lst:=[[(d*x+c)^3*(-b^2*x^2+a^2),x,2,-1/4*(-a*d+b*c)*(a*d+b*c)*(d*x+c)^4/d^3+2/5*b^2*c*(d*x+c)^5/d^3-1/6*b^2*(d*x+c)^6/d^3,1],
[(d*x+c)^2*(-b^2*x^2+a^2),x,2,-1/3*(-a*d+b*c)*(a*d+b*c)*(d*x+c)^3/d^3+1/2*b^2*c*(d*x+c)^4/d^3-1/5*b^2*(d*x+c)^5/d^3,1],
[(d*x+c)*(-b^2*x^2+a^2),x,2,a^2*c*x-1/3*b^2*c*x^3-1/4*d*(-b^2*x^2+a^2)^2/b^2,1],
[-b^2*x^2+a^2,x,1,a^2*x-1/3*b^2*x^3,1],
[(-b^2*x^2+a^2)/(d*x+c),x,2,b^2*c*x/d^2-1/2*b^2*x^2/d-(-a^2*d^2+b^2*c^2)*ln(d*x+c)/d^3,1],
[(-b^2*x^2+a^2)/(d*x+c)^2,x,2,-b^2*x/d^2+(-a*d+b*c)*(a*d+b*c)/d^3/(d*x+c)+2*b^2*c*ln(d*x+c)/d^3,1],
[(-b^2*x^2+a^2)/(d*x+c)^3,x,2,1/2*(-a*d+b*c)*(a*d+b*c)/d^3/(d*x+c)^2-2*b^2*c/d^3/(d*x+c)-b^2*ln(d*x+c)/d^3,1],
[(-b^2*x^2+a^2)/(d*x+c)^4,x,2,1/3*(-a*d+b*c)*(a*d+b*c)/d^3/(d*x+c)^3-b^2*c/d^3/(d*x+c)^2+b^2/d^3/(d*x+c),1],
[(-b^2*x^2+a^2)/(d*x+c)^5,x,2,1/4*(-a*d+b*c)*(a*d+b*c)/d^3/(d*x+c)^4-2/3*b^2*c/d^3/(d*x+c)^3+1/2*b^2/d^3/(d*x+c)^2,1],
[(d*x+c)^3*(-b^2*x^2+a^2)^2,x,2,1/4*(-a^2*d^2+b^2*c^2)^2*(d*x+c)^4/d^5-4/5*b^2*c*(-a*d+b*c)*(a*d+b*c)*(d*x+c)^5/d^5+1/3*b^2*(-a^2*d^2+3*b^2*c^2)*(d*x+c)^6/d^5-4/7*b^4*c*(d*x+c)^7/d^5+1/8*b^4*(d*x+c)^8/d^5,1],
[(d*x+c)^2*(-b^2*x^2+a^2)^2,x,2,a^4*c^2*x-1/3*a^2*(-a^2*d^2+2*b^2*c^2)*x^3+1/5*b^2*(-2*a^2*d^2+b^2*c^2)*x^5+1/7*b^4*d^2*x^7-1/3*c*d*(-b^2*x^2+a^2)^3/b^2,1],
[(d*x+c)*(-b^2*x^2+a^2)^2,x,3,a^4*c*x-2/3*a^2*b^2*c*x^3+1/5*b^4*c*x^5-1/6*d*(-b^2*x^2+a^2)^3/b^2,1],
[(-b^2*x^2+a^2)^2,x,2,a^4*x-2/3*a^2*b^2*x^3+1/5*b^4*x^5,1],
[(-b^2*x^2+a^2)^2/(d*x+c),x,2,-b^2*c*(-2*a^2*d^2+b^2*c^2)*x/d^4+1/2*b^2*(-2*a^2*d^2+b^2*c^2)*x^2/d^3-1/3*b^4*c*x^3/d^2+1/4*b^4*x^4/d+(-a^2*d^2+b^2*c^2)^2*ln(d*x+c)/d^5,1],
[(-b^2*x^2+a^2)^2/(d*x+c)^2,x,2,b^2*(-2*a^2*d^2+3*b^2*c^2)*x/d^4-b^4*c*x^2/d^3+1/3*b^4*x^3/d^2-(-a^2*d^2+b^2*c^2)^2/d^5/(d*x+c)-4*b^2*c*(-a*d+b*c)*(a*d+b*c)*ln(d*x+c)/d^5,1],
[(-b^2*x^2+a^2)^2/(d*x+c)^3,x,2,-3*b^4*c*x/d^4+1/2*b^4*x^2/d^3-1/2*(-a^2*d^2+b^2*c^2)^2/d^5/(d*x+c)^2+4*b^2*c*(-a*d+b*c)*(a*d+b*c)/d^5/(d*x+c)+2*b^2*(-a^2*d^2+3*b^2*c^2)*ln(d*x+c)/d^5,1],
[(-b^2*x^2+a^2)^2/(d*x+c)^4,x,2,b^4*x/d^4-1/3*(-a^2*d^2+b^2*c^2)^2/d^5/(d*x+c)^3+2*b^2*c*(-a*d+b*c)*(a*d+b*c)/d^5/(d*x+c)^2-2*b^2*(-a^2*d^2+3*b^2*c^2)/d^5/(d*x+c)-4*b^4*c*ln(d*x+c)/d^5,1],
[(-b^2*x^2+a^2)^2/(d*x+c)^5,x,2,-1/4*(-a^2*d^2+b^2*c^2)^2/d^5/(d*x+c)^4+4/3*b^2*c*(-a*d+b*c)*(a*d+b*c)/d^5/(d*x+c)^3-b^2*(-a^2*d^2+3*b^2*c^2)/d^5/(d*x+c)^2+4*b^4*c/d^5/(d*x+c)+b^4*ln(d*x+c)/d^5,1],
[(-b^2*x^2+a^2)^2/(d*x+c)^6,x,2,-1/5*(-a^2*d^2+b^2*c^2)^2/d^5/(d*x+c)^5+b^2*c*(-a*d+b*c)*(a*d+b*c)/d^5/(d*x+c)^4-2/3*b^2*(-a^2*d^2+3*b^2*c^2)/d^5/(d*x+c)^3+2*b^4*c/d^5/(d*x+c)^2-b^4/d^5/(d*x+c),1],
[(-b^2*x^2+a^2)^2/(d*x+c)^7,x,2,-1/6*(-a^2*d^2+b^2*c^2)^2/d^5/(d*x+c)^6+4/5*b^2*c*(-a*d+b*c)*(a*d+b*c)/d^5/(d*x+c)^5-1/2*b^2*(-a^2*d^2+3*b^2*c^2)/d^5/(d*x+c)^4+4/3*b^4*c/d^5/(d*x+c)^3-1/2*b^4/d^5/(d*x+c)^2,1],
[(d*x+c)^3*(-b^2*x^2+a^2)^3,x,2,a^6*c^3*x-a^4*c*(-a*d+b*c)*(a*d+b*c)*x^3+1/4*a^6*d^3*x^4+3/5*a^2*b^2*c*(-3*a^2*d^2+b^2*c^2)*x^5-1/2*a^4*b^2*d^3*x^6-1/7*b^4*c*(-9*a^2*d^2+b^2*c^2)*x^7+3/8*a^2*b^4*d^3*x^8-1/3*b^6*c*d^2*x^9-1/10*b^6*d^3*x^10-3/8*c^2*d*(-b^2*x^2+a^2)^4/b^2,1],
[(d*x+c)^2*(-b^2*x^2+a^2)^3,x,2,a^6*c^2*x-1/3*a^4*(-a^2*d^2+3*b^2*c^2)*x^3+3/5*a^2*b^2*(-a*d+b*c)*(a*d+b*c)*x^5-1/7*b^4*(-3*a^2*d^2+b^2*c^2)*x^7-1/9*b^6*d^2*x^9-1/4*c*d*(-b^2*x^2+a^2)^4/b^2,1],
[(d*x+c)*(-b^2*x^2+a^2)^3,x,3,a^6*c*x-a^4*b^2*c*x^3+3/5*a^2*b^4*c*x^5-1/7*b^6*c*x^7-1/8*d*(-b^2*x^2+a^2)^4/b^2,1],
[(-b^2*x^2+a^2)^3,x,2,a^6*x-a^4*b^2*x^3+3/5*a^2*b^4*x^5-1/7*b^6*x^7,1],
[(-b^2*x^2+a^2)^3/(d*x+c),x,2,b^2*c*(3*a^4*d^4-3*a^2*b^2*c^2*d^2+b^4*c^4)*x/d^6-1/2*b^2*(3*a^4*d^4-3*a^2*b^2*c^2*d^2+b^4*c^4)*x^2/d^5+1/3*b^4*c*(-3*a^2*d^2+b^2*c^2)*x^3/d^4-1/4*b^4*(-3*a^2*d^2+b^2*c^2)*x^4/d^3+1/5*b^6*c*x^5/d^2-1/6*b^6*x^6/d-(-a^2*d^2+b^2*c^2)^3*ln(d*x+c)/d^7,1],
[(-b^2*x^2+a^2)^3/(d*x+c)^2,x,2,-b^2*(3*a^4*d^4-9*a^2*b^2*c^2*d^2+5*b^4*c^4)*x/d^6+b^4*c*(-3*a^2*d^2+2*b^2*c^2)*x^2/d^5-b^4*(-a*d+b*c)*(a*d+b*c)*x^3/d^4+1/2*b^6*c*x^4/d^3-1/5*b^6*x^5/d^2+(-a^2*d^2+b^2*c^2)^3/d^7/(d*x+c)+6*b^2*c*(-a^2*d^2+b^2*c^2)^2*ln(d*x+c)/d^7,1],
[(-b^2*x^2+a^2)^3/(d*x+c)^3,x,2,b^4*c*(-9*a^2*d^2+10*b^2*c^2)*x/d^6-3/2*b^4*(-a^2*d^2+2*b^2*c^2)*x^2/d^5+b^6*c*x^3/d^4-1/4*b^6*x^4/d^3+1/2*(-a^2*d^2+b^2*c^2)^3/d^7/(d*x+c)^2-6*b^2*c*(-a^2*d^2+b^2*c^2)^2/d^7/(d*x+c)-3*b^2*(a^4*d^4-6*a^2*b^2*c^2*d^2+5*b^4*c^4)*ln(d*x+c)/d^7,1],
[(d*x+c)^4/(-b^2*x^2+a^2),x,2,-d^2*(a^2*d^2+6*b^2*c^2)*x/b^4-2*c*d^3*x^2/b^2-1/3*d^4*x^3/b^2-1/2*(a*d+b*c)^4*ln(-b*x+a)/a/b^5+1/2*(-a*d+b*c)^4*ln(b*x+a)/a/b^5,1],
[(d*x+c)^3/(-b^2*x^2+a^2),x,2,-3*c*d^2*x/b^2-1/2*d^3*x^2/b^2-1/2*(a*d+b*c)^3*ln(-b*x+a)/a/b^4+1/2*(-a*d+b*c)^3*ln(b*x+a)/a/b^4,1],
[(d*x+c)^2/(-b^2*x^2+a^2),x,2,-d^2*x/b^2-1/2*(a*d+b*c)^2*ln(-b*x+a)/a/b^3+1/2*(-a*d+b*c)^2*ln(b*x+a)/a/b^3,1],
[(d*x+c)/(-b^2*x^2+a^2),x,3,-1/2*(b*c/a+d)*ln(-b*x+a)/b^2+1/2*(b*c/a-d)*ln(b*x+a)/b^2,1],
[1/(-b^2*x^2+a^2),x,1,arctanh(b*x/a)/a/b,1],
[1/(d*x+c)/(-b^2*x^2+a^2),x,2,-1/2*ln(-b*x+a)/a/(a*d+b*c)+1/2*ln(b*x+a)/a/(-a*d+b*c)-d*ln(d*x+c)/(-a^2*d^2+b^2*c^2),1],
[1/(d*x+c)^2/(-b^2*x^2+a^2),x,2,d/(-a^2*d^2+b^2*c^2)/(d*x+c)-1/2*b*ln(-b*x+a)/a/(a*d+b*c)^2+1/2*b*ln(b*x+a)/a/(-a*d+b*c)^2-2*b^2*c*d*ln(d*x+c)/(-a^2*d^2+b^2*c^2)^2,1],
[1/(d*x+c)^3/(-b^2*x^2+a^2),x,2,1/2*d/(-a^2*d^2+b^2*c^2)/(d*x+c)^2+2*b^2*c*d/(-a^2*d^2+b^2*c^2)^2/(d*x+c)-1/2*b^2*ln(-b*x+a)/a/(a*d+b*c)^3+1/2*b^2*ln(b*x+a)/a/(-a*d+b*c)^3-b^2*d*(a^2*d^2+3*b^2*c^2)*ln(d*x+c)/(-a^2*d^2+b^2*c^2)^3,1],
[(d*x+c)^4/(-b^2*x^2+a^2)^2,x,2,d^4*x/b^4+1/4*(a*d+b*c)^4/a^2/b^5/(-b*x+a)-1/4*(-a*d+b*c)^4/a^2/b^5/(b*x+a)-1/4*(-3*a*d+b*c)*(a*d+b*c)^3*ln(-b*x+a)/a^3/b^5+1/4*(-a*d+b*c)^3*(3*a*d+b*c)*ln(b*x+a)/a^3/b^5,1],
[(d*x+c)^3/(-b^2*x^2+a^2)^2,x,2,1/4*(a*d+b*c)^3/a^2/b^4/(-b*x+a)-1/4*(-a*d+b*c)^3/a^2/b^4/(b*x+a)-1/4*(-2*a*d+b*c)*(a*d+b*c)^2*ln(-b*x+a)/a^3/b^4+1/4*(-a*d+b*c)^2*(2*a*d+b*c)*ln(b*x+a)/a^3/b^4,1],
[(d*x+c)^2/(-b^2*x^2+a^2)^2,x,2,1/2*(2*a^2*c*d+(a^2*d^2+b^2*c^2)*x)/a^2/b^2/(-b^2*x^2+a^2)+1/2*(-a*d+b*c)*(a*d+b*c)*arctanh(b*x/a)/a^3/b^3,1],
[(d*x+c)/(-b^2*x^2+a^2)^2,x,2,1/2*(b^2*c*x+a^2*d)/a^2/b^2/(-b^2*x^2+a^2)+1/2*c*arctanh(b*x/a)/a^3/b,1],
[1/(-b^2*x^2+a^2)^2,x,2,1/2*x/a^2/(-b^2*x^2+a^2)+1/2*arctanh(b*x/a)/a^3/b,1],
[1/(d*x+c)/(-b^2*x^2+a^2)^2,x,2,1/4/a^2/(a*d+b*c)/(-b*x+a)-1/4/a^2/(-a*d+b*c)/(b*x+a)-1/4*(2*a*d+b*c)*ln(-b*x+a)/a^3/(a*d+b*c)^2+1/4*(-2*a*d+b*c)*ln(b*x+a)/a^3/(-a*d+b*c)^2+d^3*ln(d*x+c)/(-a^2*d^2+b^2*c^2)^2,1],
[1/(d*x+c)^2/(-b^2*x^2+a^2)^2,x,2,1/4*b/a^2/(a*d+b*c)^2/(-b*x+a)-1/4*b/a^2/(-a*d+b*c)^2/(b*x+a)-d^3/(-a^2*d^2+b^2*c^2)^2/(d*x+c)-1/4*b*(3*a*d+b*c)*ln(-b*x+a)/a^3/(a*d+b*c)^3+1/4*b*(-3*a*d+b*c)*ln(b*x+a)/a^3/(-a*d+b*c)^3+4*b^2*c*d^3*ln(d*x+c)/(-a^2*d^2+b^2*c^2)^3,1],
[1/(d*x+c)^3/(-b^2*x^2+a^2)^2,x,2,1/4*b^2/a^2/(a*d+b*c)^3/(-b*x+a)-1/4*b^2/a^2/(-a*d+b*c)^3/(b*x+a)-1/2*d^3/(-a^2*d^2+b^2*c^2)^2/(d*x+c)^2-4*b^2*c*d^3/(-a^2*d^2+b^2*c^2)^3/(d*x+c)-1/4*b^2*(4*a*d+b*c)*ln(-b*x+a)/a^3/(a*d+b*c)^4+1/4*b^2*(-4*a*d+b*c)*ln(b*x+a)/a^3/(-a*d+b*c)^4+2*b^2*d^3*(a^2*d^2+5*b^2*c^2)*ln(d*x+c)/(-a^2*d^2+b^2*c^2)^4,1],
[(d*x+c)^4/(-b^2*x^2+a^2)^3,x,3,1/4*(4*a^2*b^2*c*d*(c^2+a^2*d^2/b^2)+(a^4*d^4+6*a^2*b^2*c^2*d^2+b^4*c^4)*x)/a^2/b^4/(-b^2*x^2+a^2)^2-1/8*(16*a^4*c*d^3-(-5*a^4*d^4-6*a^2*b^2*c^2*d^2+3*b^4*c^4)*x)/a^4/b^4/(-b^2*x^2+a^2)+3/8*(-a^2*d^2+b^2*c^2)^2*arctanh(b*x/a)/a^5/b^5,1],
[(d*x+c)^3/(-b^2*x^2+a^2)^3,x,3,1/4*(a^2*d*(3*c^2+a^2*d^2/b^2)+c*(3*a^2*d^2+b^2*c^2)*x)/a^2/b^2/(-b^2*x^2+a^2)^2-1/8*(4*a^4*d^3-3*b^2*c*(-a*d+b*c)*(a*d+b*c)*x)/a^4/b^4/(-b^2*x^2+a^2)+3/8*c*(c^2-a^2*d^2/b^2)*arctanh(b*x/a)/a^5/b,1],
[(d*x+c)^2/(-b^2*x^2+a^2)^3,x,3,1/4*(2*a^2*c*d+(a^2*d^2+b^2*c^2)*x)/a^2/b^2/(-b^2*x^2+a^2)^2+1/8*(-a^2*d^2+3*b^2*c^2)*x/a^4/b^2/(-b^2*x^2+a^2)+1/8*(-a^2*d^2+3*b^2*c^2)*arctanh(b*x/a)/a^5/b^3,1],
[(d*x+c)/(-b^2*x^2+a^2)^3,x,3,1/4*(b^2*c*x+a^2*d)/a^2/b^2/(-b^2*x^2+a^2)^2+3/8*c*x/a^4/(-b^2*x^2+a^2)+3/8*c*arctanh(b*x/a)/a^5/b,1],
[1/(-b^2*x^2+a^2)^3,x,3,1/4*x/a^2/(-b^2*x^2+a^2)^2+3/8*x/a^4/(-b^2*x^2+a^2)+3/8*arctanh(b*x/a)/a^5/b,1],
[1/(d*x+c)/(-b^2*x^2+a^2)^3,x,2,1/16/a^3/(a*d+b*c)/(-b*x+a)^2+1/16*(5*a*d+3*b*c)/a^4/(a*d+b*c)^2/(-b*x+a)-1/16/a^3/(-a*d+b*c)/(b*x+a)^2-1/16*(-5*a*d+3*b*c)/a^4/(-a*d+b*c)^2/(b*x+a)-1/16*(8*a^2*d^2+9*a*b*c*d+3*b^2*c^2)*ln(-b*x+a)/a^5/(a*d+b*c)^3+1/16*(8*a^2*d^2-9*a*b*c*d+3*b^2*c^2)*ln(b*x+a)/a^5/(-a*d+b*c)^3-d^5*ln(d*x+c)/(-a^2*d^2+b^2*c^2)^3,1],
[1/(d*x+c)^2/(-b^2*x^2+a^2)^3,x,2,1/16*b/a^3/(a*d+b*c)^2/(-b*x+a)^2+1/16*b*(7*a*d+3*b*c)/a^4/(a*d+b*c)^3/(-b*x+a)-1/16*b/a^3/(-a*d+b*c)^2/(b*x+a)^2-1/16*b*(-7*a*d+3*b*c)/a^4/(-a*d+b*c)^3/(b*x+a)+d^5/(-a^2*d^2+b^2*c^2)^3/(d*x+c)-3/16*b*(5*a^2*d^2+4*a*b*c*d+b^2*c^2)*ln(-b*x+a)/a^5/(a*d+b*c)^4+3/16*b*(5*a^2*d^2-4*a*b*c*d+b^2*c^2)*ln(b*x+a)/a^5/(-a*d+b*c)^4-6*b^2*c*d^5*ln(d*x+c)/(-a^2*d^2+b^2*c^2)^4,1],
[1/(d*x+c)^3/(-b^2*x^2+a^2)^3,x,2,1/16*b^2/a^3/(a*d+b*c)^3/(-b*x+a)^2+3/16*b^2*(3*a*d+b*c)/a^4/(a*d+b*c)^4/(-b*x+a)-1/16*b^2/a^3/(-a*d+b*c)^3/(b*x+a)^2-3/16*b^2*(-3*a*d+b*c)/a^4/(-a*d+b*c)^4/(b*x+a)+1/2*d^5/(-a^2*d^2+b^2*c^2)^3/(d*x+c)^2+6*b^2*c*d^5/(-a^2*d^2+b^2*c^2)^4/(d*x+c)-3/16*b^2*(8*a^2*d^2+5*a*b*c*d+b^2*c^2)*ln(-b*x+a)/a^5/(a*d+b*c)^5+3/16*b^2*(8*a^2*d^2-5*a*b*c*d+b^2*c^2)*ln(b*x+a)/a^5/(-a*d+b*c)^5-3*b^2*d^5*(a^2*d^2+7*b^2*c^2)*ln(d*x+c)/(-a^2*d^2+b^2*c^2)^5,1],
[(e*x+d)^4*(c*x^2+a),x,2,1/5*(a*e^2+c*d^2)*(e*x+d)^5/e^3-1/3*c*d*(e*x+d)^6/e^3+1/7*c*(e*x+d)^7/e^3,1],
[(e*x+d)^3*(c*x^2+a),x,2,1/4*(a*e^2+c*d^2)*(e*x+d)^4/e^3-2/5*c*d*(e*x+d)^5/e^3+1/6*c*(e*x+d)^6/e^3,1],
[(e*x+d)^2*(c*x^2+a),x,2,1/3*(a*e^2+c*d^2)*(e*x+d)^3/e^3-1/2*c*d*(e*x+d)^4/e^3+1/5*c*(e*x+d)^5/e^3,1],
[(e*x+d)*(c*x^2+a),x,2,a*d*x+1/3*c*d*x^3+1/4*e*(c*x^2+a)^2/c,1],
[(c*x^2+a)/(e*x+d),x,2,-c*d*x/e^2+1/2*c*x^2/e+(a*e^2+c*d^2)*ln(e*x+d)/e^3,1],
[(c*x^2+a)/(e*x+d)^2,x,2,c*x/e^2-(a*e^2+c*d^2)/e^3/(e*x+d)-2*c*d*ln(e*x+d)/e^3,1],
[(c*x^2+a)/(e*x+d)^3,x,2,1/2*(-a*e^2-c*d^2)/e^3/(e*x+d)^2+2*c*d/e^3/(e*x+d)+c*ln(e*x+d)/e^3,1],
[(c*x^2+a)/(e*x+d)^4,x,2,1/3*(-a*e^2-c*d^2)/e^3/(e*x+d)^3+c*d/e^3/(e*x+d)^2-c/e^3/(e*x+d),1],
[(c*x^2+a)/(e*x+d)^5,x,2,1/4*(-a*e^2-c*d^2)/e^3/(e*x+d)^4+2/3*c*d/e^3/(e*x+d)^3-1/2*c/e^3/(e*x+d)^2,1],
[(e*x+d)^4*(c*x^2+a)^2,x,2,1/5*(a*e^2+c*d^2)^2*(e*x+d)^5/e^5-2/3*c*d*(a*e^2+c*d^2)*(e*x+d)^6/e^5+2/7*c*(a*e^2+3*c*d^2)*(e*x+d)^7/e^5-1/2*c^2*d*(e*x+d)^8/e^5+1/9*c^2*(e*x+d)^9/e^5,1],
[(e*x+d)^3*(c*x^2+a)^2,x,2,1/4*(a*e^2+c*d^2)^2*(e*x+d)^4/e^5-4/5*c*d*(a*e^2+c*d^2)*(e*x+d)^5/e^5+1/3*c*(a*e^2+3*c*d^2)*(e*x+d)^6/e^5-4/7*c^2*d*(e*x+d)^7/e^5+1/8*c^2*(e*x+d)^8/e^5,1],
[(e*x+d)^2*(c*x^2+a)^2,x,2,a^2*d^2*x+1/3*a*(a*e^2+2*c*d^2)*x^3+1/5*c*(2*a*e^2+c*d^2)*x^5+1/7*c^2*e^2*x^7+1/3*d*e*(c*x^2+a)^3/c,1],
[(e*x+d)*(c*x^2+a)^2,x,3,a^2*d*x+2/3*a*c*d*x^3+1/5*c^2*d*x^5+1/6*e*(c*x^2+a)^3/c,1],
[(c*x^2+a)^2/(e*x+d),x,2,-c*d*(2*a*e^2+c*d^2)*x/e^4+1/2*c*(2*a*e^2+c*d^2)*x^2/e^3-1/3*c^2*d*x^3/e^2+1/4*c^2*x^4/e+(a*e^2+c*d^2)^2*ln(e*x+d)/e^5,1],
[(c*x^2+a)^2/(e*x+d)^2,x,2,c*(2*a*e^2+3*c*d^2)*x/e^4-c^2*d*x^2/e^3+1/3*c^2*x^3/e^2-(a*e^2+c*d^2)^2/e^5/(e*x+d)-4*c*d*(a*e^2+c*d^2)*ln(e*x+d)/e^5,1],
[(c*x^2+a)^2/(e*x+d)^3,x,2,-3*c^2*d*x/e^4+1/2*c^2*x^2/e^3-1/2*(a*e^2+c*d^2)^2/e^5/(e*x+d)^2+4*c*d*(a*e^2+c*d^2)/e^5/(e*x+d)+2*c*(a*e^2+3*c*d^2)*ln(e*x+d)/e^5,1],
[(c*x^2+a)^2/(e*x+d)^4,x,2,c^2*x/e^4-1/3*(a*e^2+c*d^2)^2/e^5/(e*x+d)^3+2*c*d*(a*e^2+c*d^2)/e^5/(e*x+d)^2-2*c*(a*e^2+3*c*d^2)/e^5/(e*x+d)-4*c^2*d*ln(e*x+d)/e^5,1],
[(c*x^2+a)^2/(e*x+d)^5,x,2,-1/4*(a*e^2+c*d^2)^2/e^5/(e*x+d)^4+4/3*c*d*(a*e^2+c*d^2)/e^5/(e*x+d)^3-c*(a*e^2+3*c*d^2)/e^5/(e*x+d)^2+4*c^2*d/e^5/(e*x+d)+c^2*ln(e*x+d)/e^5,1],
[(c*x^2+a)^2/(e*x+d)^6,x,2,-1/5*(a*e^2+c*d^2)^2/e^5/(e*x+d)^5+c*d*(a*e^2+c*d^2)/e^5/(e*x+d)^4-2/3*c*(a*e^2+3*c*d^2)/e^5/(e*x+d)^3+2*c^2*d/e^5/(e*x+d)^2-c^2/e^5/(e*x+d),1],
[(c*x^2+a)^2/(e*x+d)^7,x,2,-1/6*(a*e^2+c*d^2)^2/e^5/(e*x+d)^6+4/5*c*d*(a*e^2+c*d^2)/e^5/(e*x+d)^5-1/2*c*(a*e^2+3*c*d^2)/e^5/(e*x+d)^4+4/3*c^2*d/e^5/(e*x+d)^3-1/2*c^2/e^5/(e*x+d)^2,1],
[(c*x^2+a)^2/(e*x+d)^8,x,2,-1/7*(a*e^2+c*d^2)^2/e^5/(e*x+d)^7+2/3*c*d*(a*e^2+c*d^2)/e^5/(e*x+d)^6-2/5*c*(a*e^2+3*c*d^2)/e^5/(e*x+d)^5+c^2*d/e^5/(e*x+d)^4-1/3*c^2/e^5/(e*x+d)^3,1],
[(e*x+d)^6*(c*x^2+a)^3,x,2,1/7*(a*e^2+c*d^2)^3*(e*x+d)^7/e^7-3/4*c*d*(a*e^2+c*d^2)^2*(e*x+d)^8/e^7+1/3*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)*(e*x+d)^9/e^7-2/5*c^2*d*(3*a*e^2+5*c*d^2)*(e*x+d)^10/e^7+3/11*c^2*(a*e^2+5*c*d^2)*(e*x+d)^11/e^7-1/2*c^3*d*(e*x+d)^12/e^7+1/13*c^3*(e*x+d)^13/e^7,1],
[(e*x+d)^5*(c*x^2+a)^3,x,2,1/6*(a*e^2+c*d^2)^3*(e*x+d)^6/e^7-6/7*c*d*(a*e^2+c*d^2)^2*(e*x+d)^7/e^7+3/8*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)*(e*x+d)^8/e^7-4/9*c^2*d*(3*a*e^2+5*c*d^2)*(e*x+d)^9/e^7+3/10*c^2*(a*e^2+5*c*d^2)*(e*x+d)^10/e^7-6/11*c^3*d*(e*x+d)^11/e^7+1/12*c^3*(e*x+d)^12/e^7,1],
[(e*x+d)^4*(c*x^2+a)^3,x,2,1/5*(a*e^2+c*d^2)^3*(e*x+d)^5/e^7-c*d*(a*e^2+c*d^2)^2*(e*x+d)^6/e^7+3/7*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)*(e*x+d)^7/e^7-1/2*c^2*d*(3*a*e^2+5*c*d^2)*(e*x+d)^8/e^7+1/3*c^2*(a*e^2+5*c*d^2)*(e*x+d)^9/e^7-3/5*c^3*d*(e*x+d)^10/e^7+1/11*c^3*(e*x+d)^11/e^7,1],
[(e*x+d)^3*(c*x^2+a)^3,x,2,a^3*d^3*x+a^2*d*(a*e^2+c*d^2)*x^3+1/4*a^3*e^3*x^4+3/5*a*c*d*(3*a*e^2+c*d^2)*x^5+1/2*a^2*c*e^3*x^6+1/7*c^2*d*(9*a*e^2+c*d^2)*x^7+3/8*a*c^2*e^3*x^8+1/3*c^3*d*e^2*x^9+1/10*c^3*e^3*x^10+3/8*d^2*e*(c*x^2+a)^4/c,1],
[(e*x+d)^2*(c*x^2+a)^3,x,2,a^3*d^2*x+1/3*a^2*(a*e^2+3*c*d^2)*x^3+3/5*a*c*(a*e^2+c*d^2)*x^5+1/7*c^2*(3*a*e^2+c*d^2)*x^7+1/9*c^3*e^2*x^9+1/4*d*e*(c*x^2+a)^4/c,1],
[(e*x+d)*(c*x^2+a)^3,x,3,a^3*d*x+a^2*c*d*x^3+3/5*a*c^2*d*x^5+1/7*c^3*d*x^7+1/8*e*(c*x^2+a)^4/c,1],
[(c*x^2+a)^3/(e*x+d),x,2,-c*d*(3*a^2*e^4+3*a*c*d^2*e^2+c^2*d^4)*x/e^6+1/2*c*(3*a^2*e^4+3*a*c*d^2*e^2+c^2*d^4)*x^2/e^5-1/3*c^2*d*(3*a*e^2+c*d^2)*x^3/e^4+1/4*c^2*(3*a*e^2+c*d^2)*x^4/e^3-1/5*c^3*d*x^5/e^2+1/6*c^3*x^6/e+(a*e^2+c*d^2)^3*ln(e*x+d)/e^7,1],
[(c*x^2+a)^3/(e*x+d)^2,x,2,c*(3*a^2*e^4+9*a*c*d^2*e^2+5*c^2*d^4)*x/e^6-c^2*d*(3*a*e^2+2*c*d^2)*x^2/e^5+c^2*(a*e^2+c*d^2)*x^3/e^4-1/2*c^3*d*x^4/e^3+1/5*c^3*x^5/e^2-(a*e^2+c*d^2)^3/e^7/(e*x+d)-6*c*d*(a*e^2+c*d^2)^2*ln(e*x+d)/e^7,1],
[(c*x^2+a)^3/(e*x+d)^3,x,2,-c^2*d*(9*a*e^2+10*c*d^2)*x/e^6+3/2*c^2*(a*e^2+2*c*d^2)*x^2/e^5-c^3*d*x^3/e^4+1/4*c^3*x^4/e^3-1/2*(a*e^2+c*d^2)^3/e^7/(e*x+d)^2+6*c*d*(a*e^2+c*d^2)^2/e^7/(e*x+d)+3*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)*ln(e*x+d)/e^7,1],
[(c*x^2+a)^3/(e*x+d)^4,x,2,c^2*(3*a*e^2+10*c*d^2)*x/e^6-2*c^3*d*x^2/e^5+1/3*c^3*x^3/e^4-1/3*(a*e^2+c*d^2)^3/e^7/(e*x+d)^3+3*c*d*(a*e^2+c*d^2)^2/e^7/(e*x+d)^2-3*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)/e^7/(e*x+d)-4*c^2*d*(3*a*e^2+5*c*d^2)*ln(e*x+d)/e^7,1],
[(c*x^2+a)^3/(e*x+d)^5,x,2,-5*c^3*d*x/e^6+1/2*c^3*x^2/e^5-1/4*(a*e^2+c*d^2)^3/e^7/(e*x+d)^4+2*c*d*(a*e^2+c*d^2)^2/e^7/(e*x+d)^3-3/2*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)/e^7/(e*x+d)^2+4*c^2*d*(3*a*e^2+5*c*d^2)/e^7/(e*x+d)+3*c^2*(a*e^2+5*c*d^2)*ln(e*x+d)/e^7,1],
[(c*x^2+a)^3/(e*x+d)^6,x,2,c^3*x/e^6-1/5*(a*e^2+c*d^2)^3/e^7/(e*x+d)^5+3/2*c*d*(a*e^2+c*d^2)^2/e^7/(e*x+d)^4-c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)/e^7/(e*x+d)^3+2*c^2*d*(3*a*e^2+5*c*d^2)/e^7/(e*x+d)^2-3*c^2*(a*e^2+5*c*d^2)/e^7/(e*x+d)-6*c^3*d*ln(e*x+d)/e^7,1],
[(c*x^2+a)^3/(e*x+d)^7,x,2,-1/6*(a*e^2+c*d^2)^3/e^7/(e*x+d)^6+6/5*c*d*(a*e^2+c*d^2)^2/e^7/(e*x+d)^5-3/4*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)/e^7/(e*x+d)^4+4/3*c^2*d*(3*a*e^2+5*c*d^2)/e^7/(e*x+d)^3-3/2*c^2*(a*e^2+5*c*d^2)/e^7/(e*x+d)^2+6*c^3*d/e^7/(e*x+d)+c^3*ln(e*x+d)/e^7,1],
[(c*x^2+a)^3/(e*x+d)^8,x,2,-1/7*(a*e^2+c*d^2)^3/e^7/(e*x+d)^7+c*d*(a*e^2+c*d^2)^2/e^7/(e*x+d)^6-3/5*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)/e^7/(e*x+d)^5+c^2*d*(3*a*e^2+5*c*d^2)/e^7/(e*x+d)^4-c^2*(a*e^2+5*c*d^2)/e^7/(e*x+d)^3+3*c^3*d/e^7/(e*x+d)^2-c^3/e^7/(e*x+d),1],
[(c*x^2+a)^3/(e*x+d)^9,x,2,-1/8*(a*e^2+c*d^2)^3/e^7/(e*x+d)^8+6/7*c*d*(a*e^2+c*d^2)^2/e^7/(e*x+d)^7-1/2*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)/e^7/(e*x+d)^6+4/5*c^2*d*(3*a*e^2+5*c*d^2)/e^7/(e*x+d)^5-3/4*c^2*(a*e^2+5*c*d^2)/e^7/(e*x+d)^4+2*c^3*d/e^7/(e*x+d)^3-1/2*c^3/e^7/(e*x+d)^2,1],
[(c*x^2+a)^3/(e*x+d)^10,x,2,-1/9*(a*e^2+c*d^2)^3/e^7/(e*x+d)^9+3/4*c*d*(a*e^2+c*d^2)^2/e^7/(e*x+d)^8-3/7*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)/e^7/(e*x+d)^7+2/3*c^2*d*(3*a*e^2+5*c*d^2)/e^7/(e*x+d)^6-3/5*c^2*(a*e^2+5*c*d^2)/e^7/(e*x+d)^5+3/2*c^3*d/e^7/(e*x+d)^4-1/3*c^3/e^7/(e*x+d)^3,1],
[(e*x+d)^7*(c*x^2+a)^4,x,2,1/8*(a*e^2+c*d^2)^4*(e*x+d)^8/e^9-8/9*c*d*(a*e^2+c*d^2)^3*(e*x+d)^9/e^9+2/5*c*(a*e^2+c*d^2)^2*(a*e^2+7*c*d^2)*(e*x+d)^10/e^9-8/11*c^2*d*(a*e^2+c*d^2)*(3*a*e^2+7*c*d^2)*(e*x+d)^11/e^9+1/6*c^2*(3*a^2*e^4+30*a*c*d^2*e^2+35*c^2*d^4)*(e*x+d)^12/e^9-8/13*c^3*d*(3*a*e^2+7*c*d^2)*(e*x+d)^13/e^9+2/7*c^3*(a*e^2+7*c*d^2)*(e*x+d)^14/e^9-8/15*c^4*d*(e*x+d)^15/e^9+1/16*c^4*(e*x+d)^16/e^9,1],
[(e*x+d)^6*(c*x^2+a)^4,x,2,1/7*(a*e^2+c*d^2)^4*(e*x+d)^7/e^9-c*d*(a*e^2+c*d^2)^3*(e*x+d)^8/e^9+4/9*c*(a*e^2+c*d^2)^2*(a*e^2+7*c*d^2)*(e*x+d)^9/e^9-4/5*c^2*d*(a*e^2+c*d^2)*(3*a*e^2+7*c*d^2)*(e*x+d)^10/e^9+2/11*c^2*(3*a^2*e^4+30*a*c*d^2*e^2+35*c^2*d^4)*(e*x+d)^11/e^9-2/3*c^3*d*(3*a*e^2+7*c*d^2)*(e*x+d)^12/e^9+4/13*c^3*(a*e^2+7*c*d^2)*(e*x+d)^13/e^9-4/7*c^4*d*(e*x+d)^14/e^9+1/15*c^4*(e*x+d)^15/e^9,1],
[(e*x+d)^5*(c*x^2+a)^4,x,2,1/6*(a*e^2+c*d^2)^4*(e*x+d)^6/e^9-8/7*c*d*(a*e^2+c*d^2)^3*(e*x+d)^7/e^9+1/2*c*(a*e^2+c*d^2)^2*(a*e^2+7*c*d^2)*(e*x+d)^8/e^9-8/9*c^2*d*(a*e^2+c*d^2)*(3*a*e^2+7*c*d^2)*(e*x+d)^9/e^9+1/5*c^2*(3*a^2*e^4+30*a*c*d^2*e^2+35*c^2*d^4)*(e*x+d)^10/e^9-8/11*c^3*d*(3*a*e^2+7*c*d^2)*(e*x+d)^11/e^9+1/3*c^3*(a*e^2+7*c*d^2)*(e*x+d)^12/e^9-8/13*c^4*d*(e*x+d)^13/e^9+1/14*c^4*(e*x+d)^14/e^9,1],
[(e*x+d)^4*(c*x^2+a)^4,x,2,a^4*d^4*x+2/3*a^3*d^2*(3*a*e^2+2*c*d^2)*x^3+a^4*d*e^3*x^4+1/5*a^2*(a^2*e^4+24*a*c*d^2*e^2+6*c^2*d^4)*x^5+8/3*a^3*c*d*e^3*x^6+4/7*a*c*(a^2*e^4+9*a*c*d^2*e^2+c^2*d^4)*x^7+3*a^2*c^2*d*e^3*x^8+1/9*c^2*(6*a^2*e^4+24*a*c*d^2*e^2+c^2*d^4)*x^9+8/5*a*c^3*d*e^3*x^10+2/11*c^3*e^2*(2*a*e^2+3*c*d^2)*x^11+1/3*c^4*d*e^3*x^12+1/13*c^4*e^4*x^13+2/5*d^3*e*(c*x^2+a)^5/c,1],
[(e*x+d)^3*(c*x^2+a)^4,x,2,a^4*d^3*x+1/3*a^3*d*(3*a*e^2+4*c*d^2)*x^3+1/4*a^4*e^3*x^4+6/5*a^2*c*d*(2*a*e^2+c*d^2)*x^5+2/3*a^3*c*e^3*x^6+2/7*a*c^2*d*(9*a*e^2+2*c*d^2)*x^7+3/4*a^2*c^2*e^3*x^8+1/9*c^3*d*(12*a*e^2+c*d^2)*x^9+2/5*a*c^3*e^3*x^10+3/11*c^4*d*e^2*x^11+1/12*c^4*e^3*x^12+3/10*d^2*e*(c*x^2+a)^5/c,1],
[(e*x+d)^2*(c*x^2+a)^4,x,2,a^4*d^2*x+1/3*a^3*(a*e^2+4*c*d^2)*x^3+2/5*a^2*c*(2*a*e^2+3*c*d^2)*x^5+2/7*a*c^2*(3*a*e^2+2*c*d^2)*x^7+1/9*c^3*(4*a*e^2+c*d^2)*x^9+1/11*c^4*e^2*x^11+1/5*d*e*(c*x^2+a)^5/c,1],
[(e*x+d)*(c*x^2+a)^4,x,3,a^4*d*x+4/3*a^3*c*d*x^3+6/5*a^2*c^2*d*x^5+4/7*a*c^3*d*x^7+1/9*c^4*d*x^9+1/10*e*(c*x^2+a)^5/c,1],
[(c*x^2+a)^4/(e*x+d),x,2,-8*c*d*(a*e^2+c*d^2)^3*x/e^8+2*c*(a*e^2+c*d^2)^2*(a*e^2+7*c*d^2)*(e*x+d)^2/e^9-8/3*c^2*d*(a*e^2+c*d^2)*(3*a*e^2+7*c*d^2)*(e*x+d)^3/e^9+1/2*c^2*(3*a^2*e^4+30*a*c*d^2*e^2+35*c^2*d^4)*(e*x+d)^4/e^9-8/5*c^3*d*(3*a*e^2+7*c*d^2)*(e*x+d)^5/e^9+2/3*c^3*(a*e^2+7*c*d^2)*(e*x+d)^6/e^9-8/7*c^4*d*(e*x+d)^7/e^9+1/8*c^4*(e*x+d)^8/e^9+(a*e^2+c*d^2)^4*ln(e*x+d)/e^9,1],
[(c*x^2+a)^4/(e*x+d)^2,x,2,c*(4*a^3*e^6+18*a^2*c*d^2*e^4+20*a*c^2*d^4*e^2+7*c^3*d^6)*x/e^8-c^2*d*(6*a^2*e^4+8*a*c*d^2*e^2+3*c^2*d^4)*x^2/e^7+1/3*c^2*(6*a^2*e^4+12*a*c*d^2*e^2+5*c^2*d^4)*x^3/e^6-c^3*d*(2*a*e^2+c*d^2)*x^4/e^5+1/5*c^3*(4*a*e^2+3*c*d^2)*x^5/e^4-1/3*c^4*d*x^6/e^3+1/7*c^4*x^7/e^2-(a*e^2+c*d^2)^4/e^9/(e*x+d)-8*c*d*(a*e^2+c*d^2)^3*ln(e*x+d)/e^9,1],
[(x^2+2)/(2+x),x,2,-2*x+1/2*x^2+6*ln(2+x),1],
[(x^2-4)/(2+x),x,2,1/2*(2-x)^2,1],
[(4*x^2-7)/(3+2*x),x,2,-3*x+x^2+ln(3+2*x),1],
[(x^2+1)/(1+x),x,2,-x+1/2*x^2+2*ln(1+x),1],
[(e*x+d)^4/(c*x^2+a),x,5,e^2*(-a*e^2+6*c*d^2)*x/c^2+2*d*e^3*x^2/c+1/3*e^4*x^3/c+(a^2*e^4-6*a*c*d^2*e^2+c^2*d^4)*arctan(sqrt(c)*x/sqrt(a))/sqrt(a)/c^(5/2)+2*d*e*(-a*e^2+c*d^2)*ln(c*x^2+a)/c^2,1],
[(e*x+d)^3/(c*x^2+a),x,5,3*d*e^2*x/c+1/2*e^3*x^2/c+d*(-3*a*e^2+c*d^2)*arctan(sqrt(c)*x/sqrt(a))/sqrt(a)/c^(3/2)+1/2*e*(-a*e^2+3*c*d^2)*ln(c*x^2+a)/c^2,1],
[(e*x+d)^2/(c*x^2+a),x,5,e^2*x/c+(-a*e^2+c*d^2)*arctan(sqrt(c)*x/sqrt(a))/sqrt(a)/c^(3/2)+d*e*ln(c*x^2+a)/c,1],
[(e*x+d)/(c*x^2+a),x,3,d*arctan(sqrt(c)*x/sqrt(a))/sqrt(a)/sqrt(c)+1/2*e*ln(c*x^2+a)/c,1],
[1/(e*x+d)/(c*x^2+a),x,5,sqrt(c)*d*arctan(sqrt(c)*x/sqrt(a))/sqrt(a)/(a*e^2+c*d^2)+e*ln(e*x+d)/(a*e^2+c*d^2)-e*ln(c*x^2+a)/(2*a*e^2+2*c*d^2),1],
[1/(e*x+d)^2/(c*x^2+a),x,5,-e/(a*e^2+c*d^2)/(e*x+d)+sqrt(c)*(-a*e^2+c*d^2)*arctan(sqrt(c)*x/sqrt(a))/sqrt(a)/(a*e^2+c*d^2)^2+2*c*d*e*ln(e*x+d)/(a*e^2+c*d^2)^2-c*d*e*ln(c*x^2+a)/(a*e^2+c*d^2)^2,1],
[1/(e*x+d)^3/(c*x^2+a),x,5,-1/2*e/(a*e^2+c*d^2)/(e*x+d)^2-2*c*d*e/(a*e^2+c*d^2)^2/(e*x+d)+c^(3/2)*d*(-3*a*e^2+c*d^2)*arctan(sqrt(c)*x/sqrt(a))/sqrt(a)/(a*e^2+c*d^2)^3+c*e*(-a*e^2+3*c*d^2)*ln(e*x+d)/(a*e^2+c*d^2)^3-1/2*c*e*(-a*e^2+3*c*d^2)*ln(c*x^2+a)/(a*e^2+c*d^2)^3,1],
[(e*x+d)^5/(c*x^2+a)^2,x,6,5*d*e^4*x/c^2+1/2*e^5*x^2/c^2-1/2*(a*e*(a^2*e^4-10*a*c*d^2*e^2+5*c^2*d^4)-c*d*(5*a^2*e^4-10*a*c*d^2*e^2+c^2*d^4)*x)/a/c^3/(c*x^2+a)+1/2*d*(-15*a^2*e^4+10*a*c*d^2*e^2+c^2*d^4)*arctan(sqrt(c)*x/sqrt(a))/a^(3/2)/c^(5/2)+e^3*(-a*e^2+5*c*d^2)*ln(c*x^2+a)/c^3,1],
[(e*x+d)^4/(c*x^2+a)^2,x,6,e^4*x/c^2-1/2*(4*a*d*e*(-a*e^2+c*d^2)-(a^2*e^4-6*a*c*d^2*e^2+c^2*d^4)*x)/a/c^2/(c*x^2+a)+1/2*(-3*a^2*e^4+6*a*c*d^2*e^2+c^2*d^4)*arctan(sqrt(c)*x/sqrt(a))/a^(3/2)/c^(5/2)+2*d*e^3*ln(c*x^2+a)/c^2,1],
[(e*x+d)^3/(c*x^2+a)^2,x,4,-1/2*(a*e*(-a*e^2+3*c*d^2)-c*d*(-3*a*e^2+c*d^2)*x)/a/c^2/(c*x^2+a)+1/2*d*(3*a*e^2+c*d^2)*arctan(sqrt(c)*x/sqrt(a))/a^(3/2)/c^(3/2)+1/2*e^3*ln(c*x^2+a)/c^2,1],
[(e*x+d)^2/(c*x^2+a)^2,x,2,-1/2*(2*a*d*e-(-a*e^2+c*d^2)*x)/a/c/(c*x^2+a)+1/2*(a*e^2+c*d^2)*arctan(sqrt(c)*x/sqrt(a))/a^(3/2)/c^(3/2),1],
[(e*x+d)/(c*x^2+a)^2,x,2,1/2*(c*d*x-a*e)/a/c/(c*x^2+a)+1/2*d*arctan(sqrt(c)*x/sqrt(a))/a^(3/2)/sqrt(c),1],
[1/(e*x+d)/(c*x^2+a)^2,x,6,1/2*(c*d*x+a*e)/a/(a*e^2+c*d^2)/(c*x^2+a)+1/2*sqrt(c)*d*(3*a*e^2+c*d^2)*arctan(sqrt(c)*x/sqrt(a))/a^(3/2)/(a*e^2+c*d^2)^2+e^3*ln(e*x+d)/(a*e^2+c*d^2)^2-1/2*e^3*ln(c*x^2+a)/(a*e^2+c*d^2)^2,1],
[1/(e*x+d)^2/(c*x^2+a)^2,x,6,-e^3/(a*e^2+c*d^2)^2/(e*x+d)+1/2*c*(2*a*d*e+(-a*e^2+c*d^2)*x)/a/(a*e^2+c*d^2)^2/(c*x^2+a)+1/2*sqrt(c)*(-3*a^2*e^4+6*a*c*d^2*e^2+c^2*d^4)*arctan(sqrt(c)*x/sqrt(a))/a^(3/2)/(a*e^2+c*d^2)^3+4*c*d*e^3*ln(e*x+d)/(a*e^2+c*d^2)^3-2*c*d*e^3*ln(c*x^2+a)/(a*e^2+c*d^2)^3,1],
[(e*x+d)^5/(c*x^2+a)^3,x,5,-1/4*(a*e*(a^2*e^4-10*a*c*d^2*e^2+5*c^2*d^4)-c*d*(5*a^2*e^4-10*a*c*d^2*e^2+c^2*d^4)*x)/a/c^3/(c*x^2+a)^2-1/8*(8*a^2*e^3*(-a*e^2+5*c*d^2)-c*d*(-5*a*e^2+3*c*d^2)*(5*a*e^2+c*d^2)*x)/a^2/c^3/(c*x^2+a)+1/8*d*(15*a^2*e^4+10*a*c*d^2*e^2+3*c^2*d^4)*arctan(sqrt(c)*x/sqrt(a))/a^(5/2)/c^(5/2)+1/2*e^5*ln(c*x^2+a)/c^3,1],
[(e*x+d)^4/(c*x^2+a)^3,x,3,-1/4*(4*a*d*e*(-a*e^2+c*d^2)-(a^2*e^4-6*a*c*d^2*e^2+c^2*d^4)*x)/a/c^2/(c*x^2+a)^2-1/8*(16*a^2*d*e^3-(-5*a^2*e^4+6*a*c*d^2*e^2+3*c^2*d^4)*x)/a^2/c^2/(c*x^2+a)+3/8*(a*e^2+c*d^2)^2*arctan(sqrt(c)*x/sqrt(a))/a^(5/2)/c^(5/2),1],
[(e*x+d)^3/(c*x^2+a)^3,x,3,-1/4*(a*e*(-a*e^2+3*c*d^2)-c*d*(-3*a*e^2+c*d^2)*x)/a/c^2/(c*x^2+a)^2-1/8*(4*a^2*e^3-3*c*d*(a*e^2+c*d^2)*x)/a^2/c^2/(c*x^2+a)+3/8*d*(a*e^2+c*d^2)*arctan(sqrt(c)*x/sqrt(a))/a^(5/2)/c^(3/2),1],
[(e*x+d)^2/(c*x^2+a)^3,x,3,-1/4*(2*a*d*e-(-a*e^2+c*d^2)*x)/a/c/(c*x^2+a)^2+1/8*(a*e^2+3*c*d^2)*x/a^2/c/(c*x^2+a)+1/8*(a*e^2+3*c*d^2)*arctan(sqrt(c)*x/sqrt(a))/a^(5/2)/c^(3/2),1],
[(e*x+d)/(c*x^2+a)^3,x,3,1/4*(c*d*x-a*e)/a/c/(c*x^2+a)^2+3/8*d*x/a^2/(c*x^2+a)+3/8*d*arctan(sqrt(c)*x/sqrt(a))/a^(5/2)/sqrt(c),1],
[1/(e*x+d)/(c*x^2+a)^3,x,7,1/4*(c*d*x+a*e)/a/(a*e^2+c*d^2)/(c*x^2+a)^2+1/8*(4*a^2*e^3+c*d*(7*a*e^2+3*c*d^2)*x)/a^2/(a*e^2+c*d^2)^2/(c*x^2+a)+1/8*sqrt(c)*d*(15*a^2*e^4+10*a*c*d^2*e^2+3*c^2*d^4)*arctan(sqrt(c)*x/sqrt(a))/a^(5/2)/(a*e^2+c*d^2)^3+e^5*ln(e*x+d)/(a*e^2+c*d^2)^3-1/2*e^5*ln(c*x^2+a)/(a*e^2+c*d^2)^3,1],
[1/(e*x+d)^2/(c*x^2+a)^3,x,7,-e^5/(a*e^2+c*d^2)^3/(e*x+d)+1/4*c*(2*a*d*e+(-a*e^2+c*d^2)*x)/a/(a*e^2+c*d^2)^2/(c*x^2+a)^2+1/8*c*(16*a^2*d*e^3+(-7*a^2*e^4+12*a*c*d^2*e^2+3*c^2*d^4)*x)/a^2/(a*e^2+c*d^2)^3/(c*x^2+a)+3/8*sqrt(c)*(-5*a^3*e^6+15*a^2*c*d^2*e^4+5*a*c^2*d^4*e^2+c^3*d^6)*arctan(sqrt(c)*x/sqrt(a))/a^(5/2)/(a*e^2+c*d^2)^4+6*c*d*e^5*ln(e*x+d)/(a*e^2+c*d^2)^4-3*c*d*e^5*ln(c*x^2+a)/(a*e^2+c*d^2)^4,1],
[(e*x+d)^6/(c*x^2+a)^4,x,4,-1/6*(2*a*d*e*(-3*a*e^2+c*d^2)*(-a*e^2+3*c*d^2)-(-a*e^2+c*d^2)*(a^2*e^4-14*a*c*d^2*e^2+c^2*d^4)*x)/a/c^3/(c*x^2+a)^3-1/24*(24*a^2*d*e^3*(-3*a*e^2+5*c*d^2)-(13*a^3*e^6-105*a^2*c*d^2*e^4+15*a*c^2*d^4*e^2+5*c^3*d^6)*x)/a^2/c^3/(c*x^2+a)^2-1/16*(48*a^3*d*e^5-(-11*a^3*e^6+15*a^2*c*d^2*e^4+15*a*c^2*d^4*e^2+5*c^3*d^6)*x)/a^3/c^3/(c*x^2+a)+5/16*(a*e^2+c*d^2)^3*arctan(sqrt(c)*x/sqrt(a))/a^(7/2)/c^(7/2),1],
[(e*x+d)^5/(c*x^2+a)^4,x,4,-1/6*(a*e*(a^2*e^4-10*a*c*d^2*e^2+5*c^2*d^4)-c*d*(5*a^2*e^4-10*a*c*d^2*e^2+c^2*d^4)*x)/a/c^3/(c*x^2+a)^3-1/24*(12*a^2*e^3*(-a*e^2+5*c*d^2)-5*c*d*(-7*a^2*e^4+2*a*c*d^2*e^2+c^2*d^4)*x)/a^2/c^3/(c*x^2+a)^2-1/16*(8*a^3*e^5-5*c*d*(a*e^2+c*d^2)^2*x)/a^3/c^3/(c*x^2+a)+5/16*d*(a*e^2+c*d^2)^2*arctan(sqrt(c)*x/sqrt(a))/a^(7/2)/c^(5/2),1],
[(e*x+d)^4/(c*x^2+a)^4,x,4,-1/6*(4*a*d*e*(-a*e^2+c*d^2)-(a^2*e^4-6*a*c*d^2*e^2+c^2*d^4)*x)/a/c^2/(c*x^2+a)^3-1/24*(24*a^2*d*e^3-(-7*a^2*e^4+6*a*c*d^2*e^2+5*c^2*d^4)*x)/a^2/c^2/(c*x^2+a)^2+1/16*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)*x/a^3/c^2/(c*x^2+a)+1/16*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)*arctan(sqrt(c)*x/sqrt(a))/a^(7/2)/c^(5/2),1],
[(e*x+d)^3/(c*x^2+a)^4,x,4,-1/6*(a*e*(-a*e^2+3*c*d^2)-c*d*(-3*a*e^2+c*d^2)*x)/a/c^2/(c*x^2+a)^3-1/24*(6*a^2*e^3-c*d*(3*a*e^2+5*c*d^2)*x)/a^2/c^2/(c*x^2+a)^2+1/16*d*(5*d^2+3*a*e^2/c)*x/a^3/(c*x^2+a)+1/16*d*(3*a*e^2+5*c*d^2)*arctan(sqrt(c)*x/sqrt(a))/a^(7/2)/c^(3/2),1],
[(e*x+d)^2/(c*x^2+a)^4,x,4,-1/6*(2*a*d*e-(-a*e^2+c*d^2)*x)/a/c/(c*x^2+a)^3+1/24*(a*e^2+5*c*d^2)*x/a^2/c/(c*x^2+a)^2+1/16*(a*e^2+5*c*d^2)*x/a^3/c/(c*x^2+a)+1/16*(a*e^2+5*c*d^2)*arctan(sqrt(c)*x/sqrt(a))/a^(7/2)/c^(3/2),1],
[(e*x+d)/(c*x^2+a)^4,x,4,1/6*(c*d*x-a*e)/a/c/(c*x^2+a)^3+5/24*d*x/a^2/(c*x^2+a)^2+5/16*d*x/a^3/(c*x^2+a)+5/16*d*arctan(sqrt(c)*x/sqrt(a))/a^(7/2)/sqrt(c),1],
[1/(e*x+d)/(c*x^2+a)^4,x,8,1/6*(c*d*x+a*e)/a/(a*e^2+c*d^2)/(c*x^2+a)^3+1/24*(6*a^2*e^3+c*d*(11*a*e^2+5*c*d^2)*x)/a^2/(a*e^2+c*d^2)^2/(c*x^2+a)^2+1/16*(8*a^3*e^5+c*d*(19*a^2*e^4+16*a*c*d^2*e^2+5*c^2*d^4)*x)/a^3/(a*e^2+c*d^2)^3/(c*x^2+a)+1/16*sqrt(c)*d*(35*a^3*e^6+35*a^2*c*d^2*e^4+21*a*c^2*d^4*e^2+5*c^3*d^6)*arctan(sqrt(c)*x/sqrt(a))/a^(7/2)/(a*e^2+c*d^2)^4+e^7*ln(e*x+d)/(a*e^2+c*d^2)^4-1/2*e^7*ln(c*x^2+a)/(a*e^2+c*d^2)^4,1],
[1/(e*x+d)^2/(c*x^2+a)^4,x,8,-e^7/(a*e^2+c*d^2)^4/(e*x+d)+1/6*c*(2*a*d*e+(-a*e^2+c*d^2)*x)/a/(a*e^2+c*d^2)^2/(c*x^2+a)^3+1/24*c*(24*a^2*d*e^3+(-11*a^2*e^4+18*a*c*d^2*e^2+5*c^2*d^4)*x)/a^2/(a*e^2+c*d^2)^3/(c*x^2+a)^2+1/16*c*(48*a^3*d*e^5+(-19*a^3*e^6+47*a^2*c*d^2*e^4+23*a*c^2*d^4*e^2+5*c^3*d^6)*x)/a^3/(a*e^2+c*d^2)^4/(c*x^2+a)+1/16*sqrt(c)*(-35*a^4*e^8+140*a^3*c*d^2*e^6+70*a^2*c^2*d^4*e^4+28*a*c^3*d^6*e^2+5*c^4*d^8)*arctan(sqrt(c)*x/sqrt(a))/a^(7/2)/(a*e^2+c*d^2)^5+8*c*d*e^7*ln(e*x+d)/(a*e^2+c*d^2)^5-4*c*d*e^7*ln(c*x^2+a)/(a*e^2+c*d^2)^5,1],
[1/(-3+x)/(x^2+4),x,5,-3/26*arctan(1/2*x)+1/13*ln(3-x)-1/26*ln(x^2+4),1],
[1/(2+x)/(x^2+1),x,5,2/5*arctan(x)+1/5*ln(2+x)-1/10*ln(x^2+1),1],
[1/(1+x)/(x^2+1),x,5,1/2*arctan(x)+1/2*ln(1+x)-1/4*ln(x^2+1),1],
[(-3+x)*(4*x^2-7),x,2,21*x-4*x^3+1/16*(-4*x^2+7)^2,1],
[(e*x+d)^(5/2)/(-c*x^2+a),x,7,-4*d*e*sqrt(e*x+d)/c-2/3*e*(e*x+d)^(3/2)/c-(sqrt(c)*d-sqrt(a)*e)^(5/2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/sqrt(a)/c^(7/4)+(sqrt(c)*d+sqrt(a)*e)^(5/2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/sqrt(a)/c^(7/4),1],
[(e*x+d)^(3/2)/(-c*x^2+a),x,5,-2*e*sqrt(e*x+d)/c-(sqrt(c)*d-sqrt(a)*e)^(3/2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/sqrt(a)/c^(5/4)+(sqrt(c)*d+sqrt(a)*e)^(3/2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/sqrt(a)/c^(5/4),1],
[sqrt(e*x+d)/(-c*x^2+a),x,4,-sqrt(sqrt(c)*d-sqrt(a)*e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/sqrt(a)/c^(3/4)+sqrt(sqrt(c)*d+sqrt(a)*e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/sqrt(a)/c^(3/4),1],
[1/sqrt(e*x+d)/(-c*x^2+a),x,4,-arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/sqrt(a)/c^(1/4)/sqrt(sqrt(c)*d-sqrt(a)*e)+arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/sqrt(a)/c^(1/4)/sqrt(sqrt(c)*d+sqrt(a)*e),1],
[1/(e*x+d)^(3/2)/(-c*x^2+a),x,5,2*e/(-a*e^2+c*d^2)/sqrt(e*x+d)-c^(1/4)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/sqrt(a)/(sqrt(c)*d-sqrt(a)*e)^(3/2)+c^(1/4)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/sqrt(a)/(sqrt(c)*d+sqrt(a)*e)^(3/2),1],
[1/(e*x+d)^(5/2)/(-c*x^2+a),x,6,2/3*e/(-a*e^2+c*d^2)/(e*x+d)^(3/2)+4*c*d*e/(-a*e^2+c*d^2)^2/sqrt(e*x+d)-c^(3/4)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/sqrt(a)/(sqrt(c)*d-sqrt(a)*e)^(5/2)+c^(3/4)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/sqrt(a)/(sqrt(c)*d+sqrt(a)*e)^(5/2),1],
[(e*x+d)^(7/2)/(-c*x^2+a)^2,x,7,1/2*e*(5*a*e^2+c*d^2)*sqrt(e*x+d)/a/c^2+1/2*d*e*(e*x+d)^(3/2)/a/c+1/2*(c*d*x+a*e)*(e*x+d)^(5/2)/a/c/(-c*x^2+a)-1/4*(sqrt(c)*d-sqrt(a)*e)^(5/2)*(2*sqrt(c)*d+5*sqrt(a)*e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/a^(3/2)/c^(9/4)+1/4*(2*sqrt(c)*d-5*sqrt(a)*e)*(sqrt(c)*d+sqrt(a)*e)^(5/2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/a^(3/2)/c^(9/4),1],
[(e*x+d)^(5/2)/(-c*x^2+a)^2,x,7,1/2*d*e*sqrt(e*x+d)/a/c+1/2*(c*d*x+a*e)*(e*x+d)^(3/2)/a/c/(-c*x^2+a)-1/4*(sqrt(c)*d-sqrt(a)*e)^(3/2)*(2*sqrt(c)*d+3*sqrt(a)*e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/a^(3/2)/c^(7/4)+1/4*(2*sqrt(c)*d-3*sqrt(a)*e)*(sqrt(c)*d+sqrt(a)*e)^(3/2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/a^(3/2)/c^(7/4),1],
[(e*x+d)^(3/2)/(-c*x^2+a)^2,x,5,1/2*(c*d*x+a*e)*sqrt(e*x+d)/a/c/(-c*x^2+a)-1/4*sqrt(sqrt(c)*d-sqrt(a)*e)*(2*sqrt(c)*d+sqrt(a)*e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/a^(3/2)/c^(5/4)+1/4*(2*sqrt(c)*d-sqrt(a)*e)*sqrt(sqrt(c)*d+sqrt(a)*e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/a^(3/2)/c^(5/4),1],
[sqrt(e*x+d)/(-c*x^2+a)^2,x,5,1/2*x*sqrt(e*x+d)/a/(-c*x^2+a)-1/4*(2*sqrt(c)*d/sqrt(a)-e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/a/c^(3/4)/sqrt(sqrt(c)*d-sqrt(a)*e)+1/4*(2*sqrt(c)*d/sqrt(a)+e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/a/c^(3/4)/sqrt(sqrt(c)*d+sqrt(a)*e),1],
[1/sqrt(e*x+d)/(-c*x^2+a)^2,x,5,-1/2*(-c*d*x+a*e)*sqrt(e*x+d)/a/(-a*e^2+c*d^2)/(-c*x^2+a)-1/4*(2*sqrt(c)*d-3*sqrt(a)*e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/a^(3/2)/c^(1/4)/(sqrt(c)*d-sqrt(a)*e)^(3/2)+1/4*(2*sqrt(c)*d+3*sqrt(a)*e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/a^(3/2)/c^(1/4)/(sqrt(c)*d+sqrt(a)*e)^(3/2),1],
[1/(e*x+d)^(3/2)/(-c*x^2+a)^2,x,6,-1/2*e*(5*a*e^2+c*d^2)/a/(-a*e^2+c*d^2)^2/sqrt(e*x+d)-1/2*(-c*d*x+a*e)/a/(-a*e^2+c*d^2)/sqrt(e*x+d)/(-c*x^2+a)-1/4*c^(1/4)*(2*sqrt(c)*d-5*sqrt(a)*e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/a^(3/2)/(sqrt(c)*d-sqrt(a)*e)^(5/2)+1/4*c^(1/4)*(2*sqrt(c)*d+5*sqrt(a)*e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/a^(3/2)/(sqrt(c)*d+sqrt(a)*e)^(5/2),1],
[1/(e*x+d)^(5/2)/(-c*x^2+a)^2,x,7,-1/6*e*(7*a*e^2+3*c*d^2)/a/(-a*e^2+c*d^2)^2/(e*x+d)^(3/2)-1/2*c*d*e*(19*a*e^2+c*d^2)/a/(-a*e^2+c*d^2)^3/sqrt(e*x+d)-1/2*(-c*d*x+a*e)/a/(-a*e^2+c*d^2)/(e*x+d)^(3/2)/(-c*x^2+a)-1/4*c^(3/4)*(2*sqrt(c)*d-7*sqrt(a)*e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/a^(3/2)/(sqrt(c)*d-sqrt(a)*e)^(7/2)+1/4*c^(3/4)*(2*sqrt(c)*d+7*sqrt(a)*e)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/a^(3/2)/(sqrt(c)*d+sqrt(a)*e)^(7/2),1],
[(e*x+d)^(7/2)/(-c*x^2+a)^3,x,6,1/4*(c*d*x+a*e)*(e*x+d)^(5/2)/a/c/(-c*x^2+a)^2+1/16*sqrt(e*x+d)*(a*e*(-5*a*e^2+7*c*d^2)+2*c*d*(-2*a*e^2+3*c*d^2)*x)/a^2/c^2/(-c*x^2+a)-1/32*(sqrt(c)*d-sqrt(a)*e)^(3/2)*(12*c*d^2+18*sqrt(a)*sqrt(c)*d*e+5*a*e^2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/a^(5/2)/c^(9/4)+1/32*(sqrt(c)*d+sqrt(a)*e)^(3/2)*(12*c*d^2-18*sqrt(a)*sqrt(c)*d*e+5*a*e^2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/a^(5/2)/c^(9/4),1],
[(e*x+d)^(5/2)/(-c*x^2+a)^3,x,6,1/4*(c*d*x+a*e)*(e*x+d)^(3/2)/a/c/(-c*x^2+a)^2+3/16*sqrt(e*x+d)*(a*d*e+(-a*e^2+2*c*d^2)*x)/a^2/c/(-c*x^2+a)-3/32*sqrt(sqrt(c)*d-sqrt(a)*e)*(4*c*d^2+2*sqrt(a)*sqrt(c)*d*e-a*e^2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/a^(5/2)/c^(7/4)+3/32*sqrt(sqrt(c)*d+sqrt(a)*e)*(4*c*d^2-2*sqrt(a)*sqrt(c)*d*e-a*e^2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/a^(5/2)/c^(7/4),1],
[(e*x+d)^(3/2)/(-c*x^2+a)^3,x,6,1/4*(c*d*x+a*e)*sqrt(e*x+d)/a/c/(-c*x^2+a)^2-1/16*(-6*c*d*x+a*e)*sqrt(e*x+d)/a^2/c/(-c*x^2+a)-3/32*(4*c*d^2-2*sqrt(a)*sqrt(c)*d*e-a*e^2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/a^(5/2)/c^(5/4)/sqrt(sqrt(c)*d-sqrt(a)*e)+3/32*(4*c*d^2+2*sqrt(a)*sqrt(c)*d*e-a*e^2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/a^(5/2)/c^(5/4)/sqrt(sqrt(c)*d+sqrt(a)*e),1],
[sqrt(e*x+d)/(-c*x^2+a)^3,x,6,1/4*x*sqrt(e*x+d)/a/(-c*x^2+a)^2-1/16*sqrt(e*x+d)*(a*d*e-(-5*a*e^2+6*c*d^2)*x)/a^2/(-a*e^2+c*d^2)/(-c*x^2+a)-1/32*(12*c*d^2-18*sqrt(a)*sqrt(c)*d*e+5*a*e^2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/a^(5/2)/c^(3/4)/(sqrt(c)*d-sqrt(a)*e)^(3/2)+1/32*(12*c*d^2+18*sqrt(a)*sqrt(c)*d*e+5*a*e^2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/a^(5/2)/c^(3/4)/(sqrt(c)*d+sqrt(a)*e)^(3/2),1],
[1/sqrt(e*x+d)/(-c*x^2+a)^3,x,6,-1/4*(-c*d*x+a*e)*sqrt(e*x+d)/a/(-a*e^2+c*d^2)/(-c*x^2+a)^2-1/16*sqrt(e*x+d)*(a*e*(-7*a*e^2+c*d^2)-6*c*d*(-2*a*e^2+c*d^2)*x)/a^2/(-a*e^2+c*d^2)^2/(-c*x^2+a)-3/32*(4*c*d^2-10*sqrt(a)*sqrt(c)*d*e+7*a*e^2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d-sqrt(a)*e))/a^(5/2)/c^(1/4)/(sqrt(c)*d-sqrt(a)*e)^(5/2)+3/32*(4*c*d^2+10*sqrt(a)*sqrt(c)*d*e+7*a*e^2)*arctanh(c^(1/4)*sqrt(e*x+d)/sqrt(sqrt(c)*d+sqrt(a)*e))/a^(5/2)/c^(1/4)/(sqrt(c)*d+sqrt(a)*e)^(5/2),1],
[sqrt(2+3*x)/(-x^2+1),x,4,-arctan(sqrt(2+3*x))+sqrt(5)*arctanh(sqrt(2+3*x)/sqrt(5)),1],
[sqrt(d*x+c)/(-x^2+1),x,4,-sqrt(c-d)*arctanh(sqrt(d*x+c)/sqrt(c-d))+sqrt(c+d)*arctanh(sqrt(d*x+c)/sqrt(c+d)),1],
[sqrt(2+3*x)/(-b*x^2+a),x,4,-sqrt(3*sqrt(a)-2*sqrt(b))*arctan(b^(1/4)*sqrt(2+3*x)/sqrt(3*sqrt(a)-2*sqrt(b)))/sqrt(a)/b^(3/4)+sqrt(3*sqrt(a)+2*sqrt(b))*arctanh(b^(1/4)*sqrt(2+3*x)/sqrt(3*sqrt(a)+2*sqrt(b)))/sqrt(a)/b^(3/4),1],
[(e*x+d)^(5/2)*(c*x^2+a),x,2,2/7*(a*e^2+c*d^2)*(e*x+d)^(7/2)/e^3-4/9*c*d*(e*x+d)^(9/2)/e^3+2/11*c*(e*x+d)^(11/2)/e^3,1],
[(e*x+d)^(3/2)*(c*x^2+a),x,2,2/5*(a*e^2+c*d^2)*(e*x+d)^(5/2)/e^3-4/7*c*d*(e*x+d)^(7/2)/e^3+2/9*c*(e*x+d)^(9/2)/e^3,1],
[sqrt(e*x+d)*(c*x^2+a),x,2,2/3*(a*e^2+c*d^2)*(e*x+d)^(3/2)/e^3-4/5*c*d*(e*x+d)^(5/2)/e^3+2/7*c*(e*x+d)^(7/2)/e^3,1],
[(c*x^2+a)/sqrt(e*x+d),x,2,2*(a*e^2+c*d^2)*sqrt(e*x+d)/e^3-4/3*c*d*(e*x+d)^(3/2)/e^3+2/5*c*(e*x+d)^(5/2)/e^3,1],
[(c*x^2+a)/(e*x+d)^(3/2),x,2,(-2*a*e^2-2*c*d^2)/e^3/sqrt(e*x+d)-4*c*d*sqrt(e*x+d)/e^3+2/3*c*(e*x+d)^(3/2)/e^3,1],
[(c*x^2+a)/(e*x+d)^(5/2),x,2,1/3*(-2*a*e^2-2*c*d^2)/e^3/(e*x+d)^(3/2)+4*c*d/e^3/sqrt(e*x+d)+2*c*sqrt(e*x+d)/e^3,1],
[(c*x^2+a)/(e*x+d)^(7/2),x,2,1/5*(-2*a*e^2-2*c*d^2)/e^3/(e*x+d)^(5/2)+4/3*c*d/e^3/(e*x+d)^(3/2)-2*c/e^3/sqrt(e*x+d),1],
[(e*x+d)^(5/2)*(c*x^2+a)^2,x,2,2/7*(a*e^2+c*d^2)^2*(e*x+d)^(7/2)/e^5-8/9*c*d*(a*e^2+c*d^2)*(e*x+d)^(9/2)/e^5+4/11*c*(a*e^2+3*c*d^2)*(e*x+d)^(11/2)/e^5-8/13*c^2*d*(e*x+d)^(13/2)/e^5+2/15*c^2*(e*x+d)^(15/2)/e^5,1],
[(e*x+d)^(3/2)*(c*x^2+a)^2,x,2,2/5*(a*e^2+c*d^2)^2*(e*x+d)^(5/2)/e^5-8/7*c*d*(a*e^2+c*d^2)*(e*x+d)^(7/2)/e^5+4/9*c*(a*e^2+3*c*d^2)*(e*x+d)^(9/2)/e^5-8/11*c^2*d*(e*x+d)^(11/2)/e^5+2/13*c^2*(e*x+d)^(13/2)/e^5,1],
[sqrt(e*x+d)*(c*x^2+a)^2,x,2,2/3*(a*e^2+c*d^2)^2*(e*x+d)^(3/2)/e^5-8/5*c*d*(a*e^2+c*d^2)*(e*x+d)^(5/2)/e^5+4/7*c*(a*e^2+3*c*d^2)*(e*x+d)^(7/2)/e^5-8/9*c^2*d*(e*x+d)^(9/2)/e^5+2/11*c^2*(e*x+d)^(11/2)/e^5,1],
[(c*x^2+a)^2/sqrt(e*x+d),x,2,2*(a*e^2+c*d^2)^2*sqrt(e*x+d)/e^5-8/3*c*d*(a*e^2+c*d^2)*(e*x+d)^(3/2)/e^5+4/5*c*(a*e^2+3*c*d^2)*(e*x+d)^(5/2)/e^5-8/7*c^2*d*(e*x+d)^(7/2)/e^5+2/9*c^2*(e*x+d)^(9/2)/e^5,1],
[(c*x^2+a)^2/(e*x+d)^(3/2),x,2,-2*(a*e^2+c*d^2)^2/e^5/sqrt(e*x+d)-8*c*d*(a*e^2+c*d^2)*sqrt(e*x+d)/e^5+4/3*c*(a*e^2+3*c*d^2)*(e*x+d)^(3/2)/e^5-8/5*c^2*d*(e*x+d)^(5/2)/e^5+2/7*c^2*(e*x+d)^(7/2)/e^5,1],
[(c*x^2+a)^2/(e*x+d)^(5/2),x,2,-2/3*(a*e^2+c*d^2)^2/e^5/(e*x+d)^(3/2)+8*c*d*(a*e^2+c*d^2)/e^5/sqrt(e*x+d)+4*c*(a*e^2+3*c*d^2)*sqrt(e*x+d)/e^5-8/3*c^2*d*(e*x+d)^(3/2)/e^5+2/5*c^2*(e*x+d)^(5/2)/e^5,1],
[(c*x^2+a)^2/(e*x+d)^(7/2),x,2,-2/5*(a*e^2+c*d^2)^2/e^5/(e*x+d)^(5/2)+8/3*c*d*(a*e^2+c*d^2)/e^5/(e*x+d)^(3/2)-4*c*(a*e^2+3*c*d^2)/e^5/sqrt(e*x+d)-8*c^2*d*sqrt(e*x+d)/e^5+2/3*c^2*(e*x+d)^(3/2)/e^5,1],
[(e*x+d)^(5/2)*(c*x^2+a)^3,x,2,2/7*(a*e^2+c*d^2)^3*(e*x+d)^(7/2)/e^7-4/3*c*d*(a*e^2+c*d^2)^2*(e*x+d)^(9/2)/e^7+6/11*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)*(e*x+d)^(11/2)/e^7-8/13*c^2*d*(3*a*e^2+5*c*d^2)*(e*x+d)^(13/2)/e^7+2/5*c^2*(a*e^2+5*c*d^2)*(e*x+d)^(15/2)/e^7-12/17*c^3*d*(e*x+d)^(17/2)/e^7+2/19*c^3*(e*x+d)^(19/2)/e^7,1],
[(e*x+d)^(3/2)*(c*x^2+a)^3,x,2,2/5*(a*e^2+c*d^2)^3*(e*x+d)^(5/2)/e^7-12/7*c*d*(a*e^2+c*d^2)^2*(e*x+d)^(7/2)/e^7+2/3*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)*(e*x+d)^(9/2)/e^7-8/11*c^2*d*(3*a*e^2+5*c*d^2)*(e*x+d)^(11/2)/e^7+6/13*c^2*(a*e^2+5*c*d^2)*(e*x+d)^(13/2)/e^7-4/5*c^3*d*(e*x+d)^(15/2)/e^7+2/17*c^3*(e*x+d)^(17/2)/e^7,1],
[sqrt(e*x+d)*(c*x^2+a)^3,x,2,2/3*(a*e^2+c*d^2)^3*(e*x+d)^(3/2)/e^7-12/5*c*d*(a*e^2+c*d^2)^2*(e*x+d)^(5/2)/e^7+6/7*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)*(e*x+d)^(7/2)/e^7-8/9*c^2*d*(3*a*e^2+5*c*d^2)*(e*x+d)^(9/2)/e^7+6/11*c^2*(a*e^2+5*c*d^2)*(e*x+d)^(11/2)/e^7-12/13*c^3*d*(e*x+d)^(13/2)/e^7+2/15*c^3*(e*x+d)^(15/2)/e^7,1],
[(c*x^2+a)^3/sqrt(e*x+d),x,2,2*(a*e^2+c*d^2)^3*sqrt(e*x+d)/e^7-4*c*d*(a*e^2+c*d^2)^2*(e*x+d)^(3/2)/e^7+6/5*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)*(e*x+d)^(5/2)/e^7-8/7*c^2*d*(3*a*e^2+5*c*d^2)*(e*x+d)^(7/2)/e^7+2/3*c^2*(a*e^2+5*c*d^2)*(e*x+d)^(9/2)/e^7-12/11*c^3*d*(e*x+d)^(11/2)/e^7+2/13*c^3*(e*x+d)^(13/2)/e^7,1],
[(c*x^2+a)^3/(e*x+d)^(3/2),x,2,-2*(a*e^2+c*d^2)^3/e^7/sqrt(e*x+d)-12*c*d*(a*e^2+c*d^2)^2*sqrt(e*x+d)/e^7+2*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)*(e*x+d)^(3/2)/e^7-8/5*c^2*d*(3*a*e^2+5*c*d^2)*(e*x+d)^(5/2)/e^7+6/7*c^2*(a*e^2+5*c*d^2)*(e*x+d)^(7/2)/e^7-4/3*c^3*d*(e*x+d)^(9/2)/e^7+2/11*c^3*(e*x+d)^(11/2)/e^7,1],
[(c*x^2+a)^3/(e*x+d)^(5/2),x,2,-2/3*(a*e^2+c*d^2)^3/e^7/(e*x+d)^(3/2)+12*c*d*(a*e^2+c*d^2)^2/e^7/sqrt(e*x+d)+6*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)*sqrt(e*x+d)/e^7-8/3*c^2*d*(3*a*e^2+5*c*d^2)*(e*x+d)^(3/2)/e^7+6/5*c^2*(a*e^2+5*c*d^2)*(e*x+d)^(5/2)/e^7-12/7*c^3*d*(e*x+d)^(7/2)/e^7+2/9*c^3*(e*x+d)^(9/2)/e^7,1],
[(c*x^2+a)^3/(e*x+d)^(7/2),x,2,-2/5*(a*e^2+c*d^2)^3/e^7/(e*x+d)^(5/2)+4*c*d*(a*e^2+c*d^2)^2/e^7/(e*x+d)^(3/2)-6*c*(a*e^2+c*d^2)*(a*e^2+5*c*d^2)/e^7/sqrt(e*x+d)-8*c^2*d*(3*a*e^2+5*c*d^2)*sqrt(e*x+d)/e^7+2*c^2*(a*e^2+5*c*d^2)*(e*x+d)^(3/2)/e^7-12/5*c^3*d*(e*x+d)^(5/2)/e^7+2/7*c^3*(e*x+d)^(7/2)/e^7,1],
[(e*x+d)^(5/2)/(c*x^2+a),x,12,4*d*e*sqrt(e*x+d)/c+2/3*e*(e*x+d)^(3/2)/c-e*(3*c*d^2-a*e^2-2*sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/c^(7/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+e*(3*c*d^2-a*e^2-2*sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/c^(7/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))-e*(3*c*d^2-a*e^2+2*sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/c^(7/4)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[(e*x+d)^(3/2)/(c*x^2+a),x,10,2*e*sqrt(e*x+d)/c-e*(2*sqrt(c)*d-sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/c^(5/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+e*(2*sqrt(c)*d-sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/c^(5/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))-e*(2*sqrt(c)*d+sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/c^(5/4)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[sqrt(e*x+d)/(c*x^2+a),x,9,-e*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/c^(3/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+e*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/c^(3/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))-e*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/c^(3/4)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[1/sqrt(e*x+d)/(c*x^2+a),x,9,-e*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/c^(1/4)/sqrt(a*e^2+c*d^2)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+e*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/c^(1/4)/sqrt(a*e^2+c*d^2)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+e*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/c^(1/4)/sqrt(a*e^2+c*d^2)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[1/(e*x+d)^(3/2)/(c*x^2+a),x,10,-2*e/(a*e^2+c*d^2)/sqrt(e*x+d)-c^(1/4)*e*(2*sqrt(c)*d-sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/(a*e^2+c*d^2)^(3/2)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+c^(1/4)*e*(2*sqrt(c)*d-sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/(a*e^2+c*d^2)^(3/2)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+c^(1/4)*e*(2*sqrt(c)*d+sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/(a*e^2+c*d^2)^(3/2)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[1/(e*x+d)^(5/2)/(c*x^2+a),x,11,-2/3*e/(a*e^2+c*d^2)/(e*x+d)^(3/2)-4*c*d*e/(a*e^2+c*d^2)^2/sqrt(e*x+d)-c^(3/4)*e*(3*c*d^2-a*e^2-2*sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/(a*e^2+c*d^2)^(5/2)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+c^(3/4)*e*(3*c*d^2-a*e^2-2*sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/(a*e^2+c*d^2)^(5/2)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+c^(3/4)*e*(3*c*d^2-a*e^2+2*sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/(a*e^2+c*d^2)^(5/2)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[(e*x+d)^(7/2)/(c*x^2+a)^2,x,12,-1/2*e*(-5*a*e^2+c*d^2)*sqrt(e*x+d)/a/c^2-1/2*d*e*(e*x+d)^(3/2)/a/c-1/2*(-c*d*x+a*e)*(e*x+d)^(5/2)/a/c/(c*x^2+a)-1/4*e*((-5*a*e^2+c*d^2)*sqrt(a*e^2+c*d^2)+sqrt(c)*d*(13*a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/c^(9/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+1/4*e*((-5*a*e^2+c*d^2)*sqrt(a*e^2+c*d^2)+sqrt(c)*d*(13*a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/c^(9/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+1/4*e*((-5*a*e^2+c*d^2)*sqrt(a*e^2+c*d^2)-sqrt(c)*d*(13*a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/a/c^(9/4)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[(e*x+d)^(5/2)/(c*x^2+a)^2,x,12,-1/2*d*e*sqrt(e*x+d)/a/c-1/2*(-c*d*x+a*e)*(e*x+d)^(3/2)/a/c/(c*x^2+a)-1/4*e*(c*d^2+3*a*e^2+sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/c^(7/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+1/4*e*(c*d^2+3*a*e^2+sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/c^(7/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))-1/4*e*(c*d^2+3*a*e^2-sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/a/c^(7/4)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[(e*x+d)^(3/2)/(c*x^2+a)^2,x,10,-1/2*(-c*d*x+a*e)*sqrt(e*x+d)/a/c/(c*x^2+a)-1/4*e*(sqrt(c)*d+sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/c^(5/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+1/4*e*(sqrt(c)*d+sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/c^(5/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))-1/4*e*(sqrt(c)*d-sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/a/c^(5/4)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[sqrt(e*x+d)/(c*x^2+a)^2,x,10,1/2*x*sqrt(e*x+d)/a/(c*x^2+a)-1/4*e*(1+sqrt(c)*d/sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/c^(3/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+1/4*e*(1+sqrt(c)*d/sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/c^(3/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))-1/4*e*(1-sqrt(c)*d/sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/a/c^(3/4)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[1/sqrt(e*x+d)/(c*x^2+a)^2,x,10,1/2*(c*d*x+a*e)*sqrt(e*x+d)/a/(a*e^2+c*d^2)/(c*x^2+a)-1/4*e*(c*d^2+3*a*e^2+sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/c^(1/4)/(a*e^2+c*d^2)^(3/2)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+1/4*e*(c*d^2+3*a*e^2+sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/c^(1/4)/(a*e^2+c*d^2)^(3/2)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+1/4*e*(c*d^2+3*a*e^2-sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/a/c^(1/4)/(a*e^2+c*d^2)^(3/2)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[1/(e*x+d)^(3/2)/(c*x^2+a)^2,x,11,1/2*e*(-5*a*e^2+c*d^2)/a/(a*e^2+c*d^2)^2/sqrt(e*x+d)+1/2*(c*d*x+a*e)/a/(a*e^2+c*d^2)/sqrt(e*x+d)/(c*x^2+a)-1/4*c^(1/4)*e*(c*d^2-5*a*e^2+sqrt(c)*d*(13*a*e^2+c*d^2)/sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/(a*e^2+c*d^2)^2/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+1/4*c^(1/4)*e*(c*d^2-5*a*e^2+sqrt(c)*d*(13*a*e^2+c*d^2)/sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/(a*e^2+c*d^2)^2/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))-1/4*c^(1/4)*e*(c*d^2-5*a*e^2-sqrt(c)*d*(13*a*e^2+c*d^2)/sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/a/(a*e^2+c*d^2)^2/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[1/(e*x+d)^(5/2)/(c*x^2+a)^2,x,12,1/6*e*(-7*a*e^2+3*c*d^2)/a/(a*e^2+c*d^2)^2/(e*x+d)^(3/2)+1/2*c*d*e*(-19*a*e^2+c*d^2)/a/(a*e^2+c*d^2)^3/sqrt(e*x+d)+1/2*(c*d*x+a*e)/a/(a*e^2+c*d^2)/(e*x+d)^(3/2)/(c*x^2+a)-1/4*c^(3/4)*e*(sqrt(c)*d*(-19*a*e^2+c*d^2)+(-7*a^2*e^4+34*a*c*d^2*e^2+c^2*d^4)/sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/(a*e^2+c*d^2)^3/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+1/4*c^(3/4)*e*(sqrt(c)*d*(-19*a*e^2+c*d^2)+(-7*a^2*e^4+34*a*c*d^2*e^2+c^2*d^4)/sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a/(a*e^2+c*d^2)^3/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))-1/4*c^(3/4)*e*(sqrt(c)*d*(-19*a*e^2+c*d^2)-(-7*a^2*e^4+34*a*c*d^2*e^2+c^2*d^4)/sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/a/(a*e^2+c*d^2)^3/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[(e*x+d)^(9/2)/(c*x^2+a)^3,x,13,-1/4*d*e^3*sqrt(e*x+d)/a/c^2-1/4*(-c*d*x+a*e)*(e*x+d)^(7/2)/a/c/(c*x^2+a)^2-1/16*sqrt(e*x+d)*(a*d*e*(15*a*e^2+11*c*d^2)-(-7*a^2*e^4+3*a*c*d^2*e^2+6*c^2*d^4)*x)/a^2/c^2/(c*x^2+a)-3/32*e*(2*c^2*d^4+5*a*c*d^2*e^2+7*a^2*e^4+2*sqrt(c)*d*sqrt(a*e^2+c*d^2)*(2*a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a^2/c^(11/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+3/32*e*(2*c^2*d^4+5*a*c*d^2*e^2+7*a^2*e^4+2*sqrt(c)*d*sqrt(a*e^2+c*d^2)*(2*a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a^2/c^(11/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))-3/32*e*(2*c^2*d^4+5*a*c*d^2*e^2+7*a^2*e^4-2*sqrt(c)*d*sqrt(a*e^2+c*d^2)*(2*a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/a^2/c^(11/4)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[(e*x+d)^(7/2)/(c*x^2+a)^3,x,11,-1/4*(-c*d*x+a*e)*(e*x+d)^(5/2)/a/c/(c*x^2+a)^2-1/16*sqrt(e*x+d)*(a*e*(5*a*e^2+7*c*d^2)-2*c*d*(2*a*e^2+3*c*d^2)*x)/a^2/c^2/(c*x^2+a)-1/32*e*(2*sqrt(c)*d*(4*a*e^2+3*c*d^2)+sqrt(a*e^2+c*d^2)*(5*a*e^2+6*c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a^2/c^(9/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+1/32*e*(2*sqrt(c)*d*(4*a*e^2+3*c*d^2)+sqrt(a*e^2+c*d^2)*(5*a*e^2+6*c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a^2/c^(9/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))-1/32*e*(2*sqrt(c)*d*(4*a*e^2+3*c*d^2)-sqrt(a*e^2+c*d^2)*(5*a*e^2+6*c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/a^2/c^(9/4)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[(e*x+d)^(5/2)/(c*x^2+a)^3,x,11,-1/4*(-c*d*x+a*e)*(e*x+d)^(3/2)/a/c/(c*x^2+a)^2-3/16*sqrt(e*x+d)*(a*d*e-(a*e^2+2*c*d^2)*x)/a^2/c/(c*x^2+a)-3/32*e*(2*c*d^2+a*e^2+2*sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a^2/c^(7/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+3/32*e*(2*c*d^2+a*e^2+2*sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a^2/c^(7/4)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))-3/32*e*(2*c*d^2+a*e^2-2*sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/a^2/c^(7/4)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[(e*x+d)^(3/2)/(c*x^2+a)^3,x,11,-1/4*(-c*d*x+a*e)*sqrt(e*x+d)/a/c/(c*x^2+a)^2+1/16*(6*c*d*x+a*e)*sqrt(e*x+d)/a^2/c/(c*x^2+a)-3/32*e*(2*c*d^2+a*e^2+2*sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a^2/c^(5/4)/sqrt(a*e^2+c*d^2)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+3/32*e*(2*c*d^2+a*e^2+2*sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a^2/c^(5/4)/sqrt(a*e^2+c*d^2)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+3/32*e*(2*c*d^2+a*e^2-2*sqrt(c)*d*sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/a^2/c^(5/4)/sqrt(a*e^2+c*d^2)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[sqrt(e*x+d)/(c*x^2+a)^3,x,11,1/4*x*sqrt(e*x+d)/a/(c*x^2+a)^2+1/16*sqrt(e*x+d)*(a*d*e+(5*a*e^2+6*c*d^2)*x)/a^2/(a*e^2+c*d^2)/(c*x^2+a)-1/32*e*(6*c*d^2+5*a*e^2+2*sqrt(c)*d*(4*a*e^2+3*c*d^2)/sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a^2/c^(3/4)/(a*e^2+c*d^2)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+1/32*e*(6*c*d^2+5*a*e^2+2*sqrt(c)*d*(4*a*e^2+3*c*d^2)/sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a^2/c^(3/4)/(a*e^2+c*d^2)/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))-1/32*e*(6*c*d^2+5*a*e^2-2*sqrt(c)*d*(4*a*e^2+3*c*d^2)/sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/a^2/c^(3/4)/(a*e^2+c*d^2)/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[1/sqrt(e*x+d)/(c*x^2+a)^3,x,11,1/4*(c*d*x+a*e)*sqrt(e*x+d)/a/(a*e^2+c*d^2)/(c*x^2+a)^2+1/16*sqrt(e*x+d)*(a*e*(7*a*e^2+c*d^2)+6*c*d*(2*a*e^2+c*d^2)*x)/a^2/(a*e^2+c*d^2)^2/(c*x^2+a)-3/32*e*(2*sqrt(c)*d*(2*a*e^2+c*d^2)+(7*a^2*e^4+5*a*c*d^2*e^2+2*c^2*d^4)/sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))-sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a^2/c^(1/4)/(a*e^2+c*d^2)^2/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))+3/32*e*(2*sqrt(c)*d*(2*a*e^2+c*d^2)+(7*a^2*e^4+5*a*c*d^2*e^2+2*c^2*d^4)/sqrt(a*e^2+c*d^2))*arctan((sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))+sqrt(2)*c^(1/4)*sqrt(e*x+d))/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2)))/sqrt(2)/a^2/c^(1/4)/(a*e^2+c*d^2)^2/sqrt(-sqrt(c)*d+sqrt(a*e^2+c*d^2))-3/32*e*(2*sqrt(c)*d*(2*a*e^2+c*d^2)-(7*a^2*e^4+5*a*c*d^2*e^2+2*c^2*d^4)/sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2))*sqrt(e*x+d)/(sqrt(a*e^2+c*d^2)+sqrt(c)*(e*x+d)))/sqrt(2)/a^2/c^(1/4)/(a*e^2+c*d^2)^2/sqrt(sqrt(c)*d+sqrt(a*e^2+c*d^2)),1],
[sqrt(2+3*x)/(x^2+1),x,9,-3*arctan((sqrt(4+2*sqrt(13))-2*sqrt(2+3*x))/sqrt(-4+2*sqrt(13)))/sqrt(-4+2*sqrt(13))+3*arctan((sqrt(4+2*sqrt(13))+2*sqrt(2+3*x))/sqrt(-4+2*sqrt(13)))/sqrt(-4+2*sqrt(13))-3*arctanh(sqrt(4+2*sqrt(13))*sqrt(2+3*x)/(2+sqrt(13)+3*x))/sqrt(4+2*sqrt(13)),1],
[sqrt(d*x+c)/(x^2+1),x,9,-d*arctan((sqrt(c+sqrt(c^2+d^2))-sqrt(2)*sqrt(d*x+c))/sqrt(-c+sqrt(c^2+d^2)))/sqrt(2)/sqrt(-c+sqrt(c^2+d^2))+d*arctan((sqrt(c+sqrt(c^2+d^2))+sqrt(2)*sqrt(d*x+c))/sqrt(-c+sqrt(c^2+d^2)))/sqrt(2)/sqrt(-c+sqrt(c^2+d^2))-d*arctanh(sqrt(2)*sqrt(c+sqrt(c^2+d^2))*sqrt(d*x+c)/(c+sqrt(c^2+d^2)+d*x))/sqrt(2)/sqrt(c+sqrt(c^2+d^2)),1],
[sqrt(2+3*x)/(b*x^2+a),x,9,-3*arctan((sqrt(2*sqrt(b)+sqrt(9*a+4*b))-sqrt(2)*b^(1/4)*sqrt(2+3*x))/sqrt(-2*sqrt(b)+sqrt(9*a+4*b)))/sqrt(2)/b^(3/4)/sqrt(-2*sqrt(b)+sqrt(9*a+4*b))+3*arctan((sqrt(2*sqrt(b)+sqrt(9*a+4*b))+sqrt(2)*b^(1/4)*sqrt(2+3*x))/sqrt(-2*sqrt(b)+sqrt(9*a+4*b)))/sqrt(2)/b^(3/4)/sqrt(-2*sqrt(b)+sqrt(9*a+4*b))-3*arctanh(sqrt(2)*b^(1/4)*sqrt(2*sqrt(b)+sqrt(9*a+4*b))*sqrt(2+3*x)/(sqrt(9*a+4*b)+sqrt(b)*(2+3*x)))/sqrt(2)/b^(3/4)/sqrt(2*sqrt(b)+sqrt(9*a+4*b)),1],
[sqrt(1+x)/(x^2+1),x,9,-sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+x))/sqrt(-2+2*sqrt(2)))+sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+x))/sqrt(-2+2*sqrt(2)))-arctanh(sqrt(2+2*sqrt(2))*sqrt(1+x)/(1+sqrt(2)+x))/sqrt(2+2*sqrt(2)),1],
[1/sqrt(1+x)/(x^2+1),x,9,-1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+x))/sqrt(-2+2*sqrt(2)))+1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+x))/sqrt(-2+2*sqrt(2)))+1/2*arctanh(sqrt(2+2*sqrt(2))*sqrt(1+x)/(1+sqrt(2)+x))/sqrt(1+sqrt(2)),1],
[sqrt(-1+x)/(x^2+1)^3,x,11,1/4*sqrt(-1+x)*x/(x^2+1)^2-(1-11*x)*sqrt(-1+x)/(32*x^2+32)-1/64*sqrt(-527/2+373/2*sqrt(2))*arctan((sqrt(-2+2*sqrt(2))-2*sqrt(-1+x))/sqrt(2+2*sqrt(2)))+1/64*sqrt(-527/2+373/2*sqrt(2))*arctan((sqrt(-2+2*sqrt(2))+2*sqrt(-1+x))/sqrt(2+2*sqrt(2)))+1/64*sqrt(527/2+373/2*sqrt(2))*arctanh(sqrt(-2+2*sqrt(2))*sqrt(-1+x)/(1-sqrt(2)-x)),1],
[(d*x+c)^(4/3)/(b*x^2+a),x,15,3*d*(d*x+c)^(1/3)/b+1/2*sqrt(3)*(b*c^2-2*sqrt(-a)*sqrt(b)*c*d-a*d^2)*arctan((1+2*b^(1/6)*(d*x+c)^(1/3)/(sqrt(b)*c-sqrt(-a)*d)^(1/3))/sqrt(3))/sqrt(-a)/b^(7/6)/(sqrt(b)*c-sqrt(-a)*d)^(2/3)-1/2*sqrt(3)*(b*c^2+2*sqrt(-a)*sqrt(b)*c*d-a*d^2)*arctan((1+2*b^(1/6)*(d*x+c)^(1/3)/(sqrt(b)*c+sqrt(-a)*d)^(1/3))/sqrt(3))/sqrt(-a)/b^(7/6)/(sqrt(b)*c+sqrt(-a)*d)^(2/3)-1/4*(b*c^2+2*sqrt(-a)*sqrt(b)*c*d-a*d^2)*ln(sqrt(-a)-sqrt(b)*x)/sqrt(-a)/b^(7/6)/(sqrt(b)*c+sqrt(-a)*d)^(2/3)+1/4*(b*c^2-2*sqrt(-a)*sqrt(b)*c*d-a*d^2)*ln(sqrt(-a)+sqrt(b)*x)/sqrt(-a)/b^(7/6)/(sqrt(b)*c-sqrt(-a)*d)^(2/3)-3/4*(b*c^2-2*sqrt(-a)*sqrt(b)*c*d-a*d^2)*ln((sqrt(b)*c-sqrt(-a)*d)^(1/3)-b^(1/6)*(d*x+c)^(1/3))/sqrt(-a)/b^(7/6)/(sqrt(b)*c-sqrt(-a)*d)^(2/3)+3/4*(b*c^2+2*sqrt(-a)*sqrt(b)*c*d-a*d^2)*ln((sqrt(b)*c+sqrt(-a)*d)^(1/3)-b^(1/6)*(d*x+c)^(1/3))/sqrt(-a)/b^(7/6)/(sqrt(b)*c+sqrt(-a)*d)^(2/3),1],
[(d*x+c)^(2/3)/(b*x^2+a),x,17,-1/2*sqrt(3)*(sqrt(b)*c-sqrt(-a)*d)^(2/3)*arctan((1+2*b^(1/6)*(d*x+c)^(1/3)/(sqrt(b)*c-sqrt(-a)*d)^(1/3))/sqrt(3))/sqrt(-a)/b^(5/6)+1/2*sqrt(3)*(sqrt(b)*c+sqrt(-a)*d)^(2/3)*arctan((1+2*b^(1/6)*(d*x+c)^(1/3)/(sqrt(b)*c+sqrt(-a)*d)^(1/3))/sqrt(3))/sqrt(-a)/b^(5/6)-1/4*(sqrt(b)*c+sqrt(-a)*d)^(2/3)*ln(sqrt(-a)-sqrt(b)*x)/sqrt(-a)/b^(5/6)+1/4*(sqrt(b)*c-sqrt(-a)*d)^(2/3)*ln(sqrt(-a)+sqrt(b)*x)/sqrt(-a)/b^(5/6)-3/4*(sqrt(b)*c-sqrt(-a)*d)^(2/3)*ln((sqrt(b)*c-sqrt(-a)*d)^(1/3)-b^(1/6)*(d*x+c)^(1/3))/sqrt(-a)/b^(5/6)+3/4*(sqrt(b)*c+sqrt(-a)*d)^(2/3)*ln((sqrt(b)*c+sqrt(-a)*d)^(1/3)-b^(1/6)*(d*x+c)^(1/3))/sqrt(-a)/b^(5/6),1],
[(d*x+c)^(1/3)/(b*x^2+a),x,15,1/2*sqrt(3)*(sqrt(b)*c-sqrt(-a)*d)^(1/3)*arctan((1+2*b^(1/6)*(d*x+c)^(1/3)/(sqrt(b)*c-sqrt(-a)*d)^(1/3))/sqrt(3))/sqrt(-a)/b^(2/3)-1/2*sqrt(3)*(sqrt(b)*c+sqrt(-a)*d)^(1/3)*arctan((1+2*b^(1/6)*(d*x+c)^(1/3)/(sqrt(b)*c+sqrt(-a)*d)^(1/3))/sqrt(3))/sqrt(-a)/b^(2/3)-1/4*(sqrt(b)*c+sqrt(-a)*d)^(1/3)*ln(sqrt(-a)-sqrt(b)*x)/sqrt(-a)/b^(2/3)+1/4*(sqrt(b)*c-sqrt(-a)*d)^(1/3)*ln(sqrt(-a)+sqrt(b)*x)/sqrt(-a)/b^(2/3)-3/4*(sqrt(b)*c-sqrt(-a)*d)^(1/3)*ln((sqrt(b)*c-sqrt(-a)*d)^(1/3)-b^(1/6)*(d*x+c)^(1/3))/sqrt(-a)/b^(2/3)+3/4*(sqrt(b)*c+sqrt(-a)*d)^(1/3)*ln((sqrt(b)*c+sqrt(-a)*d)^(1/3)-b^(1/6)*(d*x+c)^(1/3))/sqrt(-a)/b^(2/3),1],
[1/(d*x+c)^(1/3)/(b*x^2+a),x,15,-1/2*sqrt(3)*arctan((1+2*b^(1/6)*(d*x+c)^(1/3)/(sqrt(b)*c-sqrt(-a)*d)^(1/3))/sqrt(3))/sqrt(-a)/b^(1/3)/(sqrt(b)*c-sqrt(-a)*d)^(1/3)+1/2*sqrt(3)*arctan((1+2*b^(1/6)*(d*x+c)^(1/3)/(sqrt(b)*c+sqrt(-a)*d)^(1/3))/sqrt(3))/sqrt(-a)/b^(1/3)/(sqrt(b)*c+sqrt(-a)*d)^(1/3)-1/4*ln(sqrt(-a)-sqrt(b)*x)/sqrt(-a)/b^(1/3)/(sqrt(b)*c+sqrt(-a)*d)^(1/3)+1/4*ln(sqrt(-a)+sqrt(b)*x)/sqrt(-a)/b^(1/3)/(sqrt(b)*c-sqrt(-a)*d)^(1/3)-3/4*ln((sqrt(b)*c-sqrt(-a)*d)^(1/3)-b^(1/6)*(d*x+c)^(1/3))/sqrt(-a)/b^(1/3)/(sqrt(b)*c-sqrt(-a)*d)^(1/3)+3/4*ln((sqrt(b)*c+sqrt(-a)*d)^(1/3)-b^(1/6)*(d*x+c)^(1/3))/sqrt(-a)/b^(1/3)/(sqrt(b)*c+sqrt(-a)*d)^(1/3),1],
[1/(d*x+c)^(2/3)/(b*x^2+a),x,13,1/2*sqrt(3)*arctan((1+2*b^(1/6)*(d*x+c)^(1/3)/(sqrt(b)*c-sqrt(-a)*d)^(1/3))/sqrt(3))/sqrt(-a)/b^(1/6)/(sqrt(b)*c-sqrt(-a)*d)^(2/3)-1/2*sqrt(3)*arctan((1+2*b^(1/6)*(d*x+c)^(1/3)/(sqrt(b)*c+sqrt(-a)*d)^(1/3))/sqrt(3))/sqrt(-a)/b^(1/6)/(sqrt(b)*c+sqrt(-a)*d)^(2/3)-1/4*ln(sqrt(-a)-sqrt(b)*x)/sqrt(-a)/b^(1/6)/(sqrt(b)*c+sqrt(-a)*d)^(2/3)+1/4*ln(sqrt(-a)+sqrt(b)*x)/sqrt(-a)/b^(1/6)/(sqrt(b)*c-sqrt(-a)*d)^(2/3)-3/4*ln((sqrt(b)*c-sqrt(-a)*d)^(1/3)-b^(1/6)*(d*x+c)^(1/3))/sqrt(-a)/b^(1/6)/(sqrt(b)*c-sqrt(-a)*d)^(2/3)+3/4*ln((sqrt(b)*c+sqrt(-a)*d)^(1/3)-b^(1/6)*(d*x+c)^(1/3))/sqrt(-a)/b^(1/6)/(sqrt(b)*c+sqrt(-a)*d)^(2/3),1],
[1/(d*x+c)^(4/3)/(b*x^2+a),x,15,-3*d/(a*d^2+b*c^2)/(d*x+c)^(1/3)-1/2*sqrt(3)*b^(1/6)*(sqrt(b)*c+sqrt(-a)*d)*arctan((1+2*b^(1/6)*(d*x+c)^(1/3)/(sqrt(b)*c-sqrt(-a)*d)^(1/3))/sqrt(3))/sqrt(-a)/(sqrt(b)*c-sqrt(-a)*d)^(1/3)/(a*d^2+b*c^2)-1/2*sqrt(3)*b^(1/6)*(sqrt(-a)*sqrt(b)*c+a*d)*arctan((1+2*b^(1/6)*(d*x+c)^(1/3)/(sqrt(b)*c+sqrt(-a)*d)^(1/3))/sqrt(3))/a/(sqrt(b)*c+sqrt(-a)*d)^(1/3)/(a*d^2+b*c^2)+1/4*b^(1/6)*(sqrt(-a)*sqrt(b)*c+a*d)*ln(sqrt(-a)-sqrt(b)*x)/a/(sqrt(b)*c+sqrt(-a)*d)^(1/3)/(a*d^2+b*c^2)-1/4*b^(1/6)*(sqrt(-a)*sqrt(b)*c-a*d)*ln(sqrt(-a)+sqrt(b)*x)/a/(sqrt(b)*c-sqrt(-a)*d)^(1/3)/(a*d^2+b*c^2)+3/4*b^(1/6)*(sqrt(-a)*sqrt(b)*c-a*d)*ln((sqrt(b)*c-sqrt(-a)*d)^(1/3)-b^(1/6)*(d*x+c)^(1/3))/a/(sqrt(b)*c-sqrt(-a)*d)^(1/3)/(a*d^2+b*c^2)-3/4*b^(1/6)*(sqrt(-a)*sqrt(b)*c+a*d)*ln((sqrt(b)*c+sqrt(-a)*d)^(1/3)-b^(1/6)*(d*x+c)^(1/3))/a/(sqrt(b)*c+sqrt(-a)*d)^(1/3)/(a*d^2+b*c^2),1],
[(d*x+c)^(3/4)*(-b*x^2+a),x,2,-4/7*(-a*d^2+b*c^2)*(d*x+c)^(7/4)/d^3+8/11*b*c*(d*x+c)^(11/4)/d^3-4/15*b*(d*x+c)^(15/4)/d^3,1],
[(d*x+c)^(1/4)*(-b*x^2+a),x,2,-4/5*(-a*d^2+b*c^2)*(d*x+c)^(5/4)/d^3+8/9*b*c*(d*x+c)^(9/4)/d^3-4/13*b*(d*x+c)^(13/4)/d^3,1],
[(-b*x^2+a)/(d*x+c)^(1/4),x,2,-4/3*(-a*d^2+b*c^2)*(d*x+c)^(3/4)/d^3+8/7*b*c*(d*x+c)^(7/4)/d^3-4/11*b*(d*x+c)^(11/4)/d^3,1],
[(-b*x^2+a)/(d*x+c)^(3/4),x,2,-4*(-a*d^2+b*c^2)*(d*x+c)^(1/4)/d^3+8/5*b*c*(d*x+c)^(5/4)/d^3-4/9*b*(d*x+c)^(9/4)/d^3,1],
[(-b*x^2+a)/(d*x+c)^(5/4),x,2,4*(-a*d^2+b*c^2)/d^3/(d*x+c)^(1/4)+8/3*b*c*(d*x+c)^(3/4)/d^3-4/7*b*(d*x+c)^(7/4)/d^3,1],
[(d*x+c)^(9/4)/(-b*x^2+a),x,10,-8*c*d*(d*x+c)^(1/4)/b-4/5*d*(d*x+c)^(5/4)/b-(sqrt(b)*c-sqrt(a)*d)^(9/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(13/8)+(sqrt(b)*c+sqrt(a)*d)^(9/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(13/8)-(sqrt(b)*c-sqrt(a)*d)^(9/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(13/8)+(sqrt(b)*c+sqrt(a)*d)^(9/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(13/8),1],
[(d*x+c)^(7/4)/(-b*x^2+a),x,9,-4/3*d*(d*x+c)^(3/4)/b+(sqrt(b)*c-sqrt(a)*d)^(7/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(11/8)-(sqrt(b)*c+sqrt(a)*d)^(7/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(11/8)-(sqrt(b)*c-sqrt(a)*d)^(7/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(11/8)+(sqrt(b)*c+sqrt(a)*d)^(7/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(11/8),1],
[(d*x+c)^(5/4)/(-b*x^2+a),x,9,-4*d*(d*x+c)^(1/4)/b-(sqrt(b)*c-sqrt(a)*d)^(5/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(9/8)+(sqrt(b)*c+sqrt(a)*d)^(5/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(9/8)-(sqrt(b)*c-sqrt(a)*d)^(5/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(9/8)+(sqrt(b)*c+sqrt(a)*d)^(5/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(9/8),1],
[(d*x+c)^(3/4)/(-b*x^2+a),x,8,(sqrt(b)*c-sqrt(a)*d)^(3/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(7/8)-(sqrt(b)*c+sqrt(a)*d)^(3/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(7/8)-(sqrt(b)*c-sqrt(a)*d)^(3/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(7/8)+(sqrt(b)*c+sqrt(a)*d)^(3/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(7/8),1],
[(d*x+c)^(1/4)/(-b*x^2+a),x,8,-(sqrt(b)*c-sqrt(a)*d)^(1/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(5/8)+(sqrt(b)*c+sqrt(a)*d)^(1/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(5/8)-(sqrt(b)*c-sqrt(a)*d)^(1/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(5/8)+(sqrt(b)*c+sqrt(a)*d)^(1/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(5/8),1],
[1/(d*x+c)^(1/4)/(-b*x^2+a),x,8,arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(3/8)/(sqrt(b)*c-sqrt(a)*d)^(1/4)-arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(3/8)/(sqrt(b)*c+sqrt(a)*d)^(1/4)-arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(3/8)/(sqrt(b)*c-sqrt(a)*d)^(1/4)+arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(3/8)/(sqrt(b)*c+sqrt(a)*d)^(1/4),1],
[1/(d*x+c)^(3/4)/(-b*x^2+a),x,8,-arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(1/8)/(sqrt(b)*c-sqrt(a)*d)^(3/4)+arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(1/8)/(sqrt(b)*c+sqrt(a)*d)^(3/4)-arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/b^(1/8)/(sqrt(b)*c-sqrt(a)*d)^(3/4)+arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/b^(1/8)/(sqrt(b)*c+sqrt(a)*d)^(3/4),1],
[1/(d*x+c)^(5/4)/(-b*x^2+a),x,9,4*d/(-a*d^2+b*c^2)/(d*x+c)^(1/4)+b^(1/8)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/(sqrt(b)*c-sqrt(a)*d)^(5/4)-b^(1/8)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/(sqrt(b)*c+sqrt(a)*d)^(5/4)-b^(1/8)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/(sqrt(b)*c-sqrt(a)*d)^(5/4)+b^(1/8)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/(sqrt(b)*c+sqrt(a)*d)^(5/4),1],
[1/(d*x+c)^(7/4)/(-b*x^2+a),x,9,4/3*d/(-a*d^2+b*c^2)/(d*x+c)^(3/4)-b^(3/8)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/(sqrt(b)*c-sqrt(a)*d)^(7/4)+b^(3/8)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/(sqrt(b)*c+sqrt(a)*d)^(7/4)-b^(3/8)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/(sqrt(b)*c-sqrt(a)*d)^(7/4)+b^(3/8)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/(sqrt(b)*c+sqrt(a)*d)^(7/4),1],
[1/(d*x+c)^(9/4)/(-b*x^2+a),x,10,4/5*d/(-a*d^2+b*c^2)/(d*x+c)^(5/4)+8*b*c*d/(-a*d^2+b*c^2)^2/(d*x+c)^(1/4)+b^(5/8)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/(sqrt(b)*c-sqrt(a)*d)^(9/4)-b^(5/8)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/(sqrt(b)*c+sqrt(a)*d)^(9/4)-b^(5/8)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/sqrt(a)/(sqrt(b)*c-sqrt(a)*d)^(9/4)+b^(5/8)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/sqrt(a)/(sqrt(b)*c+sqrt(a)*d)^(9/4),1],
[(d*x+c)^(13/4)/(-b*x^2+a)^2,x,11,1/2*d*(9*a*d^2+b*c^2)*(d*x+c)^(1/4)/a/b^2+1/2*c*d*(d*x+c)^(5/4)/a/b+1/2*(b*c*x+a*d)*(d*x+c)^(9/4)/a/b/(-b*x^2+a)-1/8*(sqrt(b)*c-sqrt(a)*d)^(9/4)*(4*sqrt(b)*c+9*sqrt(a)*d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(17/8)+1/8*(4*sqrt(b)*c-9*sqrt(a)*d)*(sqrt(b)*c+sqrt(a)*d)^(9/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(17/8)-1/8*(sqrt(b)*c-sqrt(a)*d)^(9/4)*(4*sqrt(b)*c+9*sqrt(a)*d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(17/8)+1/8*(4*sqrt(b)*c-9*sqrt(a)*d)*(sqrt(b)*c+sqrt(a)*d)^(9/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(17/8),1],
[(d*x+c)^(11/4)/(-b*x^2+a)^2,x,10,1/2*c*d*(d*x+c)^(3/4)/a/b+1/2*(b*c*x+a*d)*(d*x+c)^(7/4)/a/b/(-b*x^2+a)+1/8*(sqrt(b)*c-sqrt(a)*d)^(7/4)*(4*sqrt(b)*c+7*sqrt(a)*d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(15/8)-1/8*(4*sqrt(b)*c-7*sqrt(a)*d)*(sqrt(b)*c+sqrt(a)*d)^(7/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(15/8)-1/8*(sqrt(b)*c-sqrt(a)*d)^(7/4)*(4*sqrt(b)*c+7*sqrt(a)*d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(15/8)+1/8*(4*sqrt(b)*c-7*sqrt(a)*d)*(sqrt(b)*c+sqrt(a)*d)^(7/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(15/8),1],
[(d*x+c)^(9/4)/(-b*x^2+a)^2,x,10,1/2*c*d*(d*x+c)^(1/4)/a/b+1/2*(b*c*x+a*d)*(d*x+c)^(5/4)/a/b/(-b*x^2+a)-1/8*(sqrt(b)*c-sqrt(a)*d)^(5/4)*(4*sqrt(b)*c+5*sqrt(a)*d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(13/8)+1/8*(4*sqrt(b)*c-5*sqrt(a)*d)*(sqrt(b)*c+sqrt(a)*d)^(5/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(13/8)-1/8*(sqrt(b)*c-sqrt(a)*d)^(5/4)*(4*sqrt(b)*c+5*sqrt(a)*d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(13/8)+1/8*(4*sqrt(b)*c-5*sqrt(a)*d)*(sqrt(b)*c+sqrt(a)*d)^(5/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(13/8),1],
[(d*x+c)^(7/4)/(-b*x^2+a)^2,x,9,1/2*(b*c*x+a*d)*(d*x+c)^(3/4)/a/b/(-b*x^2+a)+1/8*(sqrt(b)*c-sqrt(a)*d)^(3/4)*(4*sqrt(b)*c+3*sqrt(a)*d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(11/8)-1/8*(4*sqrt(b)*c-3*sqrt(a)*d)*(sqrt(b)*c+sqrt(a)*d)^(3/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(11/8)-1/8*(sqrt(b)*c-sqrt(a)*d)^(3/4)*(4*sqrt(b)*c+3*sqrt(a)*d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(11/8)+1/8*(4*sqrt(b)*c-3*sqrt(a)*d)*(sqrt(b)*c+sqrt(a)*d)^(3/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(11/8),1],
[(d*x+c)^(5/4)/(-b*x^2+a)^2,x,9,1/2*(b*c*x+a*d)*(d*x+c)^(1/4)/a/b/(-b*x^2+a)-1/8*(sqrt(b)*c-sqrt(a)*d)^(1/4)*(4*sqrt(b)*c+sqrt(a)*d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(9/8)+1/8*(4*sqrt(b)*c-sqrt(a)*d)*(sqrt(b)*c+sqrt(a)*d)^(1/4)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(9/8)-1/8*(sqrt(b)*c-sqrt(a)*d)^(1/4)*(4*sqrt(b)*c+sqrt(a)*d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(9/8)+1/8*(4*sqrt(b)*c-sqrt(a)*d)*(sqrt(b)*c+sqrt(a)*d)^(1/4)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(9/8),1],
[(d*x+c)^(3/4)/(-b*x^2+a)^2,x,9,1/2*x*(d*x+c)^(3/4)/a/(-b*x^2+a)+1/8*(4*sqrt(b)*c/sqrt(a)-d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a/b^(7/8)/(sqrt(b)*c-sqrt(a)*d)^(1/4)-1/8*(4*sqrt(b)*c/sqrt(a)+d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a/b^(7/8)/(sqrt(b)*c+sqrt(a)*d)^(1/4)-1/8*(4*sqrt(b)*c/sqrt(a)-d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a/b^(7/8)/(sqrt(b)*c-sqrt(a)*d)^(1/4)+1/8*(4*sqrt(b)*c/sqrt(a)+d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a/b^(7/8)/(sqrt(b)*c+sqrt(a)*d)^(1/4),1],
[(d*x+c)^(1/4)/(-b*x^2+a)^2,x,9,1/2*x*(d*x+c)^(1/4)/a/(-b*x^2+a)-1/8*(4*sqrt(b)*c/sqrt(a)-3*d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a/b^(5/8)/(sqrt(b)*c-sqrt(a)*d)^(3/4)+1/8*(4*sqrt(b)*c/sqrt(a)+3*d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a/b^(5/8)/(sqrt(b)*c+sqrt(a)*d)^(3/4)-1/8*(4*sqrt(b)*c/sqrt(a)-3*d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a/b^(5/8)/(sqrt(b)*c-sqrt(a)*d)^(3/4)+1/8*(4*sqrt(b)*c/sqrt(a)+3*d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a/b^(5/8)/(sqrt(b)*c+sqrt(a)*d)^(3/4),1],
[1/(d*x+c)^(1/4)/(-b*x^2+a)^2,x,9,-1/2*(-b*c*x+a*d)*(d*x+c)^(3/4)/a/(-a*d^2+b*c^2)/(-b*x^2+a)+1/8*(4*sqrt(b)*c-5*sqrt(a)*d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(3/8)/(sqrt(b)*c-sqrt(a)*d)^(5/4)-1/8*(4*sqrt(b)*c+5*sqrt(a)*d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(3/8)/(sqrt(b)*c+sqrt(a)*d)^(5/4)-1/8*(4*sqrt(b)*c-5*sqrt(a)*d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(3/8)/(sqrt(b)*c-sqrt(a)*d)^(5/4)+1/8*(4*sqrt(b)*c+5*sqrt(a)*d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(3/8)/(sqrt(b)*c+sqrt(a)*d)^(5/4),1],
[1/(d*x+c)^(3/4)/(-b*x^2+a)^2,x,9,-1/2*(-b*c*x+a*d)*(d*x+c)^(1/4)/a/(-a*d^2+b*c^2)/(-b*x^2+a)-1/8*(4*sqrt(b)*c-7*sqrt(a)*d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(1/8)/(sqrt(b)*c-sqrt(a)*d)^(7/4)+1/8*(4*sqrt(b)*c+7*sqrt(a)*d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(1/8)/(sqrt(b)*c+sqrt(a)*d)^(7/4)-1/8*(4*sqrt(b)*c-7*sqrt(a)*d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/b^(1/8)/(sqrt(b)*c-sqrt(a)*d)^(7/4)+1/8*(4*sqrt(b)*c+7*sqrt(a)*d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/b^(1/8)/(sqrt(b)*c+sqrt(a)*d)^(7/4),1],
[1/(d*x+c)^(5/4)/(-b*x^2+a)^2,x,10,-1/2*d*(9*a*d^2+b*c^2)/a/(-a*d^2+b*c^2)^2/(d*x+c)^(1/4)-1/2*(-b*c*x+a*d)/a/(-a*d^2+b*c^2)/(d*x+c)^(1/4)/(-b*x^2+a)+1/8*b^(1/8)*(4*sqrt(b)*c-9*sqrt(a)*d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/(sqrt(b)*c-sqrt(a)*d)^(9/4)-1/8*b^(1/8)*(4*sqrt(b)*c+9*sqrt(a)*d)*arctan(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/(sqrt(b)*c+sqrt(a)*d)^(9/4)-1/8*b^(1/8)*(4*sqrt(b)*c-9*sqrt(a)*d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c-sqrt(a)*d)^(1/4))/a^(3/2)/(sqrt(b)*c-sqrt(a)*d)^(9/4)+1/8*b^(1/8)*(4*sqrt(b)*c+9*sqrt(a)*d)*arctanh(b^(1/8)*(d*x+c)^(1/4)/(sqrt(b)*c+sqrt(a)*d)^(1/4))/a^(3/2)/(sqrt(b)*c+sqrt(a)*d)^(9/4),1],
[(d*x+c)^4*sqrt(b*x^2+a),x,6,1/16*(a^2*d^4-12*a*b*c^2*d^2+8*b^2*c^4)*x*sqrt(b*x^2+a)/b^2+3/10*c*d*(d*x+c)^2*(b*x^2+a)^(3/2)/b+1/6*d*(d*x+c)^3*(b*x^2+a)^(3/2)/b+1/120*d*(8*c*(-8*a*d^2+13*b*c^2)+3*d*(-5*a*d^2+16*b*c^2)*x)*(b*x^2+a)^(3/2)/b^2+1/16*a*(a^2*d^4-12*a*b*c^2*d^2+8*b^2*c^4)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x+c)^3*sqrt(b*x^2+a),x,5,1/8*c*(-3*a*d^2+4*b*c^2)*x*sqrt(b*x^2+a)/b+1/5*d*(d*x+c)^2*(b*x^2+a)^(3/2)/b+1/60*d*(21*b*c*d*x-8*a*d^2+48*b*c^2)*(b*x^2+a)^(3/2)/b^2+1/8*a*c*(-3*a*d^2+4*b*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(d*x+c)^2*sqrt(b*x^2+a),x,4,1/8*(-a*d^2+4*b*c^2)*x*sqrt(b*x^2+a)/b+1/12*d*(3*d*x+8*c)*(b*x^2+a)^(3/2)/b+1/8*a*(-a*d^2+4*b*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(d*x+c)*sqrt(b*x^2+a),x,4,1/2*c*x*sqrt(b*x^2+a)+1/3*d*(b*x^2+a)^(3/2)/b+1/2*a*c*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b),1],
[sqrt(b*x^2+a)/(d*x+c),x,6,sqrt(b*x^2+a)/d-sqrt(b)*c*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^2-sqrt(a*d^2+b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^2,1],
[sqrt(b*x^2+a)/(d*x+c)^2,x,7,-sqrt(b*x^2+a)/d/(d*x+c)+sqrt(b)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^2+b*c*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^2/sqrt(a*d^2+b*c^2),1],
[sqrt(b*x^2+a)/(d*x+c)^3,x,3,-1/2*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)/(d*x+c)^2-1/2*a*b*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(3/2),1],
[sqrt(b*x^2+a)/(d*x+c)^4,x,4,-1/2*b*c*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^2/(d*x+c)^2-1/3*d*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)/(d*x+c)^3-1/2*a*b^2*c*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(5/2),1],
[sqrt(b*x^2+a)/(d*x+c)^5,x,5,-1/8*b*(-a*d^2+4*b*c^2)*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^3/(d*x+c)^2-1/4*d*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)/(d*x+c)^4-5/12*b*c*d*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)^2/(d*x+c)^3-1/8*a*b^2*(-a*d^2+4*b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(7/2),1],
[(d*x+c)^4*(b*x^2+a)^(3/2),x,7,3/128*a*(a^2*d^4-16*a*b*c^2*d^2+16*b^2*c^4)*x*sqrt(b*x^2+a)/b^2+1/64*(a^2*d^4-16*a*b*c^2*d^2+16*b^2*c^4)*x*(b*x^2+a)^(3/2)/b^2+11/56*c*d*(d*x+c)^2*(b*x^2+a)^(5/2)/b+1/8*d*(d*x+c)^3*(b*x^2+a)^(5/2)/b+1/560*d*(4*c*(-32*a*d^2+67*b*c^2)+5*d*(-7*a*d^2+26*b*c^2)*x)*(b*x^2+a)^(5/2)/b^2+3/128*a^2*(a^2*d^4-16*a*b*c^2*d^2+16*b^2*c^4)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x+c)^3*(b*x^2+a)^(3/2),x,6,3/16*a*c*(-a*d^2+2*b*c^2)*x*sqrt(b*x^2+a)/b+1/8*c*(-a*d^2+2*b*c^2)*x*(b*x^2+a)^(3/2)/b+1/7*d*(d*x+c)^2*(b*x^2+a)^(5/2)/b+1/70*d*(15*b*c*d*x-4*a*d^2+32*b*c^2)*(b*x^2+a)^(5/2)/b^2+3/16*a^2*c*(-a*d^2+2*b*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(d*x+c)^2*(b*x^2+a)^(3/2),x,5,1/16*a*(-a*d^2+6*b*c^2)*x*sqrt(b*x^2+a)/b+1/24*(-a*d^2+6*b*c^2)*x*(b*x^2+a)^(3/2)/b+1/30*d*(5*d*x+12*c)*(b*x^2+a)^(5/2)/b+1/16*a^2*(-a*d^2+6*b*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(d*x+c)*(b*x^2+a)^(3/2),x,5,3/8*a*c*x*sqrt(b*x^2+a)+1/4*c*x*(b*x^2+a)^(3/2)+1/5*d*(b*x^2+a)^(5/2)/b+3/8*a^2*c*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b),1],
[(b*x^2+a)^(3/2)/(d*x+c),x,7,1/2*(-b*c*d*x+2*a*d^2+2*b*c^2)*sqrt(b*x^2+a)/d^3+1/3*(b*x^2+a)^(3/2)/d-1/2*sqrt(b)*c*(3*a*d^2+2*b*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^4-(a*d^2+b*c^2)^(3/2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^4,1],
[(b*x^2+a)^(3/2)/(d*x+c)^2,x,9,-2*b*c*sqrt(b*x^2+a)/d^3+1/2*b*x*sqrt(b*x^2+a)/d^2-(a*d^2+b*c^2)*sqrt(b*x^2+a)/d^3/(d*x+c)+3/2*sqrt(b)*(a*d^2+2*b*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^4+3*b*c*sqrt(a*d^2+b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^4,1],
[(b*x^2+a)^(3/2)/(d*x+c)^3,x,9,b*sqrt(b*x^2+a)/d^3-1/2*(a*d^2+b*c^2)*sqrt(b*x^2+a)/d^3/(d*x+c)^2+5/2*b*c*sqrt(b*x^2+a)/d^3/(d*x+c)-3*b^(3/2)*c*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^4-3/2*b*(a*d^2+2*b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^4/sqrt(a*d^2+b*c^2),1],
[(b*x^2+a)^(3/2)/(d*x+c)^4,x,9,-1/3*(a*d^2+b*c^2)*sqrt(b*x^2+a)/d^3/(d*x+c)^3+7/6*b*c*sqrt(b*x^2+a)/d^3/(d*x+c)^2-1/6*b*(8*a*d^2+11*b*c^2)*sqrt(b*x^2+a)/d^3/(a*d^2+b*c^2)/(d*x+c)+b^(3/2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^4+1/2*b^2*c*(3*a*d^2+2*b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^4/(a*d^2+b*c^2)^(3/2),1],
[(b*x^2+a)^(3/2)/(d*x+c)^5,x,4,-3/8*a*b*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^2/(d*x+c)^2-1/4*(-b*c*x+a*d)*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)/(d*x+c)^4-3/8*a^2*b^2*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(5/2),1],
[(b*x^2+a)^(3/2)/(d*x+c)^6,x,5,-3/8*a*b^2*c*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^3/(d*x+c)^2-1/4*b*c*(-b*c*x+a*d)*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)^2/(d*x+c)^4-1/5*d*(b*x^2+a)^(5/2)/(a*d^2+b*c^2)/(d*x+c)^5-3/8*a^2*b^3*c*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(7/2),1],
[(b*x^2+a)^(3/2)/(d*x+c)^7,x,6,-1/16*a*b^2*(-a*d^2+6*b*c^2)*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^4/(d*x+c)^2-1/24*b*(-a*d^2+6*b*c^2)*(-b*c*x+a*d)*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)^3/(d*x+c)^4-1/6*d*(b*x^2+a)^(5/2)/(a*d^2+b*c^2)/(d*x+c)^6-7/30*b*c*d*(b*x^2+a)^(5/2)/(a*d^2+b*c^2)^2/(d*x+c)^5-1/16*a^2*b^3*(-a*d^2+6*b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(9/2),1],
[(d*x+c)^4*(b*x^2+a)^(5/2),x,8,1/256*a^2*(3*a^2*d^4-60*a*b*c^2*d^2+80*b^2*c^4)*x*sqrt(b*x^2+a)/b^2+1/384*a*(3*a^2*d^4-60*a*b*c^2*d^2+80*b^2*c^4)*x*(b*x^2+a)^(3/2)/b^2+1/480*(3*a^2*d^4-60*a*b*c^2*d^2+80*b^2*c^4)*x*(b*x^2+a)^(5/2)/b^2+13/90*c*d*(d*x+c)^2*(b*x^2+a)^(7/2)/b+1/10*d*(d*x+c)^3*(b*x^2+a)^(7/2)/b+1/5040*d*(16*c*(-40*a*d^2+103*b*c^2)+7*d*(-27*a*d^2+116*b*c^2)*x)*(b*x^2+a)^(7/2)/b^2+1/256*a^3*(3*a^2*d^4-60*a*b*c^2*d^2+80*b^2*c^4)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x+c)^3*(b*x^2+a)^(5/2),x,7,5/128*a^2*c*(-3*a*d^2+8*b*c^2)*x*sqrt(b*x^2+a)/b+5/192*a*c*(-3*a*d^2+8*b*c^2)*x*(b*x^2+a)^(3/2)/b+1/48*c*(-3*a*d^2+8*b*c^2)*x*(b*x^2+a)^(5/2)/b+1/9*d*(d*x+c)^2*(b*x^2+a)^(7/2)/b+1/504*d*(77*b*c*d*x-16*a*d^2+160*b*c^2)*(b*x^2+a)^(7/2)/b^2+5/128*a^3*c*(-3*a*d^2+8*b*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(d*x+c)^2*(b*x^2+a)^(5/2),x,6,5/128*a^2*(-a*d^2+8*b*c^2)*x*sqrt(b*x^2+a)/b+5/192*a*(-a*d^2+8*b*c^2)*x*(b*x^2+a)^(3/2)/b+1/48*(-a*d^2+8*b*c^2)*x*(b*x^2+a)^(5/2)/b+1/56*d*(7*d*x+16*c)*(b*x^2+a)^(7/2)/b+5/128*a^3*(-a*d^2+8*b*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(d*x+c)*(b*x^2+a)^(5/2),x,6,5/16*a^2*c*x*sqrt(b*x^2+a)+5/24*a*c*x*(b*x^2+a)^(3/2)+1/6*c*x*(b*x^2+a)^(5/2)+1/7*d*(b*x^2+a)^(7/2)/b+5/16*a^3*c*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b),1],
[(b*x^2+a)^(5/2)/(d*x+c),x,8,1/8*(8*(a*d^2+b*c^2)^2-b*c*d*(7*a*d^2+4*b*c^2)*x)*sqrt(b*x^2+a)/d^5+1/12*(-3*b*c*d*x+4*a*d^2+4*b*c^2)*(b*x^2+a)^(3/2)/d^3+1/5*(b*x^2+a)^(5/2)/d-1/8*sqrt(b)*c*(15*a^2*d^4+20*a*b*c^2*d^2+8*b^2*c^4)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^6-(a*d^2+b*c^2)^(5/2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^6,1],
[(b*x^2+a)^(5/2)/(d*x+c)^2,x,13,-4*b*c*(a*d^2+b*c^2)*sqrt(b*x^2+a)/d^5+3/8*b*(3*a*d^2+4*b*c^2)*x*sqrt(b*x^2+a)/d^4+1/4*b^2*x^3*sqrt(b*x^2+a)/d^2-(a*d^2+b*c^2)^2*sqrt(b*x^2+a)/d^5/(d*x+c)-2/3*b*c*(b*x^2+a)^(3/2)/d^3+5/8*sqrt(b)*(3*a^2*d^4+12*a*b*c^2*d^2+8*b^2*c^4)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^6+5*b*c*(a*d^2+b*c^2)^(3/2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^6,1],
[(b*x^2+a)^(5/2)/(d*x+c)^3,x,13,2*b*(a*d^2+3*b*c^2)*sqrt(b*x^2+a)/d^5-3/2*b^2*c*x*sqrt(b*x^2+a)/d^4-1/2*(a*d^2+b*c^2)^2*sqrt(b*x^2+a)/d^5/(d*x+c)^2+9/2*b*c*(a*d^2+b*c^2)*sqrt(b*x^2+a)/d^5/(d*x+c)+1/3*b*(b*x^2+a)^(3/2)/d^3-5/2*b^(3/2)*c*(3*a*d^2+4*b*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^6-5/2*b*sqrt(a*d^2+b*c^2)*(a*d^2+4*b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^6,1],
[(b*x^2+a)^(5/2)/(d*x+c)^4,x,11,-4*b^2*c*sqrt(b*x^2+a)/d^5+1/2*b^2*x*sqrt(b*x^2+a)/d^4-1/3*(a*d^2+b*c^2)^2*sqrt(b*x^2+a)/d^5/(d*x+c)^3+13/6*b*c*(a*d^2+b*c^2)*sqrt(b*x^2+a)/d^5/(d*x+c)^2-1/6*b*(14*a*d^2+47*b*c^2)*sqrt(b*x^2+a)/d^5/(d*x+c)+5/2*b^(3/2)*(a*d^2+4*b*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^6+5/2*b^2*c*(3*a*d^2+4*b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^6/sqrt(a*d^2+b*c^2),1],
[(b*x^2+a)^(5/2)/(d*x+c)^5,x,11,b^2*sqrt(b*x^2+a)/d^5-1/4*(a*d^2+b*c^2)^2*sqrt(b*x^2+a)/d^5/(d*x+c)^4+17/12*b*c*(a*d^2+b*c^2)*sqrt(b*x^2+a)/d^5/(d*x+c)^3-1/24*b*(27*a*d^2+86*b*c^2)*sqrt(b*x^2+a)/d^5/(d*x+c)^2+1/24*b^2*c*(139*a*d^2+154*b*c^2)*sqrt(b*x^2+a)/d^5/(a*d^2+b*c^2)/(d*x+c)-5*b^(5/2)*c*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^6-5/8*b^2*(3*a^2*d^4+12*a*b*c^2*d^2+8*b^2*c^4)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^6/(a*d^2+b*c^2)^(3/2),1],
[(b*x^2+a)^(5/2)/(d*x+c)^6,x,11,-1/5*(a*d^2+b*c^2)^2*sqrt(b*x^2+a)/d^5/(d*x+c)^5+21/20*b*c*(a*d^2+b*c^2)*sqrt(b*x^2+a)/d^5/(d*x+c)^4-1/60*b*(44*a*d^2+137*b*c^2)*sqrt(b*x^2+a)/d^5/(d*x+c)^3+1/120*b^2*c*(311*a*d^2+326*b*c^2)*sqrt(b*x^2+a)/d^5/(a*d^2+b*c^2)/(d*x+c)^2-1/120*b^2*(184*a^2*d^4+503*a*b*c^2*d^2+274*b^2*c^4)*sqrt(b*x^2+a)/d^5/(a*d^2+b*c^2)^2/(d*x+c)+b^(5/2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^6+1/8*b^3*c*(15*a^2*d^4+20*a*b*c^2*d^2+8*b^2*c^4)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^6/(a*d^2+b*c^2)^(5/2),1],
[(b*x^2+a)^(5/2)/(d*x+c)^7,x,5,-5/16*a^2*b^2*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^3/(d*x+c)^2-5/24*a*b*(-b*c*x+a*d)*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)^2/(d*x+c)^4-1/6*(-b*c*x+a*d)*(b*x^2+a)^(5/2)/(a*d^2+b*c^2)/(d*x+c)^6-5/16*a^3*b^3*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(7/2),1],
[(b*x^2+a)^(5/2)/(d*x+c)^8,x,6,-5/16*a^2*b^3*c*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^4/(d*x+c)^2-5/24*a*b^2*c*(-b*c*x+a*d)*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)^3/(d*x+c)^4-1/6*b*c*(-b*c*x+a*d)*(b*x^2+a)^(5/2)/(a*d^2+b*c^2)^2/(d*x+c)^6-1/7*d*(b*x^2+a)^(7/2)/(a*d^2+b*c^2)/(d*x+c)^7-5/16*a^3*b^4*c*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(9/2),1],
[(b*x^2+a)^(5/2)/(d*x+c)^9,x,7,-5/128*a^2*b^3*(-a*d^2+8*b*c^2)*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^5/(d*x+c)^2-5/192*a*b^2*(-a*d^2+8*b*c^2)*(-b*c*x+a*d)*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)^4/(d*x+c)^4-1/48*b*(-a*d^2+8*b*c^2)*(-b*c*x+a*d)*(b*x^2+a)^(5/2)/(a*d^2+b*c^2)^3/(d*x+c)^6-1/8*d*(b*x^2+a)^(7/2)/(a*d^2+b*c^2)/(d*x+c)^8-9/56*b*c*d*(b*x^2+a)^(7/2)/(a*d^2+b*c^2)^2/(d*x+c)^7-5/128*a^3*b^4*(-a*d^2+8*b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(11/2),1],
[sqrt(x^2+2)/(1+4*x),x,5,1/4*sqrt(x^2+2)-1/16*arcsinh(x/sqrt(2))-1/16*sqrt(33)*arctanh((8-x)/sqrt(33)/sqrt(x^2+2)),1],
[sqrt(4*x^2+2)/(5+4*x),x,5,1/2*sqrt(2*x^2+1)/sqrt(2)-5/8*arcsinh(sqrt(2)*x)-1/8*sqrt(33)*arctanh(sqrt(2/33)*(2-5*x)/sqrt(2*x^2+1)),1],
[(2+3*x)*sqrt(7*x^2-5),x,4,x*sqrt(7*x^2-5)+1/7*(7*x^2-5)^(3/2)-5*arctanh(sqrt(7)*x/sqrt(7*x^2-5))/sqrt(7),1],
[(d*x+c)^4/sqrt(b*x^2+a),x,5,7/12*c*d*(d*x+c)^2*sqrt(b*x^2+a)/b+1/4*d*(d*x+c)^3*sqrt(b*x^2+a)/b+1/24*d*(4*c*(-16*a*d^2+19*b*c^2)+d*(-9*a*d^2+26*b*c^2)*x)*sqrt(b*x^2+a)/b^2+1/8*(3*a^2*d^4-24*a*b*c^2*d^2+8*b^2*c^4)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x+c)^3/sqrt(b*x^2+a),x,4,1/3*d*(d*x+c)^2*sqrt(b*x^2+a)/b+1/6*d*(5*b*c*d*x-4*a*d^2+16*b*c^2)*sqrt(b*x^2+a)/b^2+1/2*c*(-3*a*d^2+2*b*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(d*x+c)^2/sqrt(b*x^2+a),x,3,1/2*d*(d*x+4*c)*sqrt(b*x^2+a)/b+1/2*(-a*d^2+2*b*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(d*x+c)/sqrt(b*x^2+a),x,3,d*sqrt(b*x^2+a)/b+c*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b),1],
[1/(d*x+c)/sqrt(b*x^2+a),x,2,-arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/sqrt(a*d^2+b*c^2),1],
[1/(d*x+c)^2/sqrt(b*x^2+a),x,3,-d*sqrt(b*x^2+a)/(a*d^2+b*c^2)/(d*x+c)-b*c*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(3/2),1],
[1/(d*x+c)^3/sqrt(b*x^2+a),x,4,-1/2*d*sqrt(b*x^2+a)/(a*d^2+b*c^2)/(d*x+c)^2-3/2*b*c*d*sqrt(b*x^2+a)/(a*d^2+b*c^2)^2/(d*x+c)-1/2*b*(-a*d^2+2*b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(5/2),1],
[1/(d*x+c)^4/sqrt(b*x^2+a),x,5,-1/3*d*sqrt(b*x^2+a)/(a*d^2+b*c^2)/(d*x+c)^3-5/6*b*c*d*sqrt(b*x^2+a)/(a*d^2+b*c^2)^2/(d*x+c)^2-1/6*b*d*(-4*a*d^2+11*b*c^2)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^3/(d*x+c)-1/2*b^2*c*(-3*a*d^2+2*b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(7/2),1],
[(d*x+c)^4/(b*x^2+a)^(3/2),x,5,-(4*a*c*d*(-a*d^2+b*c^2)-(a^2*d^4-6*a*b*c^2*d^2+b^2*c^4)*x)/a/b^2/sqrt(b*x^2+a)+4*c*d^3*sqrt(b*x^2+a)/b^2+1/2*d^4*x*sqrt(b*x^2+a)/b^2+3/2*d^2*(-a*d^2+4*b*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x+c)^3/(b*x^2+a)^(3/2),x,4,-(a*d*(-a*d^2+3*b*c^2)-b*c*(-3*a*d^2+b*c^2)*x)/a/b^2/sqrt(b*x^2+a)+d^3*sqrt(b*x^2+a)/b^2+3*c*d^2*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(d*x+c)^2/(b*x^2+a)^(3/2),x,3,-(2*a*c*d-(-a*d^2+b*c^2)*x)/a/b/sqrt(b*x^2+a)+d^2*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(d*x+c)/(b*x^2+a)^(3/2),x,1,-(-b*c*x+a*d)/a/b/sqrt(b*x^2+a),1],
[1/(d*x+c)/(b*x^2+a)^(3/2),x,3,(b*c*x+a*d)/a/(a*d^2+b*c^2)/sqrt(b*x^2+a)-d^2*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(3/2),1],
[1/(d*x+c)^2/(b*x^2+a)^(3/2),x,4,-d/(a*d^2+b*c^2)/(d*x+c)/sqrt(b*x^2+a)+b*(3*a*c*d+(-2*a*d^2+b*c^2)*x)/a/(a*d^2+b*c^2)^2/sqrt(b*x^2+a)-3*b*c*d^2*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(5/2),1],
[1/(d*x+c)^3/(b*x^2+a)^(3/2),x,5,-1/2*d/(a*d^2+b*c^2)/(d*x+c)^2/sqrt(b*x^2+a)-5/2*b*c*d/(a*d^2+b*c^2)^2/(d*x+c)/sqrt(b*x^2+a)+1/2*b*(3*a*d*(-a*d^2+4*b*c^2)+b*c*(-13*a*d^2+2*b*c^2)*x)/a/(a*d^2+b*c^2)^3/sqrt(b*x^2+a)-3/2*b*d^2*(-a*d^2+4*b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(7/2),1],
[1/(d*x+c)^4/(b*x^2+a)^(3/2),x,6,-1/3*d/(a*d^2+b*c^2)/(d*x+c)^3/sqrt(b*x^2+a)-7/6*b*c*d/(a*d^2+b*c^2)^2/(d*x+c)^2/sqrt(b*x^2+a)-1/6*b*d*(-8*a*d^2+27*b*c^2)/(a*d^2+b*c^2)^3/(d*x+c)/sqrt(b*x^2+a)+1/6*b^2*(15*a*c*d*(-3*a*d^2+4*b*c^2)+(16*a^2*d^4-83*a*b*c^2*d^2+6*b^2*c^4)*x)/a/(a*d^2+b*c^2)^4/sqrt(b*x^2+a)-5/2*b^2*c*d^2*(-3*a*d^2+4*b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(9/2),1],
[(d*x+c)^5/(b*x^2+a)^(5/2),x,5,-1/3*(a*d*(a^2*d^4-10*a*b*c^2*d^2+5*b^2*c^4)-b*c*(5*a^2*d^4-10*a*b*c^2*d^2+b^2*c^4)*x)/a/b^3/(b*x^2+a)^(3/2)-2/3*(3*a^2*d^3*(-a*d^2+5*b*c^2)-b*c*(-10*a^2*d^4+5*a*b*c^2*d^2+b^2*c^4)*x)/a^2/b^3/sqrt(b*x^2+a)+d^5*sqrt(b*x^2+a)/b^3+5*c*d^4*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x+c)^4/(b*x^2+a)^(5/2),x,4,-1/3*(4*a*c*d*(-a*d^2+b*c^2)-(a^2*d^4-6*a*b*c^2*d^2+b^2*c^4)*x)/a/b^2/(b*x^2+a)^(3/2)-2/3*(6*a^2*c*d^3-(-2*a^2*d^4+3*a*b*c^2*d^2+b^2*c^4)*x)/a^2/b^2/sqrt(b*x^2+a)+d^4*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x+c)^3/(b*x^2+a)^(5/2),x,2,-1/3*(a*d*(-a*d^2+3*b*c^2)-b*c*(-3*a*d^2+b*c^2)*x)/a/b^2/(b*x^2+a)^(3/2)-1/3*(3*a^2*d^3-b*c*(3*a*d^2+2*b*c^2)*x)/a^2/b^2/sqrt(b*x^2+a),1],
[(d*x+c)^2/(b*x^2+a)^(5/2),x,2,-1/3*(2*a*c*d-(-a*d^2+b*c^2)*x)/a/b/(b*x^2+a)^(3/2)+1/3*(a*d^2+2*b*c^2)*x/a^2/b/sqrt(b*x^2+a),1],
[(d*x+c)/(b*x^2+a)^(5/2),x,2,1/3*(b*c*x-a*d)/a/b/(b*x^2+a)^(3/2)+2/3*c*x/a^2/sqrt(b*x^2+a),1],
[1/(d*x+c)/(b*x^2+a)^(5/2),x,4,1/3*(b*c*x+a*d)/a/(a*d^2+b*c^2)/(b*x^2+a)^(3/2)+1/3*(3*a^2*d^3+b*c*(5*a*d^2+2*b*c^2)*x)/a^2/(a*d^2+b*c^2)^2/sqrt(b*x^2+a)-d^4*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(5/2),1],
[1/(d*x+c)^2/(b*x^2+a)^(5/2),x,5,-d/(a*d^2+b*c^2)/(d*x+c)/(b*x^2+a)^(3/2)+1/3*b*(5*a*c*d+(-4*a*d^2+b*c^2)*x)/a/(a*d^2+b*c^2)^2/(b*x^2+a)^(3/2)+1/3*b*(15*a^2*c*d^3+(-8*a^2*d^4+9*a*b*c^2*d^2+2*b^2*c^4)*x)/a^2/(a*d^2+b*c^2)^3/sqrt(b*x^2+a)-5*b*c*d^4*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(7/2),1],
[1/(d*x+c)^3/(b*x^2+a)^(5/2),x,6,-1/2*d/(a*d^2+b*c^2)/(d*x+c)^2/(b*x^2+a)^(3/2)-7/2*b*c*d/(a*d^2+b*c^2)^2/(d*x+c)/(b*x^2+a)^(3/2)+1/6*b*(5*a*d*(-a*d^2+6*b*c^2)+b*c*(-33*a*d^2+2*b*c^2)*x)/a/(a*d^2+b*c^2)^3/(b*x^2+a)^(3/2)+1/6*b*(15*a^2*d^3*(-a*d^2+6*b*c^2)+b*c*(-81*a^2*d^4+28*a*b*c^2*d^2+4*b^2*c^4)*x)/a^2/(a*d^2+b*c^2)^4/sqrt(b*x^2+a)-5/2*b*d^4*(-a*d^2+6*b*c^2)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(9/2),1],
[(d*x+c)^3/(d^2*x^2+c^2)^(3/2),x,4,-2*c*(d*x+c)/d/sqrt(d^2*x^2+c^2)+sqrt(d^2*x^2+c^2)/d+3*c*arctanh(d*x/sqrt(d^2*x^2+c^2))/d,1],
[(3+x)/sqrt(-x^2+1),x,2,-sqrt(-x^2+1)+3*arcsin(x),1],
[(1+x)/sqrt(-x^2+4),x,2,-sqrt(-x^2+4)+arcsin(1/2*x),1],
[(2+x)/sqrt(x^2+9),x,2,sqrt(x^2+9)+2*arcsinh(1/3*x),1],
[(b*x+a)^2/sqrt(-x^2+1),x,2,-1/2*b*(b*x+4*a)*sqrt(-x^2+1)+1/2*(2*a^2+b^2)*arcsin(x),1],
[(b*x+a)^2/sqrt(x^2+1),x,2,1/2*b*(b*x+4*a)*sqrt(x^2+1)+1/2*(2*a^2-b^2)*arcsinh(x),1],
[(2+3*x)/(x^2+4)^(3/2),x,1,-1/2*(6-x)/sqrt(x^2+4),1],
[(d*x+c)^(3/2)*sqrt(-b*x^2+a),x,12,-4/105*(3*c^2/d+5*a*d/b)*sqrt(d*x+c)*sqrt(-b*x^2+a)-4/35*c*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/d+2/7*(d*x+c)^(5/2)*sqrt(-b*x^2+a)/d-4/105*sqrt(a)*c*(29*a*d^2+3*b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^2/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+4/105*sqrt(a)*(-5*a^2*d^4+2*a*b*c^2*d^2+3*b^2*c^4)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^2/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(d*x+c)*sqrt(-b*x^2+a),x,11,-4/15*c*sqrt(d*x+c)*sqrt(-b*x^2+a)/d+2/5*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/d-4/15*sqrt(a)*(3*a*d^2+b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^2/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+4/15*sqrt(a)*c*(-a*d^2+b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^2/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(-b*x^2+a)/sqrt(d*x+c),x,10,2/3*sqrt(d*x+c)*sqrt(-b*x^2+a)/d-4/3*sqrt(a)*sqrt(b)*c*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^2/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+4/3*sqrt(a)*(-a*d^2+b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^2/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(-b*x^2+a)/(d*x+c)^(3/2),x,10,-2*sqrt(-b*x^2+a)/d/sqrt(d*x+c)+4*sqrt(a)*sqrt(b)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^2/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-4*sqrt(a)*sqrt(b)*c*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^2/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(-b*x^2+a)/(d*x+c)^(5/2),x,11,-2/3*sqrt(-b*x^2+a)/d/(d*x+c)^(3/2)+4/3*b*c*sqrt(-b*x^2+a)/d/(-a*d^2+b*c^2)/sqrt(d*x+c)-4/3*sqrt(a)*b^(3/2)*c*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^2/(-a*d^2+b*c^2)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+4/3*sqrt(a)*sqrt(b)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^2/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(-b*x^2+a)/(d*x+c)^(7/2),x,12,-2/5*sqrt(-b*x^2+a)/d/(d*x+c)^(5/2)+4/15*b*c*sqrt(-b*x^2+a)/d/(-a*d^2+b*c^2)/(d*x+c)^(3/2)+4/15*b*(3*a*d^2+b*c^2)*sqrt(-b*x^2+a)/d/(-a*d^2+b*c^2)^2/sqrt(d*x+c)-4/15*sqrt(a)*b^(3/2)*(3*a*d^2+b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^2/(-a*d^2+b*c^2)^2/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+4/15*sqrt(a)*b^(3/2)*c*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^2/(-a*d^2+b*c^2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(3/2)*(-b*x^2+a)^(3/2),x,13,-8/1155*(21*a*c^2-4*b*c^4/d^2+15*a^2*d^2/b)*sqrt(d*x+c)*sqrt(-b*x^2+a)/d+32/1155*c*(-4*a*d^2+b*c^2)*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/d^3-4/231*(d*x+c)^(5/2)*(-7*b*c*d*x-9*a*d^2+4*b*c^2)*sqrt(-b*x^2+a)/d^3+2/11*(d*x+c)^(5/2)*(-b*x^2+a)^(3/2)/d+32/1155*sqrt(a)*c*(-9*a*d^2+b*c^2)*(3*a*d^2+b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^4/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-8/1155*sqrt(a)*(15*a^3*d^6+6*a^2*b*c^2*d^4-25*a*b^2*c^4*d^2+4*b^3*c^6)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^4/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(d*x+c)*(-b*x^2+a)^(3/2),x,12,32/315*c*(-3*a*d^2+b*c^2)*sqrt(d*x+c)*sqrt(-b*x^2+a)/d^3-4/105*(d*x+c)^(3/2)*(-5*b*c*d*x-7*a*d^2+4*b*c^2)*sqrt(-b*x^2+a)/d^3+2/9*(d*x+c)^(3/2)*(-b*x^2+a)^(3/2)/d+8/315*sqrt(a)*(-21*a^2*d^4-15*a*b*c^2*d^2+4*b^2*c^4)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^4/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-32/315*sqrt(a)*c*(3*a^2*d^4-4*a*b*c^2*d^2+b^2*c^4)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^4/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(3/2)/sqrt(d*x+c),x,11,-4/35*sqrt(d*x+c)*(-3*b*c*d*x-5*a*d^2+4*b*c^2)*sqrt(-b*x^2+a)/d^3+2/7*sqrt(d*x+c)*(-b*x^2+a)^(3/2)/d+32/35*sqrt(a)*sqrt(b)*c*(-2*a*d^2+b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^4/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-8/35*sqrt(a)*(5*a^2*d^4-9*a*b*c^2*d^2+4*b^2*c^4)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^4/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(3/2)/(d*x+c)^(3/2),x,12,28/5*b*c*sqrt(d*x+c)*sqrt(-b*x^2+a)/d^3-12/5*b*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/d^3-2*(-b*x^2+a)^(3/2)/d/sqrt(d*x+c)-8/5*sqrt(a)*sqrt(b)*(-3*a*d^2+4*b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^4/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+32/5*sqrt(a)*sqrt(b)*c*(-a*d^2+b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^4/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(3/2)/(d*x+c)^(5/2),x,12,-4*b*c*sqrt(-b*x^2+a)/d^3/sqrt(d*x+c)-4/3*b*sqrt(d*x+c)*sqrt(-b*x^2+a)/d^3-2/3*(-b*x^2+a)^(3/2)/d/(d*x+c)^(3/2)+32/3*sqrt(a)*b^(3/2)*c*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^4/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-8/3*sqrt(a)*sqrt(b)*(-a*d^2+4*b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^4/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(3/2)/(d*x+c)^(7/2),x,12,-4/5*b*c*sqrt(-b*x^2+a)/d^3/(d*x+c)^(3/2)+4/5*b*(-3*a*d^2+5*b*c^2)*sqrt(-b*x^2+a)/d^3/(-a*d^2+b*c^2)/sqrt(d*x+c)-2/5*(-b*x^2+a)^(3/2)/d/(d*x+c)^(5/2)-8/5*sqrt(a)*b^(3/2)*(-3*a*d^2+4*b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^4/(-a*d^2+b*c^2)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+32/5*sqrt(a)*b^(3/2)*c*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^4/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(3/2)/(d*x+c)^(9/2),x,13,-12/35*b*c*sqrt(-b*x^2+a)/d^3/(d*x+c)^(5/2)+4/35*b*(-5*a*d^2+7*b*c^2)*sqrt(-b*x^2+a)/d^3/(-a*d^2+b*c^2)/(d*x+c)^(3/2)-32/35*b^2*c*(-2*a*d^2+b*c^2)*sqrt(-b*x^2+a)/d^3/(-a*d^2+b*c^2)^2/sqrt(d*x+c)-2/7*(-b*x^2+a)^(3/2)/d/(d*x+c)^(7/2)+32/35*sqrt(a)*b^(5/2)*c*(-2*a*d^2+b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^4/(-a*d^2+b*c^2)^2/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-8/35*sqrt(a)*b^(3/2)*(-5*a*d^2+4*b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^4/(-a*d^2+b*c^2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(d*x+c)*(-b*x^2+a)^(5/2),x,13,-16/9009*c*(177*a^2*d^4-113*a*b*c^2*d^2+32*b^2*c^4)*sqrt(d*x+c)*sqrt(-b*x^2+a)/d^5+8/3003*(d*x+c)^(3/2)*(32*b^2*c^4-73*a*b*c^2*d^2+77*a^2*d^4-20*b*c*d*(-5*a*d^2+2*b*c^2)*x)*sqrt(-b*x^2+a)/d^5-20/1287*(d*x+c)^(3/2)*(-9*b*c*d*x-11*a*d^2+8*b*c^2)*(-b*x^2+a)^(3/2)/d^3+2/13*(d*x+c)^(3/2)*(-b*x^2+a)^(5/2)/d-16/9009*sqrt(a)*(231*a^3*d^6+258*a^2*b*c^2*d^4-137*a*b^2*c^4*d^2+32*b^3*c^6)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^6/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+16/9009*sqrt(a)*c*(-177*a^3*d^6+290*a^2*b*c^2*d^4-145*a*b^2*c^4*d^2+32*b^3*c^6)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^6/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(5/2)/sqrt(d*x+c),x,12,8/693*sqrt(d*x+c)*(32*b^2*c^4-69*a*b*c^2*d^2+45*a^2*d^4-24*b*c*d*(-2*a*d^2+b*c^2)*x)*sqrt(-b*x^2+a)/d^5-20/693*sqrt(d*x+c)*(-7*b*c*d*x-9*a*d^2+8*b*c^2)*(-b*x^2+a)^(3/2)/d^3+2/11*sqrt(d*x+c)*(-b*x^2+a)^(5/2)/d-16/693*sqrt(a)*sqrt(b)*c*(93*a^2*d^4-93*a*b*c^2*d^2+32*b^2*c^4)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^6/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+16/693*sqrt(a)*(-45*a^3*d^6+114*a^2*b*c^2*d^4-101*a*b^2*c^4*d^2+32*b^3*c^6)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^6/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(5/2)/(d*x+c)^(3/2),x,13,-8/63*b*sqrt(d*x+c)*(c*(-33*a*d^2+32*b*c^2)-3*d*(-7*a*d^2+8*b*c^2)*x)*sqrt(-b*x^2+a)/d^5+100/21*b*c*sqrt(d*x+c)*(-b*x^2+a)^(3/2)/d^3-20/9*b*(d*x+c)^(3/2)*(-b*x^2+a)^(3/2)/d^3-2*(-b*x^2+a)^(5/2)/d/sqrt(d*x+c)+16/63*sqrt(a)*sqrt(b)*(21*a^2*d^4-57*a*b*c^2*d^2+32*b^2*c^4)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^6/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-16/63*sqrt(a)*sqrt(b)*c*(33*a^2*d^4-65*a*b*c^2*d^2+32*b^2*c^4)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^6/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(5/2)/(d*x+c)^(5/2),x,13,8/21*b*sqrt(d*x+c)*(-24*b*c*d*x-5*a*d^2+32*b*c^2)*sqrt(-b*x^2+a)/d^5-20/3*b*c*(-b*x^2+a)^(3/2)/d^3/sqrt(d*x+c)-20/21*b*sqrt(d*x+c)*(-b*x^2+a)^(3/2)/d^3-2/3*(-b*x^2+a)^(5/2)/d/(d*x+c)^(3/2)-16/21*sqrt(a)*b^(3/2)*c*(-29*a*d^2+32*b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^6/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+16/21*sqrt(a)*sqrt(b)*(5*a^2*d^4-37*a*b*c^2*d^2+32*b^2*c^4)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^6/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(5/2)/(d*x+c)^(7/2),x,13,-8/15*b^2*sqrt(d*x+c)*(c*(-17*a*d^2+32*b*c^2)-3*d*(-3*a*d^2+8*b*c^2)*x)*sqrt(-b*x^2+a)/d^5/(-a*d^2+b*c^2)-4/3*b*c*(-b*x^2+a)^(3/2)/d^3/(d*x+c)^(3/2)+4*b*(-a*d^2+3*b*c^2)*(-b*x^2+a)^(3/2)/d^3/(-a*d^2+b*c^2)/sqrt(d*x+c)-2/5*(-b*x^2+a)^(5/2)/d/(d*x+c)^(5/2)+16/15*sqrt(a)*b^(3/2)*(-9*a*d^2+32*b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^6/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-16/15*sqrt(a)*b^(3/2)*c*(-17*a*d^2+32*b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^6/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(5/2)/(d*x+c)^(9/2),x,13,8/21*b^2*(c*(-29*a*d^2+32*b*c^2)+d*(-5*a*d^2+8*b*c^2)*x)*sqrt(-b*x^2+a)/d^5/(-a*d^2+b*c^2)/sqrt(d*x+c)-4/7*b*c*(-b*x^2+a)^(3/2)/d^3/(d*x+c)^(5/2)+4/21*b*(-5*a*d^2+11*b*c^2)*(-b*x^2+a)^(3/2)/d^3/(-a*d^2+b*c^2)/(d*x+c)^(3/2)-2/7*(-b*x^2+a)^(5/2)/d/(d*x+c)^(7/2)-16/21*sqrt(a)*b^(5/2)*c*(-29*a*d^2+32*b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^6/(-a*d^2+b*c^2)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+16/21*sqrt(a)*b^(3/2)*(-5*a*d^2+32*b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^6/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(5/2)/(d*x+c)^(11/2),x,14,-16/63*b^2*(21*a^2*d^4-57*a*b*c^2*d^2+32*b^2*c^4)*sqrt(-b*x^2+a)/d^5/(-a*d^2+b*c^2)^2/sqrt(d*x+c)+8/63*b^2*(c*(-33*a*d^2+32*b*c^2)+3*d*(-7*a*d^2+8*b*c^2)*x)*sqrt(-b*x^2+a)/d^5/(-a*d^2+b*c^2)/(d*x+c)^(3/2)-20/63*b*c*(-b*x^2+a)^(3/2)/d^3/(d*x+c)^(7/2)+4/63*b*(-7*a*d^2+13*b*c^2)*(-b*x^2+a)^(3/2)/d^3/(-a*d^2+b*c^2)/(d*x+c)^(5/2)-2/9*(-b*x^2+a)^(5/2)/d/(d*x+c)^(9/2)+16/63*sqrt(a)*b^(5/2)*(21*a^2*d^4-57*a*b*c^2*d^2+32*b^2*c^4)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^6/(-a*d^2+b*c^2)^2/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-16/63*sqrt(a)*b^(5/2)*c*(-33*a*d^2+32*b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^6/(-a*d^2+b*c^2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(7/2)/sqrt(-b*x^2+a),x,12,-2/105*d*(25*a*d^2+71*b*c^2)*sqrt(d*x+c)*sqrt(-b*x^2+a)/b^2-24/35*c*d*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/b-2/7*d*(d*x+c)^(5/2)*sqrt(-b*x^2+a)/b-32/105*sqrt(a)*c*(13*a*d^2+11*b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+2/105*sqrt(a)*(-25*a^2*d^4-46*a*b*c^2*d^2+71*b^2*c^4)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(5/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(5/2)/sqrt(-b*x^2+a),x,11,-16/15*c*d*sqrt(d*x+c)*sqrt(-b*x^2+a)/b-2/5*d*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/b-2/15*sqrt(a)*(9*a*d^2+23*b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+16/15*sqrt(a)*c*(-a*d^2+b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(3/2)/sqrt(-b*x^2+a),x,10,-2/3*d*sqrt(d*x+c)*sqrt(-b*x^2+a)/b-8/3*sqrt(a)*c*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+2/3*sqrt(a)*(-a*d^2+b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(d*x+c)/sqrt(-b*x^2+a),x,4,-2*sqrt(a)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a),1],
[1/sqrt(d*x+c)/sqrt(-b*x^2+a),x,4,-2*sqrt(a)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[1/(d*x+c)^(3/2)/sqrt(-b*x^2+a),x,6,2*d*sqrt(-b*x^2+a)/(-a*d^2+b*c^2)/sqrt(d*x+c)-2*sqrt(a)*sqrt(b)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/(-a*d^2+b*c^2)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a),1],
[1/(d*x+c)^(5/2)/sqrt(-b*x^2+a),x,11,2/3*d*sqrt(-b*x^2+a)/(-a*d^2+b*c^2)/(d*x+c)^(3/2)+8/3*b*c*d*sqrt(-b*x^2+a)/(-a*d^2+b*c^2)^2/sqrt(d*x+c)-8/3*sqrt(a)*b^(3/2)*c*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/(-a*d^2+b*c^2)^2/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+2/3*sqrt(a)*sqrt(b)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/(-a*d^2+b*c^2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[1/(d*x+c)^(7/2)/sqrt(-b*x^2+a),x,12,2/5*d*sqrt(-b*x^2+a)/(-a*d^2+b*c^2)/(d*x+c)^(5/2)+16/15*b*c*d*sqrt(-b*x^2+a)/(-a*d^2+b*c^2)^2/(d*x+c)^(3/2)+2/15*b*d*(9*a*d^2+23*b*c^2)*sqrt(-b*x^2+a)/(-a*d^2+b*c^2)^3/sqrt(d*x+c)-2/15*sqrt(a)*b^(3/2)*(9*a*d^2+23*b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/(-a*d^2+b*c^2)^3/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)+16/15*sqrt(a)*b^(3/2)*c*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/(-a*d^2+b*c^2)^2/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(7/2)/(-b*x^2+a)^(3/2),x,12,(b*c*x+a*d)*(d*x+c)^(5/2)/a/b/sqrt(-b*x^2+a)+1/3*d*(5*a*d^2+3*b*c^2)*sqrt(d*x+c)*sqrt(-b*x^2+a)/a/b^2+c*d*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/a/b+1/3*c*(29*a*d^2+3*b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/b^(3/2)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-1/3*(-5*a^2*d^4+2*a*b*c^2*d^2+3*b^2*c^4)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/b^(5/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(5/2)/(-b*x^2+a)^(3/2),x,11,(b*c*x+a*d)*(d*x+c)^(3/2)/a/b/sqrt(-b*x^2+a)+c*d*sqrt(d*x+c)*sqrt(-b*x^2+a)/a/b+(3*a*d^2+b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/b^(3/2)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-c*(-a*d^2+b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/b^(3/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(3/2)/(-b*x^2+a)^(3/2),x,10,(b*c*x+a*d)*sqrt(d*x+c)/a/b/sqrt(-b*x^2+a)+c*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/sqrt(b)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-(-a*d^2+b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/b^(3/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(d*x+c)/(-b*x^2+a)^(3/2),x,11,x*sqrt(d*x+c)/a/sqrt(-b*x^2+a)+sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/sqrt(b)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-c*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/sqrt(b)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[1/sqrt(d*x+c)/(-b*x^2+a)^(3/2),x,10,-(-b*c*x+a*d)*sqrt(d*x+c)/a/(-a*d^2+b*c^2)/sqrt(-b*x^2+a)+sqrt(b)*c*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/(-a*d^2+b*c^2)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/sqrt(b)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[1/(d*x+c)^(3/2)/(-b*x^2+a)^(3/2),x,11,2*d/(-a*d^2+b*c^2)/sqrt(d*x+c)/sqrt(-b*x^2+a)-b*sqrt(d*x+c)*(4*a*c*d-(3*a*d^2+b*c^2)*x)/a/(-a*d^2+b*c^2)^2/sqrt(-b*x^2+a)+sqrt(b)*(3*a*d^2+b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/(-a*d^2+b*c^2)^2/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-sqrt(b)*c*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/(-a*d^2+b*c^2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[1/(d*x+c)^(5/2)/(-b*x^2+a)^(3/2),x,12,2/3*d/(-a*d^2+b*c^2)/(d*x+c)^(3/2)/sqrt(-b*x^2+a)+16/3*b*c*d/(-a*d^2+b*c^2)^2/sqrt(d*x+c)/sqrt(-b*x^2+a)-1/3*b*sqrt(d*x+c)*(a*d*(5*a*d^2+27*b*c^2)-b*c*(29*a*d^2+3*b*c^2)*x)/a/(-a*d^2+b*c^2)^3/sqrt(-b*x^2+a)+1/3*b^(3/2)*c*(29*a*d^2+3*b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/(-a*d^2+b*c^2)^3/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-1/3*sqrt(b)*(5*a*d^2+3*b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/(-a*d^2+b*c^2)^2/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(9/2)/(-b*x^2+a)^(5/2),x,12,1/3*(b*c*x+a*d)*(d*x+c)^(7/2)/a/b/(-b*x^2+a)^(3/2)+1/6*(d*x+c)^(3/2)*(a*d*(-7*a*d^2+b*c^2)+2*b*c*(-5*a*d^2+2*b*c^2)*x)/a^2/b^2/sqrt(-b*x^2+a)+2/3*c*d*(-3*a*d^2+b*c^2)*sqrt(d*x+c)*sqrt(-b*x^2+a)/a^2/b^2+1/6*(-21*a^2*d^4-15*a*b*c^2*d^2+4*b^2*c^4)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(5/2)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-2/3*c*(3*a^2*d^4-4*a*b*c^2*d^2+b^2*c^4)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(5/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(7/2)/(-b*x^2+a)^(5/2),x,11,1/3*(b*c*x+a*d)*(d*x+c)^(5/2)/a/b/(-b*x^2+a)^(3/2)+1/6*sqrt(d*x+c)*(a*d*(-5*a*d^2+3*b*c^2)+2*b*c*(-3*a*d^2+2*b*c^2)*x)/a^2/b^2/sqrt(-b*x^2+a)+2/3*c*(-2*a*d^2+b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(3/2)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-1/6*(5*a^2*d^4-9*a*b*c^2*d^2+4*b^2*c^4)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(5/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(5/2)/(-b*x^2+a)^(5/2),x,11,1/3*(b*c*x+a*d)*(d*x+c)^(3/2)/a/b/(-b*x^2+a)^(3/2)+1/6*sqrt(d*x+c)*(a*c*d+(-3*a*d^2+4*b*c^2)*x)/a^2/b/sqrt(-b*x^2+a)+1/6*(-3*a*d^2+4*b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(3/2)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-2/3*c*(-a*d^2+b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(3/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(3/2)/(-b*x^2+a)^(5/2),x,11,1/3*(b*c*x+a*d)*sqrt(d*x+c)/a/b/(-b*x^2+a)^(3/2)-1/6*(-4*b*c*x+a*d)*sqrt(d*x+c)/a^2/b/sqrt(-b*x^2+a)+2/3*c*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/sqrt(b)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-1/6*(-a*d^2+4*b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(3/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(d*x+c)/(-b*x^2+a)^(5/2),x,11,1/3*x*sqrt(d*x+c)/a/(-b*x^2+a)^(3/2)-1/6*sqrt(d*x+c)*(a*c*d-(-3*a*d^2+4*b*c^2)*x)/a^2/(-a*d^2+b*c^2)/sqrt(-b*x^2+a)+1/6*(-3*a*d^2+4*b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/sqrt(b)/(-a*d^2+b*c^2)/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-2/3*c*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/sqrt(b)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[1/sqrt(d*x+c)/(-b*x^2+a)^(5/2),x,11,-1/3*(-b*c*x+a*d)*sqrt(d*x+c)/a/(-a*d^2+b*c^2)/(-b*x^2+a)^(3/2)-1/6*sqrt(d*x+c)*(a*d*(-5*a*d^2+b*c^2)-4*b*c*(-2*a*d^2+b*c^2)*x)/a^2/(-a*d^2+b*c^2)^2/sqrt(-b*x^2+a)+2/3*sqrt(b)*c*(-2*a*d^2+b*c^2)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/(-a*d^2+b*c^2)^2/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-1/6*(-5*a*d^2+4*b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/sqrt(b)/(-a*d^2+b*c^2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[1/(d*x+c)^(3/2)/(-b*x^2+a)^(5/2),x,12,2*d/(-a*d^2+b*c^2)/sqrt(d*x+c)/(-b*x^2+a)^(3/2)-1/3*b*sqrt(d*x+c)*(8*a*c*d-(7*a*d^2+b*c^2)*x)/a/(-a*d^2+b*c^2)^2/(-b*x^2+a)^(3/2)-1/6*b*sqrt(d*x+c)*(a*c*d*(-33*a*d^2+b*c^2)-(-21*a^2*d^4-15*a*b*c^2*d^2+4*b^2*c^4)*x)/a^2/(-a*d^2+b*c^2)^3/sqrt(-b*x^2+a)+1/6*sqrt(b)*(-21*a^2*d^4-15*a*b*c^2*d^2+4*b^2*c^4)*sqrt(d*x+c)*sqrt(1-b*x^2/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/(-a*d^2+b*c^2)^3/sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))/sqrt(-b*x^2+a)-2/3*sqrt(b)*c*(-3*a*d^2+b*c^2)*sqrt(sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d))*sqrt(1-b*x^2/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/(-a*d^2+b*c^2)^2/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[1/(e*x+d)/(3*e^2*x^2+d^2)^(1/3),x,1,-1/2*arctan(1/sqrt(3)+2^(2/3)*(-e*x+d)/sqrt(3)/d^(1/3)/(3*e^2*x^2+d^2)^(1/3))*2^(1/3)/sqrt(3)/d^(2/3)/e-1/4*ln(e*x+d)*2^(1/3)/d^(2/3)/e+1/4*ln(3*2^(2/3)*d^(2/3)*e^2*(-e*x+d)-6*d*e^2*(3*e^2*x^2+d^2)^(1/3))*2^(1/3)/d^(2/3)/e,1],
[(2+3*x)^3/(27*x^2+4)^(1/3),x,6,1/30*(2+3*x)^2*(27*x^2+4)^(2/3)+4/35*(7+4*x)*(27*x^2+4)^(2/3)-96*x/(7*2^(2/3)*(1-sqrt(3))-7*(27*x^2+4)^(1/3))+16/63*2^(1/3)*sqrt(2+sqrt(3))*(2^(2/3)-(27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(27*x^2+4)^(1/3)+(27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)*EllipticE(sin(arcsin((2^(2/3)*(1+sqrt(3))-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/x/sqrt(-(2^(2/3)-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)-32/189*2^(5/6)*(2^(2/3)-(27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(27*x^2+4)^(1/3)+(27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)*InverseJacobiAM(arcsin((2^(2/3)*(1+sqrt(3))-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))),sqrt(-7+4*sqrt(3)))*3^(3/4)/x/sqrt(-(2^(2/3)-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2),1],
[(2+3*x)^2/(27*x^2+4)^(1/3),x,5,1/21*(7+3*x)*(27*x^2+4)^(2/3)-72*x/(7*2^(2/3)*(1-sqrt(3))-7*(27*x^2+4)^(1/3))+4/21*2^(1/3)*sqrt(2+sqrt(3))*(2^(2/3)-(27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(27*x^2+4)^(1/3)+(27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)*EllipticE(sin(arcsin((2^(2/3)*(1+sqrt(3))-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/x/sqrt(-(2^(2/3)-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)-8/63*2^(5/6)*(2^(2/3)-(27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(27*x^2+4)^(1/3)+(27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)*InverseJacobiAM(arcsin((2^(2/3)*(1+sqrt(3))-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))),sqrt(-7+4*sqrt(3)))*3^(3/4)/x/sqrt(-(2^(2/3)-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2),1],
[(2+3*x)/(27*x^2+4)^(1/3),x,5,1/12*(27*x^2+4)^(2/3)-6*x/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))+1/9*2^(1/3)*sqrt(2+sqrt(3))*(2^(2/3)-(27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(27*x^2+4)^(1/3)+(27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)*EllipticE(sin(arcsin((2^(2/3)*(1+sqrt(3))-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/x/sqrt(-(2^(2/3)-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)-2/27*2^(5/6)*(2^(2/3)-(27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(27*x^2+4)^(1/3)+(27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)*InverseJacobiAM(arcsin((2^(2/3)*(1+sqrt(3))-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))),sqrt(-7+4*sqrt(3)))*3^(3/4)/x/sqrt(-(2^(2/3)-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2),1],
[1/(2+3*x)/(27*x^2+4)^(1/3),x,1,-1/12*arctan(1/sqrt(3)+2^(1/3)*(2-3*x)/sqrt(3)/(27*x^2+4)^(1/3))*2^(2/3)/sqrt(3)-1/24*ln(2+3*x)*2^(2/3)+1/24*ln(54*2^(1/3)*(2-3*x)-108*(27*x^2+4)^(1/3))*2^(2/3),1],
[1/(2+3*x)^2/(27*x^2+4)^(1/3),x,7,-1/48*(27*x^2+4)^(2/3)/(2+3*x)-3*x/(16*2^(2/3)*(1-sqrt(3))-16*(27*x^2+4)^(1/3))-1/48*arctan(1/sqrt(3)+2^(1/3)*(2-3*x)/sqrt(3)/(27*x^2+4)^(1/3))*2^(2/3)/sqrt(3)+1/288*sqrt(2+sqrt(3))*(2^(2/3)-(27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(27*x^2+4)^(1/3)+(27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)*EllipticE(sin(arcsin((2^(2/3)*(1+sqrt(3))-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3)))),sqrt(-7+4*sqrt(3)))*2^(1/3)*3^(1/4)/x/sqrt(-(2^(2/3)-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)-1/432*(2^(2/3)-(27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(27*x^2+4)^(1/3)+(27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)*InverseJacobiAM(arcsin((2^(2/3)*(1+sqrt(3))-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))),sqrt(-7+4*sqrt(3)))*2^(5/6)*3^(3/4)/x/sqrt(-(2^(2/3)-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)-1/96*ln(2+3*x)*2^(2/3)+1/96*ln(54*2^(1/3)*(2-3*x)-108*(27*x^2+4)^(1/3))*2^(2/3),1],
[1/(2+3*x)^3/(27*x^2+4)^(1/3),x,8,-1/96*(27*x^2+4)^(2/3)/(2+3*x)^2-(27*x^2+4)^(2/3)/(192+288*x)-3*x/(32*2^(2/3)*(1-sqrt(3))-32*(27*x^2+4)^(1/3))-1/192*arctan(1/sqrt(3)+2^(1/3)*(2-3*x)/sqrt(3)/(27*x^2+4)^(1/3))*2^(2/3)/sqrt(3)+1/576*sqrt(2+sqrt(3))*(2^(2/3)-(27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(27*x^2+4)^(1/3)+(27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)*EllipticE(sin(arcsin((2^(2/3)*(1+sqrt(3))-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3)))),sqrt(-7+4*sqrt(3)))*2^(1/3)*3^(1/4)/x/sqrt(-(2^(2/3)-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)-1/864*(2^(2/3)-(27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(27*x^2+4)^(1/3)+(27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)*InverseJacobiAM(arcsin((2^(2/3)*(1+sqrt(3))-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))),sqrt(-7+4*sqrt(3)))*2^(5/6)*3^(3/4)/x/sqrt(-(2^(2/3)-(27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(27*x^2+4)^(1/3))^2)-1/384*ln(2+3*x)*2^(2/3)+1/384*ln(54*2^(1/3)*(2-3*x)-108*(27*x^2+4)^(1/3))*2^(2/3),1],
[(2+3*I*x)^3/(-27*x^2+4)^(1/3),x,6,-4/35*(7*I-4*x)*(-27*x^2+4)^(2/3)-1/30*I*(2+3*I*x)^2*(-27*x^2+4)^(2/3)-96*x/(7*2^(2/3)*(1-sqrt(3))-7*(-27*x^2+4)^(1/3))-16/63*2^(1/3)*sqrt(2+sqrt(3))*(2^(2/3)-(-27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(-27*x^2+4)^(1/3)+(-27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)*EllipticE(sin(arcsin((2^(2/3)*(1+sqrt(3))-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/x/sqrt(-(2^(2/3)-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)+32/189*2^(5/6)*(2^(2/3)-(-27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(-27*x^2+4)^(1/3)+(-27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)*InverseJacobiAM(arcsin((2^(2/3)*(1+sqrt(3))-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))),sqrt(-7+4*sqrt(3)))*3^(3/4)/x/sqrt(-(2^(2/3)-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2),1],
[(2+3*I*x)^2/(-27*x^2+4)^(1/3),x,5,-1/21*I*(7+3*I*x)*(-27*x^2+4)^(2/3)-72*x/(7*2^(2/3)*(1-sqrt(3))-7*(-27*x^2+4)^(1/3))-4/21*2^(1/3)*sqrt(2+sqrt(3))*(2^(2/3)-(-27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(-27*x^2+4)^(1/3)+(-27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)*EllipticE(sin(arcsin((2^(2/3)*(1+sqrt(3))-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/x/sqrt(-(2^(2/3)-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)+8/63*2^(5/6)*(2^(2/3)-(-27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(-27*x^2+4)^(1/3)+(-27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)*InverseJacobiAM(arcsin((2^(2/3)*(1+sqrt(3))-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))),sqrt(-7+4*sqrt(3)))*3^(3/4)/x/sqrt(-(2^(2/3)-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2),1],
[(2+3*I*x)/(-27*x^2+4)^(1/3),x,5,-1/12*I*(-27*x^2+4)^(2/3)-6*x/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))-1/9*2^(1/3)*sqrt(2+sqrt(3))*(2^(2/3)-(-27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(-27*x^2+4)^(1/3)+(-27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)*EllipticE(sin(arcsin((2^(2/3)*(1+sqrt(3))-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/x/sqrt(-(2^(2/3)-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)+2/27*2^(5/6)*(2^(2/3)-(-27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(-27*x^2+4)^(1/3)+(-27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)*InverseJacobiAM(arcsin((2^(2/3)*(1+sqrt(3))-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))),sqrt(-7+4*sqrt(3)))*3^(3/4)/x/sqrt(-(2^(2/3)-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2),1],
[1/(2+3*I*x)/(-27*x^2+4)^(1/3),x,1,1/12*I*arctan(1/sqrt(3)+2^(1/3)*(2-3*I*x)/sqrt(3)/(-27*x^2+4)^(1/3))*2^(2/3)/sqrt(3)+1/24*I*ln(2+3*I*x)*2^(2/3)-1/24*I*ln(-54*2^(1/3)*(2-3*I*x)+108*(-27*x^2+4)^(1/3))*2^(2/3),1],
[1/(2+3*I*x)^2/(-27*x^2+4)^(1/3),x,7,1/48*I*(-27*x^2+4)^(2/3)/(2+3*I*x)-3*x/(16*2^(2/3)*(1-sqrt(3))-16*(-27*x^2+4)^(1/3))+1/48*I*arctan(1/sqrt(3)+2^(1/3)*(2-3*I*x)/sqrt(3)/(-27*x^2+4)^(1/3))*2^(2/3)/sqrt(3)-1/288*2^(1/3)*sqrt(2+sqrt(3))*(2^(2/3)-(-27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(-27*x^2+4)^(1/3)+(-27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)*EllipticE(sin(arcsin((2^(2/3)*(1+sqrt(3))-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/x/sqrt(-(2^(2/3)-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)+1/432*2^(5/6)*(2^(2/3)-(-27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(-27*x^2+4)^(1/3)+(-27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)*InverseJacobiAM(arcsin((2^(2/3)*(1+sqrt(3))-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))),sqrt(-7+4*sqrt(3)))*3^(3/4)/x/sqrt(-(2^(2/3)-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)+1/96*I*ln(2+3*I*x)*2^(2/3)-1/96*I*ln(-54*2^(1/3)*(2-3*I*x)+108*(-27*x^2+4)^(1/3))*2^(2/3),1],
[1/(2+3*I*x)^3/(-27*x^2+4)^(1/3),x,8,1/96*I*(-27*x^2+4)^(2/3)/(2+3*I*x)^2+1/96*I*(-27*x^2+4)^(2/3)/(2+3*I*x)-3*x/(32*2^(2/3)*(1-sqrt(3))-32*(-27*x^2+4)^(1/3))+1/192*I*arctan(1/sqrt(3)+2^(1/3)*(2-3*I*x)/sqrt(3)/(-27*x^2+4)^(1/3))*2^(2/3)/sqrt(3)-1/576*2^(1/3)*sqrt(2+sqrt(3))*(2^(2/3)-(-27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(-27*x^2+4)^(1/3)+(-27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)*EllipticE(sin(arcsin((2^(2/3)*(1+sqrt(3))-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/x/sqrt(-(2^(2/3)-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)+1/864*2^(5/6)*(2^(2/3)-(-27*x^2+4)^(1/3))*sqrt((2*2^(1/3)+2^(2/3)*(-27*x^2+4)^(1/3)+(-27*x^2+4)^(2/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)*InverseJacobiAM(arcsin((2^(2/3)*(1+sqrt(3))-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))),sqrt(-7+4*sqrt(3)))*3^(3/4)/x/sqrt(-(2^(2/3)-(-27*x^2+4)^(1/3))/(2^(2/3)*(1-sqrt(3))-(-27*x^2+4)^(1/3))^2)+1/384*I*ln(2+3*I*x)*2^(2/3)-1/384*I*ln(-54*2^(1/3)*(2-3*I*x)+108*(-27*x^2+4)^(1/3))*2^(2/3),1],
[1/(sqrt(3)+x)/(x^2+1)^(1/3),x,1,-1/2*arctan(1/sqrt(3)+1/3*2^(2/3)*(sqrt(3)-x)/(x^2+1)^(1/3))*2^(1/3)/sqrt(3)-1/4*ln(sqrt(3)+x)*2^(1/3)+1/4*ln(2^(2/3)*(sqrt(3)-x)-2*sqrt(3)*(x^2+1)^(1/3))*2^(1/3),1],
[1/(sqrt(3)-x)/(x^2+1)^(1/3),x,1,1/2*arctan(1/sqrt(3)+1/3*2^(2/3)*(sqrt(3)+x)/(x^2+1)^(1/3))*2^(1/3)/sqrt(3)+1/4*ln(sqrt(3)-x)*2^(1/3)-1/4*ln(2^(2/3)*(sqrt(3)+x)-2*sqrt(3)*(x^2+1)^(1/3))*2^(1/3),1],
[1/(3-x)/(-x^2+1)^(1/3),x,1,-1/4*sqrt(3)*arctan(1/sqrt(3)-(1+x)/sqrt(3)/(-x^2+1)^(1/3))-1/4*ln(3-x)-1/8*ln(3+3*x)+3/8*ln(3+3*x+6*(-x^2+1)^(1/3)),1],
[1/(3+x)/(-x^2+1)^(1/3),x,1,1/4*sqrt(3)*arctan(1/sqrt(3)-(1-x)/sqrt(3)/(-x^2+1)^(1/3))+1/8*ln(3-3*x)+1/4*ln(3+x)-3/8*ln(3-3*x+6*(-x^2+1)^(1/3)),1],
[1/(d*x+c)/(-9*d^2*x^2+c^2)^(1/3),x,1,1/4*sqrt(3)*arctan(1/sqrt(3)-(-3*d*x+c)/sqrt(3)/c^(1/3)/(-9*d^2*x^2+c^2)^(1/3))/c^(2/3)/d+1/8*ln(-3*d*x+c)/c^(2/3)/d+1/4*ln(d*x+c)/c^(2/3)/d-3/8*ln(c^(2/3)*(-3*d*x+c)+2*c*(-9*d^2*x^2+c^2)^(1/3))/c^(2/3)/d,1],
[(1+x)^3/(-2*x^2+1)^(1/4),x,3,-1/7*(1+x)^2*(-2*x^2+1)^(3/4)-1/105*(100+33*x)*(-2*x^2+1)^(3/4)+8/5*sqrt(2)*EllipticE(sin(1/2*arcsin(sqrt(2)*x)),sqrt(2)),1],
[(1+x)^2/(-2*x^2+1)^(1/4),x,2,-1/15*(10+3*x)*(-2*x^2+1)^(3/4)+6/5*sqrt(2)*EllipticE(sin(1/2*arcsin(sqrt(2)*x)),sqrt(2)),1],
[(1+x)/(-2*x^2+1)^(1/4),x,2,-1/3*(-2*x^2+1)^(3/4)+sqrt(2)*EllipticE(sin(1/2*arcsin(sqrt(2)*x)),sqrt(2)),1],
[1/(-2*x^2+1)^(1/4),x,1,sqrt(2)*EllipticE(sin(1/2*arcsin(sqrt(2)*x)),sqrt(2)),1],
[1/(1+x)/(-2*x^2+1)^(1/4),x,2,1/2*(2*x^2-1)^(1/4)*arctan((2*x^2-1)^(1/4)/(1+x-sqrt(2*x^2-1)))/(-2*x^2+1)^(1/4)-1/2*(2*x^2-1)^(1/4)*arctanh((2*x^2-1)^(1/4)/(1+x+sqrt(2*x^2-1)))/(-2*x^2+1)^(1/4),1],
[1/(1+x)^2/(-2*x^2+1)^(1/4),x,5,(-2*x^2+1)^(3/4)/(1+x)+1/2*(2*x^2-1)^(1/4)*arctan((2*x^2-1)^(1/4)/(1+x-sqrt(2*x^2-1)))/(-2*x^2+1)^(1/4)-1/2*(2*x^2-1)^(1/4)*arctanh((2*x^2-1)^(1/4)/(1+x+sqrt(2*x^2-1)))/(-2*x^2+1)^(1/4)+sqrt(2)*EllipticE(sin(1/2*arcsin(sqrt(2)*x)),sqrt(2)),1],
[1/(1+x)^3/(-2*x^2+1)^(1/4),x,6,1/2*(-2*x^2+1)^(3/4)/(1+x)^2+5*(-2*x^2+1)^(3/4)/(2+2*x)+(2*x^2-1)^(1/4)*arctan((2*x^2-1)^(1/4)/(1+x-sqrt(2*x^2-1)))/(-2*x^2+1)^(1/4)-(2*x^2-1)^(1/4)*arctanh((2*x^2-1)^(1/4)/(1+x+sqrt(2*x^2-1)))/(-2*x^2+1)^(1/4)+5*EllipticE(sin(1/2*arcsin(sqrt(2)*x)),sqrt(2))/sqrt(2),1],
[(d*x+c)^3/(-2*a*d^2*x^2+a*c^2)^(1/4),x,4,-1/7*(d*x+c)^2*(-2*a*d^2*x^2+a*c^2)^(3/4)/a/d-1/105*c*(33*d*x+100*c)*(-2*a*d^2*x^2+a*c^2)^(3/4)/a/d+8/5*sqrt(2)*c^4*(1-2*d^2*x^2/c^2)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(2)*d*x/c)),sqrt(2))/d/(-2*a*d^2*x^2+a*c^2)^(1/4),1],
[(d*x+c)^2/(-2*a*d^2*x^2+a*c^2)^(1/4),x,3,-1/15*(3*d*x+10*c)*(-2*a*d^2*x^2+a*c^2)^(3/4)/a/d+6/5*sqrt(2)*c^3*(1-2*d^2*x^2/c^2)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(2)*d*x/c)),sqrt(2))/d/(-2*a*d^2*x^2+a*c^2)^(1/4),1],
[(d*x+c)/(-2*a*d^2*x^2+a*c^2)^(1/4),x,3,-1/3*(-2*a*d^2*x^2+a*c^2)^(3/4)/a/d+sqrt(2)*c^2*(1-2*d^2*x^2/c^2)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(2)*d*x/c)),sqrt(2))/d/(-2*a*d^2*x^2+a*c^2)^(1/4),1],
[1/(-2*a*d^2*x^2+a*c^2)^(1/4),x,2,sqrt(2)*c*(1-2*d^2*x^2/c^2)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(2)*d*x/c)),sqrt(2))/d/(-2*a*d^2*x^2+a*c^2)^(1/4),1],
[1/(d*x+c)/(-2*a*d^2*x^2+a*c^2)^(1/4),x,2,1/2*(2*a*d^2*x^2-a*c^2)^(1/4)*arctan(a^(1/4)*c^(3/2)*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c*(d*x+c)-c*sqrt(2*a*d^2*x^2-a*c^2)))/a^(1/4)/sqrt(c)/d/(-2*a*d^2*x^2+a*c^2)^(1/4)-1/2*(2*a*d^2*x^2-a*c^2)^(1/4)*arctanh(a^(1/4)*c^(3/2)*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c*(d*x+c)+c*sqrt(2*a*d^2*x^2-a*c^2)))/a^(1/4)/sqrt(c)/d/(-2*a*d^2*x^2+a*c^2)^(1/4),1],
[1/(d*x+c)^2/(-2*a*d^2*x^2+a*c^2)^(1/4),x,6,(-2*a*d^2*x^2+a*c^2)^(3/4)/a/c^2/d/(d*x+c)+1/2*(2*a*d^2*x^2-a*c^2)^(1/4)*arctan(a^(1/4)*c^(3/2)*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c*(d*x+c)-c*sqrt(2*a*d^2*x^2-a*c^2)))/a^(1/4)/c^(3/2)/d/(-2*a*d^2*x^2+a*c^2)^(1/4)-1/2*(2*a*d^2*x^2-a*c^2)^(1/4)*arctanh(a^(1/4)*c^(3/2)*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c*(d*x+c)+c*sqrt(2*a*d^2*x^2-a*c^2)))/a^(1/4)/c^(3/2)/d/(-2*a*d^2*x^2+a*c^2)^(1/4)+sqrt(2)*(1-2*d^2*x^2/c^2)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(2)*d*x/c)),sqrt(2))/c/d/(-2*a*d^2*x^2+a*c^2)^(1/4),1],
[1/(d*x+c)^3/(-2*a*d^2*x^2+a*c^2)^(1/4),x,7,1/2*(-2*a*d^2*x^2+a*c^2)^(3/4)/a/c^2/d/(d*x+c)^2+5/2*(-2*a*d^2*x^2+a*c^2)^(3/4)/a/c^3/d/(d*x+c)+(2*a*d^2*x^2-a*c^2)^(1/4)*arctan(a^(1/4)*c^(3/2)*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c*(d*x+c)-c*sqrt(2*a*d^2*x^2-a*c^2)))/a^(1/4)/c^(5/2)/d/(-2*a*d^2*x^2+a*c^2)^(1/4)-(2*a*d^2*x^2-a*c^2)^(1/4)*arctanh(a^(1/4)*c^(3/2)*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c*(d*x+c)+c*sqrt(2*a*d^2*x^2-a*c^2)))/a^(1/4)/c^(5/2)/d/(-2*a*d^2*x^2+a*c^2)^(1/4)+5*(1-2*d^2*x^2/c^2)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(2)*d*x/c)),sqrt(2))/sqrt(2)/c^2/d/(-2*a*d^2*x^2+a*c^2)^(1/4),1],
[(1+x)^3/(2*x^2-1)^(1/4),x,7,1/7*(1+x)^2*(2*x^2-1)^(3/4)+1/105*(100+33*x)*(2*x^2-1)^(3/4)+16*x*(2*x^2-1)^(1/4)/(5+5*sqrt(2*x^2-1))-8/5*sqrt(2)*sqrt(x^2/(1+sqrt(2*x^2-1))^2)*(1+sqrt(2*x^2-1))*EllipticE(sin(2*arctan((2*x^2-1)^(1/4))),sqrt(1/2))/x+4/5*sqrt(2)*sqrt(x^2/(1+sqrt(2*x^2-1))^2)*(1+sqrt(2*x^2-1))*InverseJacobiAM(2*arctan((2*x^2-1)^(1/4)),sqrt(1/2))/x,1],
[(1+x)^2/(2*x^2-1)^(1/4),x,6,1/15*(10+3*x)*(2*x^2-1)^(3/4)+12*x*(2*x^2-1)^(1/4)/(5+5*sqrt(2*x^2-1))-6/5*sqrt(2)*sqrt(x^2/(1+sqrt(2*x^2-1))^2)*(1+sqrt(2*x^2-1))*EllipticE(sin(2*arctan((2*x^2-1)^(1/4))),sqrt(1/2))/x+3/5*sqrt(2)*sqrt(x^2/(1+sqrt(2*x^2-1))^2)*(1+sqrt(2*x^2-1))*InverseJacobiAM(2*arctan((2*x^2-1)^(1/4)),sqrt(1/2))/x,1],
[(1+x)/(2*x^2-1)^(1/4),x,6,1/3*(2*x^2-1)^(3/4)+2*x*(2*x^2-1)^(1/4)/(1+sqrt(2*x^2-1))-sqrt(2)*sqrt(x^2/(1+sqrt(2*x^2-1))^2)*(1+sqrt(2*x^2-1))*EllipticE(sin(2*arctan((2*x^2-1)^(1/4))),sqrt(1/2))/x+sqrt(x^2/(1+sqrt(2*x^2-1))^2)*(1+sqrt(2*x^2-1))*InverseJacobiAM(2*arctan((2*x^2-1)^(1/4)),sqrt(1/2))/sqrt(2)/x,1],
[1/(2*x^2-1)^(1/4),x,5,2*x*(2*x^2-1)^(1/4)/(1+sqrt(2*x^2-1))-sqrt(2)*sqrt(x^2/(1+sqrt(2*x^2-1))^2)*(1+sqrt(2*x^2-1))*EllipticE(sin(2*arctan((2*x^2-1)^(1/4))),sqrt(1/2))/x+sqrt(x^2/(1+sqrt(2*x^2-1))^2)*(1+sqrt(2*x^2-1))*InverseJacobiAM(2*arctan((2*x^2-1)^(1/4)),sqrt(1/2))/sqrt(2)/x,1],
[1/(1+x)/(2*x^2-1)^(1/4),x,1,1/2*arctan((2*x^2-1)^(1/4)/(1+x-sqrt(2*x^2-1)))-1/2*arctanh((2*x^2-1)^(1/4)/(1+x+sqrt(2*x^2-1))),1],
[1/(1+x)^2/(2*x^2-1)^(1/4),x,8,-(2*x^2-1)^(3/4)/(1+x)+2*x*(2*x^2-1)^(1/4)/(1+sqrt(2*x^2-1))+1/2*arctan((2*x^2-1)^(1/4)/(1+x-sqrt(2*x^2-1)))-1/2*arctanh((2*x^2-1)^(1/4)/(1+x+sqrt(2*x^2-1)))-sqrt(2)*sqrt(x^2/(1+sqrt(2*x^2-1))^2)*(1+sqrt(2*x^2-1))*EllipticE(sin(2*arctan((2*x^2-1)^(1/4))),sqrt(1/2))/x+sqrt(x^2/(1+sqrt(2*x^2-1))^2)*(1+sqrt(2*x^2-1))*InverseJacobiAM(2*arctan((2*x^2-1)^(1/4)),sqrt(1/2))/sqrt(2)/x,1],
[1/(1+x)^3/(2*x^2-1)^(1/4),x,9,-1/2*(2*x^2-1)^(3/4)/(1+x)^2-5*(2*x^2-1)^(3/4)/(2+2*x)+5*x*(2*x^2-1)^(1/4)/(1+sqrt(2*x^2-1))+arctan((2*x^2-1)^(1/4)/(1+x-sqrt(2*x^2-1)))-arctanh((2*x^2-1)^(1/4)/(1+x+sqrt(2*x^2-1)))-5*sqrt(x^2/(1+sqrt(2*x^2-1))^2)*(1+sqrt(2*x^2-1))*EllipticE(sin(2*arctan((2*x^2-1)^(1/4))),sqrt(1/2))/sqrt(2)/x+5/2*sqrt(x^2/(1+sqrt(2*x^2-1))^2)*(1+sqrt(2*x^2-1))*InverseJacobiAM(2*arctan((2*x^2-1)^(1/4)),sqrt(1/2))/sqrt(2)/x,1],
[(d*x+c)^3/(2*a*d^2*x^2-a*c^2)^(1/4),x,7,1/7*(d*x+c)^2*(2*a*d^2*x^2-a*c^2)^(3/4)/a/d+1/105*c*(33*d*x+100*c)*(2*a*d^2*x^2-a*c^2)^(3/4)/a/d+16*c^3*x*(2*a*d^2*x^2-a*c^2)^(1/4)/(5*sqrt(a)*c+5*sqrt(2*a*d^2*x^2-a*c^2))-8/5*sqrt(2)*c^(7/2)*sqrt(a*d^2*x^2/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))^2)*(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))*EllipticE(sin(2*arctan((2*a*d^2*x^2-a*c^2)^(1/4)/a^(1/4)/sqrt(c))),sqrt(1/2))/a^(3/4)/d^2/x+4/5*sqrt(2)*c^(7/2)*sqrt(a*d^2*x^2/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))^2)*(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))*InverseJacobiAM(2*arctan((2*a*d^2*x^2-a*c^2)^(1/4)/a^(1/4)/sqrt(c)),sqrt(1/2))/a^(3/4)/d^2/x,1],
[(d*x+c)^2/(2*a*d^2*x^2-a*c^2)^(1/4),x,6,1/15*(3*d*x+10*c)*(2*a*d^2*x^2-a*c^2)^(3/4)/a/d+12*c^2*x*(2*a*d^2*x^2-a*c^2)^(1/4)/(5*sqrt(a)*c+5*sqrt(2*a*d^2*x^2-a*c^2))-6/5*sqrt(2)*c^(5/2)*sqrt(a*d^2*x^2/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))^2)*(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))*EllipticE(sin(2*arctan((2*a*d^2*x^2-a*c^2)^(1/4)/a^(1/4)/sqrt(c))),sqrt(1/2))/a^(3/4)/d^2/x+3/5*sqrt(2)*c^(5/2)*sqrt(a*d^2*x^2/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))^2)*(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))*InverseJacobiAM(2*arctan((2*a*d^2*x^2-a*c^2)^(1/4)/a^(1/4)/sqrt(c)),sqrt(1/2))/a^(3/4)/d^2/x,1],
[(d*x+c)/(2*a*d^2*x^2-a*c^2)^(1/4),x,6,1/3*(2*a*d^2*x^2-a*c^2)^(3/4)/a/d+2*c*x*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))-sqrt(2)*c^(3/2)*sqrt(a*d^2*x^2/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))^2)*(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))*EllipticE(sin(2*arctan((2*a*d^2*x^2-a*c^2)^(1/4)/a^(1/4)/sqrt(c))),sqrt(1/2))/a^(3/4)/d^2/x+c^(3/2)*sqrt(a*d^2*x^2/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))^2)*(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))*InverseJacobiAM(2*arctan((2*a*d^2*x^2-a*c^2)^(1/4)/a^(1/4)/sqrt(c)),sqrt(1/2))/sqrt(2)/a^(3/4)/d^2/x,1],
[1/(2*a*d^2*x^2-a*c^2)^(1/4),x,5,2*x*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))-sqrt(2)*sqrt(c)*sqrt(a*d^2*x^2/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))^2)*(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))*EllipticE(sin(2*arctan((2*a*d^2*x^2-a*c^2)^(1/4)/a^(1/4)/sqrt(c))),sqrt(1/2))/a^(3/4)/d^2/x+sqrt(c)*sqrt(a*d^2*x^2/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))^2)*(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))*InverseJacobiAM(2*arctan((2*a*d^2*x^2-a*c^2)^(1/4)/a^(1/4)/sqrt(c)),sqrt(1/2))/sqrt(2)/a^(3/4)/d^2/x,1],
[1/(d*x+c)/(2*a*d^2*x^2-a*c^2)^(1/4),x,1,1/2*arctan(a^(1/4)*c^(3/2)*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c*(d*x+c)-c*sqrt(2*a*d^2*x^2-a*c^2)))/a^(1/4)/sqrt(c)/d-1/2*arctanh(a^(1/4)*c^(3/2)*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c*(d*x+c)+c*sqrt(2*a*d^2*x^2-a*c^2)))/a^(1/4)/sqrt(c)/d,1],
[1/(d*x+c)^2/(2*a*d^2*x^2-a*c^2)^(1/4),x,8,-(2*a*d^2*x^2-a*c^2)^(3/4)/a/c^2/d/(d*x+c)+2*x*(2*a*d^2*x^2-a*c^2)^(1/4)/c^2/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))+1/2*arctan(a^(1/4)*c^(3/2)*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c*(d*x+c)-c*sqrt(2*a*d^2*x^2-a*c^2)))/a^(1/4)/c^(3/2)/d-1/2*arctanh(a^(1/4)*c^(3/2)*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c*(d*x+c)+c*sqrt(2*a*d^2*x^2-a*c^2)))/a^(1/4)/c^(3/2)/d-sqrt(2)*sqrt(a*d^2*x^2/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))^2)*(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))*EllipticE(sin(2*arctan((2*a*d^2*x^2-a*c^2)^(1/4)/a^(1/4)/sqrt(c))),sqrt(1/2))/a^(3/4)/c^(3/2)/d^2/x+sqrt(a*d^2*x^2/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))^2)*(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))*InverseJacobiAM(2*arctan((2*a*d^2*x^2-a*c^2)^(1/4)/a^(1/4)/sqrt(c)),sqrt(1/2))/sqrt(2)/a^(3/4)/c^(3/2)/d^2/x,1],
[1/(d*x+c)^3/(2*a*d^2*x^2-a*c^2)^(1/4),x,9,-1/2*(2*a*d^2*x^2-a*c^2)^(3/4)/a/c^2/d/(d*x+c)^2-5/2*(2*a*d^2*x^2-a*c^2)^(3/4)/a/c^3/d/(d*x+c)+5*x*(2*a*d^2*x^2-a*c^2)^(1/4)/c^3/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))+arctan(a^(1/4)*c^(3/2)*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c*(d*x+c)-c*sqrt(2*a*d^2*x^2-a*c^2)))/a^(1/4)/c^(5/2)/d-arctanh(a^(1/4)*c^(3/2)*(2*a*d^2*x^2-a*c^2)^(1/4)/(sqrt(a)*c*(d*x+c)+c*sqrt(2*a*d^2*x^2-a*c^2)))/a^(1/4)/c^(5/2)/d-5*sqrt(a*d^2*x^2/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))^2)*(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))*EllipticE(sin(2*arctan((2*a*d^2*x^2-a*c^2)^(1/4)/a^(1/4)/sqrt(c))),sqrt(1/2))/sqrt(2)/a^(3/4)/c^(5/2)/d^2/x+5/2*sqrt(a*d^2*x^2/(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))^2)*(sqrt(a)*c+sqrt(2*a*d^2*x^2-a*c^2))*InverseJacobiAM(2*arctan((2*a*d^2*x^2-a*c^2)^(1/4)/a^(1/4)/sqrt(c)),sqrt(1/2))/sqrt(2)/a^(3/4)/c^(5/2)/d^2/x,1],
[1/(b*x+a)/(d*x^2+c)^(1/4),x,10,arctan(sqrt(b)*(d*x^2+c)^(1/4)/(a^2*d+b^2*c)^(1/4))/sqrt(b)/(a^2*d+b^2*c)^(1/4)-arctanh(sqrt(b)*(d*x^2+c)^(1/4)/(a^2*d+b^2*c)^(1/4))/sqrt(b)/(a^2*d+b^2*c)^(1/4)-a*c^(1/4)*sqrt(-d*x^2/c)*EllipticPi(sin(arcsin((d*x^2+c)^(1/4)/c^(1/4))),-b*sqrt(c)/sqrt(a^2*d+b^2*c),sqrt(-1))/b/sqrt(a^2*d+b^2*c)/x+a*c^(1/4)*sqrt(-d*x^2/c)*EllipticPi(sin(arcsin((d*x^2+c)^(1/4)/c^(1/4))),b*sqrt(c)/sqrt(a^2*d+b^2*c),sqrt(-1))/b/sqrt(a^2*d+b^2*c)/x,1],
[1/(b*x+a)/(d*x^2+c)^(3/4),x,11,-sqrt(b)*arctan(sqrt(b)*(d*x^2+c)^(1/4)/(a^2*d+b^2*c)^(1/4))/(a^2*d+b^2*c)^(3/4)-sqrt(b)*arctanh(sqrt(b)*(d*x^2+c)^(1/4)/(a^2*d+b^2*c)^(1/4))/(a^2*d+b^2*c)^(3/4)+a*c^(1/4)*sqrt(-d*x^2/c)*EllipticPi(sin(arcsin((d*x^2+c)^(1/4)/c^(1/4))),-b*sqrt(c)/sqrt(a^2*d+b^2*c),sqrt(-1))/(a^2*d+b^2*c)/x+a*c^(1/4)*sqrt(-d*x^2/c)*EllipticPi(sin(arcsin((d*x^2+c)^(1/4)/c^(1/4))),b*sqrt(c)/sqrt(a^2*d+b^2*c),sqrt(-1))/(a^2*d+b^2*c)/x,1],
[1/(e*x+d)^(3/2)/(c*x^2+a)^(1/4),x,1,-2*(sqrt(-a)-sqrt(c)*x)*(-(sqrt(c)*d+sqrt(-a)*e)*(sqrt(-a)+sqrt(c)*x)/(sqrt(c)*d-sqrt(-a)*e)/(sqrt(-a)-sqrt(c)*x))^(1/4)*hypergeom([-1/2, 1/4],[1/2],2*sqrt(-a)*sqrt(c)*(e*x+d)/(sqrt(c)*d-sqrt(-a)*e)/(sqrt(-a)-sqrt(c)*x))/sqrt(c)/(d+sqrt(-a)*e/sqrt(c))/sqrt(e*x+d)/(c*x^2+a)^(1/4),1],
[1/(1+x)/(x^2+1)^(1/6),x,14,x*AppellF1(1/2,1,1/6,3/2,x^2,-x^2)-1/4*sqrt(3)*arctan((1-2^(5/6)*(x^2+1)^(1/6))/sqrt(3))*2^(5/6)+1/4*sqrt(3)*arctan((1+2^(5/6)*(x^2+1)^(1/6))/sqrt(3))*2^(5/6)-1/2*arctanh(1/2*2^(5/6)*(x^2+1)^(1/6))*2^(5/6)-1/4*arctanh(2^(1/6)*(x^2+1)^(1/6)/(2^(1/3)+(x^2+1)^(1/3)))*2^(5/6),1],
[(d*x+c)^m*(b*x^2+a)^3,x,2,(a*d^2+b*c^2)^3*(d*x+c)^(1+m)/d^7/(1+m)-6*b*c*(a*d^2+b*c^2)^2*(d*x+c)^(2+m)/d^7/(2+m)+3*b*(a*d^2+b*c^2)*(a*d^2+5*b*c^2)*(d*x+c)^(3+m)/d^7/(3+m)-4*b^2*c*(3*a*d^2+5*b*c^2)*(d*x+c)^(4+m)/d^7/(4+m)+3*b^2*(a*d^2+5*b*c^2)*(d*x+c)^(5+m)/d^7/(5+m)-6*b^3*c*(d*x+c)^(6+m)/d^7/(6+m)+b^3*(d*x+c)^(7+m)/d^7/(7+m),1],
[(d*x+c)^m*(b*x^2+a)^2,x,2,(a*d^2+b*c^2)^2*(d*x+c)^(1+m)/d^5/(1+m)-4*b*c*(a*d^2+b*c^2)*(d*x+c)^(2+m)/d^5/(2+m)+2*b*(a*d^2+3*b*c^2)*(d*x+c)^(3+m)/d^5/(3+m)-4*b^2*c*(d*x+c)^(4+m)/d^5/(4+m)+b^2*(d*x+c)^(5+m)/d^5/(5+m),1],
[(d*x+c)^m*(b*x^2+a),x,2,(a*d^2+b*c^2)*(d*x+c)^(1+m)/d^3/(1+m)-2*b*c*(d*x+c)^(2+m)/d^3/(2+m)+b*(d*x+c)^(3+m)/d^3/(3+m),1],
[(d*x+c)^m/(b*x^2+a),x,3,1/2*(d*x+c)^(1+m)*hypergeom([1, 1+m],[2+m],sqrt(b)*(d*x+c)/(sqrt(b)*c-sqrt(-a)*d))/(sqrt(-a)*sqrt(b)*c+a*d)/(1+m)+1/2*(d*x+c)^(1+m)*hypergeom([1, 1+m],[2+m],sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(-a)*d))/a/(sqrt(b)*c/sqrt(-a)+d)/(1+m),1],
[(d*x+c)^m/(b*x^2+a)^2,x,4,1/2*(b*c*x+a*d)*(d*x+c)^(1+m)/a/(a*d^2+b*c^2)/(b*x^2+a)-1/4*(b*c^2+a*d^2*(1-m)+sqrt(-a)*sqrt(b)*c*d*m)*(d*x+c)^(1+m)*hypergeom([1, 1+m],[2+m],sqrt(b)*(d*x+c)/(sqrt(b)*c-sqrt(-a)*d))/(-a)^(3/2)/(sqrt(b)*c-sqrt(-a)*d)/(a*d^2+b*c^2)/(1+m)+1/4*(b*c^2+a*d^2*(1-m)-sqrt(-a)*sqrt(b)*c*d*m)*(d*x+c)^(1+m)*hypergeom([1, 1+m],[2+m],sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(-a)*d))/(-a)^(3/2)/(sqrt(b)*c+sqrt(-a)*d)/(a*d^2+b*c^2)/(1+m),1],
[(d*x+c)^m/(b*x^2+a)^3,x,5,1/4*(b*c*x+a*d)*(d*x+c)^(1+m)/a/(a*d^2+b*c^2)/(b*x^2+a)^2+1/8*(d*x+c)^(1+m)*(a*d*(a*d^2*(3-m)+b*c^2*(1+m))+b*c*(3*b*c^2+a*d^2*(5-2*m))*x)/a^2/(a*d^2+b*c^2)^2/(b*x^2+a)+1/16*(3*b^2*c^4+sqrt(-a)*sqrt(b)*c*d*(3*b*c^2+a*d^2*(5-2*m))*m+a*b*c^2*d^2*(-m^2-2*m+6)+a^2*d^4*(m^2-4*m+3))*(d*x+c)^(1+m)*hypergeom([1, 1+m],[2+m],sqrt(b)*(d*x+c)/(sqrt(b)*c-sqrt(-a)*d))/(-a)^(5/2)/(sqrt(b)*c-sqrt(-a)*d)/(a*d^2+b*c^2)^2/(1+m)-1/16*(3*b^2*c^4-sqrt(-a)*sqrt(b)*c*d*(3*b*c^2+a*d^2*(5-2*m))*m+a*b*c^2*d^2*(-m^2-2*m+6)+a^2*d^4*(m^2-4*m+3))*(d*x+c)^(1+m)*hypergeom([1, 1+m],[2+m],sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(-a)*d))/(-a)^(5/2)/(sqrt(b)*c+sqrt(-a)*d)/(a*d^2+b*c^2)^2/(1+m),1],
[(d*x+c)^m*(b*x^2+a)^(3/2),x,2,(d*x+c)^(1+m)*(b*x^2+a)^(3/2)*AppellF1(1+m,-3/2,-3/2,2+m,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/d/(1+m)/(1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))^(3/2)/(1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))^(3/2),1],
[(d*x+c)^m*sqrt(b*x^2+a),x,2,(d*x+c)^(1+m)*sqrt(b*x^2+a)*AppellF1(1+m,-1/2,-1/2,2+m,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/d/(1+m)/sqrt(1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))/sqrt(1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b))),1],
[(d*x+c)^m/sqrt(b*x^2+a),x,2,(d*x+c)^(1+m)*sqrt(1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))*sqrt(1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))*AppellF1(1+m,1/2,1/2,2+m,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/d/(1+m)/sqrt(b*x^2+a),1],
[(d*x+c)^m/(b*x^2+a)^(3/2),x,2,(d*x+c)^(1+m)*(1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))^(3/2)*(1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))^(3/2)*AppellF1(1+m,3/2,3/2,2+m,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/d/(1+m)/(b*x^2+a)^(3/2),1],
[(6+8*x)^m/sqrt(-2*x^2+8),x,1,-2^(-1/2+m)*11^m*sqrt(2-x)*AppellF1(1/2,-m,1/2,3/2,8/11-4/11*x,1/2-1/4*x),1],
[(6+8*x)^m/sqrt(2*x^2+8),x,2,I*73^m*sqrt(2-I*x)*(6+8*x)^m*AppellF1(1/2,-m,1/2,3/2,(32/73-12/73*I)*(2-I*x),1/2-1/4*I*x)/sqrt(2)/(((3+8*I)*(3+4*x))^m),1],
[(3-4*x)^m/sqrt(-x^2+1),x,1,sqrt(2)*7^m*sqrt(1+x)*AppellF1(1/2,-m,1/2,3/2,4/7+4/7*x,1/2+1/2*x),1],
[(3-4*x)^m/sqrt(x^2+1),x,2,I*sqrt(2)*25^m*(3-4*x)^m*sqrt(1-I*x)*AppellF1(1/2,-m,1/2,3/2,(16/25+12/25*I)*(1-I*x),1/2-1/2*I*x)/(((3-4*I)*(3-4*x))^m),1],
[(d*x+c)^m/sqrt(-2*x^2+8),x,2,-sqrt(2-x)*(d*x+c)^m*AppellF1(1/2,-m,1/2,3/2,d*(2-x)/(c+2*d),1/2-1/4*x)/sqrt(2)/(((d*x+c)/(c+2*d))^m),1],
[(d*x+c)^m/sqrt(2*x^2+8),x,2,I*sqrt(2-I*x)*(d*x+c)^m*AppellF1(1/2,-m,1/2,3/2,d*(2-I*x)/(I*c+2*d),1/2-1/4*I*x)/sqrt(2)/(((d*x+c)/(c-2*I*d))^m),1],
[(d*x+c)^m/sqrt(-b*x^2+4),x,2,-sqrt(2-sqrt(b)*x)*(d*x+c)^m*AppellF1(1/2,-m,1/2,3/2,d*(2-sqrt(b)*x)/(sqrt(b)*c+2*d),1/2-1/4*sqrt(b)*x)/sqrt(b)/((sqrt(b)*(d*x+c)/(sqrt(b)*c+2*d))^m),1],
[(d*x+c)^m/sqrt(b*x^2+4),x,2,-sqrt(2-sqrt(-b)*x)*(d*x+c)^m*AppellF1(1/2,-m,1/2,3/2,-sqrt(-b)*d*(2-sqrt(-b)*x)/(b*c-2*sqrt(-b)*d),1/2-1/4*sqrt(-b)*x)/sqrt(-b)/((sqrt(-b)*(d*x+c)/(sqrt(-b)*c+2*d))^m),1],
[(d*x+c)^3*(b*x^2+a)^p,x,4,1/2*d*(d*x+c)^2*(b*x^2+a)^(p+1)/b/(2+p)-1/2*d*((3+2*p)*(a*d^2-b*c^2*(5+2*p))-2*b*c*d*(p+1)*(3+p)*x)*(b*x^2+a)^(p+1)/b^2/(2+p)/(2*p^2+5*p+3)+c*(c^2-3*a*d^2/(2*b*p+3*b))*x*(b*x^2+a)^p*hypergeom([1/2, -p],[3/2],-b*x^2/a)/((1+b*x^2/a)^p),1],
[(d*x+c)^2*(b*x^2+a)^p,x,3,d*(c*(3+2*p)+d*(p+1)*x)*(b*x^2+a)^(p+1)/b/(2*p^2+5*p+3)+(c^2-a*d^2/(2*b*p+3*b))*x*(b*x^2+a)^p*hypergeom([1/2, -p],[3/2],-b*x^2/a)/((1+b*x^2/a)^p),1],
[(d*x+c)*(b*x^2+a)^p,x,3,1/2*d*(b*x^2+a)^(p+1)/b/(p+1)+c*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^2+a)^p,x,2,x*(b*x^2+a)^(p+1)*hypergeom([1, 3/2+p],[3/2],-b*x^2/a)/a,1],
[(b*x^2+a)^p/(d*x+c),x,5,x*(b*x^2+a)^p*AppellF1(1/2,-p,1,3/2,-b*x^2/a,d^2*x^2/c^2)/c/((1+b*x^2/a)^p)-1/2*d*(b*x^2+a)^(p+1)*hypergeom([1, p+1],[2+p],d^2*(b*x^2+a)/(a*d^2+b*c^2))/(a*d^2+b*c^2)/(p+1),1],
[(b*x^2+a)^p/(d*x+c)^2,x,9,-(b*x^2+a)^p/d/(d*x+c)-2/3*b*p*x^3*(b*x^2+a)^p*AppellF1(3/2,1-p,1,5/2,-b*x^2/a,d^2*x^2/c^2)/a/c^2/((1+b*x^2/a)^p)+b*c*(b*x^2+a)^p*hypergeom([1, p],[p+1],d^2*(b*x^2+a)/(a*d^2+b*c^2))/d/(a*d^2+b*c^2),1],
[(b*x^2+a)^p/(d*x+c)^3,x,9,-1/2*(b*x^2+a)^p/d/(d*x+c)^2+1/2*p*(b*x^2+a)^p/d/(1-p)/(-d^2*x^2+c^2)-2/3*b*p*x^3*(b*x^2+a)^p*AppellF1(3/2,1-p,2,5/2,-b*x^2/a,d^2*x^2/c^2)/a/c^3/((1+b*x^2/a)^p)-1/2*b*(a*d^2-b*c^2*(1-2*p))*(b*x^2+a)^p*hypergeom([2, p],[p+1],d^2*(b*x^2+a)/(a*d^2+b*c^2))/d/(a*d^2+b*c^2)^2/(1-p),1],
[(d*x+c)^3*(3*x^2+2)^p,x,3,d*(d*x+c)^2*(3*x^2+2)^(p+1)/(12+6*p)-d*((3+2*p)*(2*d^2-3*c^2*(5+2*p))-6*c*d*(p+1)*(3+p)*x)*(3*x^2+2)^(p+1)/(36*p^3+162*p^2+234*p+108)-2^p*c*(2*d^2-c^2*(3+2*p))*x*hypergeom([1/2, -p],[3/2],-3/2*x^2)/(3+2*p),1],
[(d*x+c)^2*(3*x^2+2)^p,x,2,d*(c*(3+2*p)+d*(p+1)*x)*(3*x^2+2)^(p+1)/(6*p^2+15*p+9)-2^p*(2*d^2-3*c^2*(3+2*p))*x*hypergeom([1/2, -p],[3/2],-3/2*x^2)/(9+6*p),1],
[(d*x+c)*(3*x^2+2)^p,x,2,d*(3*x^2+2)^(p+1)/(6*p+6)+2^p*c*x*hypergeom([1/2, -p],[3/2],-3/2*x^2),1],
[(3*x^2+2)^p,x,1,2^p*x*hypergeom([1/2, -p],[3/2],-3/2*x^2),1],
[(3*x^2+2)^p/(d*x+c),x,4,2^p*x*AppellF1(1/2,-p,1,3/2,-3/2*x^2,d^2*x^2/c^2)/c-1/2*d*(3*x^2+2)^(p+1)*hypergeom([1, p+1],[2+p],d^2*(3*x^2+2)/(3*c^2+2*d^2))/(3*c^2+2*d^2)/(p+1),1],
[(3*x^2+2)^p/(d*x+c)^2,x,8,-(3*x^2+2)^p/d/(d*x+c)-2^p*p*x^3*AppellF1(3/2,1-p,1,5/2,-3/2*x^2,d^2*x^2/c^2)/c^2+3*c*(3*x^2+2)^p*hypergeom([1, p],[p+1],d^2*(3*x^2+2)/(3*c^2+2*d^2))/d/(3*c^2+2*d^2),1],
[(3*x^2+2)^p/(d*x+c)^3,x,8,-1/2*(3*x^2+2)^p/d/(d*x+c)^2+1/2*p*(3*x^2+2)^p/d/(1-p)/(-d^2*x^2+c^2)-2^p*p*x^3*AppellF1(3/2,1-p,2,5/2,-3/2*x^2,d^2*x^2/c^2)/c^3-3/2*(2*d^2-c^2*(3-6*p))*(3*x^2+2)^p*hypergeom([2, p],[p+1],d^2*(3*x^2+2)/(3*c^2+2*d^2))/d/(3*c^2+2*d^2)^2/(1-p),1],
[(d*x+c)^3*(-b*x^2+a)^p,x,4,-1/2*d*(a*d^2+3*b*c^2)*(-b*x^2+a)^(p+1)/b^2/(p+1)-3*c*d^2*x*(-b*x^2+a)^(p+1)/b/(3+2*p)+1/2*d^3*(-b*x^2+a)^(2+p)/b^2/(2+p)+c*(c^2+3*a*d^2/(2*b*p+3*b))*x*(-b*x^2+a)^p*hypergeom([1/2, -p],[3/2],b*x^2/a)/((1-b*x^2/a)^p),1],
[(d*x+c)^2*(-b*x^2+a)^p,x,3,-d*(c*(3+2*p)+d*(p+1)*x)*(-b*x^2+a)^(p+1)/b/(2*p^2+5*p+3)+(c^2+a*d^2/(2*b*p+3*b))*x*(-b*x^2+a)^p*hypergeom([1/2, -p],[3/2],b*x^2/a)/((1-b*x^2/a)^p),1],
[(d*x+c)*(-b*x^2+a)^p,x,3,-1/2*d*(-b*x^2+a)^(p+1)/b/(p+1)+c*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^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^2+a)^p/(d*x+c),x,5,x*(-b*x^2+a)^p*AppellF1(1/2,-p,1,3/2,b*x^2/a,d^2*x^2/c^2)/c/((1-b*x^2/a)^p)+1/2*d*(-b*x^2+a)^(p+1)*hypergeom([1, p+1],[2+p],-d^2*(-b*x^2+a)/(-a*d^2+b*c^2))/(-a*d^2+b*c^2)/(p+1),1],
[(-b*x^2+a)^p/(d*x+c)^2,x,3,-2^p*sqrt(b)*(-b*x^2+a)^p*(1-(d*x+c)/(c-sqrt(a)*d/sqrt(b)))*AppellF1(p+1,2,-p,2+p,1-(d*x+c)/(c-sqrt(a)*d/sqrt(b)),1/2*(sqrt(a)+sqrt(b)*x)/sqrt(a))/d/(sqrt(b)*c-sqrt(a)*d)/(p+1)/((1-sqrt(b)*x/sqrt(a))^p),1],
[(-b*x^2+a)^p/(d*x+c)^3,x,3,-2^p*b*(-b*x^2+a)^p*(1-(d*x+c)/(c-sqrt(a)*d/sqrt(b)))*AppellF1(p+1,3,-p,2+p,1-(d*x+c)/(c-sqrt(a)*d/sqrt(b)),1/2*(sqrt(a)+sqrt(b)*x)/sqrt(a))/d/(sqrt(b)*c-sqrt(a)*d)^2/(p+1)/((1-sqrt(b)*x/sqrt(a))^p),1],
[(d*x+c)^3*(-3*x^2+2)^p,x,3,-1/18*d*(9*c^2+2*d^2)*(-3*x^2+2)^(p+1)/(p+1)-c*d^2*x*(-3*x^2+2)^(p+1)/(3+2*p)+d^3*(-3*x^2+2)^(2+p)/(36+18*p)+2^p*c*(2*d^2+c^2*(3+2*p))*x*hypergeom([1/2, -p],[3/2],3/2*x^2)/(3+2*p),1],
[(d*x+c)^2*(-3*x^2+2)^p,x,2,-1/3*d*(c*(3+2*p)+d*(p+1)*x)*(-3*x^2+2)^(p+1)/(2*p^2+5*p+3)+2^p*(2*d^2+c^2*(9+6*p))*x*hypergeom([1/2, -p],[3/2],3/2*x^2)/(9+6*p),1],
[(d*x+c)*(-3*x^2+2)^p,x,2,-1/6*d*(-3*x^2+2)^(p+1)/(p+1)+2^p*c*x*hypergeom([1/2, -p],[3/2],3/2*x^2),1],
[(-3*x^2+2)^p,x,1,2^p*x*hypergeom([1/2, -p],[3/2],3/2*x^2),1],
[(-3*x^2+2)^p/(d*x+c),x,4,2^p*x*AppellF1(1/2,-p,1,3/2,3/2*x^2,d^2*x^2/c^2)/c+1/2*d*(-3*x^2+2)^(p+1)*hypergeom([1, p+1],[2+p],-d^2*(-3*x^2+2)/(3*c^2-2*d^2))/(3*c^2-2*d^2)/(p+1),1],
[(-3*x^2+2)^p/(d*x+c)^2,x,3,-3*4^p*(-3*x^2+2)^p*(1-3*(d*x+c)/(3*c-sqrt(6)*d))*AppellF1(p+1,2,-p,2+p,1-3*(d*x+c)/(3*c-sqrt(6)*d),-1/4*(sqrt(6)*c-2*d)*(1-3*(d*x+c)/(3*c-sqrt(6)*d))/d)/d/(3*c-sqrt(6)*d)/(p+1)/(((sqrt(6)*c+2*d)*(1-3*(d*x+c)/(3*c+sqrt(6)*d))/d)^p),1],
[(-3*x^2+2)^p/(d*x+c)^3,x,3,-9*4^p*(-3*x^2+2)^p*(1-3*(d*x+c)/(3*c-sqrt(6)*d))*AppellF1(p+1,3,-p,2+p,1-3*(d*x+c)/(3*c-sqrt(6)*d),-1/4*(sqrt(6)*c-2*d)*(1-3*(d*x+c)/(3*c-sqrt(6)*d))/d)/d/(3*c-sqrt(6)*d)^2/(p+1)/(((sqrt(6)*c+2*d)*(1-3*(d*x+c)/(3*c+sqrt(6)*d))/d)^p),1],
[(d*x+c)^(3/2)*(b*x^2+a)^p,x,2,2/5*(d*x+c)^(5/2)*(b*x^2+a)^p*AppellF1(5/2,-p,-p,7/2,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/d/((1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))^p),1],
[sqrt(d*x+c)*(b*x^2+a)^p,x,2,2/3*(d*x+c)^(3/2)*(b*x^2+a)^p*AppellF1(3/2,-p,-p,5/2,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/d/((1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))^p),1],
[(b*x^2+a)^p/sqrt(d*x+c),x,2,2*sqrt(d*x+c)*(b*x^2+a)^p*AppellF1(1/2,-p,-p,3/2,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/d/((1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))^p),1],
[(b*x^2+a)^p/(d*x+c)^(3/2),x,2,-2*(b*x^2+a)^p*AppellF1(-1/2,-p,-p,1/2,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/d/sqrt(d*x+c)/((1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))^p),1],
[(d*x+c)^(3/2)*(b*x^2+2)^p,x,2,2/5*(d*x+c)^(5/2)*(b*x^2+2)^p*AppellF1(5/2,-p,-p,7/2,(d*x+c)/(c+sqrt(2)*b*d/(-b)^(3/2)),(d*x+c)/(c+sqrt(2)*d/sqrt(-b)))/d/((1-(d*x+c)/(c+sqrt(2)*d/sqrt(-b)))^p)/((1-(d*x+c)/(c+sqrt(2)*b*d/(-b)^(3/2)))^p),1],
[sqrt(d*x+c)*(b*x^2+2)^p,x,2,2/3*(d*x+c)^(3/2)*(b*x^2+2)^p*AppellF1(3/2,-p,-p,5/2,(d*x+c)/(c+sqrt(2)*b*d/(-b)^(3/2)),(d*x+c)/(c+sqrt(2)*d/sqrt(-b)))/d/((1-(d*x+c)/(c+sqrt(2)*d/sqrt(-b)))^p)/((1-(d*x+c)/(c+sqrt(2)*b*d/(-b)^(3/2)))^p),1],
[(b*x^2+2)^p/sqrt(d*x+c),x,2,2*sqrt(d*x+c)*(b*x^2+2)^p*AppellF1(1/2,-p,-p,3/2,(d*x+c)/(c+sqrt(2)*b*d/(-b)^(3/2)),(d*x+c)/(c+sqrt(2)*d/sqrt(-b)))/d/((1-(d*x+c)/(c+sqrt(2)*d/sqrt(-b)))^p)/((1-(d*x+c)/(c+sqrt(2)*b*d/(-b)^(3/2)))^p),1],
[(b*x^2+2)^p/(d*x+c)^(3/2),x,2,-2*(b*x^2+2)^p*AppellF1(-1/2,-p,-p,1/2,(d*x+c)/(c+sqrt(2)*b*d/(-b)^(3/2)),(d*x+c)/(c+sqrt(2)*d/sqrt(-b)))/d/sqrt(d*x+c)/((1-(d*x+c)/(c+sqrt(2)*d/sqrt(-b)))^p)/((1-(d*x+c)/(c+sqrt(2)*b*d/(-b)^(3/2)))^p),1],
[(d*x+c)^(3/2)*(3*x^2+2)^p,x,2,2/5*(d*x+c)^(5/2)*(3*x^2+2)^p*AppellF1(5/2,-p,-p,7/2,3*(d*x+c)/(3*c-I*sqrt(6)*d),3*(d*x+c)/(3*c+I*sqrt(6)*d))/d/((1-3*(d*x+c)/(3*c-I*sqrt(6)*d))^p)/((1-3*(d*x+c)/(3*c+I*sqrt(6)*d))^p),1],
[sqrt(d*x+c)*(3*x^2+2)^p,x,2,2/3*(d*x+c)^(3/2)*(3*x^2+2)^p*AppellF1(3/2,-p,-p,5/2,3*(d*x+c)/(3*c-I*sqrt(6)*d),3*(d*x+c)/(3*c+I*sqrt(6)*d))/d/((1-3*(d*x+c)/(3*c-I*sqrt(6)*d))^p)/((1-3*(d*x+c)/(3*c+I*sqrt(6)*d))^p),1],
[(3*x^2+2)^p/sqrt(d*x+c),x,2,2*sqrt(d*x+c)*(3*x^2+2)^p*AppellF1(1/2,-p,-p,3/2,3*(d*x+c)/(3*c-I*sqrt(6)*d),3*(d*x+c)/(3*c+I*sqrt(6)*d))/d/((1-3*(d*x+c)/(3*c-I*sqrt(6)*d))^p)/((1-3*(d*x+c)/(3*c+I*sqrt(6)*d))^p),1],
[(3*x^2+2)^p/(d*x+c)^(3/2),x,2,-2*(3*x^2+2)^p*AppellF1(-1/2,-p,-p,1/2,3*(d*x+c)/(3*c-I*sqrt(6)*d),3*(d*x+c)/(3*c+I*sqrt(6)*d))/d/sqrt(d*x+c)/((1-3*(d*x+c)/(3*c-I*sqrt(6)*d))^p)/((1-3*(d*x+c)/(3*c+I*sqrt(6)*d))^p),1],
[(d*x+c)^(3/2)*(-b*x^2+a)^p,x,2,2/5*(d*x+c)^(5/2)*(-b*x^2+a)^p*AppellF1(5/2,-p,-p,7/2,(d*x+c)/(c-sqrt(a)*d/sqrt(b)),(d*x+c)/(c+sqrt(a)*d/sqrt(b)))/d/((1-(d*x+c)/(c-sqrt(a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(a)*d/sqrt(b)))^p),1],
[sqrt(d*x+c)*(-b*x^2+a)^p,x,2,2/3*(d*x+c)^(3/2)*(-b*x^2+a)^p*AppellF1(3/2,-p,-p,5/2,(d*x+c)/(c-sqrt(a)*d/sqrt(b)),(d*x+c)/(c+sqrt(a)*d/sqrt(b)))/d/((1-(d*x+c)/(c-sqrt(a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(a)*d/sqrt(b)))^p),1],
[(-b*x^2+a)^p/sqrt(d*x+c),x,2,2*sqrt(d*x+c)*(-b*x^2+a)^p*AppellF1(1/2,-p,-p,3/2,(d*x+c)/(c-sqrt(a)*d/sqrt(b)),(d*x+c)/(c+sqrt(a)*d/sqrt(b)))/d/((1-(d*x+c)/(c-sqrt(a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(a)*d/sqrt(b)))^p),1],
[(-b*x^2+a)^p/(d*x+c)^(3/2),x,2,-2*(-b*x^2+a)^p*AppellF1(-1/2,-p,-p,1/2,(d*x+c)/(c-sqrt(a)*d/sqrt(b)),(d*x+c)/(c+sqrt(a)*d/sqrt(b)))/d/sqrt(d*x+c)/((1-(d*x+c)/(c-sqrt(a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(a)*d/sqrt(b)))^p),1],
[(d*x+c)^(3/2)*(-b*x^2+2)^p,x,2,2/5*(d*x+c)^(5/2)*(-b*x^2+2)^p*AppellF1(5/2,-p,-p,7/2,(d*x+c)/(c-sqrt(2)*d/sqrt(b)),(d*x+c)/(c+sqrt(2)*d/sqrt(b)))/d/((1-(d*x+c)/(c-sqrt(2)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(2)*d/sqrt(b)))^p),1],
[sqrt(d*x+c)*(-b*x^2+2)^p,x,2,2/3*(d*x+c)^(3/2)*(-b*x^2+2)^p*AppellF1(3/2,-p,-p,5/2,(d*x+c)/(c-sqrt(2)*d/sqrt(b)),(d*x+c)/(c+sqrt(2)*d/sqrt(b)))/d/((1-(d*x+c)/(c-sqrt(2)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(2)*d/sqrt(b)))^p),1],
[(-b*x^2+2)^p/sqrt(d*x+c),x,2,2*sqrt(d*x+c)*(-b*x^2+2)^p*AppellF1(1/2,-p,-p,3/2,(d*x+c)/(c-sqrt(2)*d/sqrt(b)),(d*x+c)/(c+sqrt(2)*d/sqrt(b)))/d/((1-(d*x+c)/(c-sqrt(2)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(2)*d/sqrt(b)))^p),1],
[(-b*x^2+2)^p/(d*x+c)^(3/2),x,2,-2*(-b*x^2+2)^p*AppellF1(-1/2,-p,-p,1/2,(d*x+c)/(c-sqrt(2)*d/sqrt(b)),(d*x+c)/(c+sqrt(2)*d/sqrt(b)))/d/sqrt(d*x+c)/((1-(d*x+c)/(c-sqrt(2)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(2)*d/sqrt(b)))^p),1],
[(d*x+c)^(3/2)*(-3*x^2+2)^p,x,2,2/5*(d*x+c)^(5/2)*(-3*x^2+2)^p*AppellF1(5/2,-p,-p,7/2,3*(d*x+c)/(3*c-sqrt(6)*d),3*(d*x+c)/(3*c+sqrt(6)*d))/d/((1-3*(d*x+c)/(3*c-sqrt(6)*d))^p)/((1-3*(d*x+c)/(3*c+sqrt(6)*d))^p),1],
[sqrt(d*x+c)*(-3*x^2+2)^p,x,2,2/3*(d*x+c)^(3/2)*(-3*x^2+2)^p*AppellF1(3/2,-p,-p,5/2,3*(d*x+c)/(3*c-sqrt(6)*d),3*(d*x+c)/(3*c+sqrt(6)*d))/d/((1-3*(d*x+c)/(3*c-sqrt(6)*d))^p)/((1-3*(d*x+c)/(3*c+sqrt(6)*d))^p),1],
[(-3*x^2+2)^p/sqrt(d*x+c),x,2,2*sqrt(d*x+c)*(-3*x^2+2)^p*AppellF1(1/2,-p,-p,3/2,3*(d*x+c)/(3*c-sqrt(6)*d),3*(d*x+c)/(3*c+sqrt(6)*d))/d/((1-3*(d*x+c)/(3*c-sqrt(6)*d))^p)/((1-3*(d*x+c)/(3*c+sqrt(6)*d))^p),1],
[(-3*x^2+2)^p/(d*x+c)^(3/2),x,2,-2*(-3*x^2+2)^p*AppellF1(-1/2,-p,-p,1/2,3*(d*x+c)/(3*c-sqrt(6)*d),3*(d*x+c)/(3*c+sqrt(6)*d))/d/sqrt(d*x+c)/((1-3*(d*x+c)/(3*c-sqrt(6)*d))^p)/((1-3*(d*x+c)/(3*c+sqrt(6)*d))^p),1],
[(d*x+c)^m*(b*x^2+a)^p,x,2,(d*x+c)^(1+m)*(b*x^2+a)^p*AppellF1(1+m,-p,-p,2+m,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/d/(1+m)/((1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))^p),1],
[(d*x+c)^m*(b*x^2+2)^p,x,2,(d*x+c)^(1+m)*(b*x^2+2)^p*AppellF1(1+m,-p,-p,2+m,(d*x+c)/(c+sqrt(2)*b*d/(-b)^(3/2)),(d*x+c)/(c+sqrt(2)*d/sqrt(-b)))/d/(1+m)/((1-(d*x+c)/(c+sqrt(2)*d/sqrt(-b)))^p)/((1-(d*x+c)/(c+sqrt(2)*b*d/(-b)^(3/2)))^p),1],
[(d*x+c)^m*(3*x^2+2)^p,x,2,(d*x+c)^(1+m)*(3*x^2+2)^p*AppellF1(1+m,-p,-p,2+m,3*(d*x+c)/(3*c-I*sqrt(6)*d),3*(d*x+c)/(3*c+I*sqrt(6)*d))/d/(1+m)/((1-3*(d*x+c)/(3*c-I*sqrt(6)*d))^p)/((1-3*(d*x+c)/(3*c+I*sqrt(6)*d))^p),1],
[(b*x^2+a)^p/((d*x+c)^(2*p)),x,2,(d*x+c)^(1-2*p)*(b*x^2+a)^p*AppellF1(1-2*p,-p,-p,2-2*p,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/d/(1-2*p)/((1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))^p),1],
[(d*x+c)^(-1-2*p)*(b*x^2+a)^p,x,2,-1/2*(b*x^2+a)^p*AppellF1(-2*p,-p,-p,1-2*p,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/d/p/((d*x+c)^(2*p))/((1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))^p),1],
[(d*x+c)^(-2-2*p)*(b*x^2+a)^p,x,1,-(sqrt(-a)-sqrt(b)*x)*(d*x+c)^(-1-2*p)*(b*x^2+a)^p*hypergeom([-1-2*p, -p],[-2*p],2*sqrt(-a)*sqrt(b)*(d*x+c)/(sqrt(b)*c-sqrt(-a)*d)/(sqrt(-a)-sqrt(b)*x))/(sqrt(b)*c+sqrt(-a)*d)/(1+2*p)/((-(sqrt(b)*c+sqrt(-a)*d)*(sqrt(-a)+sqrt(b)*x)/(sqrt(b)*c-sqrt(-a)*d)/(sqrt(-a)-sqrt(b)*x))^p),1],
[(d*x+c)^(-3-2*p)*(b*x^2+a)^p,x,2,-1/2*d*(b*x^2+a)^(p+1)/(a*d^2+b*c^2)/(p+1)/((d*x+c)^(2*p+2))-b*c*(sqrt(-a)-sqrt(b)*x)*(d*x+c)^(-1-2*p)*(b*x^2+a)^p*hypergeom([-1-2*p, -p],[-2*p],2*sqrt(-a)*sqrt(b)*(d*x+c)/(sqrt(b)*c-sqrt(-a)*d)/(sqrt(-a)-sqrt(b)*x))/(sqrt(b)*c+sqrt(-a)*d)/(a*d^2+b*c^2)/(1+2*p)/((-(sqrt(b)*c+sqrt(-a)*d)*(sqrt(-a)+sqrt(b)*x)/(sqrt(b)*c-sqrt(-a)*d)/(sqrt(-a)-sqrt(b)*x))^p),1],
[(d*x+c)^(-4-2*p)*(b*x^2+a)^p,x,3,-d*(d*x+c)^(-3-2*p)*(b*x^2+a)^(p+1)/(a*d^2+b*c^2)/(3+2*p)-b*c*d*(2+p)*(b*x^2+a)^(p+1)/(a*d^2+b*c^2)^2/(p+1)/(3+2*p)/((d*x+c)^(2*p+2))+b*(a*d^2-b*c^2*(3+2*p))*(sqrt(-a)-sqrt(b)*x)*(d*x+c)^(-1-2*p)*(b*x^2+a)^p*hypergeom([-1-2*p, -p],[-2*p],2*sqrt(-a)*sqrt(b)*(d*x+c)/(sqrt(b)*c-sqrt(-a)*d)/(sqrt(-a)-sqrt(b)*x))/(sqrt(b)*c+sqrt(-a)*d)/(a*d^2+b*c^2)^2/(1+2*p)/(3+2*p)/((-(sqrt(b)*c+sqrt(-a)*d)*(sqrt(-a)+sqrt(b)*x)/(sqrt(b)*c-sqrt(-a)*d)/(sqrt(-a)-sqrt(b)*x))^p),1],
[(d*x+c)^m*(-b*x^2+a)^p,x,2,(d*x+c)^(1+m)*(-b*x^2+a)^p*AppellF1(1+m,-p,-p,2+m,(d*x+c)/(c-sqrt(a)*d/sqrt(b)),(d*x+c)/(c+sqrt(a)*d/sqrt(b)))/d/(1+m)/((1-(d*x+c)/(c-sqrt(a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(a)*d/sqrt(b)))^p),1],
[(d*x+c)^m*(-b*x^2+2)^p,x,2,(d*x+c)^(1+m)*(-b*x^2+2)^p*AppellF1(1+m,-p,-p,2+m,(d*x+c)/(c-sqrt(2)*d/sqrt(b)),(d*x+c)/(c+sqrt(2)*d/sqrt(b)))/d/(1+m)/((1-(d*x+c)/(c-sqrt(2)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(2)*d/sqrt(b)))^p),1],
[(d*x+c)^m*(-3*x^2+2)^p,x,2,(d*x+c)^(1+m)*(-3*x^2+2)^p*AppellF1(1+m,-p,-p,2+m,3*(d*x+c)/(3*c-sqrt(6)*d),3*(d*x+c)/(3*c+sqrt(6)*d))/d/(1+m)/((1-3*(d*x+c)/(3*c-sqrt(6)*d))^p)/((1-3*(d*x+c)/(3*c+sqrt(6)*d))^p),1],
[(-b*x^2+a)^p/((d*x+c)^(2*p)),x,2,(d*x+c)^(1-2*p)*(-b*x^2+a)^p*AppellF1(1-2*p,-p,-p,2-2*p,(d*x+c)/(c-sqrt(a)*d/sqrt(b)),(d*x+c)/(c+sqrt(a)*d/sqrt(b)))/d/(1-2*p)/((1-(d*x+c)/(c-sqrt(a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(a)*d/sqrt(b)))^p),1],
[(d*x+c)^(-1-2*p)*(-b*x^2+a)^p,x,2,-1/2*(-b*x^2+a)^p*AppellF1(-2*p,-p,-p,1-2*p,(d*x+c)/(c-sqrt(a)*d/sqrt(b)),(d*x+c)/(c+sqrt(a)*d/sqrt(b)))/d/p/((d*x+c)^(2*p))/((1-(d*x+c)/(c-sqrt(a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(a)*d/sqrt(b)))^p),1],
[(d*x+c)^(-2-2*p)*(-b*x^2+a)^p,x,1,(sqrt(a)+sqrt(b)*x)*(d*x+c)^(-1-2*p)*(-b*x^2+a)^p*hypergeom([-1-2*p, -p],[-2*p],2*sqrt(a)*sqrt(b)*(d*x+c)/(sqrt(b)*c+sqrt(a)*d)/(sqrt(a)+sqrt(b)*x))/(sqrt(b)*c-sqrt(a)*d)/(1+2*p)/((-(sqrt(b)*c-sqrt(a)*d)*(sqrt(a)-sqrt(b)*x)/(sqrt(b)*c+sqrt(a)*d)/(sqrt(a)+sqrt(b)*x))^p),1],
[(d*x+c)^(-3-2*p)*(-b*x^2+a)^p,x,2,1/2*d*(-b*x^2+a)^(p+1)/(-a*d^2+b*c^2)/(p+1)/((d*x+c)^(2*p+2))-b*c*(sqrt(a)-sqrt(b)*x)*(d*x+c)^(-1-2*p)*(-b*x^2+a)^p*hypergeom([-1-2*p, -p],[-2*p],2*sqrt(a)*sqrt(b)*(d*x+c)/(sqrt(b)*c-sqrt(a)*d)/(sqrt(a)-sqrt(b)*x))/(sqrt(b)*c+sqrt(a)*d)/(-a*d^2+b*c^2)/(1+2*p)/((-(sqrt(b)*c+sqrt(a)*d)*(sqrt(a)+sqrt(b)*x)/(sqrt(b)*c-sqrt(a)*d)/(sqrt(a)-sqrt(b)*x))^p),1],
[(d*x+c)^(-4-2*p)*(-b*x^2+a)^p,x,3,d*(d*x+c)^(-3-2*p)*(-b*x^2+a)^(p+1)/(-a*d^2+b*c^2)/(3+2*p)+b*c*d*(2+p)*(-b*x^2+a)^(p+1)/(-a*d^2+b*c^2)^2/(p+1)/(3+2*p)/((d*x+c)^(2*p+2))-b*(a*d^2+b*c^2*(3+2*p))*(sqrt(a)-sqrt(b)*x)*(d*x+c)^(-1-2*p)*(-b*x^2+a)^p*hypergeom([-1-2*p, -p],[-2*p],2*sqrt(a)*sqrt(b)*(d*x+c)/(sqrt(b)*c-sqrt(a)*d)/(sqrt(a)-sqrt(b)*x))/(sqrt(b)*c-sqrt(a)*d)^2/(sqrt(b)*c+sqrt(a)*d)^3/(4*p^2+8*p+3)/((-(sqrt(b)*c+sqrt(a)*d)*(sqrt(a)+sqrt(b)*x)/(sqrt(b)*c-sqrt(a)*d)/(sqrt(a)-sqrt(b)*x))^p),1]]: