lst:=[[(c*x^2+b*x)^4,x,3,1/5*b^4*x^5+2/3*b^3*c*x^6+6/7*b^2*c^2*x^7+1/2*b*c^3*x^8+1/9*c^4*x^9,1],
[(c*x^2+b*x)^3,x,3,1/4*b^3*x^4+3/5*b^2*c*x^5+1/2*b*c^2*x^6+1/7*c^3*x^7,1],
[(c*x^2+b*x)^2,x,3,1/3*b^2*x^3+1/2*b*c*x^4+1/5*c^2*x^5,1],
[c*x^2+b*x,x,1,1/2*b*x^2+1/3*c*x^3,1],
[1/(c*x^2+b*x),x,3,ln(x)/b-ln(c*x+b)/b,1],
[1/(c*x^2+b*x)^2,x,3,-1/b^2/x-c/b^2/(c*x+b)-2*c*ln(x)/b^3+2*c*ln(c*x+b)/b^3,1],
[1/(c*x^2+b*x)^3,x,3,-1/2/b^3/x^2+3*c/b^4/x+1/2*c^2/b^3/(c*x+b)^2+3*c^2/b^4/(c*x+b)+6*c^2*ln(x)/b^5-6*c^2*ln(c*x+b)/b^5,1],
[1/(c*x^2+b*x)^4,x,3,-1/3/b^4/x^3+2*c/b^5/x^2-10*c^2/b^6/x-1/3*c^3/b^4/(c*x+b)^3-2*c^3/b^5/(c*x+b)^2-10*c^3/b^6/(c*x+b)-20*c^3*ln(x)/b^7+20*c^3*ln(c*x+b)/b^7,1],
[(c*x^2+b*x)^(5/2),x,9,5/512*b^5*sqrt(c*x^2+b*x)/c^3-5/768*b^4*x*sqrt(c*x^2+b*x)/c^2+1/192*b^3*x^2*sqrt(c*x^2+b*x)/c+9/32*b^2*x^3*sqrt(c*x^2+b*x)+5/12*b*c*x^4*sqrt(c*x^2+b*x)+1/6*c^2*x^5*sqrt(c*x^2+b*x)-5/512*b^6*arctanh(sqrt(c)*x/sqrt(c*x^2+b*x))/c^(7/2),1],
[(c*x^2+b*x)^(3/2),x,7,-3/64*b^3*sqrt(c*x^2+b*x)/c^2+1/32*b^2*x*sqrt(c*x^2+b*x)/c+3/8*b*x^2*sqrt(c*x^2+b*x)+1/4*c*x^3*sqrt(c*x^2+b*x)+3/64*b^4*arctanh(sqrt(c)*x/sqrt(c*x^2+b*x))/c^(5/2),1],
[sqrt(c*x^2+b*x),x,5,1/4*b*sqrt(c*x^2+b*x)/c+1/2*x*sqrt(c*x^2+b*x)-1/4*b^2*arctanh(sqrt(c)*x/sqrt(c*x^2+b*x))/c^(3/2),1],
[1/sqrt(c*x^2+b*x),x,3,2*arctanh(sqrt(c)*x/sqrt(c*x^2+b*x))/sqrt(c),1],
[1/(c*x^2+b*x)^(3/2),x,3,2/b/sqrt(c*x^2+b*x)-4*sqrt(c*x^2+b*x)/b^2/x,1],
[1/(c*x^2+b*x)^(5/2),x,5,2/3/b/(c*x^2+b*x)^(3/2)+4/b^2/x/sqrt(c*x^2+b*x)-16/3*sqrt(c*x^2+b*x)/b^3/x^2+32/3*c*sqrt(c*x^2+b*x)/b^4/x,1],
[1/(c*x^2+b*x)^(7/2),x,7,2/5/b/(c*x^2+b*x)^(5/2)+4/3/b^2/x/(c*x^2+b*x)^(3/2)+32/3/b^3/x^2/sqrt(c*x^2+b*x)-64/5*sqrt(c*x^2+b*x)/b^4/x^3+256/15*c*sqrt(c*x^2+b*x)/b^5/x^2-512/15*c^2*sqrt(c*x^2+b*x)/b^6/x,1],
[1/(c*x^2+b*x)^(9/2),x,9,2/7/b/(c*x^2+b*x)^(7/2)+4/5/b^2/x/(c*x^2+b*x)^(5/2)+16/5/b^3/x^2/(c*x^2+b*x)^(3/2)+32/b^4/x^3/sqrt(c*x^2+b*x)-256/7*sqrt(c*x^2+b*x)/b^5/x^4+1536/35*c*sqrt(c*x^2+b*x)/b^6/x^3-2048/35*c^2*sqrt(c*x^2+b*x)/b^7/x^2+4096/35*c^3*sqrt(c*x^2+b*x)/b^8/x,1],
[(-4*x^2+3*x)^(5/2),x,9,-1215/32768*sqrt(3-4*x)*sqrt(x)-135/4096*sqrt(3-4*x)*x^(3/2)-9/256*sqrt(3-4*x)*x^(5/2)-39/32*sqrt(3-4*x)*x^(7/2)+5/4*(3-4*x)^(3/2)*x^(7/2)+8/3*sqrt(3-4*x)*x^(11/2)+3645/65536*arcsin(2*sqrt(x)/sqrt(3)),1],
[(-4*x^2+3*x)^(3/2),x,7,-81/1024*sqrt(3-4*x)*sqrt(x)-9/128*sqrt(3-4*x)*x^(3/2)+9/8*sqrt(3-4*x)*x^(5/2)-sqrt(3-4*x)*x^(7/2)+243/2048*arcsin(2*sqrt(x)/sqrt(3)),1],
[sqrt(-4*x^2+3*x),x,5,3/16*sqrt(3-4*x)*sqrt(x)-1/8*(3-4*x)^(3/2)*sqrt(x)+9/32*arcsin(2*sqrt(x)/sqrt(3)),1],
[1/sqrt(-4*x^2+3*x),x,3,arcsin(2*sqrt(x)/sqrt(3)),1],
[1/(-4*x^2+3*x)^(3/2),x,3,2/3/sqrt(3-4*x)/sqrt(x)-4/9*sqrt(3-4*x)/sqrt(x),1],
[1/(-4*x^2+3*x)^(5/2),x,5,2/9/(3-4*x)^(3/2)/x^(3/2)+4/9/sqrt(3-4*x)/x^(3/2)-16/81*sqrt(3-4*x)/x^(3/2)-128/243*sqrt(3-4*x)/sqrt(x),1],
[1/(-4*x^2+3*x)^(7/2),x,7,2/15/(3-4*x)^(5/2)/x^(5/2)+4/27/(3-4*x)^(3/2)/x^(5/2)+32/81/sqrt(3-4*x)/x^(5/2)-64/405*sqrt(3-4*x)/x^(5/2)-1024/3645*sqrt(3-4*x)/x^(3/2)-8192/10935*sqrt(3-4*x)/sqrt(x),1],
[1/(-4*x^2+3*x)^(9/2),x,9,2/21/(3-4*x)^(7/2)/x^(7/2)+4/45/(3-4*x)^(5/2)/x^(7/2)+16/135/(3-4*x)^(3/2)/x^(7/2)+32/81/sqrt(3-4*x)/x^(7/2)-256/1701*sqrt(3-4*x)/x^(7/2)-2048/8505*sqrt(3-4*x)/x^(5/2)-32768/76545*sqrt(3-4*x)/x^(3/2)-262144/229635*sqrt(3-4*x)/sqrt(x),1],
[(3*I*x+4*x^2)^(5/2),x,9,1215/32768*I*sqrt(3*I*x+4*x^2)-135/4096*x*sqrt(3*I*x+4*x^2)-9/256*I*x^2*sqrt(3*I*x+4*x^2)-81/32*x^3*sqrt(3*I*x+4*x^2)+5*I*x^4*sqrt(3*I*x+4*x^2)+8/3*x^5*sqrt(3*I*x+4*x^2)+3645/65536*arctanh(2*x/sqrt(3*I*x+4*x^2)),1],
[(3*I*x+4*x^2)^(3/2),x,7,81/1024*I*sqrt(3*I*x+4*x^2)-9/128*x*sqrt(3*I*x+4*x^2)+9/8*I*x^2*sqrt(3*I*x+4*x^2)+x^3*sqrt(3*I*x+4*x^2)+243/2048*arctanh(2*x/sqrt(3*I*x+4*x^2)),1],
[sqrt(3*I*x+4*x^2),x,5,3/16*I*sqrt(3*I*x+4*x^2)+1/2*x*sqrt(3*I*x+4*x^2)+9/32*arctanh(2*x/sqrt(3*I*x+4*x^2)),1],
[1/sqrt(3*I*x+4*x^2),x,3,arctanh(2*x/sqrt(3*I*x+4*x^2)),1],
[1/(3*I*x+4*x^2)^(3/2),x,3,-2/3*I/sqrt(3*I*x+4*x^2)+4/9*sqrt(3*I*x+4*x^2)/x,1],
[1/(3*I*x+4*x^2)^(5/2),x,5,-2/9*I/(3*I*x+4*x^2)^(3/2)-4/9/x/sqrt(3*I*x+4*x^2)-16/81*I*sqrt(3*I*x+4*x^2)/x^2+128/243*sqrt(3*I*x+4*x^2)/x,1],
[1/(3*I*x+4*x^2)^(7/2),x,7,-2/15*I/(3*I*x+4*x^2)^(5/2)-4/27/x/(3*I*x+4*x^2)^(3/2)+32/81*I/x^2/sqrt(3*I*x+4*x^2)-64/405*sqrt(3*I*x+4*x^2)/x^3-1024/3645*I*sqrt(3*I*x+4*x^2)/x^2+8192/10935*sqrt(3*I*x+4*x^2)/x,1],
[1/sqrt(-3*x^2+2*x),x,3,2*arcsin(sqrt(3/2)*sqrt(x))/sqrt(3),1],
[1/sqrt(-3*x^2-2*x),x,3,2*arctan(sqrt(3)*x/sqrt(-3*x^2-2*x))/sqrt(3),1],
[1/sqrt(3*x^2+2*x),x,3,2*arctanh(sqrt(3)*x/sqrt(3*x^2+2*x))/sqrt(3),1],
[1/sqrt(3*x^2-2*x),x,3,2*arcsinh(sqrt(3*x^2-2*x)/sqrt(2)/sqrt(x))/sqrt(3),1],
[1/sqrt(-b^2*x^2+b*x),x,3,-arcsin(-2*b*x+1)/b,1],
[1/sqrt(-b^2*x^2-b*x),x,3,2*arctan(b*x/sqrt(-b^2*x^2-b*x))/b,1],
[1/sqrt(b^2*x^2+b*x),x,3,2*arctanh(b*x/sqrt(b^2*x^2+b*x))/b,1],
[1/sqrt(b^2*x^2-b*x),x,3,2*arctanh(b*x/sqrt(b^2*x^2-b*x))/b,1],
[sqrt(-x^2+6*x),x,5,3/2*sqrt(6-x)*sqrt(x)-1/2*(6-x)^(3/2)*sqrt(x)+9*arcsin(sqrt(x)/sqrt(6)),1],
[sqrt(-9*x^2+5*x),x,5,5/36*sqrt(5-9*x)*sqrt(x)-1/18*(5-9*x)^(3/2)*sqrt(x)+25/108*arcsin(3*sqrt(x)/sqrt(5)),1],
[sqrt(x^2+4*x),x,5,sqrt(x^2+4*x)+1/2*x*sqrt(x^2+4*x)-4*arcsinh(1/2*sqrt(x^2+4*x)/sqrt(4+x)),1],
[sqrt(x^2-8*x),x,5,2*sqrt(x^2-8*x)+1/2*(x^2-8*x)^(3/2)/x-16*arcsinh(1/2*sqrt(x^2-8*x)/sqrt(2)/sqrt(x)),1],
[sqrt(x^2-x),x,5,1/4*sqrt(x^2-x)+1/2*(x^2-x)^(3/2)/x-1/4*arcsinh(sqrt(x^2-x)/sqrt(x)),1],
[1/sqrt(-x^2+6*x),x,3,2*arcsin(sqrt(x)/sqrt(6)),1],
[1/sqrt(x^2+4*x),x,3,2*arctanh(x/sqrt(x^2+4*x)),1],
[1/sqrt(x^2-2*x),x,3,2*arctanh(x/sqrt(x^2-2*x)),1],
[(-x^2+x)^(3/2),x,7,-3/64*sqrt(1-x)*sqrt(x)-1/32*sqrt(1-x)*x^(3/2)+3/8*sqrt(1-x)*x^(5/2)-1/4*sqrt(1-x)*x^(7/2)+3/64*arcsin(sqrt(x)),1],
[1/sqrt(3-4*x)/sqrt(x),x,2,arcsin(2*sqrt(x)/sqrt(3)),1],
[1/sqrt(-4*x^2+3*x),x,3,-1/2*arcsin(1-8/3*x),1],
[(b*x^2+a*x)^(4/3),x,2,3/7*(b*x^2+a*x)^(7/3)*hypergeom([1, 14/3],[10/3],-b*x/a)/a,1],
[(b*x^2+a*x)^(2/3),x,2,3/5*(b*x^2+a*x)^(5/3)*hypergeom([1, 10/3],[8/3],-b*x/a)/a,1],
[(b*x^2+a*x)^(1/3),x,2,3/4*(b*x^2+a*x)^(4/3)*hypergeom([1, 8/3],[7/3],-b*x/a)/a,1],
[1/(b*x^2+a*x)^(1/3),x,2,3/2*(b*x^2+a*x)^(2/3)*hypergeom([1, 4/3],[5/3],-b*x/a)/a,1],
[1/(b*x^2+a*x)^(2/3),x,2,3*(b*x^2+a*x)^(1/3)*hypergeom([2/3, 1],[4/3],-b*x/a)/a,1],
[1/(b*x^2+a*x)^(4/3),x,2,-3*hypergeom([-2/3, 1],[2/3],-b*x/a)/a/(b*x^2+a*x)^(1/3),1],
[1/(b*x^2+a*x)^(5/3),x,2,-3/2*hypergeom([-4/3, 1],[1/3],-b*x/a)/a/(b*x^2+a*x)^(2/3),1],
[(c*x^2+b*x)^(5/4),x,7,-5/84*b^3*(c*x^2+b*x)^(1/4)/c^2+1/42*b^2*x*(c*x^2+b*x)^(1/4)/c+1/7*b*x^2*(c*x^2+b*x)^(1/4)+2/7*x*(c*x^2+b*x)^(5/4)-5/84*b^(7/2)*(c*x/(c*x+b))^(3/4)*sqrt(c*x+b)*(c*x^2+b*x)^(1/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)/sqrt(c*x+b)),sqrt(2))/c^3/x,1],
[(c*x^2+b*x)^(3/4),x,5,1/5*b*(c*x^2+b*x)^(3/4)/c+2/5*x*(c*x^2+b*x)^(3/4)-3/10*b^3*(-c*x/b-c^2*x^2/b^2)^(1/4)*EllipticE(sin(1/2*arcsin(1+2*c*x/b)),sqrt(2))/sqrt(2)/c^2/(c*x^2+b*x)^(1/4),1],
[(c*x^2+b*x)^(1/4),x,5,1/3*b*(c*x^2+b*x)^(1/4)/c+2/3*x*(c*x^2+b*x)^(1/4)+1/3*b^(3/2)*(c*x/(c*x+b))^(3/4)*sqrt(c*x+b)*(c*x^2+b*x)^(1/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)/sqrt(c*x+b)),sqrt(2))/c^2/x,1],
[1/(c*x^2+b*x)^(1/4),x,3,sqrt(2)*b*(-c*x/b-c^2*x^2/b^2)^(1/4)*EllipticE(sin(1/2*arcsin(1+2*c*x/b)),sqrt(2))/c/(c*x^2+b*x)^(1/4),1],
[1/(c*x^2+b*x)^(3/4),x,3,-4*(c*x/(c*x+b))^(3/4)*(c*x+b)^(3/2)*InverseJacobiAM(1/2*arcsin(sqrt(b)/sqrt(c*x+b)),sqrt(2))/sqrt(b)/c/(c*x^2+b*x)^(3/4),1],
[1/(c*x^2+b*x)^(5/4),x,5,-4/b/(c*x^2+b*x)^(1/4)+8*(c*x/(c*x+b))^(1/4)*sqrt(c*x+b)*EllipticE(sin(1/2*arcsin(sqrt(b)/sqrt(c*x+b))),sqrt(2))/b^(3/2)/(c*x^2+b*x)^(1/4),1],
[1/(c*x^2+b*x)^(9/4),x,7,4/5/b/(c*x^2+b*x)^(5/4)+96/5*c/b^3/(c*x^2+b*x)^(1/4)+8/b^2/x/(c*x^2+b*x)^(1/4)-48/5*(c*x^2+b*x)^(3/4)/b^3/x^2-96/5*c*(c*x/(c*x+b))^(1/4)*sqrt(c*x+b)*EllipticE(sin(1/2*arcsin(sqrt(b)/sqrt(c*x+b))),sqrt(2))/b^(7/2)/(c*x^2+b*x)^(1/4),1],
[1/(c*x^2+b*x)^(13/4),x,9,4/9/b/(c*x^2+b*x)^(9/4)+8/5/b^2/x/(c*x^2+b*x)^(5/4)-896/15*c^2/b^5/(c*x^2+b*x)^(1/4)+112/5/b^3/x^2/(c*x^2+b*x)^(1/4)-224/9*(c*x^2+b*x)^(3/4)/b^4/x^3+448/15*c*(c*x^2+b*x)^(3/4)/b^5/x^2+896/15*c^2*(c*x/(c*x+b))^(1/4)*sqrt(c*x+b)*EllipticE(sin(1/2*arcsin(sqrt(b)/sqrt(c*x+b))),sqrt(2))/b^(11/2)/(c*x^2+b*x)^(1/4),1],
[1/(3*x^2+2*x)^(1/4),x,4,2/3*(-3*x^2-2*x)^(1/4)*EllipticE(sin(1/2*arcsin(1+3*x)),sqrt(2))*3^(1/4)/(3*x^2+2*x)^(1/4),1],
[1/(3*x^2-2*x)^(1/4),x,4,-2/3*(-3*x^2+2*x)^(1/4)*EllipticE(sin(1/2*arcsin(1-3*x)),sqrt(2))*3^(1/4)/(3*x^2-2*x)^(1/4),1],
[1/(a*x+3*x^2)^(1/4),x,3,1/3*sqrt(2)*a*(-x/a-3*x^2/a^2)^(1/4)*EllipticE(sin(1/2*arcsin(1+6*x/a)),sqrt(2))*3^(1/4)/(a*x+3*x^2)^(1/4),1],
[1/(-3*x^2+2*x)^(1/4),x,3,-2/3*EllipticE(sin(1/2*arcsin(1-3*x)),sqrt(2))*3^(1/4),1],
[1/(-3*x^2-2*x)^(1/4),x,3,2/3*EllipticE(sin(1/2*arcsin(1+3*x)),sqrt(2))*3^(1/4),1],
[1/(a*x-3*x^2)^(1/4),x,3,-1/3*sqrt(2)*a*(x/a-3*x^2/a^2)^(1/4)*EllipticE(sin(1/2*arcsin(1-6*x/a)),sqrt(2))*3^(1/4)/(a*x-3*x^2)^(1/4),1],
[1/(3*x^2+2*x)^(3/4),x,3,2/3*(-3*x^2-2*x)^(3/4)*InverseJacobiAM(1/2*arcsin(1+3*x),sqrt(2))*3^(3/4)/(3*x^2+2*x)^(3/4),1],
[1/(3*x^2-2*x)^(3/4),x,3,-2/3*sqrt(2)*x^(3/4)*(-2+3*x)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(2/3)/sqrt(x)),sqrt(2))*3^(3/4)/(3*x^2-2*x)^(3/4),1],
[1/(a*x+3*x^2)^(3/4),x,3,-4/3*(x/(a+3*x))^(3/4)*(a+3*x)^(3/2)*InverseJacobiAM(1/2*arcsin(sqrt(a)/sqrt(a+3*x)),sqrt(2))*3^(3/4)/sqrt(a)/(a*x+3*x^2)^(3/4),1],
[1/(-3*x^2+2*x)^(3/4),x,3,-2/3*InverseJacobiAM(1/2*arcsin(1-3*x),sqrt(2))*3^(3/4),1],
[1/(-3*x^2-2*x)^(3/4),x,3,2/3*InverseJacobiAM(1/2*arcsin(1+3*x),sqrt(2))*3^(3/4),1],
[1/(a*x-3*x^2)^(3/4),x,3,-2/3*sqrt(2)*a*(x/a-3*x^2/a^2)^(3/4)*InverseJacobiAM(1/2*arcsin(1-6*x/a),sqrt(2))*3^(3/4)/(a*x-3*x^2)^(3/4),1],
[1/(3*x^2+2*x)^(5/4),x,5,-2/(3*x^2+2*x)^(1/4)+2*sqrt(2)*3^(1/4)*x^(1/4)*(2+3*x)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(2)/sqrt(2+3*x))),sqrt(2))/(3*x^2+2*x)^(1/4),1],
[1/(3*x^2-2*x)^(5/4),x,4,-2/(3*x^2-2*x)^(1/4)+2*sqrt(2)*3^(1/4)*x^(1/4)*(-2+3*x)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(2/3)/sqrt(x))),sqrt(2))/(3*x^2-2*x)^(1/4),1],
[1/(a*x+3*x^2)^(5/4),x,5,-4/a/(a*x+3*x^2)^(1/4)+8*3^(1/4)*(x/(a+3*x))^(1/4)*sqrt(a+3*x)*EllipticE(sin(1/2*arcsin(sqrt(a)/sqrt(a+3*x))),sqrt(2))/a^(3/2)/(a*x+3*x^2)^(1/4),1],
[1/(-3*x^2+2*x)^(5/4),x,5,2/(2-3*x)^(1/4)/x^(1/4)-2*(2-3*x)^(3/4)/x^(1/4)+2*EllipticE(sin(1/2*arcsin(1-3*x)),sqrt(2))*3^(1/4),1],
[1/(-3*x^2-2*x)^(5/4),x,5,-2/(-3*x^2-2*x)^(1/4)-2*(-3*x^2-2*x)^(3/4)/x-2*EllipticE(sin(1/2*arcsin(1+3*x)),sqrt(2))*3^(1/4),1],
[1/(a*x-3*x^2)^(5/4),x,5,4/a/(a*x-3*x^2)^(1/4)-8*(a*x-3*x^2)^(3/4)/a^2/x+4*sqrt(2)*3^(1/4)*(x/a-3*x^2/a^2)^(1/4)*EllipticE(sin(1/2*arcsin(1-6*x/a)),sqrt(2))/a/(a*x-3*x^2)^(1/4),1],
[(c*x^2+b*x)^p,x,2,(c*x^2+b*x)^(p+1)*hypergeom([1, 2*p+2],[2+p],-c*x/b)/b/(p+1),1],
[(-b^2*x^2+b*x)^p,x,2,(-b^2*x^2+b*x)^(p+1)*hypergeom([1, 2*p+2],[2+p],b*x)/b/(p+1),1],
[(b^2*x^2+b*x)^p,x,2,(b^2*x^2+b*x)^(p+1)*hypergeom([1, 2*p+2],[2+p],-b*x)/b/(p+1),1],
[(-3*x^2+2*x)^p,x,2,2^p*x^(p+1)*hypergeom([-p, p+1],[2+p],3/2*x)/(p+1),1],
[(-3*x^2-2*x)^p,x,2,-1/2*(-3*x^2-2*x)^(p+1)*hypergeom([1, 2*p+2],[2+p],-3/2*x)/(p+1),1],
[(3*x^2+2*x)^p,x,2,2^p*x*(3*x^2+2*x)^p*hypergeom([-p, p+1],[2+p],-3/2*x)/(p+1)/((2+3*x)^p),1],
[(3*x^2-2*x)^p,x,2,2^p*3^(-1-p)*x^(-1-p)*(3*x^2-2*x)^(p+1)*hypergeom([-p, p+1],[2+p],1-3/2*x)/(p+1),1],
[(b*x^3+a*x^2)^4,x,3,1/9*a^4*x^9+2/5*a^3*b*x^10+6/11*a^2*b^2*x^11+1/3*a*b^3*x^12+1/13*b^4*x^13,1],
[(b*x^3+a*x^2)^3,x,3,1/7*a^3*x^7+3/8*a^2*b*x^8+1/3*a*b^2*x^9+1/10*b^3*x^10,1],
[(b*x^3+a*x^2)^2,x,3,1/5*a^2*x^5+1/3*a*b*x^6+1/7*b^2*x^7,1],
[b*x^3+a*x^2,x,1,1/3*a*x^3+1/4*b*x^4,1],
[1/(b*x^3+a*x^2),x,3,-1/a/x-b*ln(x)/a^2+b*ln(b*x+a)/a^2,1],
[1/(b*x^3+a*x^2)^2,x,3,-1/3/a^2/x^3+b/a^3/x^2-3*b^2/a^4/x-b^3/a^4/(b*x+a)-4*b^3*ln(x)/a^5+4*b^3*ln(b*x+a)/a^5,1],
[1/(b*x^3+a*x^2)^3,x,3,-1/5/a^3/x^5+3/4*b/a^4/x^4-2*b^2/a^5/x^3+5*b^3/a^6/x^2-15*b^4/a^7/x-1/2*b^5/a^6/(b*x+a)^2-6*b^5/a^7/(b*x+a)-21*b^5*ln(x)/a^8+21*b^5*ln(b*x+a)/a^8,1],
[1/(b*x^3+a*x^2)^4,x,3,-1/7/a^4/x^7+2/3*b/a^5/x^6-2*b^2/a^6/x^5+5*b^3/a^7/x^4-35/3*b^4/a^8/x^3+28*b^5/a^9/x^2-84*b^6/a^10/x-1/3*b^7/a^8/(b*x+a)^3-4*b^7/a^9/(b*x+a)^2-36*b^7/a^10/(b*x+a)-120*b^7*ln(x)/a^11+120*b^7*ln(b*x+a)/a^11,1],
[(b*x^3+a*x^2)^(7/2),x,3,-2/9*a^7*(b*x^3+a*x^2)^(9/2)/b^8/x^9+14/11*a^6*(b*x^3+a*x^2)^(11/2)/b^8/x^11-42/13*a^5*(b*x^3+a*x^2)^(13/2)/b^8/x^13+14/3*a^4*(b*x^3+a*x^2)^(15/2)/b^8/x^15-70/17*a^3*(b*x^3+a*x^2)^(17/2)/b^8/x^17+42/19*a^2*(b*x^3+a*x^2)^(19/2)/b^8/x^19-2/3*a*(b*x^3+a*x^2)^(21/2)/b^8/x^21+2/23*(b*x^3+a*x^2)^(23/2)/b^8/x^23,1],
[(b*x^3+a*x^2)^(5/2),x,3,-2/7*a^5*(b*x^3+a*x^2)^(7/2)/b^6/x^7+10/9*a^4*(b*x^3+a*x^2)^(9/2)/b^6/x^9-20/11*a^3*(b*x^3+a*x^2)^(11/2)/b^6/x^11+20/13*a^2*(b*x^3+a*x^2)^(13/2)/b^6/x^13-2/3*a*(b*x^3+a*x^2)^(15/2)/b^6/x^15+2/17*(b*x^3+a*x^2)^(17/2)/b^6/x^17,1],
[(b*x^3+a*x^2)^(3/2),x,3,-2/5*a^3*(b*x^3+a*x^2)^(5/2)/b^4/x^5+6/7*a^2*(b*x^3+a*x^2)^(7/2)/b^4/x^7-2/3*a*(b*x^3+a*x^2)^(9/2)/b^4/x^9+2/11*(b*x^3+a*x^2)^(11/2)/b^4/x^11,1],
[sqrt(b*x^3+a*x^2),x,3,-2/3*a*(b*x^3+a*x^2)^(3/2)/b^2/x^3+2/5*(b*x^3+a*x^2)^(5/2)/b^2/x^5,1],
[1/sqrt(b*x^3+a*x^2),x,3,-2*arctanh(sqrt(b*x^3+a*x^2)/sqrt(a)/x)/sqrt(a),1],
[1/(b*x^3+a*x^2)^(3/2),x,6,5/4*b/a^2/sqrt(b*x^3+a*x^2)-1/2/a/x/sqrt(b*x^3+a*x^2)+15/4*b^2*x/a^3/sqrt(b*x^3+a*x^2)-15/4*b^2*arctanh(sqrt(b*x^3+a*x^2)/sqrt(a)/x)/a^(7/2),1],
[1/(b*x^3+a*x^2)^(5/2),x,9,11/24*b/a^2/(b*x^3+a*x^2)^(3/2)-1/4/a/x/(b*x^3+a*x^2)^(3/2)-33/32*b^2*x/a^3/(b*x^3+a*x^2)^(3/2)+231/64*b^3*x^2/a^4/(b*x^3+a*x^2)^(3/2)+385/64*b^4*x^3/a^5/(b*x^3+a*x^2)^(3/2)+1155/64*b^4*x/a^6/sqrt(b*x^3+a*x^2)-1155/64*b^4*arctanh(sqrt(b*x^3+a*x^2)/sqrt(a)/x)/a^(13/2),1],
[1/(b*x^3+a*x^2)^(7/2),x,12,17/60*b/a^2/(b*x^3+a*x^2)^(5/2)-1/6/a/x/(b*x^3+a*x^2)^(5/2)-17/32*b^2*x/a^3/(b*x^3+a*x^2)^(5/2)+221/192*b^3*x^2/a^4/(b*x^3+a*x^2)^(5/2)-2431/768*b^4*x^3/a^5/(b*x^3+a*x^2)^(5/2)+7293/512*b^5*x^4/a^6/(b*x^3+a*x^2)^(5/2)+51051/2560*b^6*x^5/a^7/(b*x^3+a*x^2)^(5/2)+17017/512*b^6*x^3/a^8/(b*x^3+a*x^2)^(3/2)+51051/512*b^6*x/a^9/sqrt(b*x^3+a*x^2)-51051/512*b^6*arctanh(sqrt(b*x^3+a*x^2)/sqrt(a)/x)/a^(19/2),1],
[(b*x^3+a*x^2)^(2/3),x,5,1/9*a*(b*x^3+a*x^2)^(2/3)/b-4/27*a^2*(b*x^3+a*x^2)^(2/3)/b^2/x+1/3*x*(b*x^3+a*x^2)^(2/3)-4/27*a^3*(b*x^3+a*x^2)^(2/3)*arctan(1/sqrt(3)+2*(b*x+a)^(1/3)/sqrt(3)/b^(1/3)/x^(1/3))/sqrt(3)/b^(7/3)/x^(4/3)/(b*x+a)^(2/3)-2/81*a^3*(b*x^3+a*x^2)^(2/3)*ln(x)/b^(7/3)/x^(4/3)/(b*x+a)^(2/3)-2/27*a^3*(b*x^3+a*x^2)^(2/3)*ln(1-(b*x+a)^(1/3)/b^(1/3)/x^(1/3))/b^(7/3)/x^(4/3)/(b*x+a)^(2/3),1],
[(b*x^3+a*x^2)^(1/3),x,4,1/6*a*(b*x^3+a*x^2)^(1/3)/b+1/2*x*(b*x^3+a*x^2)^(1/3)+1/3*a^2*(b*x^3+a*x^2)^(1/3)*arctan(1/sqrt(3)+2*b^(1/3)*x^(1/3)/sqrt(3)/(b*x+a)^(1/3))/sqrt(3)/b^(5/3)/x^(2/3)/(b*x+a)^(1/3)+1/18*a^2*(b*x^3+a*x^2)^(1/3)*ln(b*x+a)/b^(5/3)/x^(2/3)/(b*x+a)^(1/3)+1/6*a^2*(b*x^3+a*x^2)^(1/3)*ln(1-b^(1/3)*x^(1/3)/(b*x+a)^(1/3))/b^(5/3)/x^(2/3)/(b*x+a)^(1/3),1],
[1/(b*x^3+a*x^2)^(1/3),x,2,-sqrt(3)*x^(2/3)*(b*x+a)^(1/3)*arctan(1/sqrt(3)+2*(b*x+a)^(1/3)/sqrt(3)/b^(1/3)/x^(1/3))/b^(1/3)/(b*x^3+a*x^2)^(1/3)-1/2*x^(2/3)*(b*x+a)^(1/3)*ln(x)/b^(1/3)/(b*x^3+a*x^2)^(1/3)-3/2*x^(2/3)*(b*x+a)^(1/3)*ln(1-(b*x+a)^(1/3)/b^(1/3)/x^(1/3))/b^(1/3)/(b*x^3+a*x^2)^(1/3),1],
[1/(b*x^3+a*x^2)^(2/3),x,2,-3*(b*x^3+a*x^2)^(1/3)/a/x,1],
[1/(b*x^3+a*x^2)^(4/3),x,4,3/a/x/(b*x^3+a*x^2)^(1/3)-18/5*(b*x^3+a*x^2)^(2/3)/a^2/x^3+27/5*b*(b*x^3+a*x^2)^(2/3)/a^3/x^2,1],
[1/(b*x^3+a*x^2)^(5/3),x,5,3/2/a/x/(b*x^3+a*x^2)^(2/3)-27/14*(b*x^3+a*x^2)^(1/3)/a^2/x^3+81/28*b*(b*x^3+a*x^2)^(1/3)/a^3/x^2-243/28*b^2*(b*x^3+a*x^2)^(1/3)/a^4/x,1],
[1/(b*x^3+a*x^2)^(7/3),x,7,3/4/a/x/(b*x^3+a*x^2)^(4/3)+45/4/a^2/x^3/(b*x^3+a*x^2)^(1/3)-135/11*(b*x^3+a*x^2)^(2/3)/a^3/x^5+1215/88*b*(b*x^3+a*x^2)^(2/3)/a^4/x^4-729/44*b^2*(b*x^3+a*x^2)^(2/3)/a^5/x^3+2187/88*b^3*(b*x^3+a*x^2)^(2/3)/a^6/x^2,1],
[(b*x^3+a*x^2)^(9/4),x,12,320/149017*a^7*(b*x^3+a*x^2)^(1/4)/b^5-160/149017*a^6*x*(b*x^3+a*x^2)^(1/4)/b^4+112/149017*a^5*x^2*(b*x^3+a*x^2)^(1/4)/b^3-8/13547*a^4*x^3*(b*x^3+a*x^2)^(1/4)/b^2+20/40641*a^3*x^4*(b*x^3+a*x^2)^(1/4)/b+20/2139*a^2*x^5*(b*x^3+a*x^2)^(1/4)+4/93*a*x^3*(b*x^3+a*x^2)^(5/4)+4/31*x*(b*x^3+a*x^2)^(9/4)-640/149017*a^(17/2)*x^(3/2)*(1+b*x/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*sqrt(x)/sqrt(a)),sqrt(2))/b^(11/2)/(b*x^3+a*x^2)^(3/4),1],
[(b*x^3+a*x^2)^(5/4),x,9,80/4389*a^4*(b*x^3+a*x^2)^(1/4)/b^3-40/4389*a^3*x*(b*x^3+a*x^2)^(1/4)/b^2+4/627*a^2*x^2*(b*x^3+a*x^2)^(1/4)/b+4/57*a*x^3*(b*x^3+a*x^2)^(1/4)+4/19*x*(b*x^3+a*x^2)^(5/4)-160/4389*a^(11/2)*x^(3/2)*(1+b*x/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*sqrt(x)/sqrt(a)),sqrt(2))/b^(7/2)/(b*x^3+a*x^2)^(3/4),1],
[(b*x^3+a*x^2)^(1/4),x,6,4/21*a*(b*x^3+a*x^2)^(1/4)/b+4/7*x*(b*x^3+a*x^2)^(1/4)-8/21*a^(5/2)*x^(3/2)*(1+b*x/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*sqrt(x)/sqrt(a)),sqrt(2))/b^(3/2)/(b*x^3+a*x^2)^(3/4),1],
[1/(b*x^3+a*x^2)^(3/4),x,5,-2*(b*x^3+a*x^2)^(1/4)/a/x-2*sqrt(b)*x^(3/2)*(1+b*x/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*sqrt(x)/sqrt(a)),sqrt(2))/sqrt(a)/(b*x^3+a*x^2)^(3/4),1],
[1/(b*x^3+a*x^2)^(7/4),x,8,4/3/a/x/(b*x^3+a*x^2)^(3/4)-26/15*(b*x^3+a*x^2)^(1/4)/a^2/x^3+13/5*b*(b*x^3+a*x^2)^(1/4)/a^3/x^2-13/2*b^2*(b*x^3+a*x^2)^(1/4)/a^4/x-13/2*b^(5/2)*x^(3/2)*(1+b*x/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*sqrt(x)/sqrt(a)),sqrt(2))/a^(7/2)/(b*x^3+a*x^2)^(3/4),1],
[1/(b*x^3+a*x^2)^(11/4),x,11,4/7/a/x/(b*x^3+a*x^2)^(7/4)+100/21/a^2/x^3/(b*x^3+a*x^2)^(3/4)-50/9*(b*x^3+a*x^2)^(1/4)/a^3/x^5+425/63*b*(b*x^3+a*x^2)^(1/4)/a^4/x^4-1105/126*b^2*(b*x^3+a*x^2)^(1/4)/a^5/x^3+1105/84*b^3*(b*x^3+a*x^2)^(1/4)/a^6/x^2-5525/168*b^4*(b*x^3+a*x^2)^(1/4)/a^7/x-5525/168*b^(9/2)*x^(3/2)*(1+b*x/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*sqrt(x)/sqrt(a)),sqrt(2))/a^(13/2)/(b*x^3+a*x^2)^(3/4),1],
[(b*x^3+a*x^2)^(7/4),x,9,224/16575*a^6*x/b^4/(b*x^3+a*x^2)^(1/4)-112/49725*a^5*x^2/b^3/(b*x^3+a*x^2)^(1/4)+56/49725*a^4*x^3/b^2/(b*x^3+a*x^2)^(1/4)-4/5525*a^3*x^4/b/(b*x^3+a*x^2)^(1/4)+4/425*a^2*x^5/(b*x^3+a*x^2)^(1/4)+4/75*a*x^3*(b*x^3+a*x^2)^(3/4)+4/25*x*(b*x^3+a*x^2)^(7/4)-448/16575*a^(13/2)*sqrt(x)*((b*x+a)/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*sqrt(x)/sqrt(a))),sqrt(2))/b^(9/2)/(b*x^3+a*x^2)^(1/4),1],
[(b*x^3+a*x^2)^(3/4),x,6,8/65*a^3*x/b^2/(b*x^3+a*x^2)^(1/4)-4/195*a^2*x^2/b/(b*x^3+a*x^2)^(1/4)+4/39*a*x^3/(b*x^3+a*x^2)^(1/4)+4/13*x*(b*x^3+a*x^2)^(3/4)-16/65*a^(7/2)*sqrt(x)*((b*x+a)/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*sqrt(x)/sqrt(a))),sqrt(2))/b^(5/2)/(b*x^3+a*x^2)^(1/4),1],
[1/(b*x^3+a*x^2)^(1/4),x,3,4*x/(b*x^3+a*x^2)^(1/4)-4*sqrt(a)*sqrt(x)*((b*x+a)/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*sqrt(x)/sqrt(a))),sqrt(2))/sqrt(b)/(b*x^3+a*x^2)^(1/4),1],
[1/(b*x^3+a*x^2)^(5/4),x,4,7/3*b/a^2/(b*x^3+a*x^2)^(1/4)-2/3/a/x/(b*x^3+a*x^2)^(1/4)+7*b^(3/2)*sqrt(x)*((b*x+a)/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*sqrt(x)/sqrt(a))),sqrt(2))/a^(5/2)/(b*x^3+a*x^2)^(1/4),1],
[1/(b*x^3+a*x^2)^(9/4),x,7,4/5/a/x/(b*x^3+a*x^2)^(5/4)+209/20*b^3/a^5/(b*x^3+a*x^2)^(1/4)-38/35/a^2/x^3/(b*x^3+a*x^2)^(1/4)+57/35*b/a^3/x^2/(b*x^3+a*x^2)^(1/4)-209/70*b^2/a^4/x/(b*x^3+a*x^2)^(1/4)+627/20*b^(7/2)*sqrt(x)*((b*x+a)/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*sqrt(x)/sqrt(a))),sqrt(2))/a^(11/2)/(b*x^3+a*x^2)^(1/4),1],
[(b*x^3+a*x^2)^p,x,2,(b*x^3+a*x^2)^(p+1)*hypergeom([1, 2+3*p],[2*p+2],-b*x/a)/a/(1+2*p)/x,1],
[(a*x^n+b*x^(1+n))^3,x,3,a*b^2*x^(3+3*n)/(1+n)+a^3*x^(1+3*n)/(1+3*n)+3*a^2*b*x^(2+3*n)/(2+3*n)+b^3*x^(4+3*n)/(4+3*n),1],
[(a*x^n+b*x^(1+n))^2,x,3,a*b*x^(2+2*n)/(1+n)+a^2*x^(1+2*n)/(1+2*n)+b^2*x^(3+2*n)/(3+2*n),1],
[a*x^n+b*x^(1+n),x,1,a*x^(1+n)/(1+n)+b*x^(2+n)/(2+n),1],
[1/(a*x^n+b*x^(1+n)),x,2,x^(1-n)*hypergeom([1, 1-n],[2-n],-b*x/a)/a/(1-n),1],
[1/(a*x^n+b*x^(1+n))^2,x,2,x^(1-2*n)*hypergeom([2, 1-2*n],[2-2*n],-b*x/a)/a^2/(1-2*n),1],
[1/(a*x^n+b*x^(1+n))^3,x,2,x^(1-3*n)*hypergeom([3, 1-3*n],[2-3*n],-b*x/a)/a^3/(1-3*n),1],
[(a*x^n+b*x^(1+n))^(5/2),x,3,2/7*(a*x^n+b*x^(1+n))^(7/2)*hypergeom([7/2, -5/2*n],[9/2],1+b*x/a)/b/(x^n)/((-b*x/a)^(5/2*n)),1],
[(a*x^n+b*x^(1+n))^(3/2),x,3,2/5*(a*x^n+b*x^(1+n))^(5/2)*hypergeom([5/2, -3/2*n],[7/2],1+b*x/a)/b/(x^n)/((-b*x/a)^(3/2*n)),1],
[sqrt(a*x^n+b*x^(1+n)),x,3,2/3*(a*x^n+b*x^(1+n))^(3/2)*hypergeom([3/2, -1/2*n],[5/2],1+b*x/a)/b/(x^n)/((-b*x/a)^(1/2*n)),1],
[1/sqrt(a*x^n+b*x^(1+n)),x,3,2*(-b*x/a)^(1/2*n)*sqrt(a*x^n+b*x^(1+n))*hypergeom([1/2, 1/2*n],[3/2],1+b*x/a)/b/(x^n),1],
[1/(a*x^n+b*x^(1+n))^(3/2),x,3,-2*(-b*x/a)^(3/2*n)*hypergeom([-1/2, 3/2*n],[1/2],1+b*x/a)/b/(x^n)/sqrt(a*x^n+b*x^(1+n)),1],
[1/(a*x^n+b*x^(1+n))^(5/2),x,3,-2/3*(-b*x/a)^(5/2*n)*hypergeom([-3/2, 5/2*n],[-1/2],1+b*x/a)/b/(x^n)/(a*x^n+b*x^(1+n))^(3/2),1],
[(a*x^n+b*x^(1+n))^p,x,2,x^(1-n)*(a*x^n+b*x^(1+n))^(p+1)*hypergeom([1, n*p+p+2],[n*p+2],-b*x/a)/a/(n*p+1),1],
[(a*x^n+b*x^(1+n))^(3/n),x,3,3*a^2*n*x^(-3-2*n)*(a*x^n+b*x^(1+n))^(2+3/n)/b^4/(3+2*n)+n*x^(-3-4*n)*(a*x^n+b*x^(1+n))^(4+3/n)/b^4/(3+4*n)-a^3*n*(b*x+a)*(a*x^n+b*x^(1+n))^(3/n)/b^4/(3+n)/x^3-a*n*(b*x+a)^3*(a*x^n+b*x^(1+n))^(3/n)/b^4/(1+n)/x^3,1],
[(a*x^n+b*x^(1+n))^(2/n),x,3,n*x^(-2-3*n)*(a*x^n+b*x^(1+n))^(3+2/n)/b^3/(2+3*n)+a^2*n*(b*x+a)*(a*x^n+b*x^(1+n))^(2/n)/b^3/(2+n)/x^2-a*n*(b*x+a)^2*(a*x^n+b*x^(1+n))^(2/n)/b^3/(1+n)/x^2,1],
[(a*x^n+b*x^(1+n))^(1/n),x,3,-a*n*x^(-1-n)*(a*x^n+b*x^(1+n))^(1+1/n)/b^2/(1+n)+n*x^(-1-2*n)*(a*x^n+b*x^(1+n))^(2+1/n)/b^2/(1+2*n),1],
[(a*x^n+b*x^(1+n))^(-1/n),x,2,n*x*(b*x+a)*hypergeom([1, -(1-n)/n],[2-1/n],1+b*x/a)/a/(1-n)/((a*x^n+b*x^(1+n))^(1/n)),1],
[(a*x^n+b*x^(1+n))^(-2/n),x,2,-b*n*x^2*(b*x+a)*hypergeom([2, -(2-n)/n],[2-2/n],1+b*x/a)/a^2/(2-n)/((a*x^n+b*x^(1+n))^(2/n)),1],
[(a*x^n+b*x^(1+n))^(-3/n),x,2,b^2*n*x^3*(b*x+a)*hypergeom([3, -(3-n)/n],[2-3/n],1+b*x/a)/a^3/(3-n)/((a*x^n+b*x^(1+n))^(3/n)),1]]: