lst:=[[(-4*b^3*x^3+27*a^2*b*x+27*a^3)^4,x,3,729/32*a^4*(2*b*x+3*a)^9/b-729/80*a^3*(2*b*x+3*a)^10/b+243/176*a^2*(2*b*x+3*a)^11/b-3/32*a*(2*b*x+3*a)^12/b+1/416*(2*b*x+3*a)^13/b,1],
[(-4*b^3*x^3+27*a^2*b*x+27*a^3)^3,x,3,729/112*a^3*(2*b*x+3*a)^7/b-243/128*a^2*(2*b*x+3*a)^8/b+3/16*a*(2*b*x+3*a)^9/b-1/160*(2*b*x+3*a)^10/b,1],
[(-4*b^3*x^3+27*a^2*b*x+27*a^3)^2,x,3,81/40*a^2*(2*b*x+3*a)^5/b-3/8*a*(2*b*x+3*a)^6/b+1/56*(2*b*x+3*a)^7/b,1],
[-4*b^3*x^3+27*a^2*b*x+27*a^3,x,1,27*a^3*x+27/2*a^2*b*x^2-b^3*x^4,1],
[1/(-4*b^3*x^3+27*a^2*b*x+27*a^3),x,3,-1/9/a/b/(2*b*x+3*a)-1/81*ln(-b*x+3*a)/a^2/b+1/81*ln(2*b*x+3*a)/a^2/b,1],
[1/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^2,x,3,1/6561/a^4/b/(-b*x+3*a)-2/243/a^2/b/(2*b*x+3*a)^3-2/729/a^3/b/(2*b*x+3*a)^2-2/2187/a^4/b/(2*b*x+3*a)-8/59049*ln(-b*x+3*a)/a^5/b+8/59049*ln(2*b*x+3*a)/a^5/b,1],
[1/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^3,x,3,1/1062882/a^6/b/(-b*x+3*a)^2+4/1594323/a^7/b/(-b*x+3*a)-4/3645/a^3/b/(2*b*x+3*a)^5-1/2187/a^4/b/(2*b*x+3*a)^4-8/59049/a^5/b/(2*b*x+3*a)^3-20/531441/a^6/b/(2*b*x+3*a)^2-20/1594323/a^7/b/(2*b*x+3*a)-28/14348907*ln(-b*x+3*a)/a^8/b+28/14348907*ln(2*b*x+3*a)/a^8/b,1],
[1/(2*sqrt(3)*b^(3/2)-9*b*x+9*x^3),x,3,1/3/sqrt(3)/sqrt(b)/(sqrt(3)*sqrt(b)-3*x)-1/27*ln(sqrt(b)-sqrt(3)*x)/b+1/27*ln(2*sqrt(b)+sqrt(3)*x)/b,1],
[(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2),x,3,-118098/7*a^5*(-b*x+3*a)*(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2)/b/(2*b*x+3*a)^5+14580*a^4*(-b*x+3*a)^2*(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2)/b/(2*b*x+3*a)^5-58320/11*a^3*(-b*x+3*a)^3*(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2)/b/(2*b*x+3*a)^5+12960/13*a^2*(-b*x+3*a)^4*(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2)/b/(2*b*x+3*a)^5-96*a*(-b*x+3*a)^5*(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2)/b/(2*b*x+3*a)^5+64/17*(-b*x+3*a)^6*(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2)/b/(2*b*x+3*a)^5,1],
[(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(3/2),x,3,-1458/5*a^3*(-b*x+3*a)*(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(3/2)/b/(2*b*x+3*a)^3+972/7*a^2*(-b*x+3*a)^2*(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(3/2)/b/(2*b*x+3*a)^3-24*a*(-b*x+3*a)^3*(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(3/2)/b/(2*b*x+3*a)^3+16/11*(-b*x+3*a)^4*(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(3/2)/b/(2*b*x+3*a)^3,1],
[sqrt(-4*b^3*x^3+27*a^2*b*x+27*a^3),x,3,-6*a*(-b*x+3*a)*sqrt(-4*b^3*x^3+27*a^2*b*x+27*a^3)/b/(2*b*x+3*a)+4/5*(-b*x+3*a)^2*sqrt(-4*b^3*x^3+27*a^2*b*x+27*a^3)/b/(2*b*x+3*a),1],
[1/sqrt(-4*b^3*x^3+27*a^2*b*x+27*a^3),x,3,-1/3*sqrt(2)*(2*b*x+3*a)*sqrt(3-b*x/a)*arctanh(1/3*sqrt(2)*sqrt(3-b*x/a))/b/sqrt(-4*b^3*x^3+27*a^2*b*x+27*a^3),1],
[1/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(3/2),x,6,-1/18*(-b*x+3*a)*(2*b*x+3*a)/a/b/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(3/2)-5/324*(-b*x+3*a)*(2*b*x+3*a)^2/a^2/b/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(3/2)+5/972*(-b*x+3*a)*(2*b*x+3*a)^3/a^3/b/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(3/2)-5/1458*(2*b*x+3*a)^3*(3-b*x/a)^(3/2)*arctanh(1/3*sqrt(2)*sqrt(3-b*x/a))/sqrt(2)/a^2/b/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(3/2),1],
[1/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2),x,9,-1/36*(-b*x+3*a)*(2*b*x+3*a)/a/b/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2)-11/1944*(-b*x+3*a)*(2*b*x+3*a)^2/a^2/b/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2)-11/7776*(-b*x+3*a)*(2*b*x+3*a)^3/a^3/b/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2)-77/139968*(-b*x+3*a)*(2*b*x+3*a)^4/a^4/b/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2)+385/3779136*(-b*x+3*a)*(2*b*x+3*a)^5/a^5/b/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2)+385/5668704*(-b*x+3*a)^2*(2*b*x+3*a)^5/a^6/b/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2)-385/8503056*(2*b*x+3*a)^5*(3-b*x/a)^(5/2)*arctanh(1/3*sqrt(2)*sqrt(3-b*x/a))/sqrt(2)/a^4/b/(-4*b^3*x^3+27*a^2*b*x+27*a^3)^(5/2),1],
[(-4*b^3*x^3+27*a^2*b*x+27*a^3)^p,x,2,-3^(2*p)*(-b*x+3*a)*(-4*b^3*x^3+27*a^2*b*x+27*a^3)^p*hypergeom([-2*p, p+1],[2+p],2/9*(-b*x+3*a)/a)/b/(p+1)/((1+2/3*b*x/a)^(2*p)),1],
[(3*x^3-4*x+2)^3,x,2,8*x-24*x^2+32*x^3-7*x^4-144/5*x^5+24*x^6+54/7*x^7-27/2*x^8+27/10*x^10,1],
[(3*x^3-4*x+2)^2,x,2,4*x-8*x^2+16/3*x^3+3*x^4-24/5*x^5+9/7*x^7,1],
[3*x^3-4*x+2,x,1,2*x-2*x^2+3/4*x^4,1],
[1/(3*x^3-4*x+2),x,6,-1/136*sqrt(3)*(17+9*sqrt(17))^(1/3)*(4+(9-sqrt(17))^(2/3))*arctan((4+(9-sqrt(17))^(2/3)-6*(9-sqrt(17))^(1/3)*x)/sqrt(3)/(4-(9-sqrt(17))^(2/3)))*17^(1/3)+(9-sqrt(17))^(2/3)*ln(4+(9-sqrt(17))^(2/3)+3*(9-sqrt(17))^(1/3)*x)/(16+4*(9-sqrt(17))^(2/3)+(9-sqrt(17))^(4/3))-(9-sqrt(17))^(2/3)*ln(16-4*(9-sqrt(17))^(2/3)+(9-sqrt(17))^(4/3)-27*x+3*sqrt(17)*x-12*(9-sqrt(17))^(1/3)*x+9*(9-sqrt(17))^(2/3)*x^2)/(32+8*(9-sqrt(17))^(2/3)+2*(9-sqrt(17))^(4/3)),1],
[1/(3*x^3-4*x+2)^2,x,8,18*(9-sqrt(17))^(1/3)/(68+17*(9-sqrt(17))^(2/3)+51*(9-sqrt(17))^(1/3)*x)+9/34*(-17+9*sqrt(17))^(1/3)*(8-3*(4+(9-sqrt(17))^(2/3))*x/(9-sqrt(17))^(1/3))*17^(1/3)/(4-(9-sqrt(17))^(2/3))/((4+(9-sqrt(17))^(2/3))/(9-sqrt(17))^(1/3)+3*x)/(4-16/(9-sqrt(17))^(2/3)-(9-sqrt(17))^(2/3)+3*(4+(9-sqrt(17))^(2/3))*x/(9-sqrt(17))^(1/3)-9*x^2)-12*(9-sqrt(17))^(5/3)*(585-97*sqrt(17)+4*(65-9*sqrt(17))*(9-sqrt(17))^(1/3))*sqrt(6/(49-9*sqrt(17)+8*(9-sqrt(17))^(2/3)-4*(9-sqrt(17))^(4/3)))*arctan((9-sqrt(17)+4*(9-sqrt(17))^(1/3)-6*(9-sqrt(17))^(2/3)*x)/sqrt(294-54*sqrt(17)+48*(9-sqrt(17))^(2/3)-24*(9-sqrt(17))^(4/3)))/(4-(9-sqrt(17))^(2/3))^2/(16+4*(9-sqrt(17))^(2/3)+(9-sqrt(17))^(4/3))^3+6*(9-sqrt(17))^(5/3)*(4+(9-sqrt(17))^(2/3))*ln(4+(9-sqrt(17))^(2/3)+3*(9-sqrt(17))^(1/3)*x)/(16+4*(9-sqrt(17))^(2/3)+(9-sqrt(17))^(4/3))^3+6*(9-sqrt(17))^(7/3)*(8-9*(9-sqrt(17))^(1/3)+2*(9-sqrt(17))^(2/3))*ln(16-4*(9-sqrt(17))^(2/3)+(9-sqrt(17))^(4/3)-3*(9-sqrt(17)+4*(9-sqrt(17))^(1/3))*x+9*(9-sqrt(17))^(2/3)*x^2)/(4-(9-sqrt(17))^(2/3))^2/(16+4*(9-sqrt(17))^(2/3)+(9-sqrt(17))^(4/3))^3,1],
[1/sqrt(3*x^3-4*x+2),x,3,1/9*(9-sqrt(17))^(1/3)*sqrt((4+(9-sqrt(17))^(2/3))/(9-sqrt(17))^(1/3)+3*x)*sqrt(-4+16/(9-sqrt(17))^(2/3)+(9-sqrt(17))^(2/3)-3*(4+(9-sqrt(17))^(2/3))*x/(9-sqrt(17))^(1/3)+9*x^2)*sqrt(-(4-16/(9-sqrt(17))^(2/3)-(9-sqrt(17))^(2/3)+3*(9-sqrt(17)+4*(9-sqrt(17))^(1/3))*x/(9-sqrt(17))^(2/3)-9*x^2)/(1+(4+(9-sqrt(17))^(2/3)+3*(9-sqrt(17))^(1/3)*x)/sqrt(48+12*(9-sqrt(17))^(2/3)+3*(9-sqrt(17))^(4/3)))^2)*(1+(4+(9-sqrt(17))^(2/3)+3*(9-sqrt(17))^(1/3)*x)/sqrt(48+12*(9-sqrt(17))^(2/3)+3*(9-sqrt(17))^(4/3)))*InverseJacobiAM(2*arctan((9-sqrt(17))^(1/6)*sqrt((4+(9-sqrt(17))^(2/3))/(9-sqrt(17))^(1/3)+3*x)/(48+12*(9-sqrt(17))^(2/3)+3*(9-sqrt(17))^(4/3))^(1/4)),sqrt(1/2+1/4*(4+(9-sqrt(17))^(2/3))*sqrt(3/(16+4*(9-sqrt(17))^(2/3)+(9-sqrt(17))^(4/3)))))*3^(3/4)/(1/(16+4*(9-sqrt(17))^(2/3)+(9-sqrt(17))^(4/3)))^(1/4)/sqrt(36-4*sqrt(17)+16*(9-sqrt(17))^(1/3)+(9-sqrt(17))^(5/3))/sqrt(-4+16/(9-sqrt(17))^(2/3)+(9-sqrt(17))^(2/3)-3*(9-sqrt(17)+4*(9-sqrt(17))^(1/3))*x/(9-sqrt(17))^(2/3)+9*x^2)/sqrt(3*x^3-4*x+2),1],
[(3*x^3-4*x+2)^p,x,3,1/3*((4+(9-sqrt(17))^(2/3))/(9-sqrt(17))^(1/3)+3*x)*(3*x^3-4*x+2)^p*AppellF1(p+1,-p,-p,2+p,2*I*(9-sqrt(17))^(1/3)*((4+(9-sqrt(17))^(2/3))/(9-sqrt(17))^(1/3)+3*x)/(12*I+4*sqrt(3)+(3*I-sqrt(3))*(9-sqrt(17))^(2/3)),2*I*(9-sqrt(17))^(1/3)*((4+(9-sqrt(17))^(2/3))/(9-sqrt(17))^(1/3)+3*x)/(12*I-4*sqrt(3)+(3*I+sqrt(3))*(9-sqrt(17))^(2/3)))/(p+1)/((1-2*I*(9-sqrt(17))^(1/3)*((4+(9-sqrt(17))^(2/3))/(9-sqrt(17))^(1/3)+3*x)/(12*I+4*sqrt(3)+(3*I-sqrt(3))*(9-sqrt(17))^(2/3)))^p)/((1-2*I*(9-sqrt(17))^(1/3)*((4+(9-sqrt(17))^(2/3))/(9-sqrt(17))^(1/3)+3*x)/(12*I-4*sqrt(3)+(3*I+sqrt(3))*(9-sqrt(17))^(2/3)))^p),1],
[(3*x^3-6*x+2)^3,x,2,8*x-36*x^2+72*x^3-45*x^4-216/5*x^5+54*x^6+54/7*x^7-81/4*x^8+27/10*x^10,1],
[(3*x^3-6*x+2)^2,x,2,4*x-12*x^2+12*x^3+3*x^4-36/5*x^5+9/7*x^7,1],
[3*x^3-6*x+2,x,1,2*x-3*x^2+3/4*x^4,1],
[1/(3*x^3-6*x+2),x,3,ln(3*x-2*sqrt(6)*sin(1/3*arcsin(1/2*sqrt(3/2))))/(6-12*cos(2/3*arcsin(1/2*sqrt(3/2))))+1/8*ln(3*x-2*sqrt(6)*cos(1/6*Pi+1/3*arcsin(1/2*sqrt(3/2))))*sec(1/3*arcsin(1/2*sqrt(3/2)))/sqrt(3)/(cos(1/6*Pi+1/3*arcsin(1/2*sqrt(3/2)))-sin(1/3*arcsin(1/2*sqrt(3/2))))+1/8*ln(3*x+2*sqrt(6)*sin(1/3*Pi+1/3*arcsin(1/2*sqrt(3/2))))*sec(1/3*arcsin(1/2*sqrt(3/2)))/sqrt(3)/(sin(1/3*arcsin(1/2*sqrt(3/2)))+sin(1/3*Pi+1/3*arcsin(1/2*sqrt(3/2)))),1],
[1/(3*x^3-6*x+2)^2,x,3,-1/64*sec(1/3*arcsin(1/2*sqrt(3/2)))^2/(3*x-2*sqrt(6)*cos(1/6*Pi+1/3*arcsin(1/2*sqrt(3/2))))/(cos(1/6*Pi+1/3*arcsin(1/2*sqrt(3/2)))-sin(1/3*arcsin(1/2*sqrt(3/2))))^2-1/3*ln(3*x-2*sqrt(6)*sin(1/3*arcsin(1/2*sqrt(3/2))))*sin(1/3*arcsin(1/2*sqrt(3/2)))/sqrt(6)/(1-2*cos(2/3*arcsin(1/2*sqrt(3/2))))^3-1/48*ln(3*x-2*sqrt(6)*cos(1/6*Pi+1/3*arcsin(1/2*sqrt(3/2))))*sec(1/3*arcsin(1/2*sqrt(3/2)))^3*(sqrt(3)*cos(1/3*arcsin(1/2*sqrt(3/2)))-sin(1/3*arcsin(1/2*sqrt(3/2))))/sqrt(6)/(cos(1/3*arcsin(1/2*sqrt(3/2)))-sqrt(3)*sin(1/3*arcsin(1/2*sqrt(3/2))))^3+1/48*ln(3*x+2*sqrt(6)*sin(1/3*Pi+1/3*arcsin(1/2*sqrt(3/2))))*sec(1/3*arcsin(1/2*sqrt(3/2)))^3*(sqrt(3)*cos(1/3*arcsin(1/2*sqrt(3/2)))+sin(1/3*arcsin(1/2*sqrt(3/2))))/sqrt(6)/(cos(1/3*arcsin(1/2*sqrt(3/2)))+sqrt(3)*sin(1/3*arcsin(1/2*sqrt(3/2))))^3-1/12/(1-2*cos(2/3*arcsin(1/2*sqrt(3/2))))^2/(3*x-2*sqrt(6)*sin(1/3*arcsin(1/2*sqrt(3/2))))-1/64*sec(1/3*arcsin(1/2*sqrt(3/2)))^2/(sin(1/3*arcsin(1/2*sqrt(3/2)))+sin(1/3*Pi+1/3*arcsin(1/2*sqrt(3/2))))^2/(3*x+2*sqrt(6)*sin(1/3*Pi+1/3*arcsin(1/2*sqrt(3/2)))),1],
[1/sqrt(3*x^3-6*x+2),x,2,-1/3*2^(3/4)*sqrt(3*x-2*sqrt(6)*cos(1/6*Pi+1/3*arcsin(1/2*sqrt(3/2))))*InverseJacobiAM(arcsin(2^(1/4)*sqrt(3*cos(1/3*arcsin(1/2*sqrt(3/2)))+3*sqrt(3)*sin(1/3*arcsin(1/2*sqrt(3/2))))/sqrt(3*x+2*sqrt(6)*sin(1/3*Pi+1/3*arcsin(1/2*sqrt(3/2))))),sqrt(sqrt(3)*cos(1/3*arcsin(1/2*sqrt(3/2)))/(sin(1/3*arcsin(1/2*sqrt(3/2)))+sin(1/3*Pi+1/3*arcsin(1/2*sqrt(3/2))))))*sqrt(3*x-2*sqrt(6)*sin(1/3*arcsin(1/2*sqrt(3/2))))*sqrt(3*x+2*sqrt(6)*sin(1/3*Pi+1/3*arcsin(1/2*sqrt(3/2))))/sqrt(3*x^3-6*x+2)/sqrt(3*cos(1/3*arcsin(1/2*sqrt(3/2)))+3*sqrt(3)*sin(1/3*arcsin(1/2*sqrt(3/2)))),1],
[(3*x^3-6*x+2)^p,x,2,1/3*(3*x^3-6*x+2)^p*AppellF1(p+1,-p,-p,2+p,-1/6*(3*x-2*sqrt(6)*cos(1/6*Pi+1/3*arcsin(1/2*sqrt(3/2))))*sec(1/3*arcsin(1/2*sqrt(3/2)))/sqrt(2),-(3*x-2*sqrt(6)*cos(1/6*Pi+1/3*arcsin(1/2*sqrt(3/2))))/sqrt(6)/(sqrt(3)*cos(1/3*arcsin(1/2*sqrt(3/2)))-3*sin(1/3*arcsin(1/2*sqrt(3/2)))))*(3*x-2*sqrt(6)*cos(1/6*Pi+1/3*arcsin(1/2*sqrt(3/2))))*(4*cos(1/3*arcsin(1/2*sqrt(3/2)))*(cos(1/3*arcsin(1/2*sqrt(3/2)))-sqrt(3)*sin(1/3*arcsin(1/2*sqrt(3/2)))))^p/(p+1)/((x-2*sqrt(2/3)*sin(1/3*arcsin(1/2*sqrt(3/2))))^p)/((x+2*sqrt(2/3)*sin(1/3*Pi+1/3*arcsin(1/2*sqrt(3/2))))^p),1],
[1/(x^3-6*x-6)^(1/3),x,4,1/2*sqrt(3)*arctan((1+2*x/(x^3-6*x-6)^(1/3))/sqrt(3))-1/2*arctan((1-2*(2+x)/(x^3-6*x-6)^(1/3))/sqrt(3))/sqrt(3)-3/4*ln(x-(x^3-6*x-6)^(1/3))+1/4*ln(2+x+(x^3-6*x-6)^(1/3)),1],
[1/(a+b*x-1/6*b^3*x^3/a^2)^(1/3),x,4,-1/2*3^(5/6)*a^(1/3)*(b*x+a)*(a*b^3*(6*a+6*b*x-b^3*x^3/a^2)/(b*x+a)^3)^(1/3)*arctan((1-2*b^2*x/a^(1/3)/(b*x+a)/(-b^3*(2-(b*x+2*a)^3/(b*x+a)^3)/a)^(1/3))/sqrt(3))*2^(1/3)/b^2/(6*a+6*b*x-b^3*x^3/a^2)^(1/3)+1/6*a^(1/3)*(b*x+a)*(a*b^3*(6*a+6*b*x-b^3*x^3/a^2)/(b*x+a)^3)^(1/3)*arctan((1+2*b*(b*x+2*a)/a^(1/3)/(b*x+a)/(-b^3*(2-(b*x+2*a)^3/(b*x+a)^3)/a)^(1/3))/sqrt(3))*2^(1/3)*3^(5/6)/b^2/(6*a+6*b*x-b^3*x^3/a^2)^(1/3)+1/2*3^(1/3)*a^(1/3)*(b*x+a)*(a*b^3*(6*a+6*b*x-b^3*x^3/a^2)/(b*x+a)^3)^(1/3)*ln(b*x+a)*2^(1/3)/b^2/(6*a+6*b*x-b^3*x^3/a^2)^(1/3)-1/4*3^(1/3)*a^(1/3)*(b*x+a)*(a*b^3*(6*a+6*b*x-b^3*x^3/a^2)/(b*x+a)^3)^(1/3)*ln(-(2*a*b+b^2*x-a^(4/3)*(b^3*(-b^3*x^3+6*a^2*b*x+6*a^3)/a/(b*x+a)^3)^(1/3)-a^(1/3)*b*x*(b^3*(-b^3*x^3+6*a^2*b*x+6*a^3)/a/(b*x+a)^3)^(1/3))/(b*x+a))*2^(1/3)/b^2/(6*a+6*b*x-b^3*x^3/a^2)^(1/3)+3/4*3^(1/3)*a^(1/3)*(b*x+a)*(a*b^3*(6*a+6*b*x-b^3*x^3/a^2)/(b*x+a)^3)^(1/3)*ln((b^2*x+a^(4/3)*(b^3*(-b^3*x^3+6*a^2*b*x+6*a^3)/a/(b*x+a)^3)^(1/3)+a^(1/3)*b*x*(b^3*(-b^3*x^3+6*a^2*b*x+6*a^3)/a/(b*x+a)^3)^(1/3))/(b*x+a))*2^(1/3)/b^2/(6*a+6*b*x-b^3*x^3/a^2)^(1/3),1],
[(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^4,x,3,3*c^4*(3*d*x+2*c)^9/d-18/5*c^3*(3*d*x+2*c)^10/d+18/11*c^2*(3*d*x+2*c)^11/d-1/3*c*(3*d*x+2*c)^12/d+1/39*(3*d*x+2*c)^13/d,1],
[(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^3,x,3,9/7*c^3*(3*d*x+2*c)^7/d-9/8*c^2*(3*d*x+2*c)^8/d+1/3*c*(3*d*x+2*c)^9/d-1/30*(3*d*x+2*c)^10/d,1],
[(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^2,x,3,3/5*c^2*(3*d*x+2*c)^5/d-1/3*c*(3*d*x+2*c)^6/d+1/21*(3*d*x+2*c)^7/d,1],
[-27*d^3*x^3-27*c*d^2*x^2+4*c^3,x,1,4*c^3*x-9*c*d^2*x^3-27/4*d^3*x^4,1],
[1/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3),x,3,-1/9/c/d/(3*d*x+2*c)-1/27*ln(-3*d*x+c)/c^2/d+1/27*ln(3*d*x+2*c)/c^2/d,1],
[1/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^2,x,3,1/243/c^4/d/(-3*d*x+c)-1/81/c^2/d/(3*d*x+2*c)^3-1/81/c^3/d/(3*d*x+2*c)^2-1/81/c^4/d/(3*d*x+2*c)-4/729*ln(-3*d*x+c)/c^5/d+4/729*ln(3*d*x+2*c)/c^5/d,1],
[1/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^3,x,3,1/4374/c^6/d/(-3*d*x+c)^2+2/2187/c^7/d/(-3*d*x+c)-1/405/c^3/d/(3*d*x+2*c)^5-1/324/c^4/d/(3*d*x+2*c)^4-2/729/c^5/d/(3*d*x+2*c)^3-5/2187/c^6/d/(3*d*x+2*c)^2-5/2187/c^7/d/(3*d*x+2*c)-7/6561*ln(-3*d*x+c)/c^8/d+7/6561*ln(3*d*x+2*c)/c^8/d,1],
[(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2),x,3,-162/7*c^5*(-3*d*x+c)*(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2)/d/(3*d*x+2*c)^5+30*c^4*(-3*d*x+c)^2*(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2)/d/(3*d*x+2*c)^5-180/11*c^3*(-3*d*x+c)^3*(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2)/d/(3*d*x+2*c)^5+60/13*c^2*(-3*d*x+c)^4*(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2)/d/(3*d*x+2*c)^5-2/3*c*(-3*d*x+c)^5*(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2)/d/(3*d*x+2*c)^5+2/51*(-3*d*x+c)^6*(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2)/d/(3*d*x+2*c)^5,1],
[(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(3/2),x,3,-18/5*c^3*(-3*d*x+c)*(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(3/2)/d/(3*d*x+2*c)^3+18/7*c^2*(-3*d*x+c)^2*(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(3/2)/d/(3*d*x+2*c)^3-2/3*c*(-3*d*x+c)^3*(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(3/2)/d/(3*d*x+2*c)^3+2/33*(-3*d*x+c)^4*(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(3/2)/d/(3*d*x+2*c)^3,1],
[sqrt(-27*d^3*x^3-27*c*d^2*x^2+4*c^3),x,3,-2/3*c*(-3*d*x+c)*sqrt(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)/d/(3*d*x+2*c)+2/15*(-3*d*x+c)^2*sqrt(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)/d/(3*d*x+2*c),1],
[1/sqrt(-27*d^3*x^3-27*c*d^2*x^2+4*c^3),x,3,-2/3*(3*d*x+2*c)*sqrt(1-3*d*x/c)*arctanh(sqrt(1-3*d*x/c)/sqrt(3))/sqrt(3)/d/sqrt(-27*d^3*x^3-27*c*d^2*x^2+4*c^3),1],
[1/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(3/2),x,6,-1/18*(-3*d*x+c)*(3*d*x+2*c)/c/d/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(3/2)-5/108*(-3*d*x+c)*(3*d*x+2*c)^2/c^2/d/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(3/2)+5/108*(-3*d*x+c)*(3*d*x+2*c)^3/c^3/d/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(3/2)-5/108*(3*d*x+2*c)^3*(1-3*d*x/c)^(3/2)*arctanh(sqrt(1-3*d*x/c)/sqrt(3))/sqrt(3)/c^2/d/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(3/2),1],
[1/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2),x,9,-1/36*(-3*d*x+c)*(3*d*x+2*c)/c/d/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2)-11/648*(-3*d*x+c)*(3*d*x+2*c)^2/c^2/d/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2)-11/864*(-3*d*x+c)*(3*d*x+2*c)^3/c^3/d/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2)-77/5184*(-3*d*x+c)*(3*d*x+2*c)^4/c^4/d/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2)+385/46656*(-3*d*x+c)*(3*d*x+2*c)^5/c^5/d/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2)+385/46656*(-3*d*x+c)^2*(3*d*x+2*c)^5/c^6/d/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2)-385/46656*(3*d*x+2*c)^5*(1-3*d*x/c)^(5/2)*arctanh(sqrt(1-3*d*x/c)/sqrt(3))/sqrt(3)/c^4/d/(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^(5/2),1],
[(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^p,x,2,-3^(-1+2*p)*(-3*d*x+c)*(-27*d^3*x^3-27*c*d^2*x^2+4*c^3)^p*hypergeom([-2*p, p+1],[2+p],1/3*(-3*d*x+c)/c)/(4^p)/d/(p+1)/((1+3/2*d*x/c)^(2*p)),1],
[(3*x^3-4*x^2+2)^3,x,2,8*x-16*x^3+9*x^4+96/5*x^5-24*x^6-10/7*x^7+18*x^8-12*x^9+27/10*x^10,1],
[(3*x^3-4*x^2+2)^2,x,2,4*x-16/3*x^3+3*x^4+16/5*x^5-4*x^6+9/7*x^7,1],
[3*x^3-4*x^2+2,x,1,2*x-4/3*x^3+3/4*x^4,1],
[1/(3*x^3-4*x^2+2),x,7,-1/2*(16+(179-9*sqrt(345))^(2/3))*arctan(((4+(179-9*sqrt(345))^(1/3))^2-18*(179-9*sqrt(345))^(1/3)*x)/sqrt(3)/(16-(179-9*sqrt(345))^(2/3)))/sqrt(115)/(179-9*sqrt(345))^(1/3)+9*(179-9*sqrt(345))^(2/3)*ln(16+(179-9*sqrt(345))^(2/3)-(179-9*sqrt(345))^(1/3)*(4-9*x))/(256+16*(179-9*sqrt(345))^(2/3)+(179-9*sqrt(345))^(4/3))-9*(179-9*sqrt(345))^(2/3)*ln(108-4*sqrt(345)+27*(179-9*sqrt(345))^(1/3)-sqrt(345)*(179-9*sqrt(345))^(1/3)-179*x+9*sqrt(345)*x-16*(179-9*sqrt(345))^(1/3)*x-8*(179-9*sqrt(345))^(2/3)*x+9*(179-9*sqrt(345))^(2/3)*x^2)/(512+32*(179-9*sqrt(345))^(2/3)+2*(179-9*sqrt(345))^(4/3)),1],
[1/(3*x^3-4*x^2+2)^2,x,9,72*(179-9*sqrt(345))^(1/3)/(1840+115*(179-9*sqrt(345))^(2/3)-115*(179-9*sqrt(345))^(1/3)*(4-9*x))-81/230*(-9315+537*sqrt(345))^(1/3)*(32+(16+(179-9*sqrt(345))^(2/3))*(4-9*x)/(179-9*sqrt(345))^(1/3))*115^(1/3)/(16-(179-9*sqrt(345))^(2/3))/(16-256/(179-9*sqrt(345))^(2/3)-(179-9*sqrt(345))^(2/3)-(16+(179-9*sqrt(345))^(2/3))*(4-9*x)/(179-9*sqrt(345))^(1/3)-(4-9*x)^2)/(4-16/(179-9*sqrt(345))^(1/3)-(179-9*sqrt(345))^(1/3)-9*x)-8748*(179-9*sqrt(345))^(5/3)*(1850681-99195*sqrt(345)+(165424-8592*sqrt(345))*(179-9*sqrt(345))^(1/3))*sqrt(6/(29993-1611*sqrt(345)+128*(179-9*sqrt(345))^(2/3)-16*(179-9*sqrt(345))^(4/3)))*arctan((179-9*sqrt(345)+16*(179-9*sqrt(345))^(1/3)+2*(179-9*sqrt(345))^(2/3)*(4-9*x))/sqrt(179958-9666*sqrt(345)+768*(179-9*sqrt(345))^(2/3)-96*(179-9*sqrt(345))^(4/3)))/(16-(179-9*sqrt(345))^(2/3))^2/(256+16*(179-9*sqrt(345))^(2/3)+(179-9*sqrt(345))^(4/3))^3+1458*(179-9*sqrt(345))^(5/3)*(16+(179-9*sqrt(345))^(2/3))*ln(16+(179-9*sqrt(345))^(2/3)-(179-9*sqrt(345))^(1/3)*(4-9*x))/(256+16*(179-9*sqrt(345))^(2/3)+(179-9*sqrt(345))^(4/3))^3+1458*(179-9*sqrt(345))^(7/3)*(128-179*(179-9*sqrt(345))^(1/3)+8*(179-9*sqrt(345))^(2/3))*ln(108-4*sqrt(345)+27*(179-9*sqrt(345))^(1/3)-sqrt(345)*(179-9*sqrt(345))^(1/3)-179*x+9*sqrt(345)*x-16*(179-9*sqrt(345))^(1/3)*x-8*(179-9*sqrt(345))^(2/3)*x+9*(179-9*sqrt(345))^(2/3)*x^2)/(16-(179-9*sqrt(345))^(2/3))^2/(256+16*(179-9*sqrt(345))^(2/3)+(179-9*sqrt(345))^(4/3))^3,1],
[1/sqrt(3*x^3-4*x^2+2),x,4,1/27*(179-9*sqrt(345))^(1/3)*sqrt((256-16*(179-9*sqrt(345))^(2/3)+(179-9*sqrt(345))^(4/3)+(179-9*sqrt(345)+16*(179-9*sqrt(345))^(1/3))*(4-9*x)+(179-9*sqrt(345))^(2/3)*(4-9*x)^2)/(1-(179-9*sqrt(345))^(1/3)*(4-16/(179-9*sqrt(345))^(1/3)-(179-9*sqrt(345))^(1/3)-9*x)/sqrt(768+48*(179-9*sqrt(345))^(2/3)+3*(179-9*sqrt(345))^(4/3)))^2)*(1-(179-9*sqrt(345))^(1/3)*(4-16/(179-9*sqrt(345))^(1/3)-(179-9*sqrt(345))^(1/3)-9*x)/sqrt(768+48*(179-9*sqrt(345))^(2/3)+3*(179-9*sqrt(345))^(4/3)))*sqrt(-4+16/(179-9*sqrt(345))^(1/3)+(179-9*sqrt(345))^(1/3)+9*x)*sqrt(-16+256/(179-9*sqrt(345))^(2/3)+(179-9*sqrt(345))^(2/3)+(16+(179-9*sqrt(345))^(2/3))*(4-9*x)/(179-9*sqrt(345))^(1/3)+(-4+9*x)^2)*InverseJacobiAM(2*arctan((179-9*sqrt(345))^(1/6)*sqrt(-4+16/(179-9*sqrt(345))^(1/3)+(179-9*sqrt(345))^(1/3)+9*x)/(768+48*(179-9*sqrt(345))^(2/3)+3*(179-9*sqrt(345))^(4/3))^(1/4)),sqrt(1/2+1/4*(16+(179-9*sqrt(345))^(2/3))*sqrt(3/(256+16*(179-9*sqrt(345))^(2/3)+(179-9*sqrt(345))^(4/3)))))*3^(3/4)/(1/(256+16*(179-9*sqrt(345))^(2/3)+(179-9*sqrt(345))^(4/3)))^(1/4)/sqrt(2864-144*sqrt(345)+256*(179-9*sqrt(345))^(1/3)+(179-9*sqrt(345))^(5/3))/sqrt(256-16*(179-9*sqrt(345))^(2/3)+(179-9*sqrt(345))^(4/3)+(179-9*sqrt(345)+16*(179-9*sqrt(345))^(1/3))*(4-9*x)+(179-9*sqrt(345))^(2/3)*(4-9*x)^2)/sqrt(3*x^3-4*x^2+2),1],
[(3*x^3-4*x^2+2)^p,x,4,-1/9*(4-16/(179-9*sqrt(345))^(1/3)-(179-9*sqrt(345))^(1/3)-9*x)*(3*x^3-4*x^2+2)^p*AppellF1(p+1,-p,-p,2+p,-2*I*(179-9*sqrt(345))^(1/3)*(4-16/(179-9*sqrt(345))^(1/3)-(179-9*sqrt(345))^(1/3)-9*x)/(48*I+16*sqrt(3)+(3*I-sqrt(3))*(179-9*sqrt(345))^(2/3)),-2*I*(179-9*sqrt(345))^(1/3)*(4-16/(179-9*sqrt(345))^(1/3)-(179-9*sqrt(345))^(1/3)-9*x)/(48*I-16*sqrt(3)+(3*I+sqrt(3))*(179-9*sqrt(345))^(2/3)))/(p+1)/((1+2*I*(179-9*sqrt(345))^(1/3)*(4-16/(179-9*sqrt(345))^(1/3)-(179-9*sqrt(345))^(1/3)-9*x)/(48*I+16*sqrt(3)+(3*I-sqrt(3))*(179-9*sqrt(345))^(2/3)))^p)/((1+2*I*(179-9*sqrt(345))^(1/3)*(4-16/(179-9*sqrt(345))^(1/3)-(179-9*sqrt(345))^(1/3)-9*x)/(48*I-16*sqrt(3)+(3*I+sqrt(3))*(179-9*sqrt(345))^(2/3)))^p),1],
[(3*x^3-6*x^2+2)^3,x,2,8*x-24*x^3+9*x^4+216/5*x^5-36*x^6-162/7*x^7+81/2*x^8-18*x^9+27/10*x^10,1],
[(3*x^3-6*x^2+2)^2,x,2,4*x-8*x^3+3*x^4+36/5*x^5-6*x^6+9/7*x^7,1],
[3*x^3-6*x^2+2,x,1,2*x-2*x^3+3/4*x^4,1],
[1/(3*x^3-6*x^2+2),x,4,ln(3*x-2-4*sin(1/3*arcsin(1/8)))/(4-8*cos(2/3*arcsin(1/8)))+sqrt(3)*ln(3*x-2-4*cos(1/6*Pi+1/3*arcsin(1/8)))*sec(1/3*arcsin(1/8))/(16*cos(1/6*Pi+1/3*arcsin(1/8))-16*sin(1/3*arcsin(1/8)))+sqrt(3)*ln(3*x-2+4*sin(1/3*Pi+1/3*arcsin(1/8)))*sec(1/3*arcsin(1/8))/(16*sin(1/3*arcsin(1/8))+16*sin(1/3*Pi+1/3*arcsin(1/8))),1],
[1/(3*x^3-6*x^2+2)^2,x,4,-9/256*sec(1/3*arcsin(1/8))^2/(3*x-2-4*cos(1/6*Pi+1/3*arcsin(1/8)))/(cos(1/6*Pi+1/3*arcsin(1/8))-sin(1/3*arcsin(1/8)))^2-3/8*ln(3*x-2-4*sin(1/3*arcsin(1/8)))*sin(1/3*arcsin(1/8))/(1-2*cos(2/3*arcsin(1/8)))^3-3/128*ln(3*x-2-4*cos(1/6*Pi+1/3*arcsin(1/8)))*sec(1/3*arcsin(1/8))^3*(sqrt(3)*cos(1/3*arcsin(1/8))-sin(1/3*arcsin(1/8)))/(cos(1/3*arcsin(1/8))-sqrt(3)*sin(1/3*arcsin(1/8)))^3+3/128*ln(3*x-2+4*sin(1/3*Pi+1/3*arcsin(1/8)))*sec(1/3*arcsin(1/8))^3*(sqrt(3)*cos(1/3*arcsin(1/8))+sin(1/3*arcsin(1/8)))/(cos(1/3*arcsin(1/8))+sqrt(3)*sin(1/3*arcsin(1/8)))^3-3/16/(1-2*cos(2/3*arcsin(1/8)))^2/(3*x-2-4*sin(1/3*arcsin(1/8)))-9/256*sec(1/3*arcsin(1/8))^2/(3*x-2+4*sin(1/3*Pi+1/3*arcsin(1/8)))/(sin(1/3*arcsin(1/8))+sin(1/3*Pi+1/3*arcsin(1/8)))^2,1],
[sqrt(3*x^3-6*x^2+2),x,8,8/15*sqrt(3*x^3-6*x^2+2)*sin(1/3*arcsin(1/8))+2/15*sqrt(3*x^3-6*x^2+2)*(3*x-2-4*sin(1/3*arcsin(1/8)))-32/5*3^(1/4)*sqrt(3*x^3-6*x^2+2)*sqrt(cos(1/3*arcsin(1/8)))*EllipticE(sin(arcsin(1/2*sqrt(3*x-2+4*sin(1/3*Pi+1/3*arcsin(1/8)))/sqrt(sin(1/3*arcsin(1/8))+sin(1/3*Pi+1/3*arcsin(1/8))))),sqrt(1/2+1/2*sqrt(3)*tan(1/3*arcsin(1/8))))*sqrt(-3*x+2+4*sin(1/3*arcsin(1/8)))/sqrt(-3*x+2+4*cos(1/6*Pi+1/3*arcsin(1/8)))/(3*x-2-4*sin(1/3*arcsin(1/8)))/sqrt(3*x-2+4*sin(1/3*Pi+1/3*arcsin(1/8)))-2/5*sqrt(3*x^3-6*x^2+2)*(1-16*cos(1/6*Pi+1/3*arcsin(1/8)))*InverseJacobiAM(arcsin(2*sqrt(sin(1/3*arcsin(1/8))+sin(1/3*Pi+1/3*arcsin(1/8)))/sqrt(3*x-2+4*sin(1/3*Pi+1/3*arcsin(1/8)))),sqrt(sqrt(3)*cos(1/3*arcsin(1/8))/(sin(1/3*arcsin(1/8))+sin(1/3*Pi+1/3*arcsin(1/8)))))/sqrt(3*x-2-4*cos(1/6*Pi+1/3*arcsin(1/8)))/sqrt(3*x-2-4*sin(1/3*arcsin(1/8)))/sqrt(3*x-2+4*sin(1/3*Pi+1/3*arcsin(1/8)))/sqrt(sin(1/3*arcsin(1/8))+sin(1/3*Pi+1/3*arcsin(1/8))),1],
[1/sqrt(3*x^3-6*x^2+2),x,3,-1/3*sqrt(3*x-2-4*cos(1/6*Pi+1/3*arcsin(1/8)))*InverseJacobiAM(arcsin(2*sqrt(sin(1/3*arcsin(1/8))+sin(1/3*Pi+1/3*arcsin(1/8)))/sqrt(3*x-2+4*sin(1/3*Pi+1/3*arcsin(1/8)))),sqrt(sqrt(3)*cos(1/3*arcsin(1/8))/(sin(1/3*arcsin(1/8))+sin(1/3*Pi+1/3*arcsin(1/8)))))*sqrt(3*x-2-4*sin(1/3*arcsin(1/8)))*sqrt(3*x-2+4*sin(1/3*Pi+1/3*arcsin(1/8)))/sqrt(3*x^3-6*x^2+2)/sqrt(sin(1/3*arcsin(1/8))+sin(1/3*Pi+1/3*arcsin(1/8))),1],
[(3*x^3-6*x^2+2)^p,x,3,3^(-1+1/2*p)*(3*x^3-6*x^2+2)^p*AppellF1(p+1,-p,-p,2+p,-1/4*(3*x-2-4*cos(1/6*Pi+1/3*arcsin(1/8)))*sec(1/3*arcsin(1/8))/sqrt(3),-1/2*(3*x-2-4*cos(1/6*Pi+1/3*arcsin(1/8)))/(sqrt(3)*cos(1/3*arcsin(1/8))-3*sin(1/3*arcsin(1/8))))*(3*x-2-4*cos(1/6*Pi+1/3*arcsin(1/8)))*(8*cos(1/3*arcsin(1/8))*(sqrt(3)*cos(1/3*arcsin(1/8))-3*sin(1/3*arcsin(1/8))))^p/(p+1)/((3*x-2-4*sin(1/3*arcsin(1/8)))^p)/((3*x-2+4*sin(1/3*Pi+1/3*arcsin(1/8)))^p),1],
[(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^3,x,2,1/10*(b*x+a)^10/b,1],
[(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^2,x,2,1/7*(b*x+a)^7/b,1],
[b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3,x,2,1/4*(b*x+a)^4/b,1],
[1/(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3),x,2,-1/2/b/(b*x+a)^2,1],
[1/(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^2,x,2,-1/5/b/(b*x+a)^5,1],
[1/(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^3,x,2,-1/8/b/(b*x+a)^8,1],
[(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^(5/2),x,2,2/17*(b*x+a)*(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^(5/2)/b,1],
[(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^(3/2),x,2,2/11*(b*x+a)*(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^(3/2)/b,1],
[sqrt(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3),x,2,2/5*(b*x+a)*sqrt(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)/b,1],
[1/sqrt(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3),x,2,(-2*b*x-2*a)/b/sqrt(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3),1],
[1/(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^(3/2),x,2,1/7*(-2*b*x-2*a)/b/(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^(3/2),1],
[1/(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^(5/2),x,2,1/13*(-2*b*x-2*a)/b/(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^(5/2),1],
[((b*x+a)^3)^p,x,2,(b*x+a)*((b*x+a)^3)^p/b/(1+3*p),1],
[(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^p,x,2,(b*x+a)*(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^p/b/(1+3*p),1],
[(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^2,x,3,-3/40*(1-6*b)*(1-sqrt(1-6*b)-6*x)^5-1/24*sqrt(1-6*b)*(1-sqrt(1-6*b)-6*x)^6-1/168*(1-sqrt(1-6*b)-6*x)^7,1],
[1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3,x,1,(1-(1-6*b)^(3/2)-9*b)*x+27*b*x^2-18*x^3+27*x^4,1],
[1/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3),x,3,-1/9/sqrt(1-6*b)/(1-sqrt(1-6*b)-6*x)-ln(1-sqrt(1-6*b)-6*x)/(27-162*b)+ln(1+2*sqrt(1-6*b)-6*x)/(27-162*b),1],
[1/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^2,x,3,2/81/(1-6*b)/(1-sqrt(1-6*b)-6*x)^3-2/81/(1-6*b)^(3/2)/(1-sqrt(1-6*b)-6*x)^2+2/81/(1-6*b)^2/(1-sqrt(1-6*b)-6*x)+2/243/(1-6*b)^2/(1+2*sqrt(1-6*b)-6*x)+8/729*ln(1-sqrt(1-6*b)-6*x)/(1-6*b)^(5/2)-8/729*ln(1+2*sqrt(1-6*b)-6*x)/(1-6*b)^(5/2),1],
[1/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^3,x,3,-4/405/(1-6*b)^(3/2)/(1-sqrt(1-6*b)-6*x)^5+1/81/(1-6*b)^2/(1-sqrt(1-6*b)-6*x)^4-8/729/(1-6*b)^(5/2)/(1-sqrt(1-6*b)-6*x)^3+20/2187/(1-6*b)^3/(1-sqrt(1-6*b)-6*x)^2-20/2187/(1-6*b)^(7/2)/(1-sqrt(1-6*b)-6*x)-2/2187/(1-6*b)^3/(1+2*sqrt(1-6*b)-6*x)^2-8/2187/(1-6*b)^(7/2)/(1+2*sqrt(1-6*b)-6*x)-28/6561*ln(1-sqrt(1-6*b)-6*x)/(1-6*b)^4+28/6561*ln(1+2*sqrt(1-6*b)-6*x)/(1-6*b)^4,1],
[(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(3/2),x,4,-9/10*sqrt(1-6*b)*(2+(1-6*x)/sqrt(1-6*b))*(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(3/2)/sqrt(2)/(1-(1-6*x)/sqrt(1-6*b))^3+9/14*sqrt(1-6*b)*(2+(1-6*x)/sqrt(1-6*b))^2*(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(3/2)/sqrt(2)/(1-(1-6*x)/sqrt(1-6*b))^3-1/6*sqrt(1-6*b)*(2+(1-6*x)/sqrt(1-6*b))^3*(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(3/2)/sqrt(2)/(1-(1-6*x)/sqrt(1-6*b))^3+1/66*sqrt(1-6*b)*(2+(1-6*x)/sqrt(1-6*b))^4*(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(3/2)/sqrt(2)/(1-(1-6*x)/sqrt(1-6*b))^3,1],
[sqrt(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3),x,4,-1/3*sqrt(1-6*b)*(2+(1-6*x)/sqrt(1-6*b))*sqrt(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)/sqrt(2)/(1-(1-6*x)/sqrt(1-6*b))+1/15*sqrt(1-6*b)*(2+(1-6*x)/sqrt(1-6*b))^2*sqrt(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)/sqrt(2)/(1-(1-6*x)/sqrt(1-6*b)),1],
[1/sqrt(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3),x,4,-1/3*sqrt(2/3)*sqrt(1-6*b)*(1-(1-6*x)/sqrt(1-6*b))*sqrt(2+(1-6*x)/sqrt(1-6*b))*arctanh(sqrt(2+(1-6*x)/sqrt(1-6*b))/sqrt(3))/sqrt(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3),1],
[1/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(3/2),x,7,-1/9*sqrt(1-6*b)*(1-(1-6*x)/sqrt(1-6*b))*(2+(1-6*x)/sqrt(1-6*b))/sqrt(2)/(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(3/2)-5/54*sqrt(1-6*b)*(1-(1-6*x)/sqrt(1-6*b))^2*(2+(1-6*x)/sqrt(1-6*b))/sqrt(2)/(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(3/2)+5/54*sqrt(1-6*b)*(1-(1-6*x)/sqrt(1-6*b))^3*(2+(1-6*x)/sqrt(1-6*b))/sqrt(2)/(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(3/2)-5/54*sqrt(1-6*b)*(1-(1-6*x)/sqrt(1-6*b))^3*(2+(1-6*x)/sqrt(1-6*b))^(3/2)*arctanh(sqrt(2+(1-6*x)/sqrt(1-6*b))/sqrt(3))/sqrt(6)/(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(3/2),1],
[1/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(5/2),x,10,-1/9*sqrt(1-6*b)*(1-(1-6*x)/sqrt(1-6*b))*(2+(1-6*x)/sqrt(1-6*b))/sqrt(2)/(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(5/2)-11/162*sqrt(1-6*b)*(1-(1-6*x)/sqrt(1-6*b))^2*(2+(1-6*x)/sqrt(1-6*b))/sqrt(2)/(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(5/2)-11/216*sqrt(1-6*b)*(1-(1-6*x)/sqrt(1-6*b))^3*(2+(1-6*x)/sqrt(1-6*b))/sqrt(2)/(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(5/2)-77/1296*sqrt(1-6*b)*(1-(1-6*x)/sqrt(1-6*b))^4*(2+(1-6*x)/sqrt(1-6*b))/sqrt(2)/(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(5/2)+385/11664*sqrt(1-6*b)*(1-(1-6*x)/sqrt(1-6*b))^5*(2+(1-6*x)/sqrt(1-6*b))/sqrt(2)/(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(5/2)+385/11664*sqrt(1-6*b)*(1-(1-6*x)/sqrt(1-6*b))^5*(2+(1-6*x)/sqrt(1-6*b))^2/sqrt(2)/(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(5/2)-385/11664*sqrt(1-6*b)*(1-(1-6*x)/sqrt(1-6*b))^5*(2+(1-6*x)/sqrt(1-6*b))^(5/2)*arctanh(sqrt(2+(1-6*x)/sqrt(1-6*b))/sqrt(3))/sqrt(6)/(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(5/2),1],
[(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^p,x,3,-2^(-1-p)*3^(-1+2*p)*sqrt(1-6*b)*(2+(1-6*x)/sqrt(1-6*b))*(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^p*hypergeom([-2*p, p+1],[2+p],2/3+1/3*(1-6*x)/sqrt(1-6*b))/(p+1)/((1-(1-6*x)/sqrt(1-6*b))^(2*p)),1],
[(c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b)^4,x,3,b^4*(-3*a*c+b^2)^4*x/c^4-b^3*(-3*a*c+b^2)^3*(c*x+b)^4/c^5+6/7*b^2*(-3*a*c+b^2)^2*(c*x+b)^7/c^5-2/5*b*(-3*a*c+b^2)*(c*x+b)^10/c^5+1/13*(c*x+b)^13/c^5,1],
[(c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b)^3,x,3,-b^3*(-3*a*c+b^2)^3*x/c^3+3/4*b^2*(-3*a*c+b^2)^2*(c*x+b)^4/c^4-3/7*b*(-3*a*c+b^2)*(c*x+b)^7/c^4+1/10*(c*x+b)^10/c^4,1],
[(c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b)^2,x,3,b^2*(-3*a*c+b^2)^2*x/c^2-1/2*b*(-3*a*c+b^2)*(c*x+b)^4/c^3+1/7*(c*x+b)^7/c^3,1],
[c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b,x,1,3*a*b*x+3/2*b^2*x^2+b*c*x^3+1/4*c^2*x^4,1],
[1/(c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b),x,7,-arctan((b^(1/3)+2*(c*x+b)/(-3*a*c+b^2)^(1/3))/sqrt(3)/b^(1/3))/sqrt(3)/b^(2/3)/(-3*a*c+b^2)^(2/3)+1/3*ln(b^(1/3)*(b^(2/3)-(-3*a*c+b^2)^(1/3))+c*x)/b^(2/3)/(-3*a*c+b^2)^(2/3)-1/6*ln(b^(2/3)*(-3*a*c+b^2)^(2/3)+b^(1/3)*(-3*a*c+b^2)^(1/3)*(c*x+b)+(c*x+b)^2)/b^(2/3)/(-3*a*c+b^2)^(2/3),1],
[1/(c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b)^2,x,8,-1/3*(c*x+b)/b/(-3*a*c+b^2)/(b*(3*a-b^2/c)+(c*x+b)^3/c)+2/3*c*arctan((b^(1/3)+2*(c*x+b)/(-3*a*c+b^2)^(1/3))/sqrt(3)/b^(1/3))/sqrt(3)/b^(5/3)/(-3*a*c+b^2)^(5/3)-2/9*c*ln(b^(1/3)*(b^(2/3)-(-3*a*c+b^2)^(1/3))+c*x)/b^(5/3)/(-3*a*c+b^2)^(5/3)+1/9*c*ln(b^(2/3)*(-3*a*c+b^2)^(2/3)+b^(1/3)*(-3*a*c+b^2)^(1/3)*(c*x+b)+(c*x+b)^2)/b^(5/3)/(-3*a*c+b^2)^(5/3),1],
[1/(c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b)^3,x,9,-1/6*(c*x+b)/b/(-3*a*c+b^2)/(b*(3*a-b^2/c)+(c*x+b)^3/c)^2+5/18*c*(c*x+b)/b^2/(-3*a*c+b^2)^2/(b*(3*a-b^2/c)+(c*x+b)^3/c)-5/9*c^2*arctan((b^(1/3)+2*(c*x+b)/(-3*a*c+b^2)^(1/3))/sqrt(3)/b^(1/3))/sqrt(3)/b^(8/3)/(-3*a*c+b^2)^(8/3)+5/27*c^2*ln(b^(1/3)*(b^(2/3)-(-3*a*c+b^2)^(1/3))+c*x)/b^(8/3)/(-3*a*c+b^2)^(8/3)-5/54*c^2*ln(b^(2/3)*(-3*a*c+b^2)^(2/3)+b^(1/3)*(-3*a*c+b^2)^(1/3)*(c*x+b)+(c*x+b)^2)/b^(8/3)/(-3*a*c+b^2)^(8/3),1],
[(c^3*x^3+3*b*c^2*x^2+3*b^2*c*x+b^3-64)^(5/2),x,5,221184/187*(c*x+b)*sqrt(-64+(c*x+b)^3)/c-1920/187*(c*x+b)*(-64+(c*x+b)^3)^(3/2)/c+2/17*(c*x+b)*(-64+(c*x+b)^3)^(5/2)/c+7077888/187*3^(3/4)*sqrt(2-sqrt(3))*(-c*x-b+4)*sqrt((16+4*c*x+4*b+(c*x+b)^2)/(4-4*sqrt(3)-b-c*x)^2)*InverseJacobiAM(arcsin((4+4*sqrt(3)-b-c*x)/(4-4*sqrt(3)-b-c*x)),sqrt(-7+4*sqrt(3)))/c/sqrt(-(-c*x-b+4)/(4-4*sqrt(3)-b-c*x)^2)/sqrt(-64+(c*x+b)^3),1],
[(c^3*x^3+3*b*c^2*x^2+3*b^2*c*x+b^3-64)^(3/2),x,4,-1152/55*(c*x+b)*sqrt(-64+(c*x+b)^3)/c+2/11*(c*x+b)*(-64+(c*x+b)^3)^(3/2)/c-36864/55*3^(3/4)*sqrt(2-sqrt(3))*(-c*x-b+4)*sqrt((16+4*c*x+4*b+(c*x+b)^2)/(4-4*sqrt(3)-b-c*x)^2)*InverseJacobiAM(arcsin((4+4*sqrt(3)-b-c*x)/(4-4*sqrt(3)-b-c*x)),sqrt(-7+4*sqrt(3)))/c/sqrt(-(-c*x-b+4)/(4-4*sqrt(3)-b-c*x)^2)/sqrt(-64+(c*x+b)^3),1],
[sqrt(c^3*x^3+3*b*c^2*x^2+3*b^2*c*x+b^3-64),x,3,2/5*(c*x+b)*sqrt(-64+(c*x+b)^3)/c+64/5*3^(3/4)*sqrt(2-sqrt(3))*(-c*x-b+4)*sqrt((16+4*c*x+4*b+(c*x+b)^2)/(4-4*sqrt(3)-b-c*x)^2)*InverseJacobiAM(arcsin((4+4*sqrt(3)-b-c*x)/(4-4*sqrt(3)-b-c*x)),sqrt(-7+4*sqrt(3)))/c/sqrt(-(-c*x-b+4)/(4-4*sqrt(3)-b-c*x)^2)/sqrt(-64+(c*x+b)^3),1],
[1/sqrt(c^3*x^3+3*b*c^2*x^2+3*b^2*c*x+b^3-64),x,2,-1/3*3^(3/4)*sqrt(2-sqrt(3))*(-c*x-b+4)*sqrt((16+4*c*x+4*b+(c*x+b)^2)/(4-4*sqrt(3)-b-c*x)^2)*InverseJacobiAM(arcsin((4+4*sqrt(3)-b-c*x)/(4-4*sqrt(3)-b-c*x)),sqrt(-7+4*sqrt(3)))/c/sqrt(-(-c*x-b+4)/(4-4*sqrt(3)-b-c*x)^2)/sqrt(-64+(c*x+b)^3),1],
[1/(c^3*x^3+3*b*c^2*x^2+3*b^2*c*x+b^3-64)^(3/2),x,3,-1/96*(c*x+b)/c/sqrt(-64+(c*x+b)^3)+1/576*3^(3/4)*sqrt(2-sqrt(3))*(-c*x-b+4)*sqrt((16+4*c*x+4*b+(c*x+b)^2)/(4-4*sqrt(3)-b-c*x)^2)*InverseJacobiAM(arcsin((4+4*sqrt(3)-b-c*x)/(4-4*sqrt(3)-b-c*x)),sqrt(-7+4*sqrt(3)))/c/sqrt(-(-c*x-b+4)/(4-4*sqrt(3)-b-c*x)^2)/sqrt(-64+(c*x+b)^3),1],
[1/(c^3*x^3+3*b*c^2*x^2+3*b^2*c*x+b^3-64)^(5/2),x,4,-1/288*(c*x+b)/c/(-64+(c*x+b)^3)^(3/2)+7/55296*(c*x+b)/c/sqrt(-64+(c*x+b)^3)-7/331776*3^(3/4)*sqrt(2-sqrt(3))*(-c*x-b+4)*sqrt((16+4*c*x+4*b+(c*x+b)^2)/(4-4*sqrt(3)-b-c*x)^2)*InverseJacobiAM(arcsin((4+4*sqrt(3)-b-c*x)/(4-4*sqrt(3)-b-c*x)),sqrt(-7+4*sqrt(3)))/c/sqrt(-(-c*x-b+4)/(4-4*sqrt(3)-b-c*x)^2)/sqrt(-64+(c*x+b)^3),1],
[1/(c^3*x^3+3*b*c^2*x^2+3*b^2*c*x+b^3-64)^(7/2),x,5,-1/480*(c*x+b)/c/(-64+(c*x+b)^3)^(5/2)+13/276480*(c*x+b)/c/(-64+(c*x+b)^3)^(3/2)-91/53084160*(c*x+b)/c/sqrt(-64+(c*x+b)^3)+91/318504960*3^(3/4)*sqrt(2-sqrt(3))*(-c*x-b+4)*sqrt((16+4*c*x+4*b+(c*x+b)^2)/(4-4*sqrt(3)-b-c*x)^2)*InverseJacobiAM(arcsin((4+4*sqrt(3)-b-c*x)/(4-4*sqrt(3)-b-c*x)),sqrt(-7+4*sqrt(3)))/c/sqrt(-(-c*x-b+4)/(4-4*sqrt(3)-b-c*x)^2)/sqrt(-64+(c*x+b)^3),1],
[(c^3*x^3+3*b*c^2*x^2+3*b^2*c*x+b^3-64)^p,x,3,64^p*(c*x+b)*(-64+(c*x+b)^3)^p*hypergeom([1/3, -p],[4/3],1/64*(c*x+b)^3)/c/((64-(c*x+b)^3)^p),1],
[(d^2*x^3+3*c*d*x^2+3*c^2*x)^p,x,3,(d*x+c)*(d^2*x^3+3*c*d*x^2+3*c^2*x)^p*hypergeom([1/3, -p],[4/3],(d*x+c)^3/c^3)/d/((1-(d*x+c)^3/c^3)^p),1],
[(d^2*x^3+3*c*d*x^2+3*c^2*x+a)^p,x,3,(d*x+c)*(a-c^3/d+(d*x+c)^3/d)^p*hypergeom([1/3, -p],[4/3],(d*x+c)^3/(c^3-a*d))/d/((1-(d*x+c)^3/(c^3-a*d))^p),1],
[(3*d^2*x^3+3*c*d*x^2+c^2*x)^p,x,3,1/3*(3*d*x+c)*(3*d^2*x^3+3*c*d*x^2+c^2*x)^p*hypergeom([1/3, -p],[4/3],(3*d*x+c)^3/c^3)/d/((1-(3*d*x+c)^3/c^3)^p),1],
[(3*d^2*x^3+3*c*d*x^2+c^2*x+a)^p,x,3,1/3*(3*d*x+c)*(3*d^2*x^3+3*c*d*x^2+c^2*x+a)^p*hypergeom([1/3, -p],[4/3],(3*d*x+c)^3/(c^3-9*a*d))/d/((1-(3*d*x+c)^3/(c^3-9*a*d))^p),1],
[(d^2*x^3+c*d*x^2+b*d*x+b*c)^4,x,3,b^4*c^4*x+2/3*b^3*c^2*d*(3*b*d+2*c^2)*x^3+b^4*c*d^3*x^4+1/5*b^2*d^2*(b^2*d^2+24*b*c^2*d+6*c^4)*x^5+8/3*b^3*c*d^4*x^6+4/7*b*d^3*(b^2*d^2+9*b*c^2*d+c^4)*x^7+3*b^2*c*d^5*x^8+1/9*d^4*(6*b^2*d^2+24*b*c^2*d+c^4)*x^9+8/5*b*c*d^6*x^10+2/11*d^6*(2*b*d+3*c^2)*x^11+1/3*c*d^7*x^12+1/13*d^8*x^13+2/5*c^3*(d*x^2+b)^5,1],
[(d^2*x^3+c*d*x^2+b*d*x+b*c)^3,x,3,b^3*c^3*x+b^2*c*d*(b*d+c^2)*x^3+1/4*b^3*d^3*x^4+3/5*b*c*d^2*(3*b*d+c^2)*x^5+1/2*b^2*d^4*x^6+1/7*c*d^3*(9*b*d+c^2)*x^7+3/8*b*d^5*x^8+1/3*c*d^5*x^9+1/10*d^6*x^10+3/8*c^2*(d*x^2+b)^4,1],
[(d^2*x^3+c*d*x^2+b*d*x+b*c)^2,x,3,b^2*c^2*x+1/3*b*d*(b*d+2*c^2)*x^3+1/5*d^2*(2*b*d+c^2)*x^5+1/7*d^4*x^7+1/3*c*(d*x^2+b)^3,1],
[d^2*x^3+c*d*x^2+b*d*x+b*c,x,1,b*c*x+1/2*b*d*x^2+1/3*c*d*x^3+1/4*d^2*x^4,1],
[1/(d^2*x^3+c*d*x^2+b*d*x+b*c),x,6,c*arctan(sqrt(d)*x/sqrt(b))/sqrt(b)/sqrt(d)/(b*d+c^2)+ln(d*x+c)/(b*d+c^2)-ln(d*x^2+b)/(2*b*d+2*c^2),1],
[1/(d^2*x^3+c*d*x^2+b*d*x+b*c)^2,x,7,1/2*(-3*b*d+c^2)/b/(b*d+c^2)^2/(d*x+c)+1/2*(c*x+b)/b/(b*d+c^2)/(d*x+c)/(d*x^2+b)+1/2*(-3*b^2*d^2+6*b*c^2*d+c^4)*arctan(sqrt(d)*x/sqrt(b))/b^(3/2)/sqrt(d)/(b*d+c^2)^3+4*c*d*ln(d*x+c)/(b*d+c^2)^3-2*c*d*ln(d*x^2+b)/(b*d+c^2)^3,1],
[1/(d^2*x^3+c*d*x^2+b*d*x+b*c)^3,x,8,3/8*(-4*b^2*d^2+5*b*c^2*d+c^4)/b^2/(b*d+c^2)^3/(d*x+c)^2+3/8*c*(-3*b*d+c^2)*(9*b*d+c^2)/b^2/(b*d+c^2)^4/(d*x+c)+1/4*(c*x+b)/b/(b*d+c^2)/(d*x+c)^2/(d*x^2+b)^2-1/8*(2*b*(-3*b*d+c^2)-c*(11*b*d+3*c^2)*x)/b^2/(b*d+c^2)^2/(d*x+c)^2/(d*x^2+b)+3/8*c*(-35*b^3*d^3+35*b^2*c^2*d^2+7*b*c^4*d+c^6)*arctan(sqrt(d)*x/sqrt(b))/b^(5/2)/sqrt(d)/(b*d+c^2)^5+3*d^2*(-b*d+7*c^2)*ln(d*x+c)/(b*d+c^2)^5-3/2*d^2*(-b*d+7*c^2)*ln(d*x^2+b)/(b*d+c^2)^5,1],
[1/(x^3+x^2+x+1),x,6,1/2*arctan(x)+1/2*ln(1+x)-1/4*ln(x^2+1),1],
[1/(16*x^3-4*x^2+4*x-1),x,6,-1/10*arctan(2*x)+1/5*ln(1-4*x)-1/10*ln(4*x^2+1),1],
[(9*x^3+3*x^2+6*x+2)^(3/2),x,11,-4/99*(9*x^3+3*x^2+6*x+2)^(3/2)+68*(9*x^3+3*x^2+6*x+2)^(3/2)/(231+693*x)+2/33*(1+3*x)*(9*x^3+3*x^2+6*x+2)^(3/2)-328/2079*(9*x^3+3*x^2+6*x+2)^(3/2)/(1+3*x)/(3*x^2+2)+148/231*x*(9*x^3+3*x^2+6*x+2)^(3/2)/(1+3*x)/(3*x^2+2)+544/189*(9*x^3+3*x^2+6*x+2)^(3/2)/(1+3*x)/(1+sqrt(7)+3*x)/(3*x^2+2)-544/189*(1+sqrt(7)+3*x)*sqrt((3*x^2+2)/(1+sqrt(7)+3*x)^2)*(9*x^3+3*x^2+6*x+2)^(3/2)*EllipticE(sin(2*arctan(1/7*sqrt(1+3*x)*7^(3/4))),sqrt(1/2+1/14*sqrt(7)))/sqrt(3)*7^(1/4)/(1+3*x)^(3/2)/(3*x^2+2)^2+8/2079*(374-41*sqrt(7))*(1+sqrt(7)+3*x)*sqrt((3*x^2+2)/(1+sqrt(7)+3*x)^2)*(9*x^3+3*x^2+6*x+2)^(3/2)*InverseJacobiAM(2*arctan(1/7*sqrt(1+3*x)*7^(3/4)),sqrt(1/2+1/14*sqrt(7)))/sqrt(3)*7^(1/4)/(1+3*x)^(3/2)/(3*x^2+2)^2,1],
[sqrt(9*x^3+3*x^2+6*x+2),x,8,-4/45*sqrt(9*x^3+3*x^2+6*x+2)+2/15*(1+3*x)*sqrt(9*x^3+3*x^2+6*x+2)+68*sqrt(9*x^3+3*x^2+6*x+2)/(45+45*sqrt(7)+135*x)-68/45*7^(1/4)*(1+sqrt(7)+3*x)*sqrt((3*x^2+2)/(1+sqrt(7)+3*x)^2)*sqrt(9*x^3+3*x^2+6*x+2)*EllipticE(sin(2*arctan(1/7*sqrt(1+3*x)*7^(3/4))),sqrt(1/2+1/14*sqrt(7)))/sqrt(3)/sqrt(1+3*x)/(3*x^2+2)+2/45*7^(1/4)*(17+sqrt(7))*(1+sqrt(7)+3*x)*sqrt((3*x^2+2)/(1+sqrt(7)+3*x)^2)*sqrt(9*x^3+3*x^2+6*x+2)*InverseJacobiAM(2*arctan(1/7*sqrt(1+3*x)*7^(3/4)),sqrt(1/2+1/14*sqrt(7)))/sqrt(3)/sqrt(1+3*x)/(3*x^2+2),1],
[1/sqrt(9*x^3+3*x^2+6*x+2),x,3,1/7*sqrt(1+3*x)*(1+sqrt(7)+3*x)*sqrt((3*x^2+2)/(1+sqrt(7)+3*x)^2)*InverseJacobiAM(2*arctan(1/7*sqrt(1+3*x)*7^(3/4)),sqrt(1/2+1/14*sqrt(7)))/sqrt(3)*7^(3/4)/sqrt(9*x^3+3*x^2+6*x+2),1],
[1/(9*x^3+3*x^2+6*x+2)^(3/2),x,8,1/14*(2+x)*(1+3*x)*(3*x^2+2)/(9*x^3+3*x^2+6*x+2)^(3/2)-17/98*(1+3*x)*(3*x^2+2)^2/(9*x^3+3*x^2+6*x+2)^(3/2)+17/98*(1+3*x)^2*(3*x^2+2)^2/(1+sqrt(7)+3*x)/(9*x^3+3*x^2+6*x+2)^(3/2)-17/98*(1+3*x)^(3/2)*(1+sqrt(7)+3*x)*(3*x^2+2)*sqrt((3*x^2+2)/(1+sqrt(7)+3*x)^2)*EllipticE(sin(2*arctan(1/7*sqrt(1+3*x)*7^(3/4))),sqrt(1/2+1/14*sqrt(7)))/sqrt(3)*7^(1/4)/(9*x^3+3*x^2+6*x+2)^(3/2)+1/196*(17+sqrt(7))*(1+3*x)^(3/2)*(1+sqrt(7)+3*x)*(3*x^2+2)*sqrt((3*x^2+2)/(1+sqrt(7)+3*x)^2)*InverseJacobiAM(2*arctan(1/7*sqrt(1+3*x)*7^(3/4)),sqrt(1/2+1/14*sqrt(7)))/sqrt(3)*7^(1/4)/(9*x^3+3*x^2+6*x+2)^(3/2),1],
[1/(9*x^3+3*x^2+6*x+2)^(5/2),x,10,1/42*(2+x)*(1+3*x)*(3*x^2+2)/(9*x^3+3*x^2+6*x+2)^(5/2)+1/588*(1+3*x)*(51+50*x)*(3*x^2+2)^2/(9*x^3+3*x^2+6*x+2)^(5/2)-205/4116*(1+3*x)*(3*x^2+2)^3/(9*x^3+3*x^2+6*x+2)^(5/2)-935/14406*(1+3*x)^2*(3*x^2+2)^3/(9*x^3+3*x^2+6*x+2)^(5/2)+935/14406*(1+3*x)^3*(3*x^2+2)^3/(1+sqrt(7)+3*x)/(9*x^3+3*x^2+6*x+2)^(5/2)-935/14406*(1+3*x)^(5/2)*(1+sqrt(7)+3*x)*(3*x^2+2)^2*sqrt((3*x^2+2)/(1+sqrt(7)+3*x)^2)*EllipticE(sin(2*arctan(1/7*sqrt(1+3*x)*7^(3/4))),sqrt(1/2+1/14*sqrt(7)))/sqrt(3)*7^(1/4)/(9*x^3+3*x^2+6*x+2)^(5/2)+5/57624*(374-41*sqrt(7))*(1+3*x)^(5/2)*(1+sqrt(7)+3*x)*(3*x^2+2)^2*sqrt((3*x^2+2)/(1+sqrt(7)+3*x)^2)*InverseJacobiAM(2*arctan(1/7*sqrt(1+3*x)*7^(3/4)),sqrt(1/2+1/14*sqrt(7)))/sqrt(3)*7^(1/4)/(9*x^3+3*x^2+6*x+2)^(5/2),1],
[(d^2*x^3+c*d*x^2+b*d*x+b*c)^p,x,2,(d*x+c)*(d^2*x^3+c*d*x^2+b*d*x+b*c)^p*AppellF1(p+1,-p,-p,2+p,(d*x+c)/(c-sqrt(-b)*sqrt(d)),(d*x+c)/(c+sqrt(-b)*sqrt(d)))/d/(p+1)/((1-(d*x+c)/(c-sqrt(-b)*sqrt(d)))^p)/((1-(d*x+c)/(c+sqrt(-b)*sqrt(d)))^p),1],
[(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^3,x,3,1/4*(-a*d+b*c)^3*(-a*f+b*e)^3*(b*x+a)^4/b^7+3/5*(-a*d+b*c)^2*(-a*f+b*e)^2*(-2*a*d*f+b*c*f+b*d*e)*(b*x+a)^5/b^7+1/2*(-a*d+b*c)*(-a*f+b*e)*(5*a^2*d^2*f^2-5*a*b*d*f*(c*f+d*e)+b^2*(c^2*f^2+3*c*d*e*f+d^2*e^2))*(b*x+a)^6/b^7+1/7*(-2*a*d*f+b*c*f+b*d*e)*(10*a^2*d^2*f^2-10*a*b*d*f*(c*f+d*e)+b^2*(c^2*f^2+8*c*d*e*f+d^2*e^2))*(b*x+a)^7/b^7+3/8*d*f*(5*a^2*d^2*f^2-5*a*b*d*f*(c*f+d*e)+b^2*(c^2*f^2+3*c*d*e*f+d^2*e^2))*(b*x+a)^8/b^7+1/3*d^2*f^2*(-2*a*d*f+b*c*f+b*d*e)*(b*x+a)^9/b^7+1/10*d^3*f^3*(b*x+a)^10/b^7,1],
[(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^2,x,3,1/3*(-a*d+b*c)^2*(-a*f+b*e)^2*(b*x+a)^3/b^5+1/2*(-a*d+b*c)*(-a*f+b*e)*(-2*a*d*f+b*c*f+b*d*e)*(b*x+a)^4/b^5+1/5*(6*a^2*d^2*f^2-6*a*b*d*f*(c*f+d*e)+b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*(b*x+a)^5/b^5+1/3*d*f*(-2*a*d*f+b*c*f+b*d*e)*(b*x+a)^6/b^5+1/7*d^2*f^2*(b*x+a)^7/b^5,1],
[a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3,x,1,a*c*e*x+1/2*(a*c*f+a*d*e+b*c*e)*x^2+1/3*(a*d*f+b*c*f+b*d*e)*x^3+1/4*b*d*f*x^4,1],
[1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3),x,3,b*ln(b*x+a)/(-a*d+b*c)/(-a*f+b*e)-d*ln(d*x+c)/(-a*d+b*c)/(-c*f+d*e)+f*ln(f*x+e)/(-a*f+b*e)/(-c*f+d*e),1],
[1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^2,x,3,-b^3/(-a*d+b*c)^2/(-a*f+b*e)^2/(b*x+a)-d^3/(-a*d+b*c)^2/(-c*f+d*e)^2/(d*x+c)-f^3/(-a*f+b*e)^2/(-c*f+d*e)^2/(f*x+e)-2*b^3*(-2*a*d*f+b*c*f+b*d*e)*ln(b*x+a)/(-a*d+b*c)^3/(-a*f+b*e)^3+2*d^3*(a*d*f-2*b*c*f+b*d*e)*ln(d*x+c)/(-a*d+b*c)^3/(-c*f+d*e)^3+2*f^3*(-a*d*f-b*c*f+2*b*d*e)*ln(f*x+e)/(-a*f+b*e)^3/(-c*f+d*e)^3,1],
[1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^3,x,3,-1/2*b^5/(-a*d+b*c)^3/(-a*f+b*e)^3/(b*x+a)^2+3*b^5*(-2*a*d*f+b*c*f+b*d*e)/(-a*d+b*c)^4/(-a*f+b*e)^4/(b*x+a)+1/2*d^5/(-a*d+b*c)^3/(-c*f+d*e)^3/(d*x+c)^2+3*d^5*(a*d*f-2*b*c*f+b*d*e)/(-a*d+b*c)^4/(-c*f+d*e)^4/(d*x+c)-1/2*f^5/(-a*f+b*e)^3/(-c*f+d*e)^3/(f*x+e)^2-3*f^5*(-a*d*f-b*c*f+2*b*d*e)/(-a*f+b*e)^4/(-c*f+d*e)^4/(f*x+e)+3*b^5*(7*a^2*d^2*f^2-7*a*b*d*f*(c*f+d*e)+b^2*(2*c^2*f^2+3*c*d*e*f+2*d^2*e^2))*ln(b*x+a)/(-a*d+b*c)^5/(-a*f+b*e)^5-3*d^5*(2*a^2*d^2*f^2+a*b*d*f*(-7*c*f+3*d*e)+b^2*(7*c^2*f^2-7*c*d*e*f+2*d^2*e^2))*ln(d*x+c)/(-a*d+b*c)^5/(-c*f+d*e)^5+3*f^5*(2*a^2*d^2*f^2-a*b*d*f*(-3*c*f+7*d*e)+b^2*(2*c^2*f^2-7*c*d*e*f+7*d^2*e^2))*ln(f*x+e)/(-a*f+b*e)^5/(-c*f+d*e)^5,1],
[sqrt(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3),x,9,2/15*(a/b+c/d-2*e/f)*sqrt(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)+2/5*(f*x+e)*sqrt(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)/f-4/15*sqrt(a*d-b*c)*(a^2*d^2*f^2-a*b*d*f*(c*f+d*e)+b^2*(c^2*f^2-c*d*e*f+d^2*e^2))*sqrt(b*(d*x+c)/(-a*d+b*c))*sqrt(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)*EllipticE(sin(arcsin(sqrt(d)*sqrt(b*x+a)/sqrt(a*d-b*c))),sqrt((-a*d+b*c)*f/d/(-a*f+b*e)))/b^2/d^(3/2)/f^2/sqrt(b*x+a)/(d*x+c)/sqrt(b*(f*x+e)/(-a*f+b*e))+2/15*sqrt(a*d-b*c)*(-a*f+b*e)*(-c*f+d*e)*(-a*d*f-b*c*f+2*b*d*e)*sqrt(b*(d*x+c)/(-a*d+b*c))*sqrt(b*(f*x+e)/(-a*f+b*e))*sqrt(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)*InverseJacobiAM(arcsin(sqrt(d)*sqrt(b*x+a)/sqrt(a*d-b*c)),sqrt((-a*d+b*c)*f/d/(-a*f+b*e)))/b^2/d^(3/2)/f^2/sqrt(b*x+a)/(d*x+c)/(f*x+e),1],
[1/sqrt(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3),x,4,2*sqrt(a*d-b*c)*sqrt(b*x+a)*sqrt(b*(d*x+c)/(-a*d+b*c))*sqrt(b*(f*x+e)/(-a*f+b*e))*InverseJacobiAM(arcsin(sqrt(d)*sqrt(b*x+a)/sqrt(a*d-b*c)),sqrt((-a*d+b*c)*f/d/(-a*f+b*e)))/b/sqrt(d)/sqrt(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3),1],
[1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^(3/2),x,10,-2*b*(b*x+a)*(d*x+c)*(f*x+e)/(-a*d+b*c)/(-a*f+b*e)/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^(3/2)-2*d*(-a*d*f-b*c*f+2*b*d*e)*(b*x+a)^2*(d*x+c)*(f*x+e)/(-a*d+b*c)^2/(-a*f+b*e)/(-c*f+d*e)/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^(3/2)-4*f*(a^2*d^2*f^2-a*b*d*f*(c*f+d*e)+b^2*(c^2*f^2-c*d*e*f+d^2*e^2))*(b*x+a)^2*(d*x+c)^2*(f*x+e)/(-a*d+b*c)^2/(-a*f+b*e)^2/(-c*f+d*e)^2/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^(3/2)+4*sqrt(d)*(a^2*d^2*f^2-a*b*d*f*(c*f+d*e)+b^2*(c^2*f^2-c*d*e*f+d^2*e^2))*(b*x+a)^(3/2)*(d*x+c)*sqrt(b*(d*x+c)/(-a*d+b*c))*(f*x+e)^2*EllipticE(sin(arcsin(sqrt(d)*sqrt(b*x+a)/sqrt(a*d-b*c))),sqrt((-a*d+b*c)*f/d/(-a*f+b*e)))/(a*d-b*c)^(3/2)/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*(f*x+e)/(-a*f+b*e))/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^(3/2)-2*sqrt(d)*(-a*d*f-b*c*f+2*b*d*e)*(b*x+a)^(3/2)*(d*x+c)*sqrt(b*(d*x+c)/(-a*d+b*c))*(f*x+e)*sqrt(b*(f*x+e)/(-a*f+b*e))*InverseJacobiAM(arcsin(sqrt(d)*sqrt(b*x+a)/sqrt(a*d-b*c)),sqrt((-a*d+b*c)*f/d/(-a*f+b*e)))/(a*d-b*c)^(3/2)/(-a*f+b*e)/(-c*f+d*e)/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^(3/2),1],
[(6*x^3-53*x^2+67*x+70)^(5/2),x,13,-35313185/817938*(6*x^3-53*x^2+67*x+70)^(5/2)/(5-2*x)^2/(7-x)^2-23231345365/1635876*(6*x^3-53*x^2+67*x+70)^(5/2)/(5-2*x)^2/(7-x)^2/(2+3*x)^2-333757603/483327*(6*x^3-53*x^2+67*x+70)^(5/2)/(5-2*x)^2/(7-x)^2/(2+3*x)+2/51*(2+3*x)*(6*x^3-53*x^2+67*x+70)^(5/2)+11420/17901*(2+3*x)*(6*x^3-53*x^2+67*x+70)^(5/2)/(7-x)^2+86851225/5316597*(2+3*x)*(6*x^3-53*x^2+67*x+70)^(5/2)/(5-2*x)^2/(7-x)^2+1348135/196911*(2+3*x)*(6*x^3-53*x^2+67*x+70)^(5/2)/(5-2*x)/(7-x)^2+65*(2+3*x)*(6*x^3-53*x^2+67*x+70)^(5/2)/(3213-459*x)+10004250047699/63799164*sqrt(19)*(6*x^3-53*x^2+67*x+70)^(5/2)*EllipticE(sin(arcsin(sqrt(2+3*x)/sqrt(23))),sqrt(46/19))/(5-2*x)^(5/2)/(7-x)^(5/2)/(2+3*x)^(5/2)+28315535033/590733*sqrt(19)*(6*x^3-53*x^2+67*x+70)^(5/2)*InverseJacobiAM(arcsin(sqrt(19/2)/sqrt(2+3*x)),sqrt(46/19))/(-7+x)^(5/2)/(-5+2*x)^(5/2)/(2+3*x)^(5/2),1],
[(6*x^3-53*x^2+67*x+70)^(3/2),x,10,-221/81*(6*x^3-53*x^2+67*x+70)^(3/2)/(5-2*x)/(7-x)+4463/1782*(6*x^3-53*x^2+67*x+70)^(3/2)/(5-2*x)/(7-x)/(2+3*x)+2/33*(2+3*x)*(6*x^3-53*x^2+67*x+70)^(3/2)+65*(2+3*x)*(6*x^3-53*x^2+67*x+70)^(3/2)/(2079-297*x)+1616/891*(2+3*x)*(6*x^3-53*x^2+67*x+70)^(3/2)/(5-2*x)/(7-x)-1738568/2673*sqrt(19)*(6*x^3-53*x^2+67*x+70)^(3/2)*EllipticE(sin(arcsin(sqrt(2+3*x)/sqrt(23))),sqrt(46/19))/(5-2*x)^(3/2)/(7-x)^(3/2)/(2+3*x)^(3/2)-124981/198*sqrt(19)*(6*x^3-53*x^2+67*x+70)^(3/2)*InverseJacobiAM(arcsin(sqrt(19/2)/sqrt(2+3*x)),sqrt(46/19))/(-7+x)^(3/2)/(-5+2*x)^(3/2)/(2+3*x)^(3/2),1],
[sqrt(6*x^3-53*x^2+67*x+70),x,7,-13/9*sqrt(6*x^3-53*x^2+67*x+70)+2/15*(2+3*x)*sqrt(6*x^3-53*x^2+67*x+70)+1603/135*sqrt(19)*sqrt(6*x^3-53*x^2+67*x+70)*EllipticE(sin(arcsin(sqrt(2+3*x)/sqrt(23))),sqrt(46/19))/sqrt(5-2*x)/sqrt(7-x)/sqrt(2+3*x)+4/5*sqrt(19)*sqrt(6*x^3-53*x^2+67*x+70)*InverseJacobiAM(arcsin(sqrt(19/2)/sqrt(2+3*x)),sqrt(46/19))/sqrt(-7+x)/sqrt(-5+2*x)/sqrt(2+3*x),1],
[1/sqrt(6*x^3-53*x^2+67*x+70),x,2,-2*sqrt(-7+x)*sqrt(-5+2*x)*sqrt(2+3*x)*InverseJacobiAM(arcsin(sqrt(19/2)/sqrt(2+3*x)),sqrt(46/19))/sqrt(19)/sqrt(6*x^3-53*x^2+67*x+70),1],
[1/(6*x^3-53*x^2+67*x+70)^(3/2),x,8,-2/207*(5-2*x)*(7-x)*(2+3*x)/(6*x^3-53*x^2+67*x+70)^(3/2)+260/35397*(5-2*x)*(7-x)^2*(2+3*x)/(6*x^3-53*x^2+67*x+70)^(3/2)-6412/5156163*(5-2*x)^2*(7-x)^2*(2+3*x)/(6*x^3-53*x^2+67*x+70)^(3/2)-6412/814131*(5-2*x)^(3/2)*(7-x)^(3/2)*(2+3*x)^(3/2)*EllipticE(sin(arcsin(sqrt(2+3*x)/sqrt(23))),sqrt(46/19))/sqrt(19)/(6*x^3-53*x^2+67*x+70)^(3/2)-16/30153*(-7+x)^(3/2)*(-5+2*x)^(3/2)*(2+3*x)^(3/2)*InverseJacobiAM(arcsin(sqrt(19/2)/sqrt(2+3*x)),sqrt(46/19))/sqrt(19)/(6*x^3-53*x^2+67*x+70)^(3/2),1],
[1/(6*x^3-53*x^2+67*x+70)^(5/2),x,11,-2/621*(5-2*x)*(7-x)*(2+3*x)/(6*x^3-53*x^2+67*x+70)^(5/2)-292/42849*(5-2*x)*(7-x)^2*(2+3*x)/(6*x^3-53*x^2+67*x+70)^(5/2)+45248/21981537*(5-2*x)*(7-x)^3*(2+3*x)/(6*x^3-53*x^2+67*x+70)^(5/2)-680680/3758842827*(5-2*x)^2*(7-x)^3*(2+3*x)/(6*x^3-53*x^2+67*x+70)^(5/2)-624820/547538105133*(5-2*x)^3*(7-x)^3*(2+3*x)/(6*x^3-53*x^2+67*x+70)^(5/2)-973598080/239274151943121*(5-2*x)^3*(7-x)^3*(2+3*x)^2/(6*x^3-53*x^2+67*x+70)^(5/2)-973598080/37780129254177*(5-2*x)^(5/2)*(7-x)^(5/2)*(2+3*x)^(5/2)*EllipticE(sin(arcsin(sqrt(2+3*x)/sqrt(23))),sqrt(46/19))/sqrt(19)/(6*x^3-53*x^2+67*x+70)^(5/2)-34994680/1399264046451*(-7+x)^(5/2)*(-5+2*x)^(5/2)*(2+3*x)^(5/2)*InverseJacobiAM(arcsin(sqrt(19/2)/sqrt(2+3*x)),sqrt(46/19))/sqrt(19)/(6*x^3-53*x^2+67*x+70)^(5/2),1],
[((b*x+a)*(d*x+c)*(f*x+e))^p,x,3,(b*x+a)*((b*x+a)*(d*x+c)*(f*x+e))^p*AppellF1(p+1,-p,-p,2+p,-d*(b*x+a)/(-a*d+b*c),-f*(b*x+a)/(-a*f+b*e))/b/(p+1)/((b*(d*x+c)/(-a*d+b*c))^p)/((b*(f*x+e)/(-a*f+b*e))^p),1],
[(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^p,x,3,(b*x+a)*(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^p*AppellF1(p+1,-p,-p,2+p,-d*(b*x+a)/(-a*d+b*c),-f*(b*x+a)/(-a*f+b*e))/b/(p+1)/((b*(d*x+c)/(-a*d+b*c))^p)/((b*(f*x+e)/(-a*f+b*e))^p),1],
[(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^3,x,3,1/4*(a*e^2-b*d*e+c*d^2)^3*(e*x+d)^4/e^7-3/5*(-b*e+2*c*d)*(a*e^2-b*d*e+c*d^2)^2*(e*x+d)^5/e^7+1/2*(a*e^2-b*d*e+c*d^2)*(5*c^2*d^2+b^2*e^2-c*e*(-a*e+5*b*d))*(e*x+d)^6/e^7-1/7*(-b*e+2*c*d)*(10*c^2*d^2+b^2*e^2-2*c*e*(-3*a*e+5*b*d))*(e*x+d)^7/e^7+3/8*c*(5*c^2*d^2+b^2*e^2-c*e*(-a*e+5*b*d))*(e*x+d)^8/e^7-1/3*c^2*(-b*e+2*c*d)*(e*x+d)^9/e^7+1/10*c^3*(e*x+d)^10/e^7,1],
[(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^2,x,3,1/3*(a*e^2-b*d*e+c*d^2)^2*(e*x+d)^3/e^5-1/2*(-b*e+2*c*d)*(a*e^2-b*d*e+c*d^2)*(e*x+d)^4/e^5+1/5*(6*c^2*d^2+b^2*e^2-2*c*e*(-a*e+3*b*d))*(e*x+d)^5/e^5-1/3*c*(-b*e+2*c*d)*(e*x+d)^6/e^5+1/7*c^2*(e*x+d)^7/e^5,1],
[a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3,x,1,a*d*x+1/2*(a*e+b*d)*x^2+1/3*(b*e+c*d)*x^3+1/4*c*e*x^4,1],
[1/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3),x,6,-(-b*e+2*c*d)*arctanh((2*c*x+b)/sqrt(-4*a*c+b^2))/sqrt(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)+e*ln(e*x+d)/(a*e^2-b*d*e+c*d^2)-e*ln(c*x^2+b*x+a)/(2*a*e^2-2*b*d*e+2*c*d^2),1],
[1/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^2,x,8,-2*e*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d))/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)-(b*c*d-b^2*e+2*a*c*e+c*(-b*e+2*c*d)*x)/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/(e*x+d)/(c*x^2+b*x+a)+2*(2*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(-3*a*e+b*d)-6*a*c^2*e^3*(a*e+2*b*d)+2*b^2*c*e^3*(3*a*e+b*d))*arctanh((2*c*x+b)/sqrt(-4*a*c+b^2))/(-4*a*c+b^2)^(3/2)/(a*e^2-b*d*e+c*d^2)^3+2*e^3*(-b*e+2*c*d)*ln(e*x+d)/(a*e^2-b*d*e+c*d^2)^3-e^3*(-b*e+2*c*d)*ln(c*x^2+b*x+a)/(a*e^2-b*d*e+c*d^2)^3,1],
[(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2),x,11,2/7293*(3*c^3*d^3+80*b^3*e^3+c^2*d*e*(-61*a*e+298*b*d)-19*b*c*e^2*(a*e+15*b*d)+11*c*e*(55*c^2*d^2+16*b^2*e^2-c*e*(9*a*e+55*b*d))*x)*(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2)/c^3/e/(e*x+d)^2+2/153153*(128*c^7*d^7+128*b^7*e^7-4*c^6*d^5*e*(-225*a*e+124*b*d)-16*b^5*c*e^6*(57*a*e+31*b*d)+3*b^3*c^2*e^5*(421*a^2*e^2+1126*a*b*d*e+197*b^2*d^2)+3*c^5*d^3*e^2*(1240*a^2*e^2-860*a*b*d*e+197*b^2*d^2)-b*c^3*e^4*(-1236*a^3*e^3+3897*a^2*b*d*e^2+4140*a*b^2*d^2*e+95*b^3*d^3)-c^4*d*e^3*(5244*a^3*e^3-5040*a^2*b*d*e^2-1050*a*b^2*d^2*e+95*b^3*d^3)-3*c*e*(32*c^6*d^6-128*b^6*e^6-4*c^5*d^4*e*(-55*a*e+24*b*d)+16*b^4*c*e^5*(67*a*e+29*b*d)+5*c^4*d^2*e^2*(-1416*a^2*e^2-88*a*b*d*e+13*b^2*d^2)-b^2*c^2*e^4*(2463*a^2*e^2+3650*a*b*d*e+495*b^2*d^2)+6*c^3*e^3*(154*a^3*e^3+1180*a^2*b*d*e^2+645*a*b^2*d^2*e+5*b^3*d^3))*x)*(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2)/c^5/e^5/(e*x+d)^2/(c*x^2+b*x+a)^2+10/153153*(16*c^5*d^5-96*b^5*e^5-c^4*d^3*e*(-96*a*e+47*b*d)+32*b^3*c*e^4*(12*a*e+11*b*d)+6*c^3*d*e^2*(-72*a^2*e^2+235*a*b*d*e+5*b^2*d^2)-b*c^2*e^3*(15*a^2*e^2+1266*a*b*d*e+383*b^2*d^2)-14*c*e*(c^4*d^4+16*b^4*e^4-8*b^2*c*e^3*(9*a*e+7*b*d)-2*c^3*d^2*e*(111*a*e+b*d)+3*c^2*e^2*(11*a^2*e^2+74*a*b*d*e+19*b^2*d^2))*x)*(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2)/c^4/e^3/(e*x+d)^2/(c*x^2+b*x+a)+4/51*e*(-b*e+2*c*d)*(c*x^2+b*x+a)*(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2)/c^2/(e*x+d)^2+2/17*e*(c*x^2+b*x+a)*(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2)/c/(e*x+d)-2/153153*sqrt(2)*sqrt(-4*a*c+b^2)*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d))*(128*c^6*d^6+128*b^6*e^6-12*c^5*d^4*e*(-115*a*e+32*b*d)-384*b^4*c*e^5*(3*a*e+b*d)+15*c^4*d^2*e^2*(568*a^2*e^2-184*a*b*d*e+9*b^2*d^2)+3*b^2*c^2*e^4*(941*a^2*e^2+1190*a*b*d*e+45*b^2*d^2)+2*c^3*e^3*(-462*a^3*e^3-4260*a^2*b*d*e^2-1095*a*b^2*d^2*e+185*b^3*d^3))*sqrt(-c*(c*x^2+b*x+a)/(-4*a*c+b^2))*(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2)*EllipticE(sin(arcsin(sqrt(1+(2*c*x+b)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(-2*sqrt(-4*a*c+b^2)*e/(2*c*d-(b+sqrt(-4*a*c+b^2))*e)))/c^6/e^6/(e*x+d)^2/sqrt(c*(e*x+d)/(2*c*d-(b+sqrt(-4*a*c+b^2))*e))/(c*x^2+b*x+a)^3+2/153153*sqrt(2)*sqrt(-4*a*c+b^2)*(-b*e+2*c*d)*(a*e^2-b*d*e+c*d^2)*(128*c^6*d^6+128*b^6*e^6-12*c^5*d^4*e*(-75*a*e+32*b*d)-48*b^4*c*e^5*(29*a*e+3*b*d)+15*c^4*d^2*e^2*(248*a^2*e^2-120*a*b*d*e+17*b^2*d^2)+3*b^2*c^2*e^4*(1621*a^2*e^2+470*a*b*d*e+5*b^2*d^2)+2*c^3*e^3*(-2622*a^3*e^3-1860*a^2*b*d*e^2-255*a*b^2*d^2*e+65*b^3*d^3))*sqrt(c*(e*x+d)/(2*c*d-(b+sqrt(-4*a*c+b^2))*e))*sqrt(-c*(c*x^2+b*x+a)/(-4*a*c+b^2))*(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2)*InverseJacobiAM(arcsin(sqrt(1+(2*c*x+b)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(-2*sqrt(-4*a*c+b^2)*e/(2*c*d-(b+sqrt(-4*a*c+b^2))*e)))/c^6/e^6/(e*x+d)^3/(c*x^2+b*x+a)^3,1],
[(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(3/2),x,9,2/231*(c^2*d^2-6*b^2*e^2+c*e*(-3*a*e+13*b*d)+14*c*e*(-b*e+2*c*d)*x)*(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(3/2)/c^2/e/(e*x+d)+2/1155*(8*c^4*d^4+8*b^4*e^4-c^3*d^2*e*(-42*a*e+19*b*d)-b^2*c*e^3*(21*a*e+19*b*d)+3*c^2*e^2*(-10*a^2*e^2+17*a*b*d*e+2*b^2*d^2)-3*c*e*(-b*e+2*c*d)*(c^2*d^2+8*b^2*e^2-c*e*(31*a*e+b*d))*x)*(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(3/2)/c^3/e^3/(e*x+d)/(c*x^2+b*x+a)+2/11*e*(c*x^2+b*x+a)*(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(3/2)/c/(e*x+d)-8/1155*sqrt(2)*sqrt(-4*a*c+b^2)*(-b*e+2*c*d)*(c^2*d^2-2*b^2*e^2-c*e*(-9*a*e+b*d))*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d))*sqrt(-c*(c*x^2+b*x+a)/(-4*a*c+b^2))*(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(3/2)*EllipticE(sin(arcsin(sqrt(1+(2*c*x+b)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(-2*sqrt(-4*a*c+b^2)*e/(2*c*d-(b+sqrt(-4*a*c+b^2))*e)))/c^4/e^4/(e*x+d)/sqrt(c*(e*x+d)/(2*c*d-(b+sqrt(-4*a*c+b^2))*e))/(c*x^2+b*x+a)^2+2/1155*sqrt(2)*sqrt(-4*a*c+b^2)*(a*e^2-b*d*e+c*d^2)*(16*c^4*d^4-8*b^4*e^4-4*c^3*d^2*e*(-21*a*e+8*b*d)+b^2*c*e^3*(51*a*e+13*b*d)+3*c^2*e^2*(-20*a^2*e^2-28*a*b*d*e+b^2*d^2))*sqrt(c*(e*x+d)/(2*c*d-(b+sqrt(-4*a*c+b^2))*e))*sqrt(-c*(c*x^2+b*x+a)/(-4*a*c+b^2))*(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(3/2)*InverseJacobiAM(arcsin(sqrt(1+(2*c*x+b)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(-2*sqrt(-4*a*c+b^2)*e/(2*c*d-(b+sqrt(-4*a*c+b^2))*e)))/c^4/e^4/(e*x+d)^2/(c*x^2+b*x+a)^2,1],
[sqrt(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3),x,8,-2/15*(-b*e+2*c*d)*sqrt(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)/c/e+2/5*(e*x+d)*sqrt(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)/e-2/15*sqrt(2)*sqrt(-4*a*c+b^2)*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d))*sqrt(-c*(c*x^2+b*x+a)/(-4*a*c+b^2))*sqrt(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)*EllipticE(sin(arcsin(sqrt(1+(2*c*x+b)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(-2*sqrt(-4*a*c+b^2)*e/(2*c*d-(b+sqrt(-4*a*c+b^2))*e)))/c^2/e^2/sqrt(c*(e*x+d)/(2*c*d-(b+sqrt(-4*a*c+b^2))*e))/(c*x^2+b*x+a)+2/15*sqrt(2)*sqrt(-4*a*c+b^2)*(-b*e+2*c*d)*(a*e^2-b*d*e+c*d^2)*sqrt(c*(e*x+d)/(2*c*d-(b+sqrt(-4*a*c+b^2))*e))*sqrt(-c*(c*x^2+b*x+a)/(-4*a*c+b^2))*sqrt(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)*InverseJacobiAM(arcsin(sqrt(1+(2*c*x+b)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(-2*sqrt(-4*a*c+b^2)*e/(2*c*d-(b+sqrt(-4*a*c+b^2))*e)))/c^2/e^2/(e*x+d)/(c*x^2+b*x+a),1],
[1/sqrt(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3),x,3,2*sqrt(2)*sqrt(-4*a*c+b^2)*sqrt(c*(e*x+d)/(2*c*d-(b+sqrt(-4*a*c+b^2))*e))*sqrt(-c*(c*x^2+b*x+a)/(-4*a*c+b^2))*InverseJacobiAM(arcsin(sqrt(1+(2*c*x+b)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(-2*sqrt(-4*a*c+b^2)*e/(2*c*d-(b+sqrt(-4*a*c+b^2))*e)))/c/sqrt(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3),1],
[1/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(3/2),x,8,-2*(e*x+d)*(b*c*d-b^2*e+2*a*c*e+c*(-b*e+2*c*d)*x)*(c*x^2+b*x+a)/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(3/2)-4*e*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d))*(e*x+d)*(c*x^2+b*x+a)^2/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)^2/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(3/2)+2*sqrt(2)*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d))*(e*x+d)^2*(c*x^2+b*x+a)*sqrt(-c*(c*x^2+b*x+a)/(-4*a*c+b^2))*EllipticE(sin(arcsin(sqrt(1+(2*c*x+b)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(-2*sqrt(-4*a*c+b^2)*e/(2*c*d-(b+sqrt(-4*a*c+b^2))*e)))/sqrt(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)^2/sqrt(c*(e*x+d)/(2*c*d-(b+sqrt(-4*a*c+b^2))*e))/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(3/2)-2*sqrt(2)*(-b*e+2*c*d)*(e*x+d)*sqrt(c*(e*x+d)/(2*c*d-(b+sqrt(-4*a*c+b^2))*e))*(c*x^2+b*x+a)*sqrt(-c*(c*x^2+b*x+a)/(-4*a*c+b^2))*InverseJacobiAM(arcsin(sqrt(1+(2*c*x+b)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(-2*sqrt(-4*a*c+b^2)*e/(2*c*d-(b+sqrt(-4*a*c+b^2))*e)))/sqrt(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(3/2),1],
[1/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2),x,10,-2/3*(e*x+d)*(b*c*d-b^2*e+2*a*c*e+c*(-b*e+2*c*d)*x)*(c*x^2+b*x+a)/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2)-2/3*(e*x+d)*(7*a*c*e*(-b*e+2*c*d)^2-(2*a*c*e-b^2*e+b*c*d)*(8*c^2*d^2-6*b^2*e^2-c*e*(-18*a*e+b*d))-2*c*(-b*e+2*c*d)*(4*c^2*d^2-3*b^2*e^2-4*c*e*(-4*a*e+b*d))*x)*(c*x^2+b*x+a)^2/(-4*a*c+b^2)^2/(a*e^2-b*d*e+c*d^2)^2/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2)+2/3*e*(16*c^4*d^4-8*b^4*e^4-4*c^3*d^2*e*(-21*a*e+8*b*d)+b^2*c*e^3*(51*a*e+13*b*d)+3*c^2*e^2*(-20*a^2*e^2-28*a*b*d*e+b^2*d^2))*(e*x+d)*(c*x^2+b*x+a)^3/(-4*a*c+b^2)^2/(a*e^2-b*d*e+c*d^2)^3/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2)+16/3*e*(-b*e+2*c*d)*(c^2*d^2-2*b^2*e^2-c*e*(-9*a*e+b*d))*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d))*(e*x+d)^2*(c*x^2+b*x+a)^3/(-4*a*c+b^2)^2/(a*e^2-b*d*e+c*d^2)^4/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2)-8/3*sqrt(2)*(-b*e+2*c*d)*(c^2*d^2-2*b^2*e^2-c*e*(-9*a*e+b*d))*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d))*(e*x+d)^3*(c*x^2+b*x+a)^2*sqrt(-c*(c*x^2+b*x+a)/(-4*a*c+b^2))*EllipticE(sin(arcsin(sqrt(1+(2*c*x+b)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(-2*sqrt(-4*a*c+b^2)*e/(2*c*d-(b+sqrt(-4*a*c+b^2))*e)))/(-4*a*c+b^2)^(3/2)/(a*e^2-b*d*e+c*d^2)^4/sqrt(c*(e*x+d)/(2*c*d-(b+sqrt(-4*a*c+b^2))*e))/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2)+2/3*sqrt(2)*(16*c^4*d^4-8*b^4*e^4-4*c^3*d^2*e*(-21*a*e+8*b*d)+b^2*c*e^3*(51*a*e+13*b*d)+3*c^2*e^2*(-20*a^2*e^2-28*a*b*d*e+b^2*d^2))*(e*x+d)^2*sqrt(c*(e*x+d)/(2*c*d-(b+sqrt(-4*a*c+b^2))*e))*(c*x^2+b*x+a)^2*sqrt(-c*(c*x^2+b*x+a)/(-4*a*c+b^2))*InverseJacobiAM(arcsin(sqrt(1+(2*c*x+b)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(-2*sqrt(-4*a*c+b^2)*e/(2*c*d-(b+sqrt(-4*a*c+b^2))*e)))/(-4*a*c+b^2)^(3/2)/(a*e^2-b*d*e+c*d^2)^3/(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^(5/2),1],
[1/sqrt(-x^3+4*x^2-8*x+8),x,3,-sqrt(2-x)*(4-x)*sqrt((x^2-2*x+4)/(4-x)^2)*InverseJacobiAM(2*arctan(sqrt(2-x)/sqrt(2)),sqrt(3/4))/sqrt(2)/sqrt(-x^3+4*x^2-8*x+8),1],
[(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^p,x,3,(e*x+d)*(a*d+(a*e+b*d)*x+(b*e+c*d)*x^2+c*e*x^3)^p*AppellF1(p+1,-p,-p,2+p,2*c*(e*x+d)/(2*c*d-(b-sqrt(-4*a*c+b^2))*e),2*c*(e*x+d)/(2*c*d-(b+sqrt(-4*a*c+b^2))*e))/e/(p+1)/((1-2*c*(e*x+d)/(2*c*d-(b-sqrt(-4*a*c+b^2))*e))^p)/((1-2*c*(e*x+d)/(2*c*d-(b+sqrt(-4*a*c+b^2))*e))^p),1],
[(x^3-5*x^2+3*x+2)^3,x,2,8*x+18*x^2-2*x^3-141/4*x^4+51/5*x^5+32*x^6-209/7*x^7+21/2*x^8-5/3*x^9+1/10*x^10,1],
[(x^3-5*x^2+3*x+2)^2,x,2,4*x+6*x^2-11/3*x^3-13/2*x^4+31/5*x^5-5/3*x^6+1/7*x^7,1],
[x^3-5*x^2+3*x+2,x,1,2*x+3/2*x^2-5/3*x^3+1/4*x^4,1],
[1/(x^3-5*x^2+3*x+2),x,4,3*ln(5-3*x-8*sin(1/3*arcsin(61/128)))/(16-32*cos(2/3*arcsin(61/128)))+3*sqrt(3)*ln(5-3*x-8*cos(1/6*Pi+1/3*arcsin(61/128)))*sec(1/3*arcsin(61/128))/(64*cos(1/6*Pi+1/3*arcsin(61/128))-64*sin(1/3*arcsin(61/128)))+3*sqrt(3)*ln(5-3*x+8*sin(1/3*Pi+1/3*arcsin(61/128)))*sec(1/3*arcsin(61/128))/(64*sin(1/3*arcsin(61/128))+64*sin(1/3*Pi+1/3*arcsin(61/128))),1],
[1/(x^3-5*x^2+3*x+2)^2,x,4,27/256/(1-2*cos(2/3*arcsin(61/128)))^2/(5-3*x-8*sin(1/3*arcsin(61/128)))+81/4096*sec(1/3*arcsin(61/128))^2/(5-3*x-8*cos(1/6*Pi+1/3*arcsin(61/128)))/(cos(1/6*Pi+1/3*arcsin(61/128))-sin(1/3*arcsin(61/128)))^2+27/256*ln(5-3*x-8*sin(1/3*arcsin(61/128)))*sin(1/3*arcsin(61/128))/(1-2*cos(2/3*arcsin(61/128)))^3+27/4096*ln(5-3*x-8*cos(1/6*Pi+1/3*arcsin(61/128)))*sec(1/3*arcsin(61/128))^3*(sqrt(3)*cos(1/3*arcsin(61/128))-sin(1/3*arcsin(61/128)))/(cos(1/3*arcsin(61/128))-sqrt(3)*sin(1/3*arcsin(61/128)))^3-27/4096*ln(5-3*x+8*sin(1/3*Pi+1/3*arcsin(61/128)))*sec(1/3*arcsin(61/128))^3*(sqrt(3)*cos(1/3*arcsin(61/128))+sin(1/3*arcsin(61/128)))/(cos(1/3*arcsin(61/128))+sqrt(3)*sin(1/3*arcsin(61/128)))^3+81/4096*sec(1/3*arcsin(61/128))^2/(sin(1/3*arcsin(61/128))+sin(1/3*Pi+1/3*arcsin(61/128)))^2/(5-3*x+8*sin(1/3*Pi+1/3*arcsin(61/128))),1],
[(x^3-5*x^2+3*x+2)^p,x,3,-3^(-1+1/2*p)*(x^3-5*x^2+3*x+2)^p*AppellF1(p+1,-p,-p,2+p,1/8*sec(1/3*arcsin(61/128))*(5-3*x+8*sin(1/3*Pi+1/3*arcsin(61/128)))/sqrt(3),(5-3*x+8*sin(1/3*Pi+1/3*arcsin(61/128)))/(8*sin(1/3*arcsin(61/128))+8*sin(1/3*Pi+1/3*arcsin(61/128))))*(32*cos(1/3*arcsin(61/128))*(sqrt(3)*cos(1/3*arcsin(61/128))+3*sin(1/3*arcsin(61/128))))^p*(5-3*x+8*sin(1/3*Pi+1/3*arcsin(61/128)))/(p+1)/((-5+3*x+8*cos(1/6*Pi+1/3*arcsin(61/128)))^p)/((-5+3*x+8*sin(1/3*arcsin(61/128)))^p),1],
[(x^3+4*x^2+3*x+2)^3,x,2,8*x+18*x^2+34*x^3+183/4*x^4+48*x^5+73/2*x^6+142/7*x^7+57/8*x^8+4/3*x^9+1/10*x^10,1],
[(x^3+4*x^2+3*x+2)^2,x,2,4*x+6*x^2+25/3*x^3+7*x^4+22/5*x^5+4/3*x^6+1/7*x^7,1],
[x^3+4*x^2+3*x+2,x,1,2*x+3/2*x^2+4/3*x^3+1/4*x^4,1],
[1/(x^3+4*x^2+3*x+2),x,7,-1/1596*(342+37*sqrt(114))^(1/3)*(7+(37-3*sqrt(114))^(2/3))*arctan((7+(37-3*sqrt(114))^(2/3)-2*(37-3*sqrt(114))^(1/3)*(4+3*x))/sqrt(3)/(7-(37-3*sqrt(114))^(2/3)))*3^(5/6)*38^(1/3)-3*(37-3*sqrt(114))^(2/3)*ln(33-4*sqrt(114)-3*(37-3*sqrt(114))^(1/3)+sqrt(114)*(37-3*sqrt(114))^(1/3)-3*(37-3*sqrt(114))^(2/3)+37*x-3*sqrt(114)*x+7*(37-3*sqrt(114))^(1/3)*x-8*(37-3*sqrt(114))^(2/3)*x-3*(37-3*sqrt(114))^(2/3)*x^2)/(98+14*(37-3*sqrt(114))^(2/3)+2*(37-3*sqrt(114))^(4/3))+3*(37-3*sqrt(114))^(2/3)*ln(7+(37-3*sqrt(114))^(2/3)+(37-3*sqrt(114))^(1/3)*(4+3*x))/(49+7*(37-3*sqrt(114))^(2/3)+(37-3*sqrt(114))^(4/3)),1],
[1/(x^3+4*x^2+3*x+2)^2,x,9,21*(37-3*sqrt(114))^(1/3)/(532+76*(37-3*sqrt(114))^(2/3)+76*(37-3*sqrt(114))^(1/3)*(4+3*x))+9/76*(-1026+111*sqrt(114))^(1/3)*(14-(7+(37-3*sqrt(114))^(2/3))*(4+3*x)/(37-3*sqrt(114))^(1/3))*38^(1/3)/(7-(37-3*sqrt(114))^(2/3))/(4+7/(37-3*sqrt(114))^(1/3)+(37-3*sqrt(114))^(1/3)+3*x)/(7-49/(37-3*sqrt(114))^(2/3)-(37-3*sqrt(114))^(2/3)+(7+(37-3*sqrt(114))^(2/3))*(4+3*x)/(37-3*sqrt(114))^(1/3)-(4+3*x)^2)-162*(37-3*sqrt(114))^(5/3)*(63307-5819*sqrt(114)+7*(1711-148*sqrt(114))*(37-3*sqrt(114))^(1/3))*sqrt(3/(2395-222*sqrt(114)+49*(37-3*sqrt(114))^(2/3)-14*(37-3*sqrt(114))^(4/3)))*arctan((37-3*sqrt(114)+7*(37-3*sqrt(114))^(1/3)-2*(37-3*sqrt(114))^(2/3)*(4+3*x))/sqrt(7185-666*sqrt(114)+147*(37-3*sqrt(114))^(2/3)-42*(37-3*sqrt(114))^(4/3)))/(7-(37-3*sqrt(114))^(2/3))^2/(49+7*(37-3*sqrt(114))^(2/3)+(37-3*sqrt(114))^(4/3))^3+27*(37-3*sqrt(114))^(7/3)*(49-74*(37-3*sqrt(114))^(1/3)+7*(37-3*sqrt(114))^(2/3))*ln(33-4*sqrt(114)-3*(37-3*sqrt(114))^(1/3)+sqrt(114)*(37-3*sqrt(114))^(1/3)-3*(37-3*sqrt(114))^(2/3)+37*x-3*sqrt(114)*x+7*(37-3*sqrt(114))^(1/3)*x-8*(37-3*sqrt(114))^(2/3)*x-3*(37-3*sqrt(114))^(2/3)*x^2)/(7-(37-3*sqrt(114))^(2/3))^2/(49+7*(37-3*sqrt(114))^(2/3)+(37-3*sqrt(114))^(4/3))^3-54*(37-3*sqrt(114))*(16765-1554*sqrt(114)+49*(37-3*sqrt(114))^(4/3)-74*(37-3*sqrt(114))^(5/3))*ln(7+(37-3*sqrt(114))^(2/3)+(37-3*sqrt(114))^(1/3)*(4+3*x))/(7-(37-3*sqrt(114))^(2/3))^2/(49+7*(37-3*sqrt(114))^(2/3)+(37-3*sqrt(114))^(4/3))^3,1],
[(x^3+4*x^2+3*x+2)^p,x,4,1/3*(4+7/(37-3*sqrt(114))^(1/3)+(37-3*sqrt(114))^(1/3)+3*x)*(x^3+4*x^2+3*x+2)^p*AppellF1(p+1,-p,-p,2+p,2*I*(37-3*sqrt(114))^(1/3)*(4+7/(37-3*sqrt(114))^(1/3)+(37-3*sqrt(114))^(1/3)+3*x)/(21*I+7*sqrt(3)+(3*I-sqrt(3))*(37-3*sqrt(114))^(2/3)),2*I*(37-3*sqrt(114))^(1/3)*(4+7/(37-3*sqrt(114))^(1/3)+(37-3*sqrt(114))^(1/3)+3*x)/(21*I-7*sqrt(3)+(3*I+sqrt(3))*(37-3*sqrt(114))^(2/3)))/(p+1)/((1-2*I*(37-3*sqrt(114))^(1/3)*(4+7/(37-3*sqrt(114))^(1/3)+(37-3*sqrt(114))^(1/3)+3*x)/(21*I+7*sqrt(3)+(3*I-sqrt(3))*(37-3*sqrt(114))^(2/3)))^p)/((1-2*I*(37-3*sqrt(114))^(1/3)*(4+7/(37-3*sqrt(114))^(1/3)+(37-3*sqrt(114))^(1/3)+3*x)/(21*I-7*sqrt(3)+(3*I+sqrt(3))*(37-3*sqrt(114))^(2/3)))^p),1],
[1/d/x^3,x,1,-1/2/d/x^2,1],
[1/(d*x^3+c*x^2),x,3,-1/c/x-d*ln(x)/c^2+d*ln(d*x+c)/c^2,1],
[1/(d*x^3+b*x),x,5,ln(x)/b-1/2*ln(d*x^2+b)/b,1],
[1/(d*x^3+c*x^2+b*x),x,6,c*arctanh((2*d*x+c)/sqrt(-4*b*d+c^2))/b/sqrt(-4*b*d+c^2)+ln(x)/b-1/2*ln(d*x^2+c*x+b)/b,1],
[1/(d*x^3+a),x,6,-arctan((a^(1/3)-2*d^(1/3)*x)/sqrt(3)/a^(1/3))/sqrt(3)/a^(2/3)/d^(1/3)+1/3*ln(a^(1/3)+d^(1/3)*x)/a^(2/3)/d^(1/3)-1/6*ln(a^(2/3)-a^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/a^(2/3)/d^(1/3),1],
[1/sqrt((b*x+a)*(d*x+c)^2),x,3,2*sqrt(b*x+a)*(d*x+c)*arctan(sqrt(d)*sqrt(b*x+a)/sqrt(-a*d+b*c))/sqrt(d)/sqrt(-a*d+b*c)/sqrt((b*x+a)*(d*x+c)^2),1],
[1/sqrt(a*c^2+c*(2*a*d+b*c)*x+d*(a*d+2*b*c)*x^2+b*d^2*x^3),x,3,2*sqrt(b*x+a)*(d*x+c)*arctan(sqrt(d)*sqrt(b*x+a)/sqrt(-a*d+b*c))/sqrt(d)/sqrt(-a*d+b*c)/sqrt(a*c^2+c*(2*a*d+b*c)*x+d*(a*d+2*b*c)*x^2+b*d^2*x^3),1],
[(d*x^3)^p,x,2,x*(d*x^3)^p/(1+3*p),1],
[(d*x^3+c*x^2)^p,x,3,x*(d*x^3+c*x^2)^p*hypergeom([-p, 1+2*p],[2*p+2],-d*x/c)/(1+2*p)/((1+d*x/c)^p),1],
[(d*x^3+b*x)^p,x,3,x*(d*x^3+b*x)^p*hypergeom([-p, 1/2*p+1/2],[3/2+1/2*p],-d*x^2/b)/(p+1)/((1+d*x^2/b)^p),1],
[(d*x^3+c*x^2+b*x)^p,x,3,x*(d*x^3+c*x^2+b*x)^p*AppellF1(p+1,-p,-p,2+p,-2*d*x/(c-sqrt(-4*b*d+c^2)),-2*d*x/(c+sqrt(-4*b*d+c^2)))/(p+1)/((1+2*d*x/(c-sqrt(-4*b*d+c^2)))^p)/((1+2*d*x/(c+sqrt(-4*b*d+c^2)))^p),1],
[(d*x^3+a)^p,x,2,x*(d*x^3+a)^(p+1)*hypergeom([1, 4/3+p],[4/3],-d*x^3/a)/a,1]]: