lst:=[[(x+sqrt(x^2-2*x-3))^3,x,3,-2/(1-x-sqrt(x^2-2*x-3))-4*x-4*sqrt(x^2-2*x-3)-(x+sqrt(x^2-2*x-3))^2+1/8*(x+sqrt(x^2-2*x-3))^4-6*ln(1-x-sqrt(x^2-2*x-3)),1],
[(x+sqrt(x^2-2*x-3))^2,x,3,-3*x-x^2+2/3*x^3-(1-x)*sqrt(x^2-2*x-3)+2/3*(x^2-2*x-3)^(3/2)+4*arctanh((1-x)/sqrt(x^2-2*x-3)),1],
[x+sqrt(x^2-2*x-3),x,4,1/2*x^2-1/2*(1-x)*sqrt(x^2-2*x-3)+2*arctanh((1-x)/sqrt(x^2-2*x-3)),1],
[1/(x+sqrt(x^2-2*x-3)),x,3,-2/(1-x-sqrt(x^2-2*x-3))+2*ln(1-x-sqrt(x^2-2*x-3))-3/2*ln(x+sqrt(x^2-2*x-3)),1],
[1/(x+sqrt(x^2-2*x-3))^2,x,3,-2/(1-x-sqrt(x^2-2*x-3))+3/(2*x+2*sqrt(x^2-2*x-3))+4*ln(1-x-sqrt(x^2-2*x-3))-4*ln(x+sqrt(x^2-2*x-3)),1],
[1/(x+sqrt(x^2-2*x-3))^3,x,3,-2/(1-x-sqrt(x^2-2*x-3))+3/4/(x+sqrt(x^2-2*x-3))^2+4/(x+sqrt(x^2-2*x-3))+6*ln(1-x-sqrt(x^2-2*x-3))-6*ln(x+sqrt(x^2-2*x-3)),1],
[(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^3,x,3,1/8*f^2*(-b*f^2+2*d*e)*(-b^2*f^2+4*a*e^2)*(e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/e^4+1/16*f^2*(-b^2*f^2+4*a*e^2)*(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^2/e^3+1/8*(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^4/e-1/32*f^2*(-b*f^2+2*d*e)^3*(-b^2*f^2+4*a*e^2)/e^5/(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))+3/32*f^2*(-b*f^2+2*d*e)^2*(-b^2*f^2+4*a*e^2)*ln(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))/e^5,1],
[(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^2,x,3,1/8*f^2*(-b^2*f^2+4*a*e^2)*(e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/e^3+1/6*(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^3/e-1/16*f^2*(-b*f^2+2*d*e)^2*(-b^2*f^2+4*a*e^2)/e^4/(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))+1/8*f^2*(-b*f^2+2*d*e)*(-b^2*f^2+4*a*e^2)*ln(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))/e^4,1],
[d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2),x,4,d*x+1/2*e*x^2+1/4*f*(b*f^2+2*e^2*x)*sqrt(a+b*x+e^2*x^2/f^2)/e^2+1/8*f^2*(-b^2*f^2+4*a*e^2)*arctanh(1/2*(b*f^2+2*e^2*x)/e/f/sqrt(a+b*x+e^2*x^2/f^2))/e^3,1],
[1/(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2)),x,3,-1/2*f^2*(-b^2*f^2+4*a*e^2)/e/(-b*f^2+2*d*e)/(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))+2*(a*e*f^2-b*d*f^2+d^2*e)*ln(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/(-b*f^2+2*d*e)^2-1/2*f^2*(-b^2*f^2+4*a*e^2)*ln(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))/e/(-b*f^2+2*d*e)^2,1],
[1/(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^2,x,3,(-2*a*e*f^2+2*b*d*f^2-2*d^2*e)/(-b*f^2+2*d*e)^2/(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))-f^2*(-b^2*f^2+4*a*e^2)/(-b*f^2+2*d*e)^2/(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))+2*f^2*(-b^2*f^2+4*a*e^2)*ln(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/(-b*f^2+2*d*e)^3-2*f^2*(-b^2*f^2+4*a*e^2)*ln(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))/(-b*f^2+2*d*e)^3,1],
[1/(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^3,x,3,-(a*e*f^2-b*d*f^2+d^2*e)/(-b*f^2+2*d*e)^2/(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^2-2*f^2*(-b^2*f^2+4*a*e^2)/(-b*f^2+2*d*e)^3/(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))-2*e*f^2*(-b^2*f^2+4*a*e^2)/(-b*f^2+2*d*e)^3/(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))+6*e*f^2*(-b^2*f^2+4*a*e^2)*ln(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/(-b*f^2+2*d*e)^4-6*e*f^2*(-b^2*f^2+4*a*e^2)*ln(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))/(-b*f^2+2*d*e)^4,1],
[(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^(5/2),x,6,1/4*f^2*(-b*f^2+2*d*e)*(-b^2*f^2+4*a*e^2)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/e^4+1/12*f^2*(-b^2*f^2+4*a*e^2)*(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^(3/2)/e^3+1/7*(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^(7/2)/e-1/16*f^2*(-b*f^2+2*d*e)^2*(-b^2*f^2+4*a*e^2)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/e^4/(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))-5/16*f^2*(-b*f^2+2*d*e)^(3/2)*(-b^2*f^2+4*a*e^2)*arctanh(sqrt(2)*sqrt(e)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/sqrt(-b*f^2+2*d*e))/sqrt(2)/e^(9/2),1],
[(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^(3/2),x,6,1/4*f^2*(-b^2*f^2+4*a*e^2)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/e^3+1/5*(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^(5/2)/e-1/8*f^2*(-b*f^2+2*d*e)*(-b^2*f^2+4*a*e^2)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/e^3/(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))-3/8*f^2*sqrt(-b*f^2+2*d*e)*(-b^2*f^2+4*a*e^2)*arctanh(sqrt(2)*sqrt(e)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/sqrt(-b*f^2+2*d*e))/sqrt(2)/e^(7/2),1],
[sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2)),x,6,1/3*(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^(3/2)/e-f^2*(4*a-b^2*f^2/e^2)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/(4*b*f^2+8*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))-1/4*f^2*(-b^2*f^2+4*a*e^2)*arctanh(sqrt(2)*sqrt(e)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/sqrt(-b*f^2+2*d*e))/sqrt(2)/e^(5/2)/sqrt(-b*f^2+2*d*e),1],
[1/sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2)),x,6,sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/e-1/2*f^2*(-b^2*f^2+4*a*e^2)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/e/(-b*f^2+2*d*e)/(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))+1/2*f^2*(-b^2*f^2+4*a*e^2)*arctanh(sqrt(2)*sqrt(e)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/sqrt(-b*f^2+2*d*e))/sqrt(2)/e^(3/2)/(-b*f^2+2*d*e)^(3/2),1],
[1/(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^(3/2),x,5,(-4*a*e*f^2+4*b*d*f^2-4*d^2*e)/(-b*f^2+2*d*e)^2/sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))-f^2*(-b^2*f^2+4*a*e^2)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/(-b*f^2+2*d*e)^2/(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))+3*f^2*(-b^2*f^2+4*a*e^2)*arctanh(sqrt(2)*sqrt(e)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/sqrt(-b*f^2+2*d*e))/sqrt(2)/sqrt(e)/(-b*f^2+2*d*e)^(5/2),1],
[1/(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^(5/2),x,6,1/3*(-4*a*e*f^2+4*b*d*f^2-4*d^2*e)/(-b*f^2+2*d*e)^2/(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^(3/2)-4*f^2*(-b^2*f^2+4*a*e^2)/(-b*f^2+2*d*e)^3/sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))-2*e*f^2*(-b^2*f^2+4*a*e^2)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/(-b*f^2+2*d*e)^3/(b*f^2+2*e*(e*x+f*sqrt(a+x*(b*f^2+e^2*x)/f^2)))+5*sqrt(2)*sqrt(e)*f^2*(-b^2*f^2+4*a*e^2)*arctanh(sqrt(2)*sqrt(e)*sqrt(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/sqrt(-b*f^2+2*d*e))/(-b*f^2+2*d*e)^(7/2),1],
[(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^p,x,4,1/2*(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^(p+1)/e/(p+1)+1/2*f^2*(-b^2*f^2+4*a*e^2)*(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))^(p+1)*hypergeom([2, p+1],[2+p],2*e*(d+e*x+f*sqrt(a+b*x+e^2*x^2/f^2))/(-b*f^2+2*d*e))/e/(-b*f^2+2*d*e)^2/(p+1),1],
[(x+sqrt(-x^2-2*x+3))^2,x,6,3*x-x^2-(1+x)*sqrt(-x^2-2*x+3)-2/3*(-x^2-2*x+3)^(3/2)+4*arcsin(-1/2-1/2*x),1],
[x+sqrt(-x^2-2*x+3),x,4,1/2*x^2+1/2*(1+x)*sqrt(-x^2-2*x+3)-2*arcsin(-1/2-1/2*x),1],
[1/(x+sqrt(-x^2-2*x+3)),x,10,arctan((sqrt(3)-sqrt(-x^2-2*x+3))/x)-1/2*ln(-(3-x-sqrt(3)*sqrt(-x^2-2*x+3))/x^2)+1/14*(7+sqrt(7))*ln(1+sqrt(3)-sqrt(7)-sqrt(3)*(sqrt(3)-sqrt(-x^2-2*x+3))/x)+1/14*(7-sqrt(7))*ln(1+sqrt(3)+sqrt(7)-sqrt(3)*(sqrt(3)-sqrt(-x^2-2*x+3))/x),1],
[1/(x+sqrt(-x^2-2*x+3))^2,x,4,2*(4-sqrt(3)+3*(sqrt(3)-sqrt(-x^2-2*x+3))/x)/(14-7*sqrt(3)-14*(1+sqrt(3))*(sqrt(3)-sqrt(-x^2-2*x+3))/x+7*sqrt(3)*(sqrt(3)-sqrt(-x^2-2*x+3))^2/x^2)+8/7*arctanh((3-x-sqrt(3)*x-sqrt(3)*sqrt(-x^2-2*x+3))/sqrt(7)/x)/sqrt(7),1],
[1/(x+sqrt(-x^2-2*x+3))^3,x,5,1/21*(-36+20*sqrt(3)-4*(21+5*sqrt(3))*(sqrt(3)-sqrt(-x^2-2*x+3))/x)/(2-sqrt(3)-2*(1+sqrt(3))*(sqrt(3)-sqrt(-x^2-2*x+3))/x+sqrt(3)*(sqrt(3)-sqrt(-x^2-2*x+3))^2/x^2)^2-2/49*(43-6*sqrt(3)+(49+6*sqrt(3))*(sqrt(3)-sqrt(-x^2-2*x+3))/x)/sqrt(3)/(2-sqrt(3)-2*(1+sqrt(3))*(sqrt(3)-sqrt(-x^2-2*x+3))/x+sqrt(3)*(sqrt(3)-sqrt(-x^2-2*x+3))^2/x^2)+12/49*arctanh((3-x-sqrt(3)*x-sqrt(3)*sqrt(-x^2-2*x+3))/sqrt(7)/x)/sqrt(7),1],
[(d+e*x+f*sqrt(c*x^2+b*x+a))^2,x,9,(a*f^2+d^2)*x+1/2*(b*f^2+2*d*e)*x^2+1/3*(c*f^2+e^2)*x^3+2/3*e*f*(c*x^2+b*x+a)^(3/2)/c-1/4*(b*e-2*c*d)*f*(2*c*x+b)*sqrt(a+x*(c*x+b))/c^2+1/8*(-4*a*c+b^2)*(b*e-2*c*d)*f*arctanh(1/2*(2*c*x+b)/sqrt(c)/sqrt(a+x*(c*x+b)))/c^(5/2),1],
[d+e*x+f*sqrt(c*x^2+b*x+a),x,4,d*x+1/2*e*x^2+1/4*f*(2*c*x+b)*sqrt(c*x^2+b*x+a)/c-1/8*(-4*a*c+b^2)*f*arctanh(1/2*(2*c*x+b)/sqrt(c)/sqrt(c*x^2+b*x+a))/c^(3/2),1],
[1/(d+e*x+f*sqrt(c*x^2+b*x+a)),x,10,2*sqrt(c)*f*arctanh((sqrt(a)-sqrt(c*x^2+b*x+a))/sqrt(c)/x)/(-c*f^2+e^2)+2*(-b*e+2*c*d)*f*arctanh((2*a*f+b*f*x+2*d*sqrt(a+x*(c*x+b))-2*sqrt(a)*(d+e*x+f*sqrt(a+x*(c*x+b))))/sqrt(-4*b*d*e+4*a*e^2+b^2*f^2+4*c*(-a*f^2+d^2))/x)/(-c*f^2+e^2)/sqrt(-4*b*d*e+4*a*e^2+b^2*f^2+4*c*(-a*f^2+d^2))-e*ln(c-(sqrt(a)-sqrt(c*x^2+b*x+a))^2/x^2)/(-c*f^2+e^2)+e*ln(b*e-c*(d+sqrt(a)*f)+(2*sqrt(a)*e-b*f)*(sqrt(a)-sqrt(c*x^2+b*x+a))/x+(d-sqrt(a)*f)*(sqrt(a)-sqrt(c*x^2+b*x+a))^2/x^2)/(-c*f^2+e^2),1],
[1/(d+e*x+f*sqrt(c*x^2+b*x+a))^2,x,4,(-4*b*(a*e^2+c*d^2)+8*a^(3/2)*c*e*f+2*b^2*(2*d*e-sqrt(a)*e*f)-2*(4*a^(3/2)*e^2+4*sqrt(a)*d*(-b*e+c*d)+b^2*d*f-4*a*c*d*f)*(sqrt(a)-sqrt(c*x^2+b*x+a))/x)/(d-sqrt(a)*f)/(4*b*d*e-4*a*e^2-b^2*f^2-4*c*(-a*f^2+d^2))/(b*e-c*(d+sqrt(a)*f)+(2*sqrt(a)*e-b*f)*(sqrt(a)-sqrt(c*x^2+b*x+a))/x+(d-sqrt(a)*f)*(sqrt(a)-sqrt(c*x^2+b*x+a))^2/x^2)+4*(-4*a*c+b^2)*f*arctanh((2*a*f+b*f*x+2*d*sqrt(a+x*(c*x+b))-2*sqrt(a)*(d+e*x+f*sqrt(a+x*(c*x+b))))/sqrt(-4*b*d*e+4*a*e^2+b^2*f^2+4*c*(-a*f^2+d^2))/x)/(-4*b*d*e+4*a*e^2+b^2*f^2+4*c*(-a*f^2+d^2))^(3/2),1],
[1/(d+e*x+f*sqrt(c*x^2+b*x+a))^3,x,5,(b^4*d*e*f^2-b^3*(d+sqrt(a)*f)*(2*d*e^2+sqrt(a)*e^2*f+c*d*f^2)-4*b*(2*sqrt(a)*c^2*d^3*f+a^(3/2)*c*d*f*(-c*f^2+3*e^2)+a*c*d^2*(-c*f^2+4*e^2)+a^2*(-c*e^2*f^2+2*e^4))+8*a*c*e*(a*e^2*(d+sqrt(a)*f)+c*(d^3-a^(3/2)*f^3))+2*b^2*(a*e^3*(5*d+sqrt(a)*f)+c*e*(d^3+6*sqrt(a)*d^2*f-2*a*d*f^2+a^(3/2)*f^3))+(4*sqrt(a)*b*d*(-b*e+c*d)*(-b*f^2+2*d*e)-16*a^(5/2)*(-c*e^2*f^2+e^4)+a^2*(-4*b*c*e*f^3-8*c^2*d*f^3+8*b*e^3*f)-b^2*d*f*(2*c*d^2-b*(-b*f^2+3*d*e))+4*a^(3/2)*(4*c^2*d^2*f^2+b*e^2*(-b*f^2+6*d*e)-4*c*d*e*(b*f^2+d*e))-a*f*(8*c^2*d^3+b^2*e*(-b*f^2+12*d*e)-6*b*c*d*(b*f^2+2*d*e)))*(sqrt(a)-sqrt(c*x^2+b*x+a))/x)/(d-sqrt(a)*f)^3/(4*b*d*e-4*a*e^2-b^2*f^2-4*c*(-a*f^2+d^2))/(b*e-c*(d+sqrt(a)*f)+(2*sqrt(a)*e-b*f)*(sqrt(a)-sqrt(c*x^2+b*x+a))/x+(d-sqrt(a)*f)*(sqrt(a)-sqrt(c*x^2+b*x+a))^2/x^2)^2+((b^5*d*f^4-b^4*e*f^2*(5*d^2+6*sqrt(a)*d*f-a*f^2)-16*a*e*(2*a^2*e^4+4*a*c*e^2*(-a*f^2+d^2)+c^2*(d-sqrt(a)*f)^2*(2*d^2+7*sqrt(a)*d*f+2*a*f^2))-2*b^3*(3*a^(3/2)*e^2*f^3-a*d*f^2*(-7*c*f^2+18*e^2)+3*sqrt(a)*d^2*f*(-2*c*f^2+e^2)-d^3*(c*f^2+8*e^2))+8*b*(10*a^2*d*e^4+c^2*d*(d-sqrt(a)*f)^2*(2*d^2+4*sqrt(a)*d*f+5*a*f^2)+3*a*c*e^2*(4*d^3+sqrt(a)*d^2*f-6*a*d*f^2+a^(3/2)*f^3))-4*b^2*(4*a*e^3*(a*f^2+4*d^2)+c*e*(8*d^4-3*sqrt(a)*d^3*f+5*a*d^2*f^2-9*a^(3/2)*d*f^3-a^2*f^4)))/(d-sqrt(a)*f)^2+2*(3*b^2*d^2*(-b*e+2*c*d)*f-12*a^2*c*(-b*e+2*c*d)*f^3-3*a*(-b*e+2*c*d)*f*(-b^2*f^2+4*c*d^2)+16*a^(5/2)*(-c*f^2+e^2)^2+8*a^(3/2)*(2*c^2*d^2*f^2-b*e^2*(-b*f^2+4*d*e)+c*(-b^2*f^4+b*d*e*f^2+4*d^2*e^2))+sqrt(a)*(16*c^2*d^4-4*b*c*d^2*(b*f^2+8*d*e)+b^2*(b^2*f^4-2*b*d*e*f^2+16*d^2*e^2)))*(sqrt(a)-sqrt(c*x^2+b*x+a))/(d-sqrt(a)*f)/x)/(d-sqrt(a)*f)/(4*b*d*e-4*a*e^2-b^2*f^2-4*c*(-a*f^2+d^2))^2/(b*e-c*(d+sqrt(a)*f)+(2*sqrt(a)*e-b*f)*(sqrt(a)-sqrt(c*x^2+b*x+a))/x+(d-sqrt(a)*f)*(sqrt(a)-sqrt(c*x^2+b*x+a))^2/x^2)+12*(-4*a*c+b^2)*(-b*e+2*c*d)*f*arctanh((2*a*f+b*f*x+2*d*sqrt(a+x*(c*x+b))-2*sqrt(a)*(d+e*x+f*sqrt(a+x*(c*x+b))))/sqrt(-4*b*d*e+4*a*e^2+b^2*f^2+4*c*(-a*f^2+d^2))/x)/(-4*b*d*e+4*a*e^2+b^2*f^2+4*c*(-a*f^2+d^2))^(5/2),1],
[(x+sqrt(4*x^2-2*x-3))^3,x,14,-9/2*x^2-2*x^3+13/4*x^4+105/512*(1-4*x)*sqrt(4*x^2-2*x-3)+1/64*(4*x^2-2*x-3)^(3/2)+7/16*x*(4*x^2-2*x-3)^(3/2)-1365/1024*arctanh(1/2*(1-4*x)/sqrt(4*x^2-2*x-3)),1],
[(x+sqrt(4*x^2-2*x-3))^2,x,6,-3*x-x^2+5/3*x^3-1/16*(1-4*x)*sqrt(4*x^2-2*x-3)+1/6*(4*x^2-2*x-3)^(3/2)+13/32*arctanh(1/2*(1-4*x)/sqrt(4*x^2-2*x-3)),1],
[x+sqrt(4*x^2-2*x-3),x,4,1/2*x^2-1/8*(1-4*x)*sqrt(4*x^2-2*x-3)+13/16*arctanh(1/2*(1-4*x)/sqrt(4*x^2-2*x-3)),1],
[1/(x+sqrt(4*x^2-2*x-3)),x,6,-1/30*(10-sqrt(10))*ln(1-sqrt(10)-6*x-3*sqrt(4*x^2-2*x-3))-1/30*(10+sqrt(10))*ln(1+sqrt(10)-6*x-3*sqrt(4*x^2-2*x-3))+ln(1-4*x-2*sqrt(4*x^2-2*x-3)),1],
[1/(x+sqrt(4*x^2-2*x-3))^2,x,6,(3-38*x-19*sqrt(4*x^2-2*x-3))/(45+60*x+30*sqrt(4*x^2-2*x-3)-45*(2*x+sqrt(4*x^2-2*x-3))^2)-13/10*ln(1-sqrt(10)-6*x-3*sqrt(4*x^2-2*x-3))/sqrt(10)+13/10*ln(1+sqrt(10)-6*x-3*sqrt(4*x^2-2*x-3))/sqrt(10),1],
[1/(x+sqrt(4*x^2-2*x-3))^3,x,7,1/45*(123+2*x+sqrt(4*x^2-2*x-3))/(3+4*x+2*sqrt(4*x^2-2*x-3)-3*(2*x+sqrt(4*x^2-2*x-3))^2)^2+(917-702*x-351*sqrt(4*x^2-2*x-3))/(2700+3600*x+1800*sqrt(4*x^2-2*x-3)-2700*(2*x+sqrt(4*x^2-2*x-3))^2)-39/200*ln(1-sqrt(10)-6*x-3*sqrt(4*x^2-2*x-3))/sqrt(10)+39/200*ln(1+sqrt(10)-6*x-3*sqrt(4*x^2-2*x-3))/sqrt(10),1],
[(d+e*x+f*sqrt(c*x^2+b*x-a))^2,x,9,(-a*f^2+d^2)*x+1/2*(b*f^2+2*d*e)*x^2+1/3*(c*f^2+e^2)*x^3+1/2*d*f*(2*c*x+b)*sqrt(c*x^2+b*x-a)/c-1/4*b*e*f*(2*c*x+b)*sqrt(c*x^2+b*x-a)/c^2+2/3*e*f*(c*x^2+b*x-a)^(3/2)/c-1/4*(4*a*c+b^2)*d*f*arctanh(1/2*(2*c*x+b)/sqrt(c)/sqrt(c*x^2+b*x-a))/c^(3/2)+1/8*b*(4*a*c+b^2)*e*f*arctanh(1/2*(2*c*x+b)/sqrt(c)/sqrt(c*x^2+b*x-a))/c^(5/2),1],
[d+e*x+f*sqrt(c*x^2+b*x-a),x,4,d*x+1/2*e*x^2+1/4*f*(2*c*x+b)*sqrt(c*x^2+b*x-a)/c-1/8*(4*a*c+b^2)*f*arctanh(1/2*(2*c*x+b)/sqrt(c)/sqrt(c*x^2+b*x-a))/c^(3/2),1],
[1/(d+e*x+f*sqrt(c*x^2+b*x-a)),x,7,-2*(-b*e+2*c*d)*f*arctanh((b*f+2*c*f*x+2*e*sqrt(-a+x*(c*x+b))+2*sqrt(c)*(d+e*x+f*sqrt(-a+x*(c*x+b))))/sqrt(-4*b*d*e-4*a*e^2+b^2*f^2+4*c*(a*f^2+d^2)))/(-c*f^2+e^2)/sqrt(-4*b*d*e-4*a*e^2+b^2*f^2+4*c*(a*f^2+d^2))-ln(b+2*c*x+2*sqrt(c)*sqrt(-a+x*(c*x+b)))/(e-sqrt(c)*f)+e*ln(b*d+a*(e-sqrt(c)*f)+(2*sqrt(c)*d+b*f)*(sqrt(c)*x+sqrt(c*x^2+b*x-a))+(e+sqrt(c)*f)*(sqrt(c)*x+sqrt(c*x^2+b*x-a))^2)/(-c*f^2+e^2),1],
[1/(d+e*x+f*sqrt(c*x^2+b*x-a))^2,x,4,2*(2*b*(-a*e^2+c*d^2)-4*a*c^(3/2)*d*f-b^2*d*(2*e+sqrt(c)*f)+(4*c^(3/2)*d^2-4*sqrt(c)*e*(a*e+b*d)-b^2*e*f-4*a*c*e*f)*(sqrt(c)*x+sqrt(c*x^2+b*x-a)))/(e+sqrt(c)*f)/(4*b*d*e+4*a*e^2-b^2*f^2-4*c*(a*f^2+d^2))/(b*d+a*(e-sqrt(c)*f)+(2*sqrt(c)*d+b*f)*(sqrt(c)*x+sqrt(c*x^2+b*x-a))+(e+sqrt(c)*f)*(sqrt(c)*x+sqrt(c*x^2+b*x-a))^2)-4*(4*a*c+b^2)*f*arctanh((b*f+2*c*f*x+2*e*sqrt(-a+x*(c*x+b))+2*sqrt(c)*(d+e*x+f*sqrt(-a+x*(c*x+b))))/sqrt(-4*b*d*e-4*a*e^2+b^2*f^2+4*c*(a*f^2+d^2)))/(-4*b*d*e-4*a*e^2+b^2*f^2+4*c*(a*f^2+d^2))^(3/2),1],
[1/(d+e*x+f*sqrt(c*x^2+b*x-a))^3,x,5,-(b^3*d*(2*e^2+sqrt(c)*e*f+c*f^2)+4*b*c*d*(2*c*d^2-4*a*e^2+a*sqrt(c)*e*f+a*c*f^2)-2*b^2*(5*c*d^2*e-a*e^3+c^(3/2)*d^2*f-a*c*e*f^2)-8*a*c*(a*e^3+c^(3/2)*d^2*f-c*e*(a*f^2+d^2))-(-b*e+2*c*d)*(b^2*e*f+4*a*c*e*f-4*c^(3/2)*(a*f^2+2*d^2)+sqrt(c)*(-b^2*f^2+8*a*e^2+8*b*d*e))*(sqrt(c)*x+sqrt(c*x^2+b*x-a)))/(e+sqrt(c)*f)^2/(4*b*d*e+4*a*e^2-b^2*f^2-4*c*(a*f^2+d^2))/(b*d+a*(e-sqrt(c)*f)+(2*sqrt(c)*d+b*f)*(sqrt(c)*x+sqrt(c*x^2+b*x-a))+(e+sqrt(c)*f)*(sqrt(c)*x+sqrt(c*x^2+b*x-a))^2)^2-((8*c*(e+sqrt(c)*f)*(b*d+a*(e-sqrt(c)*f))*(4*b*d*e+4*a*e^2-b^2*f^2-4*c*(a*f^2+d^2))+(2*sqrt(c)*d+b*f)*(3*b^3*e^2*f+3*b^3*sqrt(c)*e*f^2-2*b*c*f*(-b^2*f^2-2*a*e^2+7*b*d*e)+8*c^(5/2)*(-a*d*f^2+2*d^3)-2*c^(3/2)*(-6*a*b*e*f^2+b^2*d*f^2+8*a*d*e^2+8*b*d^2*e)-8*c^2*f*(3*a*d*e-b*(a*f^2+d^2))))/(e+sqrt(c)*f)^2-6*(4*a*c+b^2)*(-b*e+2*c*d)*f*(sqrt(c)*x+sqrt(c*x^2+b*x-a)))/(4*b*d*e+4*a*e^2-b^2*f^2-4*c*(a*f^2+d^2))^2/(b*d+a*(e-sqrt(c)*f)+(2*sqrt(c)*d+b*f)*(sqrt(c)*x+sqrt(c*x^2+b*x-a))+(e+sqrt(c)*f)*(sqrt(c)*x+sqrt(c*x^2+b*x-a))^2)-12*(4*a*c+b^2)*(-b*e+2*c*d)*f*arctanh((b*f+2*c*f*x+2*e*sqrt(-a+x*(c*x+b))+2*sqrt(c)*(d+e*x+f*sqrt(-a+x*(c*x+b))))/sqrt(-4*b*d*e-4*a*e^2+b^2*f^2+4*c*(a*f^2+d^2)))/(-4*b*d*e-4*a*e^2+b^2*f^2+4*c*(a*f^2+d^2))^(5/2),1],
[(x+sqrt(-x^2-4*x-3))^2,x,6,-3*x-2*x^2-2*(2+x)*sqrt(-x^2-4*x-3)-2/3*(-x^2-4*x-3)^(3/2)-2*arcsin(2+x),1],
[x+sqrt(-x^2-4*x-3),x,4,1/2*x^2+1/2*(2+x)*sqrt(-x^2-4*x-3)+1/2*arcsin(2+x),1],
[1/(x+sqrt(-x^2-4*x-3)),x,9,-arctan(sqrt(-x^2-4*x-3)/(3+x))-sqrt(2)*arctan((1-3*sqrt(-x^2-4*x-3)/(3+x))/sqrt(2))+1/2*ln(3+x)+1/2*ln((x+sqrt(-x^2-4*x-3))/(3+x)),1],
[1/(x+sqrt(-x^2-4*x-3))^2,x,4,(1-sqrt(-x^2-4*x-3)/(3+x))/(1-2*sqrt(-x^2-4*x-3)/(3+x)-3*(x^2+4*x+3)/(3+x)^2)+arctan((1-3*sqrt(-x^2-4*x-3)/(3+x))/sqrt(2))/sqrt(2),1],
[1/(x+sqrt(-x^2-4*x-3))^3,x,5,1/9*(-4+2*sqrt(-x^2-4*x-3)/(3+x))/(1-2*sqrt(-x^2-4*x-3)/(3+x)-3*(x^2+4*x+3)/(3+x)^2)^2-(13-27*sqrt(-x^2-4*x-3)/(3+x))/(18-36*sqrt(-x^2-4*x-3)/(3+x)-54*(x^2+4*x+3)/(3+x)^2)-3/2*arctan((1-3*sqrt(-x^2-4*x-3)/(3+x))/sqrt(2))/sqrt(2),1],
[(d+e*x+f*sqrt(-c*x^2+b*x-a))^2,x,9,(-a*f^2+d^2)*x+1/2*(b*f^2+2*d*e)*x^2+1/3*(-c*f^2+e^2)*x^3-1/2*d*f*(-2*c*x+b)*sqrt(-c*x^2+b*x-a)/c-1/4*b*e*f*(-2*c*x+b)*sqrt(-c*x^2+b*x-a)/c^2-2/3*e*f*(-c*x^2+b*x-a)^(3/2)/c-1/4*(-4*a*c+b^2)*d*f*arctan(1/2*(-2*c*x+b)/sqrt(c)/sqrt(-c*x^2+b*x-a))/c^(3/2)-1/8*b*(-4*a*c+b^2)*e*f*arctan(1/2*(-2*c*x+b)/sqrt(c)/sqrt(-c*x^2+b*x-a))/c^(5/2),1],
[d+e*x+f*sqrt(-c*x^2+b*x-a),x,4,d*x+1/2*e*x^2-1/4*f*(-2*c*x+b)*sqrt(-c*x^2+b*x-a)/c-1/8*(-4*a*c+b^2)*f*arctan(1/2*(-2*c*x+b)/sqrt(c)/sqrt(-c*x^2+b*x-a))/c^(3/2),1],
[1/(d+e*x+f*sqrt(-c*x^2+b*x-a)),x,10,2*sqrt(c)*f*arctan(2*sqrt(c)*sqrt(-c*x^2+b*x-a)/(b-sqrt(-4*a*c+b^2)-2*c*x))/(c*f^2+e^2)+2*(b*e+2*c*d)*f*arctan((sqrt(-4*a*c+b^2)*f-4*c*d*sqrt(-c*x^2+b*x-a)/(b-sqrt(-4*a*c+b^2)-2*c*x)-2*(b-sqrt(-4*a*c+b^2))*e*sqrt(-c*x^2+b*x-a)/(b-sqrt(-4*a*c+b^2)-2*c*x))/sqrt(4*b*d*e+4*a*e^2-b^2*f^2+4*c*(a*f^2+d^2)))/(c*f^2+e^2)/sqrt(4*b*d*e+4*a*e^2-b^2*f^2+4*c*(a*f^2+d^2))-e*ln(c*(b^2-4*a*c-b*sqrt(-4*a*c+b^2)+2*c*sqrt(-4*a*c+b^2)*x)/(b-sqrt(-4*a*c+b^2)-2*c*x)^2)/(c*f^2+e^2)+e*ln((c^2*(b^2-4*a*c-b*sqrt(-4*a*c+b^2))*d+2*c^3*sqrt(-4*a*c+b^2)*d*x+b^2*c^2*e*x-4*a*c^3*e*x-b*c^2*sqrt(-4*a*c+b^2)*e*x+2*c^3*sqrt(-4*a*c+b^2)*e*x^2+b^2*c^2*f*sqrt(-c*x^2+b*x-a)-4*a*c^3*f*sqrt(-c*x^2+b*x-a)-b*c^2*sqrt(-4*a*c+b^2)*f*sqrt(-c*x^2+b*x-a)+2*c^3*sqrt(-4*a*c+b^2)*f*x*sqrt(-c*x^2+b*x-a))/(b-sqrt(-4*a*c+b^2)-2*c*x)^2)/(c*f^2+e^2),1],
[1/(d+e*x+f*sqrt(-c*x^2+b*x-a))^2,x,5,4*sqrt(-4*a*c+b^2)*(2*c*d+(b+sqrt(-4*a*c+b^2))*e-2*c*sqrt(-4*a*c+b^2)*f*sqrt(-c*x^2+b*x-a)/(b-sqrt(-4*a*c+b^2)-2*c*x))/(4*b*d*e+4*a*e^2-b^2*f^2+4*c*(a*f^2+d^2))/(2*c*d+(b+sqrt(-4*a*c+b^2))*e-4*c*sqrt(-4*a*c+b^2)*f*sqrt(-c*x^2+b*x-a)/(b-sqrt(-4*a*c+b^2)-2*c*x)-4*c*(2*c*d+(b-sqrt(-4*a*c+b^2))*e)*(c*x^2-b*x+a)/(b-sqrt(-4*a*c+b^2)-2*c*x)^2)+4*(-4*a*c+b^2)*f*arctan((sqrt(-4*a*c+b^2)*f-4*c*d*sqrt(-c*x^2+b*x-a)/(b-sqrt(-4*a*c+b^2)-2*c*x)-2*(b-sqrt(-4*a*c+b^2))*e*sqrt(-c*x^2+b*x-a)/(b-sqrt(-4*a*c+b^2)-2*c*x))/sqrt(4*b*d*e+4*a*e^2-b^2*f^2+4*c*(a*f^2+d^2)))/(4*b*d*e+4*a*e^2-b^2*f^2+4*c*(a*f^2+d^2))^(3/2),1],
[1/(d+e*x+f*sqrt(-c*x^2+b*x-a))^3,x,6,-8*sqrt(-4*a*c+b^2)*(c^4*(8*a*c^2*d*f^2+e*(4*b*sqrt(-4*a*c+b^2)*d*e+4*a*sqrt(-4*a*c+b^2)*e^2-b^3*f^2-b^2*sqrt(-4*a*c+b^2)*f^2)+c*(4*sqrt(-4*a*c+b^2)*d^2*e-2*b^2*d*f^2+4*a*(b+sqrt(-4*a*c+b^2))*e*f^2))-2*c^4*f*(b^2*(b-sqrt(-4*a*c+b^2))*e^2+4*c^2*(sqrt(-4*a*c+b^2)*d^2-2*a*d*e+2*a*sqrt(-4*a*c+b^2)*f^2)+c*(8*a*sqrt(-4*a*c+b^2)*e^2+4*b*e*(sqrt(-4*a*c+b^2)*d-a*e)+2*b^2*(d*e-sqrt(-4*a*c+b^2)*f^2)))*sqrt(-c*x^2+b*x-a)/(b-sqrt(-4*a*c+b^2)-2*c*x))/(2*c*d+(b-sqrt(-4*a*c+b^2))*e)^2/(4*b*d*e+4*a*e^2-b^2*f^2+4*c*(a*f^2+d^2))/(c*(2*c*d+(b+sqrt(-4*a*c+b^2))*e)-4*c^2*sqrt(-4*a*c+b^2)*f*sqrt(-c*x^2+b*x-a)/(b-sqrt(-4*a*c+b^2)-2*c*x)-4*c^2*(2*c*d+(b-sqrt(-4*a*c+b^2))*e)*(c*x^2-b*x+a)/(b-sqrt(-4*a*c+b^2)-2*c*x)^2)^2+4*sqrt(-4*a*c+b^2)*(c^2*(3*b^3*(b-sqrt(-4*a*c+b^2))*e^2*f^2+16*c^3*(2*a^2*f^4+a*d^2*f^2+2*d^4)+2*c*(16*a^2*e^4-2*b^3*d*e*f^2+b^4*f^4+2*a*b*e^2*(16*d*e+3*sqrt(-4*a*c+b^2)*f^2)+b^2*e*(16*d^2*e-3*sqrt(-4*a*c+b^2)*d*f^2-14*a*e*f^2))+c^2*(16*b*d*e*(a*f^2+4*d^2)-4*b^2*f^2*(4*a*f^2+d^2)+8*a*e*(8*d^2*e+3*sqrt(-4*a*c+b^2)*d*f^2+8*a*e*f^2)))/(2*c*d+(b-sqrt(-4*a*c+b^2))*e)^2+6*c^2*(b*e+2*c*d)*(b*(b-sqrt(-4*a*c+b^2))*e-2*c*(sqrt(-4*a*c+b^2)*d+2*a*e))*f*sqrt(-c*x^2+b*x-a)/(2*c*d+(b-sqrt(-4*a*c+b^2))*e)/(b-sqrt(-4*a*c+b^2)-2*c*x))/(4*b*d*e+4*a*e^2-b^2*f^2+4*c*(a*f^2+d^2))^2/(c*(2*c*d+(b+sqrt(-4*a*c+b^2))*e)-4*c^2*sqrt(-4*a*c+b^2)*f*sqrt(-c*x^2+b*x-a)/(b-sqrt(-4*a*c+b^2)-2*c*x)-4*c^2*(2*c*d+(b-sqrt(-4*a*c+b^2))*e)*(c*x^2-b*x+a)/(b-sqrt(-4*a*c+b^2)-2*c*x)^2)-12*sqrt(-4*a*c+b^2)*(b*e+2*c*d)*(b*(b-sqrt(-4*a*c+b^2))*e-2*c*(sqrt(-4*a*c+b^2)*d+2*a*e))*f*arctan((sqrt(-4*a*c+b^2)*f-4*c*d*sqrt(-c*x^2+b*x-a)/(b-sqrt(-4*a*c+b^2)-2*c*x)-2*(b-sqrt(-4*a*c+b^2))*e*sqrt(-c*x^2+b*x-a)/(b-sqrt(-4*a*c+b^2)-2*c*x))/sqrt(4*b*d*e+4*a*e^2-b^2*f^2+4*c*(a*f^2+d^2)))/(2*c*d+(b-sqrt(-4*a*c+b^2))*e)/(4*b*d*e+4*a*e^2-b^2*f^2+4*c*(a*f^2+d^2))^(5/2),1]]: