lst:=[[sqrt(x^2+2*x+1)/sqrt(x^2+1),x,3,sqrt(x^2+1)*sqrt(x^2+2*x+1)/(1+x)+sqrt(x^2+2*x+1)*arcsinh(x)/(1+x),1],
[1/(-x^2+1)/(c*x^2+b*x+a),x,8,(-2*a*c+b^2-2*c^2)*arctanh((2*c*x+b)/sqrt(-4*a*c+b^2))/(a-b+c)/(a+b+c)/sqrt(-4*a*c+b^2)-ln(1-x)/(2*a+2*b+2*c)+ln(1+x)/(2*a-2*b+2*c)-1/2*b*ln(c*x^2+b*x+a)/(a-b+c)/(a+b+c),1],
[1/(1-x)/(1+x)/(c*x^2+b*x+a),x,9,(-2*a*c+b^2-2*c^2)*arctanh((2*c*x+b)/sqrt(-4*a*c+b^2))/(a-b+c)/(a+b+c)/sqrt(-4*a*c+b^2)-ln(1-x)/(2*a+2*b+2*c)+ln(1+x)/(2*a-2*b+2*c)-1/2*b*ln(c*x^2+b*x+a)/(a-b+c)/(a+b+c),1],
[(-a*x^2+2*b*x+a)^4/(x^2-1)^5,x,3,-1/8*b^4/(1-x)^4-1/12*(8*a-3*b)*b^3/(1-x)^3-1/16*b^2*(24*a^2-16*a*b-b^2)/(1-x)^2-b*(32*a^3-24*a^2*b-16*a*b^2+3*b^3)/(16-16*x)+1/8*b^4/(1+x)^4-1/12*b^3*(8*a+3*b)/(1+x)^3+1/16*b^2*(24*a^2+16*a*b-b^2)/(1+x)^2-b*(32*a^3+24*a^2*b-16*a*b^2-3*b^3)/(16+16*x)-1/8*(8*a^4-24*a^2*b^2+3*b^4)*arctanh(x),1],
[sqrt(f*x^2+e*x+d)/(c*x^2+a)^2,x,6,1/2*x*sqrt(f*x^2+e*x+d)/a/(c*x^2+a)+1/4*sqrt(c*d+a*f-sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2)))*sqrt(2*c*d^2+a*e^2-2*a*d*f-2*d*sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2)))*arctan((a*e*(c*d+a*f-sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2)))-c*(a*e^2+2*d*(c*d-a*f-sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2))))*x)/sqrt(2)/sqrt(a)/sqrt(c)/sqrt(c*d+a*f-sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2)))/sqrt(2*c*d^2+a*e^2-2*a*d*f-2*d*sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2)))/sqrt(f*x^2+e*x+d))/sqrt(2)/a^(3/2)/sqrt(c)/sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2))-1/4*sqrt(c*d+a*f+sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2)))*sqrt(2*c*d^2+a*e^2-2*a*d*f+2*d*sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2)))*arctan((a*e*(c*d+a*f+sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2)))-c*(a*e^2+2*d*(c*d-a*f+sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2))))*x)/sqrt(2)/sqrt(a)/sqrt(c)/sqrt(c*d+a*f+sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2)))/sqrt(2*c*d^2+a*e^2-2*a*d*f+2*d*sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2)))/sqrt(f*x^2+e*x+d))/sqrt(2)/a^(3/2)/sqrt(c)/sqrt(c^2*d^2+a^2*f^2+a*c*(-2*d*f+e^2)),1],
[1/(x^2-1)^2/sqrt(x^2+x-1),x,6,sqrt(x^2+x-1)/(-2*x^2+2)-1/8*arctan(1/2*(3+x)/sqrt(x^2+x-1))-5/8*arctanh(1/2*(1-3*x)/sqrt(x^2+x-1)),1],
[1/sqrt(c*x^2+b*x+a)/sqrt(f*x^2+d),x,3,-(b^2*d+b*sqrt(-4*a*c+b^2)*d-2*a*(-a*f+c*d))^(1/4)*(b+sqrt(-4*a*c+b^2)+2*c*x)^(3/2)*sqrt(2*a+(b+sqrt(-4*a*c+b^2))*x)*sqrt((4*a*c-(b+sqrt(-4*a*c+b^2))^2)^2*(f*x^2+d)/((b+sqrt(-4*a*c+b^2))^2*d+4*a^2*f)/(b+sqrt(-4*a*c+b^2)+2*c*x)^2)*(1+sqrt(2*c^2*d-2*a*c*f+b*(b+sqrt(-4*a*c+b^2))*f)*(2*a+(b+sqrt(-4*a*c+b^2))*x)/sqrt(b^2*d+b*sqrt(-4*a*c+b^2)*d-2*a*(-a*f+c*d))/(b+sqrt(-4*a*c+b^2)+2*c*x))*sqrt((1-4*(b+sqrt(-4*a*c+b^2))*(a*f+c*d)*(2*a+(b+sqrt(-4*a*c+b^2))*x)/((b+sqrt(-4*a*c+b^2))^2*d+4*a^2*f)/(b+sqrt(-4*a*c+b^2)+2*c*x)+(4*c^2*d+(b+sqrt(-4*a*c+b^2))^2*f)*(2*a+(b+sqrt(-4*a*c+b^2))*x)^2/((b+sqrt(-4*a*c+b^2))^2*d+4*a^2*f)/(b+sqrt(-4*a*c+b^2)+2*c*x)^2)/(1+sqrt(2*c^2*d-2*a*c*f+b*(b+sqrt(-4*a*c+b^2))*f)*(2*a+(b+sqrt(-4*a*c+b^2))*x)/sqrt(b^2*d+b*sqrt(-4*a*c+b^2)*d-2*a*(-a*f+c*d))/(b+sqrt(-4*a*c+b^2)+2*c*x))^2)*InverseJacobiAM(2*arctan((2*c^2*d-2*a*c*f+b*(b+sqrt(-4*a*c+b^2))*f)^(1/4)*sqrt(2*a+(b+sqrt(-4*a*c+b^2))*x)/(b^2*d+b*sqrt(-4*a*c+b^2)*d-2*a*(-a*f+c*d))^(1/4)/sqrt(b+sqrt(-4*a*c+b^2)+2*c*x)),sqrt(1/2+1/2*(b+sqrt(-4*a*c+b^2))*(a*f+c*d)/sqrt(2*c^2*d-2*a*c*f+b*(b+sqrt(-4*a*c+b^2))*f)/sqrt(b^2*d+b*sqrt(-4*a*c+b^2)*d-2*a*(-a*f+c*d))))/(4*a*c-(b+sqrt(-4*a*c+b^2))^2)/(2*c^2*d-2*a*c*f+b*(b+sqrt(-4*a*c+b^2))*f)^(1/4)/sqrt(c*x^2+b*x+a)/sqrt(f*x^2+d)/sqrt(1-4*(b+sqrt(-4*a*c+b^2))*(a*f+c*d)*(2*a+(b+sqrt(-4*a*c+b^2))*x)/((b+sqrt(-4*a*c+b^2))^2*d+4*a^2*f)/(b+sqrt(-4*a*c+b^2)+2*c*x)+(4*c^2*d+(b+sqrt(-4*a*c+b^2))^2*f)*(2*a+(b+sqrt(-4*a*c+b^2))*x)^2/((b+sqrt(-4*a*c+b^2))^2*d+4*a^2*f)/(b+sqrt(-4*a*c+b^2)+2*c*x)^2),1],
[(c*x^2+b*x+a)^3*(f*x^2+d)^q,x,9,1/2*b*(3*c^2*d^2-6*a*c*d*f-f*(-3*a^2*f+b^2*d))*(f*x^2+d)^(1+q)/f^3/(1+q)+3*(5*c^3*d^2-3*a*c^2*d*f*(7+2*q)+a*b^2*f^2*(4*q^2+24*q+35)-c*f*(7+2*q)*(3*b^2*d-a^2*f*(5+2*q)))*x*(f*x^2+d)^(1+q)/f^3/(3+2*q)/(5+2*q)/(7+2*q)-c*(5*c^2*d-3*b^2*f*(7+2*q)-3*a*c*f*(7+2*q))*x^3*(f*x^2+d)^(1+q)/f^2/(5+2*q)/(7+2*q)+c^3*x^5*(f*x^2+d)^(1+q)/f/(7+2*q)-1/2*b*(-6*a*c*f-b^2*f+6*c^2*d)*(f*x^2+d)^(2+q)/f^3/(2+q)+3/2*b*c^2*(f*x^2+d)^(3+q)/f^3/(3+q)-(15*c^3*d^3-9*a*c^2*d^2*f*(7+2*q)+a*f^2*(4*q^2+24*q+35)*(3*b^2*d-a^2*f*(3+2*q))-3*c*d*f*(7+2*q)*(3*b^2*d-a^2*f*(5+2*q)))*x*(f*x^2+d)^q*hypergeom([1/2, -q],[3/2],-f*x^2/d)/f^3/(3+2*q)/(5+2*q)/(7+2*q)/((1+f*x^2/d)^q),1],
[(c*x^2+b*x+a)^2*(f*x^2+d)^q,x,8,-b*(-a*f+c*d)*(f*x^2+d)^(1+q)/f^2/(1+q)-(3*c^2*d-b^2*f*(5+2*q)-2*a*c*f*(5+2*q))*x*(f*x^2+d)^(1+q)/f^2/(3+2*q)/(5+2*q)+c^2*x^3*(f*x^2+d)^(1+q)/f/(5+2*q)+b*c*(f*x^2+d)^(2+q)/f^2/(2+q)+(3*c^2*d^2-2*a*c*d*f*(5+2*q)-f*(5+2*q)*(b^2*d-a^2*f*(3+2*q)))*x*(f*x^2+d)^q*hypergeom([1/2, -q],[3/2],-f*x^2/d)/f^2/(3+2*q)/(5+2*q)/((1+f*x^2/d)^q),1],
[(c*x^2+b*x+a)*(f*x^2+d)^q,x,4,1/2*b*(f*x^2+d)^(1+q)/f/(1+q)+c*x*(f*x^2+d)^(1+q)/f/(3+2*q)+(a-c*d/(2*f*q+3*f))*x*(f*x^2+d)^q*hypergeom([1/2, -q],[3/2],-f*x^2/d)/((1+f*x^2/d)^q),1],
[(f*x^2+d)^q,x,2,x*(f*x^2+d)^q*hypergeom([1/2, -q],[3/2],-f*x^2/d)/((1+f*x^2/d)^q),1],
[(f*x^2+d)^q/(c*x^2+b*x+a),x,14,-2*c*x*(f*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-f*x^2/d,4*c^2*x^2/(b-sqrt(-4*a*c+b^2))^2)/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))/((1+f*x^2/d)^q)-2*c*x*(f*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-f*x^2/d,4*c^2*x^2/(b+sqrt(-4*a*c+b^2))^2)/(b^2-4*a*c+b*sqrt(-4*a*c+b^2))/((1+f*x^2/d)^q)-2*c^2*(f*x^2+d)^(1+q)*hypergeom([1, 1+q],[2+q],4*c^2*(f*x^2+d)/(4*c^2*d+(b-sqrt(-4*a*c+b^2))^2*f))/sqrt(-4*a*c+b^2)/(4*c^2*d+(b-sqrt(-4*a*c+b^2))^2*f)/(1+q)+2*c^2*(f*x^2+d)^(1+q)*hypergeom([1, 1+q],[2+q],4*c^2*(f*x^2+d)/(4*c^2*d+(b+sqrt(-4*a*c+b^2))^2*f))/sqrt(-4*a*c+b^2)/(4*c^2*d+(b+sqrt(-4*a*c+b^2))^2*f)/(1+q),1],
[(f*x^2+d)^q/(c*x^2+b*x+a)^2,x,19,-(b*(b^2*f+c*(-3*a*f+c*d))+c*(-2*a*c*f+b^2*f+2*c^2*d)*x)*(f*x^2+d)^(1+q)/(-4*a*c+b^2)/(b^2*d*f+(-a*f+c*d)^2)/(c*x^2+b*x+a)+2*c*(2*c^3*d^2-4*a*c^2*d*f*(1-q)+a*b*(b+sqrt(-4*a*c+b^2))*f^2*q+c*f*(2*a^2*f*(1-2*q)+b^2*d*(2-q)+b*sqrt(-4*a*c+b^2)*d*q))*x*(f*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-f*x^2/d,4*c^2*x^2/(b-sqrt(-4*a*c+b^2))^2)/(-4*a*c+b^2)/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))/(b^2*d*f+(-a*f+c*d)^2)/((1+f*x^2/d)^q)+2*c*(2*c^3*d^2-4*a*c^2*d*f*(1-q)+a*b*(b-sqrt(-4*a*c+b^2))*f^2*q+c*f*(2*a^2*f*(1-2*q)+b^2*d*(2-q)-b*sqrt(-4*a*c+b^2)*d*q))*x*(f*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-f*x^2/d,4*c^2*x^2/(b+sqrt(-4*a*c+b^2))^2)/(-4*a*c+b^2)/(b^2-4*a*c+b*sqrt(-4*a*c+b^2))/(b^2*d*f+(-a*f+c*d)^2)/((1+f*x^2/d)^q)+f*(-2*a*c*f+b^2*f+2*c^2*d)*(1+2*q)*x*(f*x^2+d)^q*hypergeom([1/2, -q],[3/2],-f*x^2/d)/(-4*a*c+b^2)/(b^2*d*f+(-a*f+c*d)^2)/((1+f*x^2/d)^q)+2*c^2*(2*c^3*d^2-4*a*c^2*d*f*(1-q)+a*b*(b+sqrt(-4*a*c+b^2))*f^2*q+c*f*(2*a^2*f*(1-2*q)+b^2*d*(2-q)+b*sqrt(-4*a*c+b^2)*d*q))*(f*x^2+d)^(1+q)*hypergeom([1, 1+q],[2+q],4*c^2*(f*x^2+d)/(4*c^2*d+(b-sqrt(-4*a*c+b^2))^2*f))/(-4*a*c+b^2)^(3/2)/(4*c^2*d+(b-sqrt(-4*a*c+b^2))^2*f)/(b^2*d*f+(-a*f+c*d)^2)/(1+q)+2*c^2*(b*f*(a*f+c*d)*q-(2*c^3*d^2+c*f*(2*a^2*f*(1-2*q)+b^2*d*(2-q))-4*a*c^2*d*f*(1-q)+a*b^2*f^2*q)/sqrt(-4*a*c+b^2))*(f*x^2+d)^(1+q)*hypergeom([1, 1+q],[2+q],4*c^2*(f*x^2+d)/(4*c^2*d+(b+sqrt(-4*a*c+b^2))^2*f))/(-4*a*c+b^2)/(4*c^2*d+(b+sqrt(-4*a*c+b^2))^2*f)/(b^2*d*f+(-a*f+c*d)^2)/(1+q),1]]: