lst:=[[(b*x^5+a)^3,x,2,a^3*x+1/2*a^2*b*x^6+3/11*a*b^2*x^11+1/16*b^3*x^16,1],
[(b*x^5+a)^2,x,2,a^2*x+1/3*a*b*x^6+1/11*b^2*x^11,1],
[b*x^5+a,x,1,a*x+1/6*b*x^6,1],
[1/(b*x^5+a),x,6,-1/5*sqrt(5/2+1/2*sqrt(5))*arctan(((1-sqrt(5))*a^(1/5)-4*b^(1/5)*x)/sqrt(10+2*sqrt(5))/a^(1/5))/a^(4/5)/b^(1/5)-1/5*sqrt(5/2-1/2*sqrt(5))*arctan(((1+sqrt(5))*a^(1/5)-4*b^(1/5)*x)/sqrt(10-2*sqrt(5))/a^(1/5))/a^(4/5)/b^(1/5)+1/5*ln(a^(1/5)+b^(1/5)*x)/a^(4/5)/b^(1/5)-1/20*(1-sqrt(5))*ln(2*a^(2/5)-(1-sqrt(5))*a^(1/5)*b^(1/5)*x+2*b^(2/5)*x^2)/a^(4/5)/b^(1/5)-1/20*(1+sqrt(5))*ln(2*a^(2/5)-(1+sqrt(5))*a^(1/5)*b^(1/5)*x+2*b^(2/5)*x^2)/a^(4/5)/b^(1/5),1],
[1/(x^5+1),x,6,-1/5*sqrt(5/2+1/2*sqrt(5))*arctan((1-sqrt(5)-4*x)/sqrt(10+2*sqrt(5)))-1/5*sqrt(5/2-1/2*sqrt(5))*arctan(1/2*sqrt(1/2+1/10*sqrt(5))*(1+sqrt(5)-4*x))+1/5*ln(1+x)-1/20*(1-sqrt(5))*ln(1-1/2*(1-sqrt(5))*x+x^2)-1/20*(1+sqrt(5))*ln(1-1/2*(1+sqrt(5))*x+x^2),1],
[(b*x^5+a)^(3/2),x,2,a*x*sqrt(b*x^5+a)*hypergeom([-3/2, 1/5],[6/5],-b*x^5/a)/sqrt(1+b*x^5/a),1],
[sqrt(b*x^5+a),x,2,x*sqrt(b*x^5+a)*hypergeom([-1/2, 1/5],[6/5],-b*x^5/a)/sqrt(1+b*x^5/a),1],
[1/sqrt(b*x^5+a),x,2,x*sqrt(1+b*x^5/a)*hypergeom([1/5, 1/2],[6/5],-b*x^5/a)/sqrt(b*x^5+a),1],
[1/(b*x^5+a)^(3/2),x,2,x*sqrt(1+b*x^5/a)*hypergeom([1/5, 3/2],[6/5],-b*x^5/a)/a/sqrt(b*x^5+a),1],
[(b*x^6+a)^4,x,2,a^4*x+4/7*a^3*b*x^7+6/13*a^2*b^2*x^13+4/19*a*b^3*x^19+1/25*b^4*x^25,1],
[(b*x^6+a)^3,x,2,a^3*x+3/7*a^2*b*x^7+3/13*a*b^2*x^13+1/19*b^3*x^19,1],
[(b*x^6+a)^2,x,2,a^2*x+2/7*a*b*x^7+1/13*b^2*x^13,1],
[b*x^6+a,x,1,a*x+1/7*b*x^7,1],
[1/(b*x^6+a),x,10,1/3*arctan(b^(1/6)*x/a^(1/6))/a^(5/6)/b^(1/6)-1/6*arctan(sqrt(3)-2*b^(1/6)*x/a^(1/6))/a^(5/6)/b^(1/6)+1/6*arctan(sqrt(3)+2*b^(1/6)*x/a^(1/6))/a^(5/6)/b^(1/6)+1/2*arctanh(sqrt(3)*a^(1/6)*b^(1/6)*x/(a^(1/3)+b^(1/3)*x^2))/sqrt(3)/a^(5/6)/b^(1/6),1],
[1/(b*x^6+a)^2,x,11,1/6*x/a/(b*x^6+a)+5/18*arctan(b^(1/6)*x/a^(1/6))/a^(11/6)/b^(1/6)-5/36*arctan(sqrt(3)-2*b^(1/6)*x/a^(1/6))/a^(11/6)/b^(1/6)+5/36*arctan(sqrt(3)+2*b^(1/6)*x/a^(1/6))/a^(11/6)/b^(1/6)+5/12*arctanh(sqrt(3)*a^(1/6)*b^(1/6)*x/(a^(1/3)+b^(1/3)*x^2))/sqrt(3)/a^(11/6)/b^(1/6),1],
[1/(-3*x^6+2),x,10,-1/12*arctan(1/sqrt(3)-1/3*2^(5/6)*x*3^(2/3))*2^(1/6)*3^(1/3)+1/12*arctan(1/sqrt(3)+1/3*2^(5/6)*x*3^(2/3))*2^(1/6)*3^(1/3)+1/18*arctanh(1/2*3^(1/6)*2^(5/6)*x)*3^(5/6)*2^(1/6)+1/36*arctanh(6^(1/6)*x/(2^(1/3)+3^(1/3)*x^2))*3^(5/6)*2^(1/6),1],
[sqrt(x^6+2),x,2,1/4*x*sqrt(x^6+2)+1/8*3^(3/4)*x*(2^(1/3)+x^2)*sqrt((2^(2/3)-2^(1/3)*x^2+x^4)/(2^(1/3)+(1+sqrt(3))*x^2)^2)*InverseJacobiAM(arccos((2^(1/3)+(1-sqrt(3))*x^2)/(2^(1/3)+(1+sqrt(3))*x^2)),sqrt(1/2+1/4*sqrt(3)))*2^(2/3)/sqrt(x^2*(2^(1/3)+x^2)/(2^(1/3)+(1+sqrt(3))*x^2)^2)/sqrt(x^6+2),1],
[1/sqrt(x^6+2),x,1,1/12*3^(3/4)*x*(2^(1/3)+x^2)*sqrt((2^(2/3)-2^(1/3)*x^2+x^4)/(2^(1/3)+(1+sqrt(3))*x^2)^2)*InverseJacobiAM(arccos((2^(1/3)+(1-sqrt(3))*x^2)/(2^(1/3)+(1+sqrt(3))*x^2)),sqrt(1/2+1/4*sqrt(3)))*2^(2/3)/sqrt(x^2*(2^(1/3)+x^2)/(2^(1/3)+(1+sqrt(3))*x^2)^2)/sqrt(x^6+2),1],
[1/(x^6+2)^(3/2),x,2,1/6*x/sqrt(x^6+2)+1/36*3^(3/4)*x*(2^(1/3)+x^2)*sqrt((2^(2/3)-2^(1/3)*x^2+x^4)/(2^(1/3)+(1+sqrt(3))*x^2)^2)*InverseJacobiAM(arccos((2^(1/3)+(1-sqrt(3))*x^2)/(2^(1/3)+(1+sqrt(3))*x^2)),sqrt(1/2+1/4*sqrt(3)))*2^(2/3)/sqrt(x^2*(2^(1/3)+x^2)/(2^(1/3)+(1+sqrt(3))*x^2)^2)/sqrt(x^6+2),1],
[1/(-x^7+1),x,6,2/7*arctan(sec(1/14*Pi)*(x+sin(1/14*Pi)))*cos(1/14*Pi)+2/7*arctan(sec(3/14*Pi)*(x-sin(3/14*Pi)))*cos(3/14*Pi)-1/7*ln(1-x)+1/7*cos(1/7*Pi)*ln(1+x^2+2*x*cos(1/7*Pi))+1/7*ln(1+x^2+2*x*sin(1/14*Pi))*sin(1/14*Pi)+2/7*arctan((x+cos(1/7*Pi))*csc(1/7*Pi))*sin(1/7*Pi)-1/7*ln(1+x^2-2*x*sin(3/14*Pi))*sin(3/14*Pi),1],
[1/(x^7+1),x,6,2/7*arctan(sec(1/14*Pi)*(x-sin(1/14*Pi)))*cos(1/14*Pi)+2/7*arctan(sec(3/14*Pi)*(x+sin(3/14*Pi)))*cos(3/14*Pi)+1/7*ln(1+x)-1/7*cos(1/7*Pi)*ln(1+x^2-2*x*cos(1/7*Pi))-1/7*ln(1+x^2-2*x*sin(1/14*Pi))*sin(1/14*Pi)+2/7*arctan((x-cos(1/7*Pi))*csc(1/7*Pi))*sin(1/7*Pi)+1/7*ln(1+x^2+2*x*sin(3/14*Pi))*sin(3/14*Pi),1],
[(b*x^6+a)^(4/3),x,4,8/27*a*x*(b*x^6+a)^(1/3)+1/9*x*(b*x^6+a)^(4/3)+8/81*a*x*(b*x^6+a)^(1/3)*(1-b^(1/3)*x^2/(b*x^6+a)^(1/3))*sqrt((1+b^(2/3)*x^4/(b*x^6+a)^(2/3)+b^(1/3)*x^2/(b*x^6+a)^(1/3))/(1-(1+sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))^2)*InverseJacobiAM(arccos((1-(1-sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))/(1-(1+sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/sqrt(-b^(1/3)*x^2*(1-b^(1/3)*x^2/(b*x^6+a)^(1/3))/(b*x^6+a)^(1/3)/(1-(1+sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))^2),1],
[(b*x^6+a)^(1/3),x,3,1/3*x*(b*x^6+a)^(1/3)+1/9*x*(b*x^6+a)^(1/3)*(1-b^(1/3)*x^2/(b*x^6+a)^(1/3))*sqrt((1+b^(2/3)*x^4/(b*x^6+a)^(2/3)+b^(1/3)*x^2/(b*x^6+a)^(1/3))/(1-(1+sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))^2)*InverseJacobiAM(arccos((1-(1-sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))/(1-(1+sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/sqrt(-b^(1/3)*x^2*(1-b^(1/3)*x^2/(b*x^6+a)^(1/3))/(b*x^6+a)^(1/3)/(1-(1+sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))^2),1],
[1/(b*x^6+a)^(2/3),x,2,1/6*x*(b*x^6+a)^(1/3)*(1-b^(1/3)*x^2/(b*x^6+a)^(1/3))*sqrt((1+b^(2/3)*x^4/(b*x^6+a)^(2/3)+b^(1/3)*x^2/(b*x^6+a)^(1/3))/(1-(1+sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))^2)*InverseJacobiAM(arccos((1-(1-sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))/(1-(1+sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/a/sqrt(-b^(1/3)*x^2*(1-b^(1/3)*x^2/(b*x^6+a)^(1/3))/(b*x^6+a)^(1/3)/(1-(1+sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))^2),1],
[1/(b*x^6+a)^(5/3),x,3,1/4*x/a/(b*x^6+a)^(2/3)+1/8*3^(3/4)*x*(b*x^6+a)^(1/3)*(1-b^(1/3)*x^2/(b*x^6+a)^(1/3))*sqrt((1+b^(2/3)*x^4/(b*x^6+a)^(2/3)+b^(1/3)*x^2/(b*x^6+a)^(1/3))/(1-(1+sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))^2)*InverseJacobiAM(arccos((1-(1-sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))/(1-(1+sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))),sqrt(1/2+1/4*sqrt(3)))/a^2/sqrt(-b^(1/3)*x^2*(1-b^(1/3)*x^2/(b*x^6+a)^(1/3))/(b*x^6+a)^(1/3)/(1-(1+sqrt(3))*b^(1/3)*x^2/(b*x^6+a)^(1/3))^2),1],
[(b*x^6+a)^(5/3),x,2,a*x*(b*x^6+a)^(2/3)*hypergeom([-5/3, 1/6],[7/6],-b*x^6/a)/(1+b*x^6/a)^(2/3),1],
[(b*x^6+a)^(2/3),x,2,x*(b*x^6+a)^(2/3)*hypergeom([-2/3, 1/6],[7/6],-b*x^6/a)/(1+b*x^6/a)^(2/3),1],
[1/(b*x^6+a)^(1/3),x,2,x*(1+b*x^6/a)^(1/3)*hypergeom([1/6, 1/3],[7/6],-b*x^6/a)/(b*x^6+a)^(1/3),1],
[1/(b*x^6+a)^(4/3),x,2,x*(1+b*x^6/a)^(1/3)*hypergeom([1/6, 4/3],[7/6],-b*x^6/a)/a/(b*x^6+a)^(1/3),1],
[1/(b*x^8+a),x,12,-1/4*arctan(b^(1/8)*x/(-a)^(1/8))/(-a)^(7/8)/b^(1/8)+1/4*arctan(1-sqrt(2)*b^(1/8)*x/(-a)^(1/8))/sqrt(2)/(-a)^(7/8)/b^(1/8)-1/4*arctan(1+sqrt(2)*b^(1/8)*x/(-a)^(1/8))/sqrt(2)/(-a)^(7/8)/b^(1/8)-1/4*arctanh(b^(1/8)*x/(-a)^(1/8))/(-a)^(7/8)/b^(1/8)-1/4*arctanh(sqrt(2)*(-a)^(1/8)*b^(1/8)*x/((-a)^(1/4)+b^(1/4)*x^2))/sqrt(2)/(-a)^(7/8)/b^(1/8),1],
[1/(-b*x^8+a),x,12,1/4*arctan(b^(1/8)*x/a^(1/8))/a^(7/8)/b^(1/8)-1/4*arctan(1-sqrt(2)*b^(1/8)*x/a^(1/8))/sqrt(2)/a^(7/8)/b^(1/8)+1/4*arctan(1+sqrt(2)*b^(1/8)*x/a^(1/8))/sqrt(2)/a^(7/8)/b^(1/8)+1/4*arctanh(b^(1/8)*x/a^(1/8))/a^(7/8)/b^(1/8)+1/4*arctanh(sqrt(2)*a^(1/8)*b^(1/8)*x/(a^(1/4)+b^(1/4)*x^2))/sqrt(2)/a^(7/8)/b^(1/8),1],
[sqrt(b*x^8+a),x,4,1/5*x*sqrt(b*x^8+a)+2/5*a*b^(1/4)*x^3*sqrt((a^(1/4)+b^(1/4)*x^2)^2/a^(1/4)/b^(1/4)/x^2)*sqrt(-(b*x^8+a)/sqrt(a)/sqrt(b)/x^4)*InverseJacobiAM(arcsin(1/2*sqrt(-a^(1/4)*(sqrt(2)-2*b^(1/4)*x^2/a^(1/4)+sqrt(2)*sqrt(b)*x^4/sqrt(a))/b^(1/4)/x^2)),sqrt(-2+2*sqrt(2)))/sqrt(2+sqrt(2))/(a^(1/4)+b^(1/4)*x^2)/sqrt(b*x^8+a)-2/5*a*b^(1/4)*x^3*sqrt(-(a^(1/4)-b^(1/4)*x^2)^2/a^(1/4)/b^(1/4)/x^2)*sqrt(-(b*x^8+a)/sqrt(a)/sqrt(b)/x^4)*InverseJacobiAM(arcsin(1/2*sqrt(a^(1/4)*(sqrt(2)+2*b^(1/4)*x^2/a^(1/4)+sqrt(2)*sqrt(b)*x^4/sqrt(a))/b^(1/4)/x^2)),sqrt(-2+2*sqrt(2)))/sqrt(2+sqrt(2))/(a^(1/4)-b^(1/4)*x^2)/sqrt(b*x^8+a),1],
[1/sqrt(b*x^8+a),x,3,1/2*b^(1/4)*x^3*sqrt((a^(1/4)+b^(1/4)*x^2)^2/a^(1/4)/b^(1/4)/x^2)*sqrt(-(b*x^8+a)/sqrt(a)/sqrt(b)/x^4)*InverseJacobiAM(arcsin(1/2*sqrt(-a^(1/4)*(sqrt(2)-2*b^(1/4)*x^2/a^(1/4)+sqrt(2)*sqrt(b)*x^4/sqrt(a))/b^(1/4)/x^2)),sqrt(-2+2*sqrt(2)))/sqrt(2+sqrt(2))/(a^(1/4)+b^(1/4)*x^2)/sqrt(b*x^8+a)-1/2*b^(1/4)*x^3*sqrt(-(a^(1/4)-b^(1/4)*x^2)^2/a^(1/4)/b^(1/4)/x^2)*sqrt(-(b*x^8+a)/sqrt(a)/sqrt(b)/x^4)*InverseJacobiAM(arcsin(1/2*sqrt(a^(1/4)*(sqrt(2)+2*b^(1/4)*x^2/a^(1/4)+sqrt(2)*sqrt(b)*x^4/sqrt(a))/b^(1/4)/x^2)),sqrt(-2+2*sqrt(2)))/sqrt(2+sqrt(2))/(a^(1/4)-b^(1/4)*x^2)/sqrt(b*x^8+a),1],
[1/(b*x^8+a)^(3/2),x,4,1/4*x/a/sqrt(b*x^8+a)+3/8*b^(1/4)*x^3*sqrt((a^(1/4)+b^(1/4)*x^2)^2/a^(1/4)/b^(1/4)/x^2)*sqrt(-(b*x^8+a)/sqrt(a)/sqrt(b)/x^4)*InverseJacobiAM(arcsin(1/2*sqrt(-a^(1/4)*(sqrt(2)-2*b^(1/4)*x^2/a^(1/4)+sqrt(2)*sqrt(b)*x^4/sqrt(a))/b^(1/4)/x^2)),sqrt(-2+2*sqrt(2)))/sqrt(2+sqrt(2))/a/(a^(1/4)+b^(1/4)*x^2)/sqrt(b*x^8+a)-3/8*b^(1/4)*x^3*sqrt(-(a^(1/4)-b^(1/4)*x^2)^2/a^(1/4)/b^(1/4)/x^2)*sqrt(-(b*x^8+a)/sqrt(a)/sqrt(b)/x^4)*InverseJacobiAM(arcsin(1/2*sqrt(a^(1/4)*(sqrt(2)+2*b^(1/4)*x^2/a^(1/4)+sqrt(2)*sqrt(b)*x^4/sqrt(a))/b^(1/4)/x^2)),sqrt(-2+2*sqrt(2)))/sqrt(2+sqrt(2))/a/(a^(1/4)-b^(1/4)*x^2)/sqrt(b*x^8+a),1],
[1/(-x^10+1),x,10,1/20*sqrt(10-2*sqrt(5))*arctan(sqrt(10-2*sqrt(5))*x/(-2*x^2+2))+1/20*sqrt(10+2*sqrt(5))*arctan(sqrt(10+2*sqrt(5))*x/(-2*x^2+2))+1/5*arctanh(x)+1/20*(1-sqrt(5))*arctanh((1-sqrt(5))*x/(2*x^2+2))+1/20*(1+sqrt(5))*arctanh((1+sqrt(5))*x/(2*x^2+2)),1],
[(b*x^3+a)^p,x,2,x*(b*x^3+a)^p*hypergeom([1/3, -p],[4/3],-b*x^3/a)/((1+b*x^3/a)^p),1],
[(b*x^2+a)^p,x,2,x*(b*x^2+a)^p*hypergeom([1/2, -p],[3/2],-b*x^2/a)/((1+b*x^2/a)^p),1],
[(b*x+a)^p,x,1,(b*x+a)^(p+1)/b/(p+1),1],
[(a+b/x)^p,x,2,-b*(a+b/x)^(p+1)*hypergeom([2, p+1],[2+p],1+b/a/x)/a^2/(p+1),1],
[(a+b/x^2)^p,x,3,(a+b/x^2)^p*x*hypergeom([-1/2, -p],[1/2],-b/a/x^2)/((1+b/a/x^2)^p),1],
[(a+b/x^3)^p,x,3,(a+b/x^3)^p*x*hypergeom([-1/3, -p],[2/3],-b/a/x^3)/((1+b/a/x^3)^p),1],
[(3*a*x^2+a)^p,x,2,x*(3*a*x^2+a)^p*hypergeom([1/2, -p],[3/2],-3*x^2)/((3*x^2+1)^p),1],
[(2*a*x^2+a)^p,x,2,x*(2*a*x^2+a)^p*hypergeom([1/2, -p],[3/2],-2*x^2)/((2*x^2+1)^p),1],
[(a*x^2+a)^p,x,2,x*(a*x^2+a)^p*hypergeom([1/2, -p],[3/2],-x^2)/((x^2+1)^p),1],
[(-a*x^2+a)^p,x,2,x*(-a*x^2+a)^p*hypergeom([1/2, -p],[3/2],x^2)/((-x^2+1)^p),1],
[(-2*a*x^2+a)^p,x,2,x*(-2*a*x^2+a)^p*hypergeom([1/2, -p],[3/2],2*x^2)/((-2*x^2+1)^p),1],
[(-3*a*x^2+a)^p,x,2,x*(-3*a*x^2+a)^p*hypergeom([1/2, -p],[3/2],3*x^2)/((-3*x^2+1)^p),1],
[(a+b*sqrt(x))^5,x,3,-1/3*a*(a+b*sqrt(x))^6/b^2+2/7*(a+b*sqrt(x))^7/b^2,1],
[(a+b*sqrt(x))^4,x,3,-2/5*a*(a+b*sqrt(x))^5/b^2+1/3*(a+b*sqrt(x))^6/b^2,1],
[(a+b*sqrt(x))^3,x,3,-1/2*a*(a+b*sqrt(x))^4/b^2+2/5*(a+b*sqrt(x))^5/b^2,1],
[(a+b*sqrt(x))^2,x,3,a^2*x+4/3*a*b*x^(3/2)+1/2*b^2*x^2,1],
[a+b*sqrt(x),x,1,a*x+2/3*b*x^(3/2),1],
[1/(a+b*sqrt(x)),x,3,2*sqrt(x)/b-2*a*ln(a+b*sqrt(x))/b^2,1],
[1/(a+b*sqrt(x))^2,x,3,2*a/b^2/(a+b*sqrt(x))+2*ln(a+b*sqrt(x))/b^2,1],
[1/(a+b*sqrt(x))^3,x,1,x/a/(a+b*sqrt(x))^2,1],
[1/(a+b*sqrt(x))^4,x,3,2/3*a/b^2/(a+b*sqrt(x))^3-1/b^2/(a+b*sqrt(x))^2,1],
[1/(a+b*sqrt(x))^5,x,3,1/2*a/b^2/(a+b*sqrt(x))^4-2/3/b^2/(a+b*sqrt(x))^3,1],
[(a+b*x^(3/2))^3,x,2,a^3*x+6/5*a^2*b*x^(5/2)+3/4*a*b^2*x^4+2/11*b^3*x^(11/2),1],
[(a+b*x^(3/2))^2,x,2,a^2*x+4/5*a*b*x^(5/2)+1/4*b^2*x^4,1],
[a+b*x^(3/2),x,1,a*x+2/5*b*x^(5/2),1],
[1/(a+b*x^(3/2)),x,7,-2*arctan((a^(1/3)-2*b^(1/3)*sqrt(x))/sqrt(3)/a^(1/3))/sqrt(3)/a^(1/3)/b^(2/3)-2/3*ln(a^(1/3)+b^(1/3)*sqrt(x))/a^(1/3)/b^(2/3)+1/3*ln(a^(2/3)-a^(1/3)*b^(1/3)*sqrt(x)+b^(2/3)*x)/a^(1/3)/b^(2/3),1],
[1/(a+b*x^(3/2))^2,x,8,2/3*x/a/(a+b*x^(3/2))-2/3*arctan((a^(1/3)-2*b^(1/3)*sqrt(x))/sqrt(3)/a^(1/3))/sqrt(3)/a^(4/3)/b^(2/3)-2/9*ln(a^(1/3)+b^(1/3)*sqrt(x))/a^(4/3)/b^(2/3)+1/9*ln(a^(2/3)-a^(1/3)*b^(1/3)*sqrt(x)+b^(2/3)*x)/a^(4/3)/b^(2/3),1],
[1/(a+b*x^(3/2))^3,x,9,1/3*x/a/(a+b*x^(3/2))^2+4/9*x/a^2/(a+b*x^(3/2))-4/9*arctan((a^(1/3)-2*b^(1/3)*sqrt(x))/sqrt(3)/a^(1/3))/sqrt(3)/a^(7/3)/b^(2/3)-4/27*ln(a^(1/3)+b^(1/3)*sqrt(x))/a^(7/3)/b^(2/3)+2/27*ln(a^(2/3)-a^(1/3)*b^(1/3)*sqrt(x)+b^(2/3)*x)/a^(7/3)/b^(2/3),1],
[1/(a+b*x^(3/2))^4,x,10,2/9*x/a/(a+b*x^(3/2))^3+7/27*x/a^2/(a+b*x^(3/2))^2+28/81*x/a^3/(a+b*x^(3/2))-28/81*arctan((a^(1/3)-2*b^(1/3)*sqrt(x))/sqrt(3)/a^(1/3))/sqrt(3)/a^(10/3)/b^(2/3)-28/243*ln(a^(1/3)+b^(1/3)*sqrt(x))/a^(10/3)/b^(2/3)+14/243*ln(a^(2/3)-a^(1/3)*b^(1/3)*sqrt(x)+b^(2/3)*x)/a^(10/3)/b^(2/3),1],
[(a+b/sqrt(x))^4,x,4,-b^4/x-8*a*b^3/sqrt(x)+8*a^3*b*sqrt(x)+a^4*x+6*a^2*b^2*ln(x),1],
[(a+b/sqrt(x))^3,x,4,-2*b^3/sqrt(x)+6*a^2*b*sqrt(x)+a^3*x+3*a*b^2*ln(x),1],
[(a+b/sqrt(x))^2,x,4,4*a*b*sqrt(x)+a^2*x+b^2*ln(x),1],
[a+b/sqrt(x),x,1,2*b*sqrt(x)+a*x,1],
[1/(a+b/sqrt(x)),x,4,-2*b*sqrt(x)/a^2+x/a+2*b^2*ln(b+a*sqrt(x))/a^3,1],
[1/(a+b/sqrt(x))^2,x,4,2*b^3/a^4/(b+a*sqrt(x))-4*b*sqrt(x)/a^3+x/a^2+6*b^2*ln(b+a*sqrt(x))/a^4,1],
[1/(a+b/sqrt(x))^3,x,4,-b^4/a^5/(b+a*sqrt(x))^2+8*b^3/a^5/(b+a*sqrt(x))-6*b*sqrt(x)/a^4+x/a^3+12*b^2*ln(b+a*sqrt(x))/a^5,1],
[1/(a+b/sqrt(x))^4,x,4,2/3*b^5/a^6/(b+a*sqrt(x))^3-5*b^4/a^6/(b+a*sqrt(x))^2+20*b^3/a^6/(b+a*sqrt(x))-8*b*sqrt(x)/a^5+x/a^4+20*b^2*ln(b+a*sqrt(x))/a^6,1],
[(a+b/x^(3/2))^4,x,2,-1/5*b^4/x^5-8/7*a*b^3/x^(7/2)-3*a^2*b^2/x^2-8*a^3*b/sqrt(x)+a^4*x,1],
[(a+b/x^(3/2))^3,x,2,-2/7*b^3/x^(7/2)-3/2*a*b^2/x^2-6*a^2*b/sqrt(x)+a^3*x,1],
[(a+b/x^(3/2))^2,x,2,-1/2*b^2/x^2-4*a*b/sqrt(x)+a^2*x,1],
[a+b/x^(3/2),x,1,-2*b/sqrt(x)+a*x,1],
[1/(a+b/x^(3/2)),x,9,x/a+2*b^(2/3)*arctan((b^(1/3)-2*a^(1/3)*sqrt(x))/sqrt(3)/b^(1/3))/sqrt(3)/a^(5/3)+2/3*b^(2/3)*ln(b^(1/3)+a^(1/3)*sqrt(x))/a^(5/3)-1/3*b^(2/3)*ln(b^(2/3)-a^(1/3)*b^(1/3)*sqrt(x)+a^(2/3)*x)/a^(5/3),1],
[1/(a+b/x^(3/2))^2,x,11,x/a^2+2/3*b*x/a^2/(b+a*x^(3/2))+10/3*b^(2/3)*arctan((b^(1/3)-2*a^(1/3)*sqrt(x))/sqrt(3)/b^(1/3))/sqrt(3)/a^(8/3)+10/9*b^(2/3)*ln(b^(1/3)+a^(1/3)*sqrt(x))/a^(8/3)-5/9*b^(2/3)*ln(b^(2/3)-a^(1/3)*b^(1/3)*sqrt(x)+a^(2/3)*x)/a^(8/3),1],
[1/(a+b/x^(3/2))^3,x,12,x/a^3-1/3*b^2*x/a^3/(b+a*x^(3/2))^2+14/9*b*x/a^3/(b+a*x^(3/2))+40/9*b^(2/3)*arctan((b^(1/3)-2*a^(1/3)*sqrt(x))/sqrt(3)/b^(1/3))/sqrt(3)/a^(11/3)+40/27*b^(2/3)*ln(b^(1/3)+a^(1/3)*sqrt(x))/a^(11/3)-20/27*b^(2/3)*ln(b^(2/3)-a^(1/3)*b^(1/3)*sqrt(x)+a^(2/3)*x)/a^(11/3),1],
[(a+b*x^(5/2))^p,x,2,x*(a+b*x^(5/2))^p*hypergeom([2/5, -p],[7/5],-b*x^(5/2)/a)/((1+b*x^(5/2)/a)^p),1],
[(a+b*x^(3/2))^p,x,2,x*(a+b*x^(3/2))^p*hypergeom([2/3, -p],[5/3],-b*x^(3/2)/a)/((1+b*x^(3/2)/a)^p),1],
[(a+b*sqrt(x))^p,x,3,-2*a*(a+b*sqrt(x))^(p+1)/b^2/(p+1)+2*(a+b*sqrt(x))^(2+p)/b^2/(2+p),1],
[(a+b/sqrt(x))^p,x,3,2*b^2*(a+b/sqrt(x))^(p+1)*hypergeom([3, p+1],[2+p],1+b/a/sqrt(x))/a^3/(p+1),1],
[(a+b/x^(3/2))^p,x,2,(a+b/x^(3/2))^p*x*hypergeom([-2/3, -p],[1/3],-b/a/x^(3/2))/((1+b/a/x^(3/2))^p),1],
[(a+b/x^(5/2))^p,x,2,(a+b/x^(5/2))^p*x*hypergeom([-2/5, -p],[3/5],-b/a/x^(5/2))/((1+b/a/x^(5/2))^p),1],
[(a+b*x^(1/3))^6,x,3,3/7*a^2*(a+b*x^(1/3))^7/b^3-3/4*a*(a+b*x^(1/3))^8/b^3+1/3*(a+b*x^(1/3))^9/b^3,1],
[(a+b*x^(1/3))^5,x,3,1/2*a^2*(a+b*x^(1/3))^6/b^3-6/7*a*(a+b*x^(1/3))^7/b^3+3/8*(a+b*x^(1/3))^8/b^3,1],
[(a+b*x^(1/3))^4,x,3,3/5*a^2*(a+b*x^(1/3))^5/b^3-a*(a+b*x^(1/3))^6/b^3+3/7*(a+b*x^(1/3))^7/b^3,1],
[(a+b*x^(1/3))^3,x,3,a^3*x+9/4*a^2*b*x^(4/3)+9/5*a*b^2*x^(5/3)+1/2*b^3*x^2,1],
[(a+b*x^(1/3))^2,x,3,a^2*x+3/2*a*b*x^(4/3)+3/5*b^2*x^(5/3),1],
[a+b*x^(1/3),x,1,a*x+3/4*b*x^(4/3),1],
[1/(a+b*x^(1/3)),x,3,-3*a*x^(1/3)/b^2+3/2*x^(2/3)/b+3*a^2*ln(a+b*x^(1/3))/b^3,1],
[1/(a+b*x^(1/3))^2,x,3,-3*a^2/b^3/(a+b*x^(1/3))+3*x^(1/3)/b^2-6*a*ln(a+b*x^(1/3))/b^3,1],
[1/(a+b*x^(1/3))^3,x,3,-3/2*a^2/b^3/(a+b*x^(1/3))^2+6*a/b^3/(a+b*x^(1/3))+3*ln(a+b*x^(1/3))/b^3,1],
[1/(a+b*x^(1/3))^4,x,1,x/a/(a+b*x^(1/3))^3,1],
[1/(a+b*x^(1/3))^5,x,3,3/4*x/a/(a+b*x^(1/3))^4+1/4*x/a^2/(a+b*x^(1/3))^3,1],
[1/(a+b*x^(1/3))^6,x,3,-3/5*a^2/b^3/(a+b*x^(1/3))^5+3/2*a/b^3/(a+b*x^(1/3))^4-1/b^3/(a+b*x^(1/3))^3,1],
[(a+b*x^(2/3))^3,x,2,a^3*x+9/5*a^2*b*x^(5/3)+9/7*a*b^2*x^(7/3)+1/3*b^3*x^3,1],
[(a+b*x^(2/3))^2,x,2,a^2*x+6/5*a*b*x^(5/3)+3/7*b^2*x^(7/3),1],
[a+b*x^(2/3),x,1,a*x+3/5*b*x^(5/3),1],
[1/(a+b*x^(2/3)),x,3,3*x^(1/3)/b-3*sqrt(a)*arctan(sqrt(b)*x^(1/3)/sqrt(a))/b^(3/2),1],
[1/(a+b*x^(2/3))^2,x,3,-3/2*x^(1/3)/b/(a+b*x^(2/3))+3/2*arctan(sqrt(b)*x^(1/3)/sqrt(a))/sqrt(a)/b^(3/2),1],
[1/(a+b*x^(2/3))^3,x,4,-3/4*x^(1/3)/b/(a+b*x^(2/3))^2+3/8*x^(1/3)/a/b/(a+b*x^(2/3))+3/8*arctan(sqrt(b)*x^(1/3)/sqrt(a))/a^(3/2)/b^(3/2),1],
[(a+b*x^(4/3))^3,x,2,a^3*x+9/7*a^2*b*x^(7/3)+9/11*a*b^2*x^(11/3)+1/5*b^3*x^5,1],
[(a+b*x^(4/3))^2,x,2,a^2*x+6/7*a*b*x^(7/3)+3/11*b^2*x^(11/3),1],
[a+b*x^(4/3),x,1,a*x+3/7*b*x^(7/3),1],
[1/(a+b*x^(4/3)),x,9,-3/2*arctan(1-sqrt(2)*b^(1/4)*x^(1/3)/a^(1/4))/sqrt(2)/a^(1/4)/b^(3/4)+3/2*arctan(1+sqrt(2)*b^(1/4)*x^(1/3)/a^(1/4))/sqrt(2)/a^(1/4)/b^(3/4)-3/2*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x^(1/3)/(sqrt(a)+sqrt(b)*x^(2/3)))/sqrt(2)/a^(1/4)/b^(3/4),1],
[1/(a+b*x^(4/3))^2,x,10,3/4*x/a/(a+b*x^(4/3))-3/8*arctan(1-sqrt(2)*b^(1/4)*x^(1/3)/a^(1/4))/sqrt(2)/a^(5/4)/b^(3/4)+3/8*arctan(1+sqrt(2)*b^(1/4)*x^(1/3)/a^(1/4))/sqrt(2)/a^(5/4)/b^(3/4)-3/8*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x^(1/3)/(sqrt(a)+sqrt(b)*x^(2/3)))/sqrt(2)/a^(5/4)/b^(3/4),1],
[1/(a+b*x^(4/3))^3,x,11,3/8*x/a/(a+b*x^(4/3))^2+15/32*x/a^2/(a+b*x^(4/3))-15/64*arctan(1-sqrt(2)*b^(1/4)*x^(1/3)/a^(1/4))/sqrt(2)/a^(9/4)/b^(3/4)+15/64*arctan(1+sqrt(2)*b^(1/4)*x^(1/3)/a^(1/4))/sqrt(2)/a^(9/4)/b^(3/4)-15/64*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x^(1/3)/(sqrt(a)+sqrt(b)*x^(2/3)))/sqrt(2)/a^(9/4)/b^(3/4),1],
[(a+b/x^(1/3))^3,x,4,9*a*b^2*x^(1/3)+9/2*a^2*b*x^(2/3)+a^3*x+b^3*ln(x),1],
[(a+b/x^(1/3))^2,x,2,(b+a*x^(1/3))^3/a,1],
[a+b/x^(1/3),x,1,3/2*b*x^(2/3)+a*x,1],
[1/(a+b/x^(1/3)),x,4,3*b^2*x^(1/3)/a^3-3/2*b*x^(2/3)/a^2+x/a-3*b^3*ln(b+a*x^(1/3))/a^4,1],
[1/(a+b/x^(1/3))^2,x,4,-3*b^4/a^5/(b+a*x^(1/3))+9*b^2*x^(1/3)/a^4-3*b*x^(2/3)/a^3+x/a^2-12*b^3*ln(b+a*x^(1/3))/a^5,1],
[1/(a+b/x^(1/3))^3,x,4,3/2*b^5/a^6/(b+a*x^(1/3))^2-15*b^4/a^6/(b+a*x^(1/3))+18*b^2*x^(1/3)/a^5-9/2*b*x^(2/3)/a^4+x/a^3-30*b^3*ln(b+a*x^(1/3))/a^6,1],
[(a+b/x^(2/3))^3,x,2,-b^3/x-9*a*b^2/x^(1/3)+9*a^2*b*x^(1/3)+a^3*x,1],
[(a+b/x^(2/3))^2,x,2,-3*b^2/x^(1/3)+6*a*b*x^(1/3)+a^2*x,1],
[a+b/x^(2/3),x,1,3*b*x^(1/3)+a*x,1],
[1/(a+b/x^(2/3)),x,5,-3*b*x^(1/3)/a^2+x/a+3*b^(3/2)*arctan(sqrt(a)*x^(1/3)/sqrt(b))/a^(5/2),1],
[1/(a+b/x^(2/3))^2,x,6,-6*b*x^(1/3)/a^3-3/2*b^2*x^(1/3)/a^3/(b+a*x^(2/3))+x/a^2+15/2*b^(3/2)*arctan(sqrt(a)*x^(1/3)/sqrt(b))/a^(7/2),1],
[1/(a+b/x^(2/3))^3,x,7,-9*b*x^(1/3)/a^4+3/4*b^3*x^(1/3)/a^4/(b+a*x^(2/3))^2-39/8*b^2*x^(1/3)/a^4/(b+a*x^(2/3))+x/a^3+105/8*b^(3/2)*arctan(sqrt(a)*x^(1/3)/sqrt(b))/a^(9/2),1],
[(a+b/x^(4/3))^3,x,2,-1/3*b^3/x^3-9/5*a*b^2/x^(5/3)-9*a^2*b/x^(1/3)+a^3*x,1],
[(a+b/x^(4/3))^2,x,2,-3/5*b^2/x^(5/3)-6*a*b/x^(1/3)+a^2*x,1],
[a+b/x^(4/3),x,1,-3*b/x^(1/3)+a*x,1],
[1/(a+b/x^(4/3)),x,11,x/a+3/2*b^(3/4)*arctan(1-sqrt(2)*a^(1/4)*x^(1/3)/b^(1/4))/sqrt(2)/a^(7/4)-3/2*b^(3/4)*arctan(1+sqrt(2)*a^(1/4)*x^(1/3)/b^(1/4))/sqrt(2)/a^(7/4)+3/2*b^(3/4)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x^(1/3)/(sqrt(b)+sqrt(a)*x^(2/3)))/sqrt(2)/a^(7/4),1],
[1/(a+b/x^(4/3))^2,x,13,x/a^2+3/4*b*x/a^2/(b+a*x^(4/3))+21/8*b^(3/4)*arctan(1-sqrt(2)*a^(1/4)*x^(1/3)/b^(1/4))/sqrt(2)/a^(11/4)-21/8*b^(3/4)*arctan(1+sqrt(2)*a^(1/4)*x^(1/3)/b^(1/4))/sqrt(2)/a^(11/4)+21/8*b^(3/4)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x^(1/3)/(sqrt(b)+sqrt(a)*x^(2/3)))/sqrt(2)/a^(11/4),1],
[1/(a+b/x^(4/3))^3,x,14,x/a^3-3/8*b^2*x/a^3/(b+a*x^(4/3))^2+57/32*b*x/a^3/(b+a*x^(4/3))+231/64*b^(3/4)*arctan(1-sqrt(2)*a^(1/4)*x^(1/3)/b^(1/4))/sqrt(2)/a^(15/4)-231/64*b^(3/4)*arctan(1+sqrt(2)*a^(1/4)*x^(1/3)/b^(1/4))/sqrt(2)/a^(15/4)+231/64*b^(3/4)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x^(1/3)/(sqrt(b)+sqrt(a)*x^(2/3)))/sqrt(2)/a^(15/4),1],
[(a+b/x^(1/3))^2,x,2,(b+a*x^(1/3))^3/a,1],
[(b+a*x^(1/3))^2/x^(2/3),x,1,(b+a*x^(1/3))^3/a,1],
[(a+b*x^(1/3))^(3/2),x,3,6/5*a^2*(a+b*x^(1/3))^(5/2)/b^3-12/7*a*(a+b*x^(1/3))^(7/2)/b^3+2/3*(a+b*x^(1/3))^(9/2)/b^3,1],
[sqrt(a+b*x^(1/3)),x,3,2*a^2*(a+b*x^(1/3))^(3/2)/b^3-12/5*a*(a+b*x^(1/3))^(5/2)/b^3+6/7*(a+b*x^(1/3))^(7/2)/b^3,1],
[1/sqrt(a+b*x^(1/3)),x,3,6*a^2*sqrt(a+b*x^(1/3))/b^3-4*a*(a+b*x^(1/3))^(3/2)/b^3+6/5*(a+b*x^(1/3))^(5/2)/b^3,1],
[1/(a+b*x^(1/3))^(3/2),x,3,-6*a^2/b^3/sqrt(a+b*x^(1/3))-12*a*sqrt(a+b*x^(1/3))/b^3+2*(a+b*x^(1/3))^(3/2)/b^3,1],
[1/(a+b*x^(1/3))^(5/2),x,3,-2*a^2/b^3/(a+b*x^(1/3))^(3/2)+12*a/b^3/sqrt(a+b*x^(1/3))+6*sqrt(a+b*x^(1/3))/b^3,1],
[(a+b*x^(2/3))^(3/2),x,6,3/16*a^2*sqrt(a+b*x^(2/3))*x^(1/3)/b+3/8*a*sqrt(a+b*x^(2/3))*x+1/2*(a+b*x^(2/3))^(3/2)*x-3/16*a^3*arctanh(sqrt(b)*x^(1/3)/sqrt(a+b*x^(2/3)))/b^(3/2),1],
[sqrt(a+b*x^(2/3)),x,5,3/8*a*sqrt(a+b*x^(2/3))*x^(1/3)/b+3/4*sqrt(a+b*x^(2/3))*x-3/8*a^2*arctanh(sqrt(b)*x^(1/3)/sqrt(a+b*x^(2/3)))/b^(3/2),1],
[1/sqrt(a+b*x^(2/3)),x,4,3/2*sqrt(a+b*x^(2/3))*x^(1/3)/b-3/2*a*arctanh(sqrt(b)*x^(1/3)/sqrt(a+b*x^(2/3)))/b^(3/2),1],
[1/(a+b*x^(2/3))^(3/2),x,4,-3*x^(1/3)/b/sqrt(a+b*x^(2/3))+3*arctanh(sqrt(b)*x^(1/3)/sqrt(a+b*x^(2/3)))/b^(3/2),1],
[1/(a+b*x^(2/3))^(5/2),x,1,x/a/(a+b*x^(2/3))^(3/2),1],
[1/(a+b*x^(2/3))^(7/2),x,2,3/5*x/a/(a+b*x^(2/3))^(5/2)+2/5*x/a^2/(a+b*x^(2/3))^(3/2),1],
[1/(a+b*x^(2/3))^(9/2),x,3,3/7*x/a/(a+b*x^(2/3))^(7/2)+12/35*x/a^2/(a+b*x^(2/3))^(5/2)+8/35*x/a^3/(a+b*x^(2/3))^(3/2),1],
[(a+b*x^(4/3))^(3/2),x,7,4/5*a^2*x^(1/3)*sqrt(a+b*x^(4/3))/sqrt(b)/(sqrt(a)+sqrt(b)*x^(2/3))+2/5*a*x*sqrt(a+b*x^(4/3))+1/3*x*(a+b*x^(4/3))^(3/2)-4/5*a^(9/4)*(sqrt(a)+sqrt(b)*x^(2/3))*sqrt((a+b*x^(4/3))/(sqrt(a)+sqrt(b)*x^(2/3))^2)*EllipticE(sin(2*arctan(b^(1/4)*x^(1/3)/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(a+b*x^(4/3))+2/5*a^(9/4)*(sqrt(a)+sqrt(b)*x^(2/3))*sqrt((a+b*x^(4/3))/(sqrt(a)+sqrt(b)*x^(2/3))^2)*InverseJacobiAM(2*arctan(b^(1/4)*x^(1/3)/a^(1/4)),sqrt(1/2))/b^(3/4)/sqrt(a+b*x^(4/3)),1],
[sqrt(a+b*x^(4/3)),x,6,6/5*a*x^(1/3)*sqrt(a+b*x^(4/3))/sqrt(b)/(sqrt(a)+sqrt(b)*x^(2/3))+3/5*x*sqrt(a+b*x^(4/3))-6/5*a^(5/4)*(sqrt(a)+sqrt(b)*x^(2/3))*sqrt((a+b*x^(4/3))/(sqrt(a)+sqrt(b)*x^(2/3))^2)*EllipticE(sin(2*arctan(b^(1/4)*x^(1/3)/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(a+b*x^(4/3))+3/5*a^(5/4)*(sqrt(a)+sqrt(b)*x^(2/3))*sqrt((a+b*x^(4/3))/(sqrt(a)+sqrt(b)*x^(2/3))^2)*InverseJacobiAM(2*arctan(b^(1/4)*x^(1/3)/a^(1/4)),sqrt(1/2))/b^(3/4)/sqrt(a+b*x^(4/3)),1],
[1/sqrt(a+b*x^(4/3)),x,5,3*x^(1/3)*sqrt(a+b*x^(4/3))/sqrt(b)/(sqrt(a)+sqrt(b)*x^(2/3))-3*a^(1/4)*(sqrt(a)+sqrt(b)*x^(2/3))*sqrt((a+b*x^(4/3))/(sqrt(a)+sqrt(b)*x^(2/3))^2)*EllipticE(sin(2*arctan(b^(1/4)*x^(1/3)/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(a+b*x^(4/3))+3/2*a^(1/4)*(sqrt(a)+sqrt(b)*x^(2/3))*sqrt((a+b*x^(4/3))/(sqrt(a)+sqrt(b)*x^(2/3))^2)*InverseJacobiAM(2*arctan(b^(1/4)*x^(1/3)/a^(1/4)),sqrt(1/2))/b^(3/4)/sqrt(a+b*x^(4/3)),1],
[1/(a+b*x^(4/3))^(3/2),x,6,3/2*x/a/sqrt(a+b*x^(4/3))-3/2*x^(1/3)*sqrt(a+b*x^(4/3))/a/sqrt(b)/(sqrt(a)+sqrt(b)*x^(2/3))+3/2*(sqrt(a)+sqrt(b)*x^(2/3))*sqrt((a+b*x^(4/3))/(sqrt(a)+sqrt(b)*x^(2/3))^2)*EllipticE(sin(2*arctan(b^(1/4)*x^(1/3)/a^(1/4))),sqrt(1/2))/a^(3/4)/b^(3/4)/sqrt(a+b*x^(4/3))-3/4*(sqrt(a)+sqrt(b)*x^(2/3))*sqrt((a+b*x^(4/3))/(sqrt(a)+sqrt(b)*x^(2/3))^2)*InverseJacobiAM(2*arctan(b^(1/4)*x^(1/3)/a^(1/4)),sqrt(1/2))/a^(3/4)/b^(3/4)/sqrt(a+b*x^(4/3)),1],
[(a+b/x^(1/3))^(7/2),x,8,-6*b^3*sqrt(a+b/x^(1/3))+87/8*a*b^2*sqrt(a+b/x^(1/3))*x^(1/3)+19/4*a^2*b*sqrt(a+b/x^(1/3))*x^(2/3)+a^3*sqrt(a+b/x^(1/3))*x+105/8*sqrt(a)*b^3*arctanh(sqrt(a+b/x^(1/3))/sqrt(a)),1],
[(a+b/x^(1/3))^(5/2),x,7,33/8*b^2*sqrt(a+b/x^(1/3))*x^(1/3)+13/4*a*b*sqrt(a+b/x^(1/3))*x^(2/3)+a^2*sqrt(a+b/x^(1/3))*x+15/8*b^3*arctanh(sqrt(a+b/x^(1/3))/sqrt(a))/sqrt(a),1],
[(a+b/x^(1/3))^(3/2),x,7,3/8*b^2*sqrt(a+b/x^(1/3))*x^(1/3)/a+7/4*b*sqrt(a+b/x^(1/3))*x^(2/3)+a*sqrt(a+b/x^(1/3))*x-3/8*b^3*arctanh(sqrt(a+b/x^(1/3))/sqrt(a))/a^(3/2),1],
[sqrt(a+b/x^(1/3)),x,7,-3/8*b^2*sqrt(a+b/x^(1/3))*x^(1/3)/a^2+1/4*b*sqrt(a+b/x^(1/3))*x^(2/3)/a+sqrt(a+b/x^(1/3))*x+3/8*b^3*arctanh(sqrt(a+b/x^(1/3))/sqrt(a))/a^(5/2),1],
[1/sqrt(a+b/x^(1/3)),x,7,15/8*b^2*sqrt(a+b/x^(1/3))*x^(1/3)/a^3-5/4*b*sqrt(a+b/x^(1/3))*x^(2/3)/a^2+sqrt(a+b/x^(1/3))*x/a-15/8*b^3*arctanh(sqrt(a+b/x^(1/3))/sqrt(a))/a^(7/2),1],
[1/(a+b/x^(1/3))^(3/2),x,8,105/8*b^3/a^4/sqrt(a+b/x^(1/3))+35/8*b^2*x^(1/3)/a^3/sqrt(a+b/x^(1/3))-7/4*b*x^(2/3)/a^2/sqrt(a+b/x^(1/3))+x/a/sqrt(a+b/x^(1/3))-105/8*b^3*arctanh(sqrt(a+b/x^(1/3))/sqrt(a))/a^(9/2),1],
[(a+b/x^(2/3))^(5/2),x,7,-3/2*b^2*sqrt(a+b/x^(2/3))/x^(1/3)+7*a*b*sqrt(a+b/x^(2/3))*x^(1/3)+a^2*sqrt(a+b/x^(2/3))*x-15/2*a*b^(3/2)*arctanh(sqrt(b)/sqrt(a+b/x^(2/3))/x^(1/3)),1],
[(a+b/x^(2/3))^(3/2),x,6,4*b*sqrt(a+b/x^(2/3))*x^(1/3)+a*sqrt(a+b/x^(2/3))*x-3*b^(3/2)*arctanh(sqrt(b)/sqrt(a+b/x^(2/3))/x^(1/3)),1],
[sqrt(a+b/x^(2/3)),x,1,(a+b/x^(2/3))^(3/2)*x/a,1],
[1/sqrt(a+b/x^(2/3)),x,2,3*sqrt(a+b/x^(2/3))*x/a-2*(a+b/x^(2/3))^(3/2)*x/a^2,1],
[1/(a+b/x^(2/3))^(3/2),x,3,-3*x/a/sqrt(a+b/x^(2/3))+12*sqrt(a+b/x^(2/3))*x/a^2-8*(a+b/x^(2/3))^(3/2)*x/a^3,1],
[(a+b/x^(4/3))^(3/2),x,5,-b*sqrt(a+b/x^(4/3))/x^(1/3)+a*sqrt(a+b/x^(4/3))*x-2*a^(3/4)*b^(3/4)*sqrt((a+b/x^(4/3))/(sqrt(a)+sqrt(b)/x^(2/3))^2)*(sqrt(a)+sqrt(b)/x^(2/3))*InverseJacobiAM(2*arccot(a^(1/4)*x^(1/3)/b^(1/4)),sqrt(1/2))/sqrt(a+b/x^(4/3)),1],
[sqrt(a+b/x^(4/3)),x,4,sqrt(a+b/x^(4/3))*x-b^(3/4)*sqrt((a+b/x^(4/3))/(sqrt(a)+sqrt(b)/x^(2/3))^2)*(sqrt(a)+sqrt(b)/x^(2/3))*InverseJacobiAM(2*arccot(a^(1/4)*x^(1/3)/b^(1/4)),sqrt(1/2))/a^(1/4)/sqrt(a+b/x^(4/3)),1],
[1/sqrt(a+b/x^(4/3)),x,4,sqrt(a+b/x^(4/3))*x/a+1/2*b^(3/4)*sqrt((a+b/x^(4/3))/(sqrt(a)+sqrt(b)/x^(2/3))^2)*(sqrt(a)+sqrt(b)/x^(2/3))*InverseJacobiAM(2*arccot(a^(1/4)*x^(1/3)/b^(1/4)),sqrt(1/2))/a^(5/4)/sqrt(a+b/x^(4/3)),1],
[1/(a+b/x^(4/3))^(3/2),x,5,-3/2*x/a/sqrt(a+b/x^(4/3))+5/2*sqrt(a+b/x^(4/3))*x/a^2+5/4*b^(3/4)*sqrt((a+b/x^(4/3))/(sqrt(a)+sqrt(b)/x^(2/3))^2)*(sqrt(a)+sqrt(b)/x^(2/3))*InverseJacobiAM(2*arccot(a^(1/4)*x^(1/3)/b^(1/4)),sqrt(1/2))/a^(9/4)/sqrt(a+b/x^(4/3)),1],
[(a+b*x^(4/3))^p,x,2,x*(a+b*x^(4/3))^p*hypergeom([3/4, -p],[7/4],-b*x^(4/3)/a)/((1+b*x^(4/3)/a)^p),1],
[(a+b*x^(2/3))^p,x,2,(a+b*x^(2/3))^p*x*hypergeom([3/2, -p],[5/2],-b*x^(2/3)/a)/((1+b*x^(2/3)/a)^p),1],
[(a+b*x^(1/3))^p,x,3,3*a^2*(a+b*x^(1/3))^(p+1)/b^3/(p+1)-6*a*(a+b*x^(1/3))^(2+p)/b^3/(2+p)+3*(a+b*x^(1/3))^(3+p)/b^3/(3+p),1],
[(a+b/x^(1/3))^p,x,3,-3*b^3*(a+b/x^(1/3))^(p+1)*hypergeom([4, p+1],[2+p],1+b/a/x^(1/3))/a^4/(p+1),1],
[(a+b/x^(2/3))^p,x,2,(a+b/x^(2/3))^p*x*hypergeom([-3/2, -p],[-1/2],-b/a/x^(2/3))/((1+b/a/x^(2/3))^p),1],
[(a+b/x^(4/3))^p,x,2,(a+b/x^(4/3))^p*x*hypergeom([-3/4, -p],[1/4],-b/a/x^(4/3))/((1+b/a/x^(4/3))^p),1],
[(a+b/x^(1/4))^3,x,2,(b+a*x^(1/4))^4/a,1],
[(b+a*x^(1/4))^3/x^(3/4),x,1,(b+a*x^(1/4))^4/a,1],
[1/(1+x^(1/5)),x,3,-5*x^(1/5)+5/2*x^(2/5)-5/3*x^(3/5)+5/4*x^(4/5)+5*ln(1+x^(1/5)),1],
[(a+b/x^(3/5))^(2/3),x,1,(a+b/x^(3/5))^(5/3)*x/a,1],
[(a+b*x^n)^3,x,2,a^3*x+3*a^2*b*x^(1+n)/(1+n)+3*a*b^2*x^(1+2*n)/(1+2*n)+b^3*x^(1+3*n)/(1+3*n),1],
[(a+b*x^n)^2,x,2,a^2*x+2*a*b*x^(1+n)/(1+n)+b^2*x^(1+2*n)/(1+2*n),1],
[a+b*x^n,x,1,a*x+b*x^(1+n)/(1+n),1],
[1/(a+b*x^n),x,1,x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a,1],
[1/(a+b*x^n)^2,x,1,x*hypergeom([2, 1/n],[1+1/n],-b*x^n/a)/a^2,1],
[1/(a+b*x^n)^10,x,1,x*hypergeom([10, 1/n],[1+1/n],-b*x^n/a)/a^10,1],
[(a+b*x^n)^(3/2),x,2,a*x*sqrt(a+b*x^n)*hypergeom([-3/2, 1/n],[1+1/n],-b*x^n/a)/sqrt(1+b*x^n/a),1],
[sqrt(a+b*x^n),x,2,x*sqrt(a+b*x^n)*hypergeom([-1/2, 1/n],[1+1/n],-b*x^n/a)/sqrt(1+b*x^n/a),1],
[1/sqrt(a+b*x^n),x,2,x*sqrt(1+b*x^n/a)*hypergeom([1/2, 1/n],[1+1/n],-b*x^n/a)/sqrt(a+b*x^n),1],
[1/(a+b*x^n)^(3/2),x,2,x*sqrt(1+b*x^n/a)*hypergeom([3/2, 1/n],[1+1/n],-b*x^n/a)/a/sqrt(a+b*x^n),1],
[1/(a+b*x^n)^(5/2),x,2,x*sqrt(1+b*x^n/a)*hypergeom([5/2, 1/n],[1+1/n],-b*x^n/a)/a^2/sqrt(a+b*x^n),1],
[(a+b*x^n)^p,x,2,x*(a+b*x^n)^p*hypergeom([1/n, -p],[1+1/n],-b*x^n/a)/((1+b*x^n/a)^p),1],
[(a+b*x^(-1/(p+1)))^p,x,1,x/a*(a+b*x^(-1/(p+1)))^(p+1),1],
[(a+b*x^n)^(-4-1/n),x,4,x*(a+b*x^n)^(-3-1/n)/a/(1+3*n)+3*n*x*(a+b*x^n)^(-2-1/n)/a^2/(6*n^2+5*n+1)+6*n^2*x*(a+b*x^n)^(-1-1/n)/a^3/(1+n)/(1+2*n)/(1+3*n)+6*n^3*x/a^4/(1+n)/(1+2*n)/(1+3*n)/((a+b*x^n)^(1/n)),1],
[(a+b*x^n)^(-3-1/n),x,3,x*(a+b*x^n)^(-2-1/n)/a/(1+2*n)+2*n*x*(a+b*x^n)^(-1-1/n)/a^2/(1+n)/(1+2*n)+2*n^2*x/a^3/(1+n)/(1+2*n)/((a+b*x^n)^(1/n)),1],
[(a+b*x^n)^(-2-1/n),x,2,x*(a+b*x^n)^(-1-1/n)/a/(1+n)+n*x/a^2/(1+n)/((a+b*x^n)^(1/n)),1],
[(a+b*x^n)^(-1-1/n),x,1,x/a/((a+b*x^n)^(1/n)),1],
[(a+b*x^n)^(-1/n),x,2,x*(1+b*x^n/a)^(1/n)*hypergeom([1/n, 1/n],[1+1/n],-b*x^n/a)/((a+b*x^n)^(1/n)),1],
[(a+b*x^n)^(1-1/n),x,2,a*x*(1+b*x^n/a)^(1/n)*hypergeom([-1+1/n, 1/n],[1+1/n],-b*x^n/a)/((a+b*x^n)^(1/n)),1],
[(a+b*x^n)^(2-1/n),x,2,a^2*x*(1+b*x^n/a)^(1/n)*hypergeom([-2+1/n, 1/n],[1+1/n],-b*x^n/a)/((a+b*x^n)^(1/n)),1],
[(a+b*x^n)^(-(1+4*n)/n),x,4,x*(a+b*x^n)^(-3-1/n)/a/(1+3*n)+3*n*x*(a+b*x^n)^(-2-1/n)/a^2/(6*n^2+5*n+1)+6*n^3*x/a^4/(1+n)/(1+2*n)/(1+3*n)/((a+b*x^n)^(1/n))+6*n^2*x/a^3/(1+n)/(1+2*n)/(1+3*n)/((a+b*x^n)^((1+n)/n)),1],
[(a+b*x^n)^(-(1+3*n)/n),x,3,x*(a+b*x^n)^(-2-1/n)/a/(1+2*n)+2*n^2*x/a^3/(1+n)/(1+2*n)/((a+b*x^n)^(1/n))+2*n*x/a^2/(1+n)/(1+2*n)/((a+b*x^n)^((1+n)/n)),1],
[(a+b*x^n)^(-(1+2*n)/n),x,2,n*x/a^2/(1+n)/((a+b*x^n)^(1/n))+x/a/(1+n)/((a+b*x^n)^((1+n)/n)),1],
[(a+b*x^n)^(-(1+n)/n),x,1,x/a/((a+b*x^n)^(1/n)),1],
[(a+b*x^n)^(-1/n),x,2,x*(1+b*x^n/a)^(1/n)*hypergeom([1/n, 1/n],[1+1/n],-b*x^n/a)/((a+b*x^n)^(1/n)),1],
[(a+b*x^n)^(-(1-n)/n),x,2,x*(1+b*x^n/a)^(-1+1/n)*hypergeom([-1+1/n, 1/n],[1+1/n],-b*x^n/a)/((a+b*x^n)^((1-n)/n)),1],
[(a+b*x^n)^(-(1-2*n)/n),x,2,x*(a+b*x^n)^(2-1/n)*(1+b*x^n/a)^(-2+1/n)*hypergeom([-2+1/n, 1/n],[1+1/n],-b*x^n/a),1]]: