/8/x^2/LambertW(a/x)^2+3/4/x^2/LambertW(a/x)+1/2*LambertW(a/x)/x^2-1/2*LambertW(a/x)^2/x^2,1],
[LambertW(a/x)^2/x^4,x,7,-8/27/x^3+16/243/x^3/LambertW(a/x)^3-16/81/x^3/LambertW(a/x)^2+8/27/x^3/LambertW(a/x)+2/9*LambertW(a/x)/x^3-1/3*LambertW(a/x)^2/x^3,1],
[LambertW(a/x)^2/x^5,x,8,-5/32/x^4-15/1024/x^4/LambertW(a/x)^4+15/256/x^4/LambertW(a/x)^3-15/128/x^4/LambertW(a/x)^2+5/32/x^4/LambertW(a/x)+1/8*LambertW(a/x)/x^4-1/4*LambertW(a/x)^2/x^4,1],
[x^3*sqrt(LambertW(a/x)),x,6,-256/105*a^4*sqrt(Pi)*erf(2*sqrt(LambertW(a/x)))+2/7*x^4*sqrt(LambertW(a/x))-2/35*x^4*LambertW(a/x)^(3/2)+16/105*x^4*LambertW(a/x)^(5/2)-128/105*x^4*LambertW(a/x)^(7/2),1],
[x^2*sqrt(LambertW(a/x)),x,5,4/5*a^3*sqrt(3*Pi)*erf(sqrt(3)*sqrt(LambertW(a/x)))+2/5*x^3*sqrt(LambertW(a/x))-2/15*x^3*LambertW(a/x)^(3/2)+4/5*x^3*LambertW(a/x)^(5/2),1],
[x*sqrt(LambertW(a/x)),x,4,-2/3*a^2*sqrt(2*Pi)*erf(sqrt(2)*sqrt(LambertW(a/x)))+2/3*x^2*sqrt(LambertW(a/x))-2/3*x^2*LambertW(a/x)^(3/2),1],
[sqrt(LambertW(a/x)),x,3,a*sqrt(Pi)*erf(sqrt(LambertW(a/x)))+2*x*sqrt(LambertW(a/x)),1],
[sqrt(LambertW(a/x))/x,x,3,-2*sqrt(LambertW(a/x))-2/3*LambertW(a/x)^(3/2),1],
[sqrt(LambertW(a/x))/x^2,x,4,-1/4*sqrt(Pi)*erfi(sqrt(LambertW(a/x)))/a+1/2/x/sqrt(LambertW(a/x))-sqrt(LambertW(a/x))/x,1],
[sqrt(LambertW(a/x))/x^3,x,5,3/64*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(LambertW(a/x)))/a^2-3/32/x^2/LambertW(a/x)^(3/2)+1/8/x^2/sqrt(LambertW(a/x))-1/2*sqrt(LambertW(a/x))/x^2,1],
[sqrt(LambertW(a/x))/x^4,x,6,-5/432*sqrt(1/3*Pi)*erfi(sqrt(3)*sqrt(LambertW(a/x)))/a^3+5/216/x^3/LambertW(a/x)^(5/2)-5/108/x^3/LambertW(a/x)^(3/2)+1/18/x^3/sqrt(LambertW(a/x))-1/3*sqrt(LambertW(a/x))/x^3,1],
[x^3/sqrt(LambertW(a/x)),x,7,-2048/945*a^4*sqrt(Pi)*erf(2*sqrt(LambertW(a/x)))+2/9*x^4/sqrt(LambertW(a/x))+2/63*x^4*sqrt(LambertW(a/x))-16/315*x^4*LambertW(a/x)^(3/2)+128/945*x^4*LambertW(a/x)^(5/2)-1024/945*x^4*LambertW(a/x)^(7/2),1],
[x^2/sqrt(LambertW(a/x)),x,6,24/35*a^3*sqrt(3*Pi)*erf(sqrt(3)*sqrt(LambertW(a/x)))+2/7*x^3/sqrt(LambertW(a/x))+2/35*x^3*sqrt(LambertW(a/x))-4/35*x^3*LambertW(a/x)^(3/2)+24/35*x^3*LambertW(a/x)^(5/2),1],
[x/sqrt(LambertW(a/x)),x,5,-8/15*a^2*sqrt(2*Pi)*erf(sqrt(2)*sqrt(LambertW(a/x)))+2/5*x^2/sqrt(LambertW(a/x))+2/15*x^2*sqrt(LambertW(a/x))-8/15*x^2*LambertW(a/x)^(3/2),1],
[1/sqrt(LambertW(a/x)),x,4,2/3*a*sqrt(Pi)*erf(sqrt(LambertW(a/x)))+2/3*x/sqrt(LambertW(a/x))+2/3*x*sqrt(LambertW(a/x)),1],
[1/x/sqrt(LambertW(a/x)),x,3,2/sqrt(LambertW(a/x))-2*sqrt(LambertW(a/x)),1],
[1/x^2/sqrt(LambertW(a/x)),x,3,-1/2*sqrt(Pi)*erfi(sqrt(LambertW(a/x)))/a-1/x/sqrt(LambertW(a/x)),1],
[1/x^3/sqrt(LambertW(a/x)),x,4,1/16*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(LambertW(a/x)))/a^2-1/8/x^2/LambertW(a/x)^(3/2)-1/2/x^2/sqrt(LambertW(a/x)),1],
[1/x^4/sqrt(LambertW(a/x)),x,5,-1/72*sqrt(1/3*Pi)*erfi(sqrt(3)*sqrt(LambertW(a/x)))/a^3+1/36/x^3/LambertW(a/x)^(5/2)-1/18/x^3/LambertW(a/x)^(3/2)-1/3/x^3/sqrt(LambertW(a/x)),1],
[x^2*(c*LambertW(a/x))^p,x,4,3^(3-p)*exp(4*LambertW(a/x))*x^4*GAMMA(-3+p,3*LambertW(a/x))*LambertW(a/x)^(4-p)*(c*LambertW(a/x))^p/a+3^(2-p)*exp(4*LambertW(a/x))*x^4*GAMMA(-2+p,3*LambertW(a/x))*LambertW(a/x)^(3-p)*(c*LambertW(a/x))^(p+1)/a/c,1],
[x*(c*LambertW(a/x))^p,x,4,2^(2-p)*exp(3*LambertW(a/x))*x^3*GAMMA(-2+p,2*LambertW(a/x))*LambertW(a/x)^(3-p)*(c*LambertW(a/x))^p/a+2^(1-p)*exp(3*LambertW(a/x))*x^3*GAMMA(-1+p,2*LambertW(a/x))*LambertW(a/x)^(2-p)*(c*LambertW(a/x))^(p+1)/a/c,1],
[(c*LambertW(a/x))^p/x,x,3,-(c*LambertW(a/x))^p/p-(c*LambertW(a/x))^(p+1)/c/(p+1),1],
[(c*LambertW(a/x))^p/x^2,x,3,-(c*LambertW(a/x))^p/x+p*GAMMA(p+1,-LambertW(a/x))*(c*LambertW(a/x))^p/a/((-LambertW(a/x))^p),1],
[(c*LambertW(a/x))^p/x^3,x,4,-2^(-2-p)*GAMMA(2+p,-2*LambertW(a/x))*(-LambertW(a/x))^(-1-p)*(c*LambertW(a/x))^p/a/exp(LambertW(a/x))/x-2^(-3-p)*GAMMA(3+p,-2*LambertW(a/x))*(-LambertW(a/x))^(-2-p)*(c*LambertW(a/x))^(p+1)/a/c/exp(LambertW(a/x))/x,1],
[LambertW(a/x^(1/4))^5,x,3,5/4*x*LambertW(a/x^(1/4))^4+x*LambertW(a/x^(1/4))^5,1],
[LambertW(a/x^(1/3))^4,x,3,4/3*x*LambertW(a/x^(1/3))^3+x*LambertW(a/x^(1/3))^4,1],
[LambertW(a/sqrt(x))^3,x,3,3/2*x*LambertW(a/sqrt(x))^2+x*LambertW(a/sqrt(x))^3,1],
[LambertW(a/x)^2,x,3,2*x*LambertW(a/x)+x*LambertW(a/x)^2,1],
[1/LambertW(a*sqrt(x)),x,3,1/2*x/LambertW(a*sqrt(x))^2+x/LambertW(a*sqrt(x)),1],
[1/LambertW(a*x^(1/3))^2,x,3,2/3*x/LambertW(a*x^(1/3))^3+x/LambertW(a*x^(1/3))^2,1],
[1/LambertW(a*x^(1/4))^3,x,3,3/4*x/LambertW(a*x^(1/4))^4+x/LambertW(a*x^(1/4))^3,1],
[LambertW(a/x^(1/5))^4,x,3,20*a^5*Ei(-5*LambertW(a/x^(1/5)))+5*x*LambertW(a/x^(1/5))^4,1],
[LambertW(a/x^(1/4))^3,x,3,12*a^4*Ei(-4*LambertW(a/x^(1/4)))+4*x*LambertW(a/x^(1/4))^3,1],
[LambertW(a/x^(1/3))^2,x,3,6*a^3*Ei(-3*LambertW(a/x^(1/3)))+3*x*LambertW(a/x^(1/3))^2,1],
[LambertW(a/sqrt(x)),x,3,2*a^2*Ei(-2*LambertW(a/sqrt(x)))+2*x*LambertW(a/sqrt(x)),1],
[1/LambertW(a*x)^2,x,2,2*Ei(LambertW(a*x))/a-x/LambertW(a*x)^2,1],
[1/LambertW(a*sqrt(x))^3,x,3,6*Ei(2*LambertW(a*sqrt(x)))/a^2-2*x/LambertW(a*sqrt(x))^3,1],
[1/LambertW(a*x^(1/3))^4,x,3,12*Ei(3*LambertW(a*x^(1/3)))/a^3-3*x/LambertW(a*x^(1/3))^4,1],
[1/LambertW(a*x^(1/4))^5,x,3,20*Ei(4*LambertW(a*x^(1/4)))/a^4-4*x/LambertW(a*x^(1/4))^5,1],
[x^m*LambertW(a*x^n)^2,x,4,exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA(3+(1+m)/n,-(1+m)*LambertW(a*x^n)/n)*LambertW(a*x^n)^3*(-(1+m)*LambertW(a*x^n)/n)^(-2-(1+m)/n)/a/(1+m)+exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA(2+(1+m)/n,-(1+m)*LambertW(a*x^n)/n)*LambertW(a*x^n)^2/a/(1+m)/((-(1+m)*LambertW(a*x^n)/n)^((1+m+n)/n)),1],
[x^m*LambertW(a*x^n),x,4,exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA((1+m+n)/n,-(1+m)*LambertW(a*x^n)/n)*LambertW(a*x^n)/a/(1+m)/((-(1+m)*LambertW(a*x^n)/n)^((1+m)/n))+exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA(2+(1+m)/n,-(1+m)*LambertW(a*x^n)/n)*LambertW(a*x^n)^2/a/(1+m)/((-(1+m)*LambertW(a*x^n)/n)^((1+m+n)/n)),1],
[x^m/LambertW(a*x^n),x,4,exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA((1+m)/n,-(1+m)*LambertW(a*x^n)/n)*(-(1+m)*LambertW(a*x^n)/n)^(1-(1+m)/n)/a/(1+m)+exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA(-1+(1+m)/n,-(1+m)*LambertW(a*x^n)/n)*(-(1+m)*LambertW(a*x^n)/n)^(2-(1+m)/n)/a/(1+m)/LambertW(a*x^n),1],
[x^m/LambertW(a*x^n)^2,x,4,exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA(-1+(1+m)/n,-(1+m)*LambertW(a*x^n)/n)*(-(1+m)*LambertW(a*x^n)/n)^(2-(1+m)/n)/a/(1+m)/LambertW(a*x^n)+exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA(-2+(1+m)/n,-(1+m)*LambertW(a*x^n)/n)*(-(1+m)*LambertW(a*x^n)/n)^(3-(1+m)/n)/a/(1+m)/LambertW(a*x^n)^2,1],
[x^m/LambertW(a*x^n)^3,x,4,exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA(-2+(1+m)/n,-(1+m)*LambertW(a*x^n)/n)*(-(1+m)*LambertW(a*x^n)/n)^(3-(1+m)/n)/a/(1+m)/LambertW(a*x^n)^2+exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA(-3+(1+m)/n,-(1+m)*LambertW(a*x^n)/n)*(-(1+m)*LambertW(a*x^n)/n)^(4-(1+m)/n)/a/(1+m)/LambertW(a*x^n)^3,1],
[x^(-1-3*n)*LambertW(a*x^n)^4,x,3,-4/9*LambertW(a*x^n)^3/n/(x^(3*n))-1/3*LambertW(a*x^n)^4/n/(x^(3*n)),1],
[x^(-1-2*n)*LambertW(a*x^n)^3,x,3,-3/4*LambertW(a*x^n)^2/n/(x^(2*n))-1/2*LambertW(a*x^n)^3/n/(x^(2*n)),1],
[x^(-1-n)*LambertW(a*x^n)^2,x,3,-2*LambertW(a*x^n)/n/(x^n)-LambertW(a*x^n)^2/n/(x^n),1],
[x^(-1+2*n)/LambertW(a*x^n),x,3,1/4*x^(2*n)/n/LambertW(a*x^n)^2+1/2*x^(2*n)/n/LambertW(a*x^n),1],
[x^(-1+3*n)/LambertW(a*x^n)^2,x,3,2/9*x^(3*n)/n/LambertW(a*x^n)^3+1/3*x^(3*n)/n/LambertW(a*x^n)^2,1],
[x^(-1-n)*(c*LambertW(a*x^n))^(9/2),x,6,135/16*a*c^(9/2)*sqrt(Pi)*erf(sqrt(c*LambertW(a*x^n))/sqrt(c))/n-135/8*c^3*(c*LambertW(a*x^n))^(3/2)/n/(x^n)-45/4*c^2*(c*LambertW(a*x^n))^(5/2)/n/(x^n)-9/2*c*(c*LambertW(a*x^n))^(7/2)/n/(x^n)-(c*LambertW(a*x^n))^(9/2)/n/(x^n),1],
[x^(-1-n)*(c*LambertW(a*x^n))^(7/2),x,5,21/8*a*c^(7/2)*sqrt(Pi)*erf(sqrt(c*LambertW(a*x^n))/sqrt(c))/n-21/4*c^2*(c*LambertW(a*x^n))^(3/2)/n/(x^n)-7/2*c*(c*LambertW(a*x^n))^(5/2)/n/(x^n)-(c*LambertW(a*x^n))^(7/2)/n/(x^n),1],
[x^(-1-n)*(c*LambertW(a*x^n))^(5/2),x,4,5/4*a*c^(5/2)*sqrt(Pi)*erf(sqrt(c*LambertW(a*x^n))/sqrt(c))/n-5/2*c*(c*LambertW(a*x^n))^(3/2)/n/(x^n)-(c*LambertW(a*x^n))^(5/2)/n/(x^n),1],
[x^(-1-n)*(c*LambertW(a*x^n))^(3/2),x,3,3/2*a*c^(3/2)*sqrt(Pi)*erf(sqrt(c*LambertW(a*x^n))/sqrt(c))/n-(c*LambertW(a*x^n))^(3/2)/n/(x^n),1],
[x^(-1-n)*sqrt(c*LambertW(a*x^n)),x,3,-a*sqrt(c)*sqrt(Pi)*erf(sqrt(c*LambertW(a*x^n))/sqrt(c))/n-2*sqrt(c*LambertW(a*x^n))/n/(x^n),1],
[x^(-1-n)/sqrt(c*LambertW(a*x^n)),x,4,-2/3*a*sqrt(Pi)*erf(sqrt(c*LambertW(a*x^n))/sqrt(c))/sqrt(c)/n-2/3/n/(x^n)/sqrt(c*LambertW(a*x^n))-2/3*sqrt(c*LambertW(a*x^n))/c/n/(x^n),1],
[x^(-1-n)/(c*LambertW(a*x^n))^(3/2),x,5,4/5*a*sqrt(Pi)*erf(sqrt(c*LambertW(a*x^n))/sqrt(c))/c^(3/2)/n-2/5/n/(x^n)/(c*LambertW(a*x^n))^(3/2)-2/5/c/n/(x^n)/sqrt(c*LambertW(a*x^n))+4/5*sqrt(c*LambertW(a*x^n))/c^2/n/(x^n),1],
[x^(-1-n)/(c*LambertW(a*x^n))^(5/2),x,6,-8/21*a*sqrt(Pi)*erf(sqrt(c*LambertW(a*x^n))/sqrt(c))/c^(5/2)/n-2/7/n/(x^n)/(c*LambertW(a*x^n))^(5/2)-2/7/c/n/(x^n)/(c*LambertW(a*x^n))^(3/2)+4/21/c^2/n/(x^n)/sqrt(c*LambertW(a*x^n))-8/21*sqrt(c*LambertW(a*x^n))/c^3/n/(x^n),1],
[x^(-1-2*n)*(c*LambertW(a*x^n))^(11/2),x,6,165/256*a^2*c^(11/2)*sqrt(1/2*Pi)*erf(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/n-165/128*c^3*(c*LambertW(a*x^n))^(5/2)/n/(x^(2*n))-55/32*c^2*(c*LambertW(a*x^n))^(7/2)/n/(x^(2*n))-11/8*c*(c*LambertW(a*x^n))^(9/2)/n/(x^(2*n))-1/2*(c*LambertW(a*x^n))^(11/2)/n/(x^(2*n)),1],
[x^(-1-2*n)*(c*LambertW(a*x^n))^(9/2),x,5,27/64*a^2*c^(9/2)*sqrt(1/2*Pi)*erf(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/n-27/32*c^2*(c*LambertW(a*x^n))^(5/2)/n/(x^(2*n))-9/8*c*(c*LambertW(a*x^n))^(7/2)/n/(x^(2*n))-1/2*(c*LambertW(a*x^n))^(9/2)/n/(x^(2*n)),1],
[x^(-1-2*n)*(c*LambertW(a*x^n))^(7/2),x,4,7/16*a^2*c^(7/2)*sqrt(1/2*Pi)*erf(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/n-7/8*c*(c*LambertW(a*x^n))^(5/2)/n/(x^(2*n))-1/2*(c*LambertW(a*x^n))^(7/2)/n/(x^(2*n)),1],
[x^(-1-2*n)*(c*LambertW(a*x^n))^(5/2),x,3,5/4*a^2*c^(5/2)*sqrt(1/2*Pi)*erf(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/n-1/2*(c*LambertW(a*x^n))^(5/2)/n/(x^(2*n)),1],
[x^(-1-2*n)*(c*LambertW(a*x^n))^(3/2),x,3,-3*a^2*c^(3/2)*sqrt(1/2*Pi)*erf(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/n-2*(c*LambertW(a*x^n))^(3/2)/n/(x^(2*n)),1],
[x^(-1-2*n)*sqrt(c*LambertW(a*x^n)),x,4,2/3*a^2*sqrt(c)*sqrt(2*Pi)*erf(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/n-2/3*sqrt(c*LambertW(a*x^n))/n/(x^(2*n))+2/3*(c*LambertW(a*x^n))^(3/2)/c/n/(x^(2*n)),1],
[x^(-1-2*n)/sqrt(c*LambertW(a*x^n)),x,5,8/15*a^2*sqrt(2*Pi)*erf(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/sqrt(c)/n-2/5/n/(x^(2*n))/sqrt(c*LambertW(a*x^n))-2/15*sqrt(c*LambertW(a*x^n))/c/n/(x^(2*n))+8/15*(c*LambertW(a*x^n))^(3/2)/c^2/n/(x^(2*n)),1],
[x^(-1-2*n)/(c*LambertW(a*x^n))^(3/2),x,6,-32/35*a^2*sqrt(2*Pi)*erf(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/c^(3/2)/n-2/7/n/(x^(2*n))/(c*LambertW(a*x^n))^(3/2)-6/35/c/n/(x^(2*n))/sqrt(c*LambertW(a*x^n))+8/35*sqrt(c*LambertW(a*x^n))/c^2/n/(x^(2*n))-32/35*(c*LambertW(a*x^n))^(3/2)/c^3/n/(x^(2*n)),1],
[x^(-1+n)*(c*LambertW(a*x^n))^(5/2),x,6,75/16*c^(5/2)*sqrt(Pi)*erfi(sqrt(c*LambertW(a*x^n))/sqrt(c))/a/n-75/8*c^3*x^n/n/sqrt(c*LambertW(a*x^n))+25/4*c^2*x^n*sqrt(c*LambertW(a*x^n))/n-5/2*c*x^n*(c*LambertW(a*x^n))^(3/2)/n+x^n*(c*LambertW(a*x^n))^(5/2)/n,1],
[x^(-1+n)*(c*LambertW(a*x^n))^(3/2),x,5,-9/8*c^(3/2)*sqrt(Pi)*erfi(sqrt(c*LambertW(a*x^n))/sqrt(c))/a/n+9/4*c^2*x^n/n/sqrt(c*LambertW(a*x^n))-3/2*c*x^n*sqrt(c*LambertW(a*x^n))/n+x^n*(c*LambertW(a*x^n))^(3/2)/n,1],
[x^(-1+n)*sqrt(c*LambertW(a*x^n)),x,4,1/4*sqrt(c)*sqrt(Pi)*erfi(sqrt(c*LambertW(a*x^n))/sqrt(c))/a/n-1/2*c*x^n/n/sqrt(c*LambertW(a*x^n))+x^n*sqrt(c*LambertW(a*x^n))/n,1],
[x^(-1+n)/sqrt(c*LambertW(a*x^n)),x,3,1/2*sqrt(Pi)*erfi(sqrt(c*LambertW(a*x^n))/sqrt(c))/a/sqrt(c)/n+x^n/n/sqrt(c*LambertW(a*x^n)),1],
[x^(-1+n)/(c*LambertW(a*x^n))^(3/2),x,3,3*sqrt(Pi)*erfi(sqrt(c*LambertW(a*x^n))/sqrt(c))/a/c^(3/2)/n-2*x^n/n/(c*LambertW(a*x^n))^(3/2),1],
[x^(-1+n)/(c*LambertW(a*x^n))^(5/2),x,4,10/3*sqrt(Pi)*erfi(sqrt(c*LambertW(a*x^n))/sqrt(c))/a/c^(5/2)/n-2/3*x^n/n/(c*LambertW(a*x^n))^(5/2)-10/3*x^n/c/n/(c*LambertW(a*x^n))^(3/2),1],
[x^(-1+n)/(c*LambertW(a*x^n))^(7/2),x,5,28/15*sqrt(Pi)*erfi(sqrt(c*LambertW(a*x^n))/sqrt(c))/a/c^(7/2)/n-2/5*x^n/n/(c*LambertW(a*x^n))^(7/2)-14/15*x^n/c/n/(c*LambertW(a*x^n))^(5/2)-28/15*x^n/c^2/n/(c*LambertW(a*x^n))^(3/2),1],
[x^(-1+n)/(c*LambertW(a*x^n))^(9/2),x,6,24/35*sqrt(Pi)*erfi(sqrt(c*LambertW(a*x^n))/sqrt(c))/a/c^(9/2)/n-2/7*x^n/n/(c*LambertW(a*x^n))^(9/2)-18/35*x^n/c/n/(c*LambertW(a*x^n))^(7/2)-12/35*x^n/c^2/n/(c*LambertW(a*x^n))^(5/2)-24/35*x^n/c^3/n/(c*LambertW(a*x^n))^(3/2),1],
[x^(-1+2*n)*(c*LambertW(a*x^n))^(3/2),x,6,45/256*c^(3/2)*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/a^2/n-45/128*c^3*x^(2*n)/n/(c*LambertW(a*x^n))^(3/2)+15/32*c^2*x^(2*n)/n/sqrt(c*LambertW(a*x^n))-3/8*c*x^(2*n)*sqrt(c*LambertW(a*x^n))/n+1/2*x^(2*n)*(c*LambertW(a*x^n))^(3/2)/n,1],
[x^(-1+2*n)*sqrt(c*LambertW(a*x^n)),x,5,-3/64*sqrt(c)*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/a^2/n+3/32*c^2*x^(2*n)/n/(c*LambertW(a*x^n))^(3/2)-1/8*c*x^(2*n)/n/sqrt(c*LambertW(a*x^n))+1/2*x^(2*n)*sqrt(c*LambertW(a*x^n))/n,1],
[x^(-1+2*n)/sqrt(c*LambertW(a*x^n)),x,4,-1/16*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/a^2/sqrt(c)/n+1/8*c*x^(2*n)/n/(c*LambertW(a*x^n))^(3/2)+1/2*x^(2*n)/n/sqrt(c*LambertW(a*x^n)),1],
[x^(-1+2*n)/(c*LambertW(a*x^n))^(3/2),x,3,3/4*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/a^2/c^(3/2)/n+1/2*x^(2*n)/n/(c*LambertW(a*x^n))^(3/2),1],
[x^(-1+2*n)/(c*LambertW(a*x^n))^(5/2),x,3,5*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/a^2/c^(5/2)/n-2*x^(2*n)/n/(c*LambertW(a*x^n))^(5/2),1],
[x^(-1+2*n)/(c*LambertW(a*x^n))^(7/2),x,4,14/3*sqrt(2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/a^2/c^(7/2)/n-2/3*x^(2*n)/n/(c*LambertW(a*x^n))^(7/2)-14/3*x^(2*n)/c/n/(c*LambertW(a*x^n))^(5/2),1],
[x^(-1+2*n)/(c*LambertW(a*x^n))^(9/2),x,5,24/5*sqrt(2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/a^2/c^(9/2)/n-2/5*x^(2*n)/n/(c*LambertW(a*x^n))^(9/2)-6/5*x^(2*n)/c/n/(c*LambertW(a*x^n))^(7/2)-24/5*x^(2*n)/c^2/n/(c*LambertW(a*x^n))^(5/2),1],
[x^(-1+2*n)/(c*LambertW(a*x^n))^(11/2),x,6,352/105*sqrt(2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(a*x^n))/sqrt(c))/a^2/c^(11/2)/n-2/7*x^(2*n)/n/(c*LambertW(a*x^n))^(11/2)-22/35*x^(2*n)/c/n/(c*LambertW(a*x^n))^(9/2)-88/105*x^(2*n)/c^2/n/(c*LambertW(a*x^n))^(7/2)-352/105*x^(2*n)/c^3/n/(c*LambertW(a*x^n))^(5/2),1],
[x*(c*LambertW(a*x^n))^p,x,4,2^(-1-2/n-p)*x^(2-n)*GAMMA(1+2/n+p,-2*LambertW(a*x^n)/n)*(c*LambertW(a*x^n))^(p+1)*(-LambertW(a*x^n)/n)^(-2/n-p)/a/c/exp((2-n)*LambertW(a*x^n)/n)+2^(-2/n-p)*x^(2-n)*GAMMA(2/n+p,-2*LambertW(a*x^n)/n)*(c*LambertW(a*x^n))^p*(-LambertW(a*x^n)/n)^(1-2/n-p)/a/exp((2-n)*LambertW(a*x^n)/n),1],
[(c*LambertW(a*x^n))^p,x,4,x^(1-n)*GAMMA(1+1/n+p,-LambertW(a*x^n)/n)*(c*LambertW(a*x^n))^(p+1)*(-LambertW(a*x^n)/n)^(-1/n-p)/a/c/exp((1-n)*LambertW(a*x^n)/n)+x^(1-n)*GAMMA(1/n+p,-LambertW(a*x^n)/n)*(c*LambertW(a*x^n))^p*(-LambertW(a*x^n)/n)^(1-1/n-p)/a/exp((1-n)*LambertW(a*x^n)/n),1],
[(c*LambertW(a*x^n))^p/x,x,3,(c*LambertW(a*x^n))^p/n/p+(c*LambertW(a*x^n))^(p+1)/c/n/(p+1),1],
[(c*LambertW(a*x^n))^p/x^2,x,4,-exp((1+1/n)*LambertW(a*x^n))*x^(-1-n)*GAMMA(1-1/n+p,LambertW(a*x^n)/n)*(c*LambertW(a*x^n))^(p+1)*(LambertW(a*x^n)/n)^(1/n-p)/a/c-exp((1+1/n)*LambertW(a*x^n))*x^(-1-n)*GAMMA(-1/n+p,LambertW(a*x^n)/n)*(c*LambertW(a*x^n))^p*(LambertW(a*x^n)/n)^(1+1/n-p)/a,1],
[(c*LambertW(a*x^n))^p/x^3,x,4,-2^(-1+2/n-p)*exp((2+n)*LambertW(a*x^n)/n)*x^(-2-n)*GAMMA(1-2/n+p,2*LambertW(a*x^n)/n)*(c*LambertW(a*x^n))^(p+1)*(LambertW(a*x^n)/n)^(2/n-p)/a/c-2^(2/n-p)*exp((2+n)*LambertW(a*x^n)/n)*x^(-2-n)*GAMMA(-2/n+p,2*LambertW(a*x^n)/n)*(c*LambertW(a*x^n))^p*(LambertW(a*x^n)/n)^(1+2/n-p)/a,1],
[LambertW(a*x^n)^((-1+n)/n),x,5,(1-n)*x/(LambertW(a*x^n)^(1/n))+x/(LambertW(a*x^n)^((1-n)/n)),1],
[LambertW(a*x^(1/(1-p)))^p,x,3,-p*x*LambertW(a*x^(1/(1-p)))^(-1+p)/(1-p)+x*LambertW(a*x^(1/(1-p)))^p,1],
[x^m*(c*LambertW(a*x^n))^p,x,4,exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA((1+m)/n+p,-(1+m)*LambertW(a*x^n)/n)*(c*LambertW(a*x^n))^p*(-(1+m)*LambertW(a*x^n)/n)^(1-(1+m)/n-p)/a/(1+m)+exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA(1+(1+m)/n+p,-(1+m)*LambertW(a*x^n)/n)*(c*LambertW(a*x^n))^(p+1)/a/c/(1+m)/((-(1+m)*LambertW(a*x^n)/n)^((n*p+m+1)/n)),1],
[x^(-1-n*(p+1))*(c*LambertW(a*x^n))^p,x,3,-(c*LambertW(a*x^n))^p/n/(x^(n*(p+1)))+exp((2+p)*LambertW(a*x^n))*p*GAMMA(0,(p+1)*LambertW(a*x^n))*LambertW(a*x^n)*(c*LambertW(a*x^n))^(p+1)/a/c/n/(x^(n*(2+p))),1],
[x^(-n*p-1)*(c*LambertW(a*x^n))^p,x,3,-(c*LambertW(a*x^n))^p/n/p/(x^(n*p))-exp((p+1)*LambertW(a*x^n))*GAMMA(0,p*LambertW(a*x^n))*LambertW(a*x^n)*(c*LambertW(a*x^n))^p/a/n/(x^(n*(p+1))),1],
[x^(-1+n*(1-p))*(c*LambertW(a*x^n))^p,x,3,-c*p*x^(n*(1-p))*(c*LambertW(a*x^n))^(-1+p)/n/(1-p)^2+x^(n*(1-p))*(c*LambertW(a*x^n))^p/n/(1-p),1],
[x^(-1+n*(2-p))*(c*LambertW(a*x^n))^p,x,4,c^2*p*x^(n*(2-p))*(c*LambertW(a*x^n))^(-2+p)/n/(2-p)^3-c*p*x^(n*(2-p))*(c*LambertW(a*x^n))^(-1+p)/n/(2-p)^2+x^(n*(2-p))*(c*LambertW(a*x^n))^p/n/(2-p),1],
[x^(-1+n*(3-p))*(c*LambertW(a*x^n))^p,x,5,-2*c^3*p*x^(n*(3-p))*(c*LambertW(a*x^n))^(-3+p)/n/(3-p)^4+2*c^2*p*x^(n*(3-p))*(c*LambertW(a*x^n))^(-2+p)/n/(3-p)^3-c*p*x^(n*(3-p))*(c*LambertW(a*x^n))^(-1+p)/n/(3-p)^2+x^(n*(3-p))*(c*LambertW(a*x^n))^p/n/(3-p),1],
[x^3/(1+LambertW(a*x)),x,4,-3/128*x^4/LambertW(a*x)^4+3/32*x^4/LambertW(a*x)^3-3/16*x^4/LambertW(a*x)^2+1/4*x^4/LambertW(a*x),1],
[x^2/(1+LambertW(a*x)),x,3,2/27*x^3/LambertW(a*x)^3-2/9*x^3/LambertW(a*x)^2+1/3*x^3/LambertW(a*x),1],
[x/(1+LambertW(a*x)),x,2,-1/4*x^2/LambertW(a*x)^2+1/2*x^2/LambertW(a*x),1],
[1/(1+LambertW(a*x)),x,1,x/LambertW(a*x),1],
[1/x/(1+LambertW(a*x)),x,1,ln(LambertW(a*x)),1],
[1/x^2/(1+LambertW(a*x)),x,2,-1/x-a*Ei(-LambertW(a*x)),1],
[1/x^3/(1+LambertW(a*x)),x,3,-1/2/x^2+2*a^2*Ei(-2*LambertW(a*x))+LambertW(a*x)/x^2,1],
[1/x^4/(1+LambertW(a*x)),x,4,-1/3/x^3-9/2*a^3*Ei(-3*LambertW(a*x))+1/2*LambertW(a*x)/x^3-3/2*LambertW(a*x)^2/x^3,1],
[x^5/(1+LambertW(a*x^2)),x,4,1/27*x^6/LambertW(a*x^2)^3-1/9*x^6/LambertW(a*x^2)^2+1/6*x^6/LambertW(a*x^2),1],
[x^3/(1+LambertW(a*x^2)),x,3,-1/8*x^4/LambertW(a*x^2)^2+1/4*x^4/LambertW(a*x^2),1],
[x/(1+LambertW(a*x^2)),x,2,1/2*x^2/LambertW(a*x^2),1],
[1/x/(1+LambertW(a*x^2)),x,2,1/2*ln(LambertW(a*x^2)),1],
[1/x^3/(1+LambertW(a*x^2)),x,3,-1/2/x^2-1/2*a*Ei(-LambertW(a*x^2)),1],
[1/x^5/(1+LambertW(a*x^2)),x,4,-1/4/x^4+a^2*Ei(-2*LambertW(a*x^2))+1/2*LambertW(a*x^2)/x^4,1],
[x^4/(1+LambertW(a*x^2)),x,4,-3/25*x^5/LambertW(a*x^2)^2+3/25*x^3*GAMMA(1/2,-5/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/sqrt(10)/a/exp(3/2*LambertW(a*x^2))/LambertW(a*x^2)^2+1/5*x^5/LambertW(a*x^2),1],
[x^2/(1+LambertW(a*x^2)),x,3,1/3*x^3/LambertW(a*x^2)-1/3*x*GAMMA(1/2,-3/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/sqrt(6)/a/exp(1/2*LambertW(a*x^2))/LambertW(a*x^2),1],
[1/(1+LambertW(a*x^2)),x,2,exp(1/2*LambertW(a*x^2))*GAMMA(1/2,-1/2*LambertW(a*x^2))*sqrt(-LambertW(a*x^2))/sqrt(2)/a/x,1],
[1/x^2/(1+LambertW(a*x^2)),x,3,-1/x+exp(3/2*LambertW(a*x^2))*GAMMA(1/2,1/2*LambertW(a*x^2))*LambertW(a*x^2)^(3/2)/sqrt(2)/a/x^3,1],
[1/x^4/(1+LambertW(a*x^2)),x,4,-1/3/x^3+LambertW(a*x^2)/x^3-sqrt(3/2)*exp(5/2*LambertW(a*x^2))*GAMMA(1/2,3/2*LambertW(a*x^2))*LambertW(a*x^2)^(5/2)/a/x^5,1],
[x^2/(1+LambertW(a/x)),x,5,1/3*x^3+9/2*a^3*Ei(-3*LambertW(a/x))-1/2*x^3*LambertW(a/x)+3/2*x^3*LambertW(a/x)^2,1],
[x/(1+LambertW(a/x)),x,4,1/2*x^2-2*a^2*Ei(-2*LambertW(a/x))-x^2*LambertW(a/x),1],
[1/(1+LambertW(a/x)),x,3,x+a*Ei(-LambertW(a/x)),1],
[1/x/(1+LambertW(a/x)),x,2,-ln(LambertW(a/x)),1],
[1/x^2/(1+LambertW(a/x)),x,2,-1/x/LambertW(a/x),1],
[1/x^3/(1+LambertW(a/x)),x,3,1/4/x^2/LambertW(a/x)^2-1/2/x^2/LambertW(a/x),1],
[1/x^4/(1+LambertW(a/x)),x,4,-2/27/x^3/LambertW(a/x)^3+2/9/x^3/LambertW(a/x)^2-1/3/x^3/LambertW(a/x),1],
[x^5/(1+LambertW(a/x^2)),x,5,1/6*x^6+9/4*a^3*Ei(-3*LambertW(a/x^2))-1/4*x^6*LambertW(a/x^2)+3/4*x^6*LambertW(a/x^2)^2,1],
[x^3/(1+LambertW(a/x^2)),x,4,1/4*x^4-a^2*Ei(-2*LambertW(a/x^2))-1/2*x^4*LambertW(a/x^2),1],
[x/(1+LambertW(a/x^2)),x,4,1/2*x^2+1/2*a*Ei(-LambertW(a/x^2)),1],
[1/x/(1+LambertW(a/x^2)),x,2,-1/2*ln(LambertW(a/x^2)),1],
[1/x^3/(1+LambertW(a/x^2)),x,2,-1/2/x^2/LambertW(a/x^2),1],
[1/x^5/(1+LambertW(a/x^2)),x,3,1/8/x^4/LambertW(a/x^2)^2-1/4/x^4/LambertW(a/x^2),1],
[1/x^7/(1+LambertW(a/x^2)),x,4,-1/27/x^6/LambertW(a/x^2)^3+1/9/x^6/LambertW(a/x^2)^2-1/6/x^6/LambertW(a/x^2),1],
[x^4/(1+LambertW(a/x^2)),x,5,1/5*x^5-1/3*x^5*LambertW(a/x^2)+5/3*x^5*LambertW(a/x^2)^2-5/3*sqrt(5/2)*exp(7/2*LambertW(a/x^2))*x^7*GAMMA(1/2,5/2*LambertW(a/x^2))*LambertW(a/x^2)^(7/2)/a,1],
[x^2/(1+LambertW(a/x^2)),x,4,1/3*x^3-x^3*LambertW(a/x^2)+sqrt(3/2)*exp(5/2*LambertW(a/x^2))*x^5*GAMMA(1/2,3/2*LambertW(a/x^2))*LambertW(a/x^2)^(5/2)/a,1],
[1/(1+LambertW(a/x^2)),x,3,x-exp(3/2*LambertW(a/x^2))*x^3*GAMMA(1/2,1/2*LambertW(a/x^2))*LambertW(a/x^2)^(3/2)/sqrt(2)/a,1],
[1/x^2/(1+LambertW(a/x^2)),x,2,-exp(1/2*LambertW(a/x^2))*x*GAMMA(1/2,-1/2*LambertW(a/x^2))*sqrt(-LambertW(a/x^2))/sqrt(2)/a,1],
[1/x^4/(1+LambertW(a/x^2)),x,3,-1/3/x^3/LambertW(a/x^2)+1/3*GAMMA(1/2,-3/2*LambertW(a/x^2))*sqrt(-LambertW(a/x^2))/sqrt(6)/a/exp(1/2*LambertW(a/x^2))/x/LambertW(a/x^2),1],
[x^m/(d+d*LambertW(a*x^3)),x,2,3^(-2/3+1/3*m)*exp(1/3*(2-m)*LambertW(a*x^3))*x^(-2+m)*GAMMA(1/3+1/3*m,-1/3*(1+m)*LambertW(a*x^3))*(-(1+m)*LambertW(a*x^3))^(2/3-1/3*m)/a/d/(1+m),1],
[x^m/(d+d*LambertW(a*x^2)),x,2,2^(-1/2+1/2*m)*exp(1/2*(1-m)*LambertW(a*x^2))*x^(-1+m)*GAMMA(1/2+1/2*m,-1/2*(1+m)*LambertW(a*x^2))*(-(1+m)*LambertW(a*x^2))^(1/2-1/2*m)/a/d/(1+m),1],
[x^m/(d+d*LambertW(a*x)),x,1,x^m*GAMMA(1+m,(-1-m)*LambertW(a*x))/a/d/exp(m*LambertW(a*x))/(1+m)/(((-1-m)*LambertW(a*x))^m),1],
[x^m/(d+d*LambertW(a/x)),x,2,exp((2+m)*LambertW(a/x))*x^(2+m)*GAMMA(-1-m,(1+m)*LambertW(a/x))*((1+m)*LambertW(a/x))^(2+m)/a/d/(1+m),1],
[x^m/(d+d*LambertW(a/x^2)),x,2,2^(-3/2-1/2*m)*exp(1/2*(3+m)*LambertW(a/x^2))*x^(3+m)*GAMMA(-1/2-1/2*m,1/2*(1+m)*LambertW(a/x^2))*((1+m)*LambertW(a/x^2))^(3/2+1/2*m)/a/d/(1+m),1],
[x^m/(d+d*LambertW(a*x^n)),x,2,exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA((1+m)/n,-(1+m)*LambertW(a*x^n)/n)*(-(1+m)*LambertW(a*x^n)/n)^(1-(1+m)/n)/a/d/(1+m),1],
[LambertW(a/x^(1/4))^5/(1+LambertW(a/x^(1/4))),x,2,x*LambertW(a/x^(1/4))^4,1],
[LambertW(a/x^(1/3))^4/(1+LambertW(a/x^(1/3))),x,2,x*LambertW(a/x^(1/3))^3,1],
[LambertW(a/sqrt(x))^3/(1+LambertW(a/sqrt(x))),x,2,x*LambertW(a/sqrt(x))^2,1],
[LambertW(a/x)^2/(1+LambertW(a/x)),x,2,x*LambertW(a/x),1],
[1/LambertW(a*sqrt(x))/(1+LambertW(a*sqrt(x))),x,2,x/LambertW(a*sqrt(x))^2,1],
[1/LambertW(a*x^(1/3))^2/(1+LambertW(a*x^(1/3))),x,2,x/LambertW(a*x^(1/3))^3,1],
[1/LambertW(a*x^(1/4))^3/(1+LambertW(a*x^(1/4))),x,2,x/LambertW(a*x^(1/4))^4,1],
[LambertW(a/x^(1/4))^4/(1+LambertW(a/x^(1/4))),x,2,-4*a^4*Ei(-4*LambertW(a/x^(1/4))),1],
[LambertW(a/x^(1/3))^3/(1+LambertW(a/x^(1/3))),x,2,-3*a^3*Ei(-3*LambertW(a/x^(1/3))),1],
[LambertW(a/sqrt(x))^2/(1+LambertW(a/sqrt(x))),x,2,-2*a^2*Ei(-2*LambertW(a/sqrt(x))),1],
[LambertW(a/x)/(1+LambertW(a/x)),x,2,-a*Ei(-LambertW(a/x)),1],
[1/LambertW(a*x)/(1+LambertW(a*x)),x,1,Ei(LambertW(a*x))/a,1],
[1/LambertW(a*sqrt(x))^2/(1+LambertW(a*sqrt(x))),x,2,2*Ei(2*LambertW(a*sqrt(x)))/a^2,1],
[1/LambertW(a*x^(1/3))^3/(1+LambertW(a*x^(1/3))),x,2,3*Ei(3*LambertW(a*x^(1/3)))/a^3,1],
[1/LambertW(a*x^(1/4))^4/(1+LambertW(a*x^(1/4))),x,2,4*Ei(4*LambertW(a*x^(1/4)))/a^4,1],
[LambertW(a*x^n)^p/(d+d*LambertW(a*x^n)),x,2,x^(1-n)*GAMMA(1/n+p,-LambertW(a*x^n)/n)*LambertW(a*x^n)^p*(-LambertW(a*x^n)/n)^(1-1/n-p)/a/d/exp((1-n)*LambertW(a*x^n)/n),1],
[LambertW(a*x^n)^(1-1/n)/(1+LambertW(a*x^n)),x,2,x/(LambertW(a*x^n)^(1/n)),1],
[LambertW(a*x^(1/(1-p)))^p/(1+LambertW(a*x^(1/(1-p)))),x,2,x*LambertW(a*x^(1/(1-p)))^(-1+p),1],
[x^m*LambertW(a*x^n)^p/(d+d*LambertW(a*x^n)),x,2,exp((1-(1+m)/n)*LambertW(a*x^n))*x^(1+m-n)*GAMMA((1+m)/n+p,-(1+m)*LambertW(a*x^n)/n)*LambertW(a*x^n)^p*(-(1+m)*LambertW(a*x^n)/n)^(1-(1+m)/n-p)/a/d/(1+m),1],
[LambertW(b*x+a)^4,x,6,96*x-96*(b*x+a)/b/LambertW(b*x+a)-48*(b*x+a)*LambertW(b*x+a)/b+16*(b*x+a)*LambertW(b*x+a)^2/b-4*(b*x+a)*LambertW(b*x+a)^3/b+(b*x+a)*LambertW(b*x+a)^4/b,1],
[LambertW(b*x+a)^3,x,5,-18*x+18*(b*x+a)/b/LambertW(b*x+a)+9*(b*x+a)*LambertW(b*x+a)/b-3*(b*x+a)*LambertW(b*x+a)^2/b+(b*x+a)*LambertW(b*x+a)^3/b,1],
[LambertW(b*x+a)^2,x,4,4*x-4*(b*x+a)/b/LambertW(b*x+a)-2*(b*x+a)*LambertW(b*x+a)/b+(b*x+a)*LambertW(b*x+a)^2/b,1],
[LambertW(b*x+a),x,3,-x+(b*x+a)/b/LambertW(b*x+a)+(b*x+a)*LambertW(b*x+a)/b,1],
[1/LambertW(b*x+a),x,2,Ei(LambertW(b*x+a))/b+(b*x+a)/b/LambertW(b*x+a),1],
[1/LambertW(b*x+a)^2,x,2,2*Ei(LambertW(b*x+a))/b-(b*x+a)/b/LambertW(b*x+a)^2,1],
[1/LambertW(b*x+a)^3,x,3,3/2*Ei(LambertW(b*x+a))/b-1/2*(b*x+a)/b/LambertW(b*x+a)^3-3/2*(b*x+a)/b/LambertW(b*x+a)^2,1],
[1/LambertW(b*x+a)^4,x,4,2/3*Ei(LambertW(b*x+a))/b-1/3*(b*x+a)/b/LambertW(b*x+a)^4-2/3*(b*x+a)/b/LambertW(b*x+a)^3-2/3*(b*x+a)/b/LambertW(b*x+a)^2,1],
[1/LambertW(b*x+a)^5,x,5,5/24*Ei(LambertW(b*x+a))/b-1/4*(b*x+a)/b/LambertW(b*x+a)^5-5/12*(b*x+a)/b/LambertW(b*x+a)^4-5/24*(b*x+a)/b/LambertW(b*x+a)^3-5/24*(b*x+a)/b/LambertW(b*x+a)^2,1],
[(c*LambertW(b*x+a))^(5/2),x,5,75/16*c^(5/2)*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b-75/8*c^3*(b*x+a)/b/sqrt(c*LambertW(b*x+a))+25/4*c^2*(b*x+a)*sqrt(c*LambertW(b*x+a))/b-5/2*c*(b*x+a)*(c*LambertW(b*x+a))^(3/2)/b+(b*x+a)*(c*LambertW(b*x+a))^(5/2)/b,1],
[(c*LambertW(b*x+a))^(3/2),x,4,-9/8*c^(3/2)*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b+9/4*c^2*(b*x+a)/b/sqrt(c*LambertW(b*x+a))-3/2*c*(b*x+a)*sqrt(c*LambertW(b*x+a))/b+(b*x+a)*(c*LambertW(b*x+a))^(3/2)/b,1],
[sqrt(c*LambertW(b*x+a)),x,3,1/4*sqrt(c)*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b-1/2*c*(b*x+a)/b/sqrt(c*LambertW(b*x+a))+(b*x+a)*sqrt(c*LambertW(b*x+a))/b,1],
[1/sqrt(c*LambertW(b*x+a)),x,2,1/2*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b/sqrt(c)+(b*x+a)/b/sqrt(c*LambertW(b*x+a)),1],
[1/(c*LambertW(b*x+a))^(3/2),x,2,3*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b/c^(3/2)-2*(b*x+a)/b/(c*LambertW(b*x+a))^(3/2),1],
[1/(c*LambertW(b*x+a))^(5/2),x,3,10/3*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b/c^(5/2)-2/3*(b*x+a)/b/(c*LambertW(b*x+a))^(5/2)-10/3*(b*x+a)/b/c/(c*LambertW(b*x+a))^(3/2),1],
[1/(c*LambertW(b*x+a))^(7/2),x,4,28/15*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b/c^(7/2)-2/5*(b*x+a)/b/(c*LambertW(b*x+a))^(7/2)-14/15*(b*x+a)/b/c/(c*LambertW(b*x+a))^(5/2)-28/15*(b*x+a)/b/c^2/(c*LambertW(b*x+a))^(3/2),1],
[(-c*LambertW(b*x+a))^(5/2),x,5,75/16*c^(5/2)*sqrt(Pi)*erf(sqrt(-c*LambertW(b*x+a))/sqrt(c))/b+75/8*c^3*(b*x+a)/b/sqrt(-c*LambertW(b*x+a))+25/4*c^2*(b*x+a)*sqrt(-c*LambertW(b*x+a))/b+5/2*c*(b*x+a)*(-c*LambertW(b*x+a))^(3/2)/b+(b*x+a)*(-c*LambertW(b*x+a))^(5/2)/b,1],
[(-c*LambertW(b*x+a))^(3/2),x,4,9/8*c^(3/2)*sqrt(Pi)*erf(sqrt(-c*LambertW(b*x+a))/sqrt(c))/b+9/4*c^2*(b*x+a)/b/sqrt(-c*LambertW(b*x+a))+3/2*c*(b*x+a)*sqrt(-c*LambertW(b*x+a))/b+(b*x+a)*(-c*LambertW(b*x+a))^(3/2)/b,1],
[sqrt(-c*LambertW(b*x+a)),x,3,1/4*sqrt(c)*sqrt(Pi)*erf(sqrt(-c*LambertW(b*x+a))/sqrt(c))/b+1/2*c*(b*x+a)/b/sqrt(-c*LambertW(b*x+a))+(b*x+a)*sqrt(-c*LambertW(b*x+a))/b,1],
[1/sqrt(-c*LambertW(b*x+a)),x,2,-1/2*sqrt(Pi)*erf(sqrt(-c*LambertW(b*x+a))/sqrt(c))/b/sqrt(c)+(b*x+a)/b/sqrt(-c*LambertW(b*x+a)),1],
[1/(-c*LambertW(b*x+a))^(3/2),x,2,3*sqrt(Pi)*erf(sqrt(-c*LambertW(b*x+a))/sqrt(c))/b/c^(3/2)-2*(b*x+a)/b/(-c*LambertW(b*x+a))^(3/2),1],
[1/(-c*LambertW(b*x+a))^(5/2),x,3,-10/3*sqrt(Pi)*erf(sqrt(-c*LambertW(b*x+a))/sqrt(c))/b/c^(5/2)-2/3*(b*x+a)/b/(-c*LambertW(b*x+a))^(5/2)+10/3*(b*x+a)/b/c/(-c*LambertW(b*x+a))^(3/2),1],
[1/(-c*LambertW(b*x+a))^(7/2),x,4,28/15*sqrt(Pi)*erf(sqrt(-c*LambertW(b*x+a))/sqrt(c))/b/c^(7/2)-2/5*(b*x+a)/b/(-c*LambertW(b*x+a))^(7/2)+14/15*(b*x+a)/b/c/(-c*LambertW(b*x+a))^(5/2)-28/15*(b*x+a)/b/c^2/(-c*LambertW(b*x+a))^(3/2),1],
[(c*LambertW(b*x+a))^n,x,2,(b*x+a)*(c*LambertW(b*x+a))^n/b-n*GAMMA(1+n,-LambertW(b*x+a))*(c*LambertW(b*x+a))^n/b/((-LambertW(b*x+a))^n),1],
[x^3*LambertW(b*x+a),x,20,a^3*x/b^3-3/4*a^2*(b*x+a)^2/b^4+1/3*a*(b*x+a)^3/b^4-1/16*(b*x+a)^4/b^4-3/512*(b*x+a)^4/b^4/LambertW(b*x+a)^4-2/27*a*(b*x+a)^3/b^4/LambertW(b*x+a)^3+3/128*(b*x+a)^4/b^4/LambertW(b*x+a)^3-3/8*a^2*(b*x+a)^2/b^4/LambertW(b*x+a)^2+2/9*a*(b*x+a)^3/b^4/LambertW(b*x+a)^2-3/64*(b*x+a)^4/b^4/LambertW(b*x+a)^2-a^3*(b*x+a)/b^4/LambertW(b*x+a)+3/4*a^2*(b*x+a)^2/b^4/LambertW(b*x+a)-1/3*a*(b*x+a)^3/b^4/LambertW(b*x+a)+1/16*(b*x+a)^4/b^4/LambertW(b*x+a)-a^3*(b*x+a)*LambertW(b*x+a)/b^4+3/2*a^2*(b*x+a)^2*LambertW(b*x+a)/b^4-a*(b*x+a)^3*LambertW(b*x+a)/b^4+1/4*(b*x+a)^4*LambertW(b*x+a)/b^4,1],
[x^2*LambertW(b*x+a),x,14,-a^2*x/b^2+1/2*a*(b*x+a)^2/b^3-1/9*(b*x+a)^3/b^3+2/81*(b*x+a)^3/b^3/LambertW(b*x+a)^3+1/4*a*(b*x+a)^2/b^3/LambertW(b*x+a)^2-2/27*(b*x+a)^3/b^3/LambertW(b*x+a)^2+a^2*(b*x+a)/b^3/LambertW(b*x+a)-1/2*a*(b*x+a)^2/b^3/LambertW(b*x+a)+1/9*(b*x+a)^3/b^3/LambertW(b*x+a)+a^2*(b*x+a)*LambertW(b*x+a)/b^3-a*(b*x+a)^2*LambertW(b*x+a)/b^3+1/3*(b*x+a)^3*LambertW(b*x+a)/b^3,1],
[x*LambertW(b*x+a),x,9,a*x/b-1/4*(b*x+a)^2/b^2-1/8*(b*x+a)^2/b^2/LambertW(b*x+a)^2-a*(b*x+a)/b^2/LambertW(b*x+a)+1/4*(b*x+a)^2/b^2/LambertW(b*x+a)-a*(b*x+a)*LambertW(b*x+a)/b^2+1/2*(b*x+a)^2*LambertW(b*x+a)/b^2,1],
[LambertW(b*x+a),x,3,-x+(b*x+a)/b/LambertW(b*x+a)+(b*x+a)*LambertW(b*x+a)/b,1],
[LambertW(b*x+a)/x,x,0,Defer(Int)(LambertW(b*x+a)/x,x),0],
[LambertW(b*x+a)/x^2,x,0,Defer(Int)(LambertW(b*x+a)/x^2,x),0],
[x^3*LambertW(b*x+a)^2,x,24,-4*a^3*x/b^3+9/4*a^2*(b*x+a)^2/b^4-8/9*a*(b*x+a)^3/b^4+5/32*(b*x+a)^4/b^4+15/1024*(b*x+a)^4/b^4/LambertW(b*x+a)^4+16/81*a*(b*x+a)^3/b^4/LambertW(b*x+a)^3-15/256*(b*x+a)^4/b^4/LambertW(b*x+a)^3+9/8*a^2*(b*x+a)^2/b^4/LambertW(b*x+a)^2-16/27*a*(b*x+a)^3/b^4/LambertW(b*x+a)^2+15/128*(b*x+a)^4/b^4/LambertW(b*x+a)^2+4*a^3*(b*x+a)/b^4/LambertW(b*x+a)-9/4*a^2*(b*x+a)^2/b^4/LambertW(b*x+a)+8/9*a*(b*x+a)^3/b^4/LambertW(b*x+a)-5/32*(b*x+a)^4/b^4/LambertW(b*x+a)+2*a^3*(b*x+a)*LambertW(b*x+a)/b^4-3/2*a^2*(b*x+a)^2*LambertW(b*x+a)/b^4+2/3*a*(b*x+a)^3*LambertW(b*x+a)/b^4-1/8*(b*x+a)^4*LambertW(b*x+a)/b^4-a^3*(b*x+a)*LambertW(b*x+a)^2/b^4+3/2*a^2*(b*x+a)^2*LambertW(b*x+a)^2/b^4-a*(b*x+a)^3*LambertW(b*x+a)^2/b^4+1/4*(b*x+a)^4*LambertW(b*x+a)^2/b^4,1],
[x^2*LambertW(b*x+a)^2,x,17,4*a^2*x/b^2-3/2*a*(b*x+a)^2/b^3+8/27*(b*x+a)^3/b^3-16/243*(b*x+a)^3/b^3/LambertW(b*x+a)^3-3/4*a*(b*x+a)^2/b^3/LambertW(b*x+a)^2+16/81*(b*x+a)^3/b^3/LambertW(b*x+a)^2-4*a^2*(b*x+a)/b^3/LambertW(b*x+a)+3/2*a*(b*x+a)^2/b^3/LambertW(b*x+a)-8/27*(b*x+a)^3/b^3/LambertW(b*x+a)-2*a^2*(b*x+a)*LambertW(b*x+a)/b^3+a*(b*x+a)^2*LambertW(b*x+a)/b^3-2/9*(b*x+a)^3*LambertW(b*x+a)/b^3+a^2*(b*x+a)*LambertW(b*x+a)^2/b^3-a*(b*x+a)^2*LambertW(b*x+a)^2/b^3+1/3*(b*x+a)^3*LambertW(b*x+a)^2/b^3,1],
[x*LambertW(b*x+a)^2,x,11,-4*a*x/b+3/4*(b*x+a)^2/b^2+3/8*(b*x+a)^2/b^2/LambertW(b*x+a)^2+4*a*(b*x+a)/b^2/LambertW(b*x+a)-3/4*(b*x+a)^2/b^2/LambertW(b*x+a)+2*a*(b*x+a)*LambertW(b*x+a)/b^2-1/2*(b*x+a)^2*LambertW(b*x+a)/b^2-a*(b*x+a)*LambertW(b*x+a)^2/b^2+1/2*(b*x+a)^2*LambertW(b*x+a)^2/b^2,1],
[LambertW(b*x+a)^2,x,4,4*x-4*(b*x+a)/b/LambertW(b*x+a)-2*(b*x+a)*LambertW(b*x+a)/b+(b*x+a)*LambertW(b*x+a)^2/b,1],
[LambertW(b*x+a)^2/x,x,0,Defer(Int)(LambertW(b*x+a)^2/x,x),0],
[LambertW(b*x+a)^2/x^2,x,0,Defer(Int)(LambertW(b*x+a)^2/x^2,x),0],
[x^3*sqrt(c*LambertW(b*x+a)),x,20,-1/4*a^3*sqrt(c)*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b^4-105/65536*sqrt(c)*sqrt(Pi)*erfi(2*sqrt(c*LambertW(b*x+a))/sqrt(c))/b^4-9/64*a^2*sqrt(c)*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(b*x+a))/sqrt(c))/b^4-5/144*a*sqrt(c)*sqrt(1/3*Pi)*erfi(sqrt(3)*sqrt(c*LambertW(b*x+a))/sqrt(c))/b^4+105/16384*c^4*(b*x+a)^4/b^4/(c*LambertW(b*x+a))^(7/2)+5/72*a*c^3*(b*x+a)^3/b^4/(c*LambertW(b*x+a))^(5/2)-35/2048*c^3*(b*x+a)^4/b^4/(c*LambertW(b*x+a))^(5/2)+9/32*a^2*c^2*(b*x+a)^2/b^4/(c*LambertW(b*x+a))^(3/2)-5/36*a*c^2*(b*x+a)^3/b^4/(c*LambertW(b*x+a))^(3/2)+7/256*c^2*(b*x+a)^4/b^4/(c*LambertW(b*x+a))^(3/2)+1/2*a^3*c*(b*x+a)/b^4/sqrt(c*LambertW(b*x+a))-3/8*a^2*c*(b*x+a)^2/b^4/sqrt(c*LambertW(b*x+a))+1/6*a*c*(b*x+a)^3/b^4/sqrt(c*LambertW(b*x+a))-1/32*c*(b*x+a)^4/b^4/sqrt(c*LambertW(b*x+a))-a^3*(b*x+a)*sqrt(c*LambertW(b*x+a))/b^4+3/2*a^2*(b*x+a)^2*sqrt(c*LambertW(b*x+a))/b^4-a*(b*x+a)^3*sqrt(c*LambertW(b*x+a))/b^4+1/4*(b*x+a)^4*sqrt(c*LambertW(b*x+a))/b^4,1],
[x^2*sqrt(c*LambertW(b*x+a)),x,14,1/4*a^2*sqrt(c)*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b^3+3/32*a*sqrt(c)*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(b*x+a))/sqrt(c))/b^3+5/432*sqrt(c)*sqrt(1/3*Pi)*erfi(sqrt(3)*sqrt(c*LambertW(b*x+a))/sqrt(c))/b^3-5/216*c^3*(b*x+a)^3/b^3/(c*LambertW(b*x+a))^(5/2)-3/16*a*c^2*(b*x+a)^2/b^3/(c*LambertW(b*x+a))^(3/2)+5/108*c^2*(b*x+a)^3/b^3/(c*LambertW(b*x+a))^(3/2)-1/2*a^2*c*(b*x+a)/b^3/sqrt(c*LambertW(b*x+a))+1/4*a*c*(b*x+a)^2/b^3/sqrt(c*LambertW(b*x+a))-1/18*c*(b*x+a)^3/b^3/sqrt(c*LambertW(b*x+a))+a^2*(b*x+a)*sqrt(c*LambertW(b*x+a))/b^3-a*(b*x+a)^2*sqrt(c*LambertW(b*x+a))/b^3+1/3*(b*x+a)^3*sqrt(c*LambertW(b*x+a))/b^3,1],
[x*sqrt(c*LambertW(b*x+a)),x,9,-1/4*a*sqrt(c)*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b^2-3/64*sqrt(c)*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(b*x+a))/sqrt(c))/b^2+3/32*c^2*(b*x+a)^2/b^2/(c*LambertW(b*x+a))^(3/2)+1/2*a*c*(b*x+a)/b^2/sqrt(c*LambertW(b*x+a))-1/8*c*(b*x+a)^2/b^2/sqrt(c*LambertW(b*x+a))-a*(b*x+a)*sqrt(c*LambertW(b*x+a))/b^2+1/2*(b*x+a)^2*sqrt(c*LambertW(b*x+a))/b^2,1],
[sqrt(c*LambertW(b*x+a)),x,3,1/4*sqrt(c)*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b-1/2*c*(b*x+a)/b/sqrt(c*LambertW(b*x+a))+(b*x+a)*sqrt(c*LambertW(b*x+a))/b,1],
[sqrt(c*LambertW(b*x+a))/x,x,2,sqrt(c*LambertW(b*x+a))*Defer(Int)(sqrt(LambertW(b*x+a))/x,x)/sqrt(LambertW(b*x+a)),0],
[sqrt(c*LambertW(b*x+a))/x^2,x,2,sqrt(c*LambertW(b*x+a))*Defer(Int)(sqrt(LambertW(b*x+a))/x^2,x)/sqrt(LambertW(b*x+a)),0],
[x^3/sqrt(c*LambertW(b*x+a)),x,16,-1/2*a^3*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b^4/sqrt(c)-15/8192*sqrt(Pi)*erfi(2*sqrt(c*LambertW(b*x+a))/sqrt(c))/b^4/sqrt(c)-3/16*a^2*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(b*x+a))/sqrt(c))/b^4/sqrt(c)-1/24*a*sqrt(1/3*Pi)*erfi(sqrt(3)*sqrt(c*LambertW(b*x+a))/sqrt(c))/b^4/sqrt(c)+15/2048*c^3*(b*x+a)^4/b^4/(c*LambertW(b*x+a))^(7/2)+1/12*a*c^2*(b*x+a)^3/b^4/(c*LambertW(b*x+a))^(5/2)-5/256*c^2*(b*x+a)^4/b^4/(c*LambertW(b*x+a))^(5/2)+3/8*a^2*c*(b*x+a)^2/b^4/(c*LambertW(b*x+a))^(3/2)-1/6*a*c*(b*x+a)^3/b^4/(c*LambertW(b*x+a))^(3/2)+1/32*c*(b*x+a)^4/b^4/(c*LambertW(b*x+a))^(3/2)-a^3*(b*x+a)/b^4/sqrt(c*LambertW(b*x+a))+3/2*a^2*(b*x+a)^2/b^4/sqrt(c*LambertW(b*x+a))-a*(b*x+a)^3/b^4/sqrt(c*LambertW(b*x+a))+1/4*(b*x+a)^4/b^4/sqrt(c*LambertW(b*x+a)),1],
[x^2/sqrt(c*LambertW(b*x+a)),x,11,1/2*a^2*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b^3/sqrt(c)+1/8*a*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(b*x+a))/sqrt(c))/b^3/sqrt(c)+1/72*sqrt(1/3*Pi)*erfi(sqrt(3)*sqrt(c*LambertW(b*x+a))/sqrt(c))/b^3/sqrt(c)-1/36*c^2*(b*x+a)^3/b^3/(c*LambertW(b*x+a))^(5/2)-1/4*a*c*(b*x+a)^2/b^3/(c*LambertW(b*x+a))^(3/2)+1/18*c*(b*x+a)^3/b^3/(c*LambertW(b*x+a))^(3/2)+a^2*(b*x+a)/b^3/sqrt(c*LambertW(b*x+a))-a*(b*x+a)^2/b^3/sqrt(c*LambertW(b*x+a))+1/3*(b*x+a)^3/b^3/sqrt(c*LambertW(b*x+a)),1],
[x/sqrt(c*LambertW(b*x+a)),x,7,-1/2*a*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b^2/sqrt(c)-1/16*sqrt(1/2*Pi)*erfi(sqrt(2)*sqrt(c*LambertW(b*x+a))/sqrt(c))/b^2/sqrt(c)+1/8*c*(b*x+a)^2/b^2/(c*LambertW(b*x+a))^(3/2)-a*(b*x+a)/b^2/sqrt(c*LambertW(b*x+a))+1/2*(b*x+a)^2/b^2/sqrt(c*LambertW(b*x+a)),1],
[1/sqrt(c*LambertW(b*x+a)),x,2,1/2*sqrt(Pi)*erfi(sqrt(c*LambertW(b*x+a))/sqrt(c))/b/sqrt(c)+(b*x+a)/b/sqrt(c*LambertW(b*x+a)),1],
[1/x/sqrt(c*LambertW(b*x+a)),x,2,sqrt(LambertW(b*x+a))*Defer(Int)(1/x/sqrt(LambertW(b*x+a)),x)/sqrt(c*LambertW(b*x+a)),0],
[1/x^2/sqrt(c*LambertW(b*x+a)),x,2,sqrt(LambertW(b*x+a))*Defer(Int)(1/x^2/sqrt(LambertW(b*x+a)),x)/sqrt(c*LambertW(b*x+a)),0],
[x^3/sqrt(-c*LambertW(b*x+a)),x,16,1/2*a^3*sqrt(Pi)*erf(sqrt(-c*LambertW(b*x+a))/sqrt(c))/b^4/sqrt(c)+15/8192*sqrt(Pi)*erf(2*sqrt(-c*LambertW(b*x+a))/sqrt(c))/b^4/sqrt(c)+3/16*a^2*sqrt(1/2*Pi)*erf(sqrt(2)*sqrt(-c*LambertW(b*x+a))/sqrt(c))/b^4/sqrt(c)+1/24*a*sqrt(1/3*Pi)*erf(sqrt(3)*sqrt(-c*LambertW(b*x+a))/sqrt(c))/b^4/sqrt(c)-15/2048*c^3*(b*x+a)^4/b^4/(-c*LambertW(b*x+a))^(7/2)+1/12*a*c^2*(b*x+a)^3/b^4/(-c*LambertW(b*x+a))^(5/2)-5/256*c^2*(b*x+a)^4/b^4/(-c*LambertW(b*x+a))^(5/2)-3/8*a^2*c*(b*x+a)^2/b^4/(-c*LambertW(b*x+a))^(3/2)+1/6*a*c*(b*x+a)^3/b^4/(-c*LambertW(b*x+a))^(3/2)-1/32*c*(b*x+a)^4/b^4/(-c*LambertW(b*x+a))^(3/2)-a^3*(b*x+a)/b^4/sqrt(-c*LambertW(b*x+a))+3/2*a^2*(b*x+a)^2/b^4/sqrt(-c*LambertW(b*x+a))-a*(b*x+a)^3/b^4/sqrt(-c*LambertW(b*x+a))+1/4*(b*x+a)^4/b^4/sqrt(-c*LambertW(b*x+a)),1],
[x^2/sqrt(-c*LambertW(b*x+a)),x,11,-1/2*a^2*sqrt(Pi)*erf(sqrt(-c*LambertW(b*x+a))/sqrt(c))/b^3/sqrt(c)-1/8*a*sqrt(1/2*Pi)*erf(sqrt(2)*sqrt(-c*LambertW(b*x+a))/sqrt(c))/b^3/sqrt(c)-1/72*sqrt(1/3*Pi)*erf(sqrt(3)*sqrt(-c*LambertW(b*x+a))/sqrt(c))/b^3/sqrt(c)-1/36*c^2*(b*x+a)^3/b^3/(-c*LambertW(b*x+a))^(5/2)+1/4*a*c*(b*x+a)^2/b^3/(-c*LambertW(b*x+a))^(3/2)-1/18*c*(b*x+a)^3/b^3/(-c*LambertW(b*x+a))^(3/2)+a^2*(b*x+a)/b^3/sqrt(-c*LambertW(b*x+a))-a*(b*x+a)^2/b^3/sqrt(-c*LambertW(b*x+a))+1/3*(b*x+a)^3/b^3/sqrt(-c*LambertW(b*x+a)),1],
[x/sqrt(-c*LambertW(b*x+a)),x,7,1/2*a*sqrt(Pi)*erf(sqrt(-c*LambertW(b*x+a))/sqrt(c))/b^2/sqrt(c)+1/16*sqrt(1/2*Pi)*erf(sqrt(2)*sqrt(-c*LambertW(b*x+a))/sqrt(c))/b^2/sqrt(c)-1/8*c*(b*x+a)^2/b^2/(-c*LambertW(b*x+a))^(3/2)-a*(b*x+a)/b^2/sqrt(-c*LambertW(b*x+a))+1/2*(b*x+a)^2/b^2/sqrt(-c*LambertW(b*x+a)),1],
[1/sqrt(-c*LambertW(b*x+a)),x,2,-1/2*sqrt(Pi)*erf(sqrt(-c*LambertW(b*x+a))/sqrt(c))/b/sqrt(c)+(b*x+a)/b/sqrt(-c*LambertW(b*x+a)),1],
[1/x/sqrt(-c*LambertW(b*x+a)),x,2,sqrt(LambertW(b*x+a))*Defer(Int)(1/x/sqrt(LambertW(b*x+a)),x)/sqrt(-c*LambertW(b*x+a)),0],
[1/x^2/sqrt(-c*LambertW(b*x+a)),x,2,sqrt(LambertW(b*x+a))*Defer(Int)(1/x^2/sqrt(LambertW(b*x+a)),x)/sqrt(-c*LambertW(b*x+a)),0],
[x^3/(d+d*LambertW(b*x+a)),x,12,-3/128*(b*x+a)^4/b^4/d/LambertW(b*x+a)^4-2/9*a*(b*x+a)^3/b^4/d/LambertW(b*x+a)^3+3/32*(b*x+a)^4/b^4/d/LambertW(b*x+a)^3-3/4*a^2*(b*x+a)^2/b^4/d/LambertW(b*x+a)^2+2/3*a*(b*x+a)^3/b^4/d/LambertW(b*x+a)^2-3/16*(b*x+a)^4/b^4/d/LambertW(b*x+a)^2-a^3*(b*x+a)/b^4/d/LambertW(b*x+a)+3/2*a^2*(b*x+a)^2/b^4/d/LambertW(b*x+a)-a*(b*x+a)^3/b^4/d/LambertW(b*x+a)+1/4*(b*x+a)^4/b^4/d/LambertW(b*x+a),1],
[x^2/(d+d*LambertW(b*x+a)),x,8,2/27*(b*x+a)^3/b^3/d/LambertW(b*x+a)^3+1/2*a*(b*x+a)^2/b^3/d/LambertW(b*x+a)^2-2/9*(b*x+a)^3/b^3/d/LambertW(b*x+a)^2+a^2*(b*x+a)/b^3/d/LambertW(b*x+a)-a*(b*x+a)^2/b^3/d/LambertW(b*x+a)+1/3*(b*x+a)^3/b^3/d/LambertW(b*x+a),1],
[x/(d+d*LambertW(b*x+a)),x,5,-1/4*(b*x+a)^2/b^2/d/LambertW(b*x+a)^2-a*(b*x+a)/b^2/d/LambertW(b*x+a)+1/2*(b*x+a)^2/b^2/d/LambertW(b*x+a),1],
[1/(d+d*LambertW(b*x+a)),x,1,(b*x+a)/b/d/LambertW(b*x+a),1],
[1/x/(d+d*LambertW(b*x+a)),x,2,Defer(Int)(1/x/(1+LambertW(b*x+a)),x)/d,0],
[1/x^2/(d+d*LambertW(b*x+a)),x,2,Defer(Int)(1/x^2/(1+LambertW(b*x+a)),x)/d,0]]: