lst:=[[x^5*sqrt(c+d*x^2+e*sqrt(b*x^2+a)),x,9,-1/1024*e*(32*a*b*c*d^3+16*a^2*d^4-120*b^3*c*d*e^2+33*b^4*e^4+8*b^2*d^2*(a*e^2+10*c^2))*(b*e+2*d*sqrt(b*x^2+a))*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/b^2/d^6+1/13440*(1536*a*c*d^3-3276*b^2*c*d*e^2+1155*b^3*e^4+4*b*d^2*(-161*a*e^2+256*c^2))*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)/b/d^5+1/7*x^4*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)/d+1/2240*e*(-231*b^2*e^2+340*a*d^2+444*b*c*d)*sqrt(b*x^2+a)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)/b/d^4-1/280*(-33*b*e^2+32*c*d)*(b*x^2+a)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)/b/d^3-11/84*e*(b*x^2+a)^(3/2)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)/b/d^2-1/2048*e*(-b^2*e^2-4*a*d^2+4*b*c*d)*(32*a*b*c*d^3+16*a^2*d^4-120*b^3*c*d*e^2+33*b^4*e^4+8*b^2*d^2*(a*e^2+10*c^2))*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/b^(5/2)/d^(13/2),1],
[x^3*sqrt(c+d*x^2+e*sqrt(b*x^2+a)),x,6,1/128*e*(-7*b^2*e^2+4*a*d^2+12*b*c*d)*(b*e+2*d*sqrt(b*x^2+a))*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/b/d^4+1/5*(b*x^2+a)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)/b/d-1/240*(32*c*d+48*a*d^2/b-35*b*e^2+42*d*e*sqrt(b*x^2+a))*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)/d^3+1/256*e*(-7*b^2*e^2+4*a*d^2+12*b*c*d)*(-b^2*e^2-4*a*d^2+4*b*c*d)*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/b^(3/2)/d^(9/2),1],
[x*sqrt(c+d*x^2+e*sqrt(b*x^2+a)),x,7,-1/8*e*(b*e+2*d*sqrt(b*x^2+a))*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/d^2+1/3*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)/d-1/16*e*(-b^2*e^2-4*a*d^2+4*b*c*d)*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(b)/d^(5/2),1],
[sqrt(c+d*x^2+e*sqrt(b*x^2+a))/x,x,11,sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)+1/2*sqrt(b)*e*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(d)-1/2*sqrt(c-sqrt(a)*e)*arctanh(1/2*(2*c-2*a*d/b-sqrt(a)*e-(2*sqrt(a)*d/b-e)*sqrt(b*x^2+a))/sqrt(c-sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))-1/2*sqrt(c+sqrt(a)*e)*arctanh(1/2*(2*c-2*a*d/b+sqrt(a)*e+(2*sqrt(a)*d/b+e)*sqrt(b*x^2+a))/sqrt(c+sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)),1],
[sqrt(c+d*x^2+e*sqrt(b*x^2+a))/x^3,x,7,-1/2*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/x^2-1/8*(2*sqrt(a)*d-b*e)*arctanh(1/2*(2*c-2*a*d/b-sqrt(a)*e-(2*sqrt(a)*d/b-e)*sqrt(b*x^2+a))/sqrt(c-sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(a)/sqrt(c-sqrt(a)*e)-1/8*(2*sqrt(a)*d+b*e)*arctanh(1/2*(2*c-2*a*d/b+sqrt(a)*e+(2*sqrt(a)*d/b+e)*sqrt(b*x^2+a))/sqrt(c+sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(a)/sqrt(c+sqrt(a)*e),1],
[sqrt(c+d*x^2+e*sqrt(b*x^2+a))/x^5,x,8,-1/4*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/x^4-1/16*(a*(-b*e^2+2*c*d)+(-2*a*d+b*c)*e*sqrt(b*x^2+a))*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/a/(-a*e^2+c^2)/x^2+1/64*(4*a^(3/2)*d^2-2*b^2*c*e-4*a*b*d*e+3*sqrt(a)*b^2*e^2)*arctanh(1/2*(2*c-2*a*d/b-sqrt(a)*e-(2*sqrt(a)*d/b-e)*sqrt(b*x^2+a))/sqrt(c-sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/a^(3/2)/(c-sqrt(a)*e)^(3/2)+1/64*(4*a^(3/2)*d^2+2*b^2*c*e+4*a*b*d*e+3*sqrt(a)*b^2*e^2)*arctanh(1/2*(2*c-2*a*d/b+sqrt(a)*e+(2*sqrt(a)*d/b+e)*sqrt(b*x^2+a))/sqrt(c+sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/a^(3/2)/(c+sqrt(a)*e)^(3/2),1],
[x^5*(c+d*x^2+e*sqrt(b*x^2+a))^(3/2),x,10,-1/32768*e*(-b^2*e^2-4*a*d^2+4*b*c*d)*(288*a*b*c*d^3+240*a^2*d^4-440*b^3*c*d*e^2+143*b^4*e^4+8*b^2*d^2*(-17*a*e^2+30*c^2))*(b*e+2*d*sqrt(b*x^2+a))*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/b^3/d^7-1/12288*e*(288*a*b*c*d^3+240*a^2*d^4-440*b^3*c*d*e^2+143*b^4*e^4+8*b^2*d^2*(-17*a*e^2+30*c^2))*(b*e+2*d*sqrt(b*x^2+a))*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)/b^2/d^6+1/80640*(5120*a*c*d^3-7524*b^2*c*d*e^2+3003*b^3*e^4+4*b*d^2*(-1143*a*e^2+512*c^2))*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(5/2)/b/d^5+1/9*x^4*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(5/2)/d+1/8064*e*(-429*b^2*e^2+980*a*d^2+748*b*c*d)*sqrt(b*x^2+a)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(5/2)/b/d^4-1/2016*(-143*b*e^2+128*c*d)*(b*x^2+a)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(5/2)/b/d^3-13/144*e*(b*x^2+a)^(3/2)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(5/2)/b/d^2-1/65536*e*(-b^2*e^2-4*a*d^2+4*b*c*d)^2*(288*a*b*c*d^3+240*a^2*d^4-440*b^3*c*d*e^2+143*b^4*e^4+8*b^2*d^2*(-17*a*e^2+30*c^2))*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/b^(7/2)/d^(15/2),1],
[x^3*(c+d*x^2+e*sqrt(b*x^2+a))^(3/2),x,7,3/1024*e*(-3*b^2*e^2+4*a*d^2+4*b*c*d)*(-b^2*e^2-4*a*d^2+4*b*c*d)*(b*e+2*d*sqrt(b*x^2+a))*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/b^2/d^5+1/128*e*(-3*b^2*e^2+4*a*d^2+4*b*c*d)*(b*e+2*d*sqrt(b*x^2+a))*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)/b/d^4+1/7*(b*x^2+a)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(5/2)/b/d-1/280*(16*c*d+40*a*d^2/b-21*b*e^2+30*d*e*sqrt(b*x^2+a))*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(5/2)/d^3+3/2048*e*(-3*b^2*e^2+4*a*d^2+4*b*c*d)*(-b^2*e^2-4*a*d^2+4*b*c*d)^2*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/b^(5/2)/d^(11/2),1],
[x*(c+d*x^2+e*sqrt(b*x^2+a))^(3/2),x,8,-3/128*e*(-b^2*e^2-4*a*d^2+4*b*c*d)*(b*e+2*d*sqrt(b*x^2+a))*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/b/d^3-1/16*e*(b*e+2*d*sqrt(b*x^2+a))*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)/d^2+1/5*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(5/2)/d-3/256*e*(-b^2*e^2-4*a*d^2+4*b*c*d)^2*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/b^(3/2)/d^(7/2),1],
[(c+d*x^2+e*sqrt(b*x^2+a))^(3/2)/x,x,13,1/8*(b*e^2+8*c*d)*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/d+1/4*e*sqrt(b*x^2+a)*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)+1/3*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)+1/16*e*(-b^2*e^2+12*a*d^2+12*b*c*d)*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(b)/d^(3/2)-1/2*(c-sqrt(a)*e)^(3/2)*arctanh(1/2*(2*c-2*a*d/b-sqrt(a)*e-(2*sqrt(a)*d/b-e)*sqrt(b*x^2+a))/sqrt(c-sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))-1/2*(c+sqrt(a)*e)^(3/2)*arctanh(1/2*(2*c-2*a*d/b+sqrt(a)*e+(2*sqrt(a)*d/b+e)*sqrt(b*x^2+a))/sqrt(c+sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)),1],
[(c+d*x^2+e*sqrt(b*x^2+a))^(3/2)/x^3,x,12,3/2*d*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)-1/2*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)/x^2+3/2*sqrt(b)*sqrt(d)*e*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))-3/8*sqrt(c-sqrt(a)*e)*(2*sqrt(a)*d-b*e)*arctanh(1/2*(2*c-2*a*d/b-sqrt(a)*e-(2*sqrt(a)*d/b-e)*sqrt(b*x^2+a))/sqrt(c-sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(a)-3/8*sqrt(c+sqrt(a)*e)*(2*sqrt(a)*d+b*e)*arctanh(1/2*(2*c-2*a*d/b+sqrt(a)*e+(2*sqrt(a)*d/b+e)*sqrt(b*x^2+a))/sqrt(c+sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(a),1],
[(c+d*x^2+e*sqrt(b*x^2+a))^(3/2)/x^5,x,8,-3/16*(2*a*d+b*e*sqrt(b*x^2+a))*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/a/x^2-1/4*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(3/2)/x^4-3/64*(4*a^(3/2)*d^2+2*b^2*c*e-4*a*b*d*e-sqrt(a)*b^2*e^2)*arctanh(1/2*(2*c-2*a*d/b-sqrt(a)*e-(2*sqrt(a)*d/b-e)*sqrt(b*x^2+a))/sqrt(c-sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/a^(3/2)/sqrt(c-sqrt(a)*e)-3/64*(4*a^(3/2)*d^2-2*b^2*c*e+4*a*b*d*e-sqrt(a)*b^2*e^2)*arctanh(1/2*(2*c-2*a*d/b+sqrt(a)*e+(2*sqrt(a)*d/b+e)*sqrt(b*x^2+a))/sqrt(c+sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/a^(3/2)/sqrt(c+sqrt(a)*e),1],
[x^5/sqrt(c+d*x^2+e*sqrt(b*x^2+a)),x,8,1/1920*(512*a*c*d^3-2940*b^2*c*d*e^2+945*b^3*e^4+4*b*d^2*(135*a*e^2+256*c^2))*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/b/d^5+1/5*x^4*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/d+1/960*e*(-315*b^2*e^2+156*a*d^2+644*b*c*d)*sqrt(b*x^2+a)*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/b/d^4-1/240*(-63*b*e^2+64*c*d)*(b*x^2+a)*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/b/d^3-9/40*e*(b*x^2+a)^(3/2)*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/b/d^2+1/256*e*(96*a*b*c*d^3+16*a^2*d^4+280*b^3*c*d*e^2-63*b^4*e^4-120*b^2*d^2*(a*e^2+2*c^2))*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/b^(3/2)/d^(11/2),1],
[x^3/sqrt(c+d*x^2+e*sqrt(b*x^2+a)),x,5,1/3*(b*x^2+a)*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/b/d-1/24*(16*c*d+8*a*d^2/b-15*b*e^2+10*d*e*sqrt(b*x^2+a))*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/d^3+1/16*e*(-5*b^2*e^2-4*a*d^2+12*b*c*d)*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(b)/d^(7/2),1],
[x/sqrt(c+d*x^2+e*sqrt(b*x^2+a)),x,6,sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/d-1/2*sqrt(b)*e*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/d^(3/2),1],
[1/x/sqrt(c+d*x^2+e*sqrt(b*x^2+a)),x,6,-1/2*arctanh(1/2*(2*c-2*a*d/b-sqrt(a)*e-(2*sqrt(a)*d/b-e)*sqrt(b*x^2+a))/sqrt(c-sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(c-sqrt(a)*e)-1/2*arctanh(1/2*(2*c-2*a*d/b+sqrt(a)*e+(2*sqrt(a)*d/b+e)*sqrt(b*x^2+a))/sqrt(c+sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(c+sqrt(a)*e),1],
[1/x^3/sqrt(c+d*x^2+e*sqrt(b*x^2+a)),x,7,-1/2*(c-e*sqrt(b*x^2+a))*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/(-a*e^2+c^2)/x^2+1/8*(2*sqrt(a)*d-b*e)*arctanh(1/2*(2*c-2*a*d/b-sqrt(a)*e-(2*sqrt(a)*d/b-e)*sqrt(b*x^2+a))/sqrt(c-sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(a)/(c-sqrt(a)*e)^(3/2)+1/8*(2*sqrt(a)*d+b*e)*arctanh(1/2*(2*c-2*a*d/b+sqrt(a)*e+(2*sqrt(a)*d/b+e)*sqrt(b*x^2+a))/sqrt(c+sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(a)/(c+sqrt(a)*e)^(3/2),1],
[x^5/(c+d*x^2+e*sqrt(b*x^2+a))^(3/2),x,11,-2*b*x^4*(2*c-2*a*d/b+e*sqrt(b*x^2+a))/(-b^2*e^2-4*a*d^2+4*b*c*d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)+1/3*(-7*b^2*e^2-16*a*d^2+16*b*c*d)*(b*x^2+a)*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/b/d^2/(-b^2*e^2-4*a*d^2+4*b*c*d)+2*e*(b*x^2+a)^(3/2)*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/d/(-b^2*e^2-4*a*d^2+4*b*c*d)+1/24*(128*a*c*d^3+128*a^2*d^4/b+460*b^2*c*d*e^2-105*b^3*e^4-4*b*d^2*(79*a*e^2+64*c^2)-2*d*e*(-35*b^2*e^2-68*a*d^2+116*b*c*d)*sqrt(b*x^2+a))*sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/d^4/(-b^2*e^2-4*a*d^2+4*b*c*d)+1/16*e*(-35*b^2*e^2-12*a*d^2+60*b*c*d)*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(b)/d^(9/2),1],
[x^3/(c+d*x^2+e*sqrt(b*x^2+a))^(3/2),x,5,2*((-a*d+b*c)*(-b*e^2+2*c*d)+e*(-b^2*e^2-2*a*d^2+3*b*c*d)*sqrt(b*x^2+a))/d^2/(-b^2*e^2-4*a*d^2+4*b*c*d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)+sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)/d^2-3/2*sqrt(b)*e*arctanh(1/2*(b*e+2*d*sqrt(b*x^2+a))/sqrt(b)/sqrt(d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/d^(5/2),1],
[x/(c+d*x^2+e*sqrt(b*x^2+a))^(3/2),x,4,-2*b*(2*c-2*a*d/b+e*sqrt(b*x^2+a))/(-b^2*e^2-4*a*d^2+4*b*c*d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b),1],
[1/x/(c+d*x^2+e*sqrt(b*x^2+a))^(3/2),x,7,2*((-a*d+b*c)*(-b*e^2+2*c*d)-d*(-2*a*d+b*c)*e*sqrt(b*x^2+a))/(-a*e^2+c^2)/(-b^2*e^2-4*a*d^2+4*b*c*d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)-1/2*arctanh(1/2*(2*c-2*a*d/b-sqrt(a)*e-(2*sqrt(a)*d/b-e)*sqrt(b*x^2+a))/sqrt(c-sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/(c-sqrt(a)*e)^(3/2)-1/2*arctanh(1/2*(2*c-2*a*d/b+sqrt(a)*e+(2*sqrt(a)*d/b+e)*sqrt(b*x^2+a))/sqrt(c+sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/(c+sqrt(a)*e)^(3/2),1],
[1/x^3/(c+d*x^2+e*sqrt(b*x^2+a))^(3/2),x,8,-1/2*(c-e*sqrt(b*x^2+a))/(-a*e^2+c^2)/x^2/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)-1/2*(6*b^3*c*e^4-12*a*d^3*(a*e^2+c^2)-5*b^2*d*e^2*(a*e^2+5*c^2)+12*b*c*d^2*(3*a*e^2+c^2)+2*d*e*(12*a*c*d^2+3*b^2*c*e^2-2*b*d*(a*e^2+5*c^2))*sqrt(b*x^2+a))/(-a*e^2+c^2)^2/(-b^2*e^2-4*a*d^2+4*b*c*d)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)+3/8*(2*sqrt(a)*d-b*e)*arctanh(1/2*(2*c-2*a*d/b-sqrt(a)*e-(2*sqrt(a)*d/b-e)*sqrt(b*x^2+a))/sqrt(c-sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(a)/(c-sqrt(a)*e)^(5/2)+3/8*(2*sqrt(a)*d+b*e)*arctanh(1/2*(2*c-2*a*d/b+sqrt(a)*e+(2*sqrt(a)*d/b+e)*sqrt(b*x^2+a))/sqrt(c+sqrt(a)*e)/sqrt(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b))/sqrt(a)/(c+sqrt(a)*e)^(5/2),1],
[x^5*(c+d*x^2+e*sqrt(b*x^2+a))^p,x,7,-1/8*(6*b^2*c*d*e^2*(3*p^3+26*p^2+71*p+60)-8*a*c*d^3*(4*p^3+20*p^2+31*p+15)-b^3*e^4*(p^4+14*p^3+71*p^2+154*p+120)-2*b*d^2*(4*c^2*(4*p^2+16*p+15)-a*e^2*p*(4*p^3+33*p^2+86*p+69)))*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(p+1)/b/d^5/(p+1)/(2+p)/(3+p)/(3+2*p)/(5+2*p)+1/2*x^4*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(p+1)/d/(3+p)+1/4*e*(2*b*c*d*(7*p^2+43*p+60)-b^2*e^2*(p^3+12*p^2+47*p+60)+2*a*d^2*(4*p^3+27*p^2+53*p+30))*sqrt(b*x^2+a)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(p+1)/b/d^4/(2+p)/(3+p)/(3+2*p)/(5+2*p)-1/4*(4*c*d*(5+2*p)-b*e^2*(p^2+9*p+20))*(b*x^2+a)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(p+1)/b/d^3/(2+p)/(3+p)/(5+2*p)-1/2*e*(5+p)*(b*x^2+a)^(3/2)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(p+1)/b/d^2/(3+p)/(5+2*p)+2^(-2+p)*e*(48*a*b*c*d^3*p+16*a^2*d^4*p*(p+1)-20*b^3*c*d*e^2*(4+p)+b^4*e^4*(p^2+9*p+20)+4*b^2*d^2*(15*c^2+a*e^2*(-2*p^2-6*p+5)))*(-(b*e-sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/sqrt(b^2*e^2+4*a*d^2-4*b*c*d))^(-1-p)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(p+1)*hypergeom([-p, p+1],[2+p],1/2*(b*e+sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/sqrt(b^2*e^2+4*a*d^2-4*b*c*d))/b/d^5/sqrt(b^2*e^2+4*a*d^2-4*b*c*d)/(p+1)/(3+2*p)/(5+2*p),1],
[x^3*(c+d*x^2+e*sqrt(b*x^2+a))^p,x,4,1/2*(b*x^2+a)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(p+1)/b/d/(2+p)+1/4*(b*(e^2*(2+p)*(3+p)-2*d*(3+2*p)*(b*c+a*d*(p+1))/b^2)-2*d*e*(p+1)*(3+p)*sqrt(b*x^2+a))*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(p+1)/d^3/(p+1)/(2+p)/(3+2*p)-2^(-1+p)*e*(6*b*c*d+4*a*d^2*p-b^2*e^2*(3+p))*(-(b*e-sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/sqrt(b^2*e^2+4*a*d^2-4*b*c*d))^(-1-p)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(p+1)*hypergeom([-p, p+1],[2+p],1/2*(b*e+sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/sqrt(b^2*e^2+4*a*d^2-4*b*c*d))/d^3/sqrt(b^2*e^2+4*a*d^2-4*b*c*d)/(p+1)/(3+2*p),1],
[x*(c+d*x^2+e*sqrt(b*x^2+a))^p,x,5,1/2*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(p+1)/d/(p+1)+2^p*b*e*(-(b*e-sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/sqrt(b^2*e^2+4*a*d^2-4*b*c*d))^(-1-p)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(p+1)*hypergeom([-p, p+1],[2+p],1/2*(b*e+sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/sqrt(b^2*e^2+4*a*d^2-4*b*c*d))/d/sqrt(b^2*e^2+4*a*d^2-4*b*c*d)/(p+1),1],
[(c+d*x^2+e*sqrt(b*x^2+a))^p/x,x,7,4^(-1+p)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^p*AppellF1(-2*p,-p,-p,1-2*p,1/2*(2*sqrt(a)*d+b*e-sqrt(b^2*e^2+4*a*d^2-4*b*c*d))/d/(sqrt(a)-sqrt(b*x^2+a)),1/2*(2*sqrt(a)*d+b*e+sqrt(b^2*e^2+4*a*d^2-4*b*c*d))/d/(sqrt(a)-sqrt(b*x^2+a)))/p/((-(b*e-sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/d/(sqrt(a)-sqrt(b*x^2+a)))^p)/((-(b*e+sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/d/(sqrt(a)-sqrt(b*x^2+a)))^p)+4^(-1+p)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^p*AppellF1(-2*p,-p,-p,1-2*p,1/2*(2*sqrt(a)*d-b*e-sqrt(b^2*e^2+4*a*d^2-4*b*c*d))/d/(sqrt(a)+sqrt(b*x^2+a)),1/2*(2*sqrt(a)*d-b*e+sqrt(b^2*e^2+4*a*d^2-4*b*c*d))/d/(sqrt(a)+sqrt(b*x^2+a)))/p/(((b*e-sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/d/(sqrt(a)+sqrt(b*x^2+a)))^p)/(((b*e+sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/d/(sqrt(a)+sqrt(b*x^2+a)))^p),1],
[(c+d*x^2+e*sqrt(b*x^2+a))^p/x^3,x,11,-1/2*(c-e*sqrt(b*x^2+a))*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(p+1)/(-a*e^2+c^2)/x^2+2^(-3+2*p)*(2*sqrt(a)*d+b*e)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^p*AppellF1(-2*p,-p,-p,1-2*p,1/2*(2*sqrt(a)*d+b*e-sqrt(b^2*e^2+4*a*d^2-4*b*c*d))/d/(sqrt(a)-sqrt(b*x^2+a)),1/2*(2*sqrt(a)*d+b*e+sqrt(b^2*e^2+4*a*d^2-4*b*c*d))/d/(sqrt(a)-sqrt(b*x^2+a)))/sqrt(a)/(c+sqrt(a)*e)/((-(b*e-sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/d/(sqrt(a)-sqrt(b*x^2+a)))^p)/((-(b*e+sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/d/(sqrt(a)-sqrt(b*x^2+a)))^p)+2^(-3+2*p)*(2*sqrt(a)*d-b*e)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^p*AppellF1(-2*p,-p,-p,1-2*p,1/2*(2*sqrt(a)*d-b*e-sqrt(b^2*e^2+4*a*d^2-4*b*c*d))/d/(sqrt(a)+sqrt(b*x^2+a)),1/2*(2*sqrt(a)*d-b*e+sqrt(b^2*e^2+4*a*d^2-4*b*c*d))/d/(sqrt(a)+sqrt(b*x^2+a)))/sqrt(a)/(c-sqrt(a)*e)/(((b*e-sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/d/(sqrt(a)+sqrt(b*x^2+a)))^p)/(((b*e+sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/d/(sqrt(a)+sqrt(b*x^2+a)))^p)+2^p*b*d*e*(1+2*p)*(-(b*e-sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/sqrt(b^2*e^2+4*a*d^2-4*b*c*d))^(-1-p)*(c-a*d/b+e*sqrt(b*x^2+a)+d*(b*x^2+a)/b)^(p+1)*hypergeom([-p, p+1],[2+p],1/2*(b*e+sqrt(b^2*e^2+4*a*d^2-4*b*c*d)+2*d*sqrt(b*x^2+a))/sqrt(b^2*e^2+4*a*d^2-4*b*c*d))/(-a*e^2+c^2)/sqrt(b^2*e^2+4*a*d^2-4*b*c*d)/(p+1),1]]: