lst:=[[x^3*(d+I*c*d*x)*(a+b*arctan(c*x)),x,7,1/4*b*d*x/c^3+1/10*I*b*d*x^2/c^2-1/12*b*d*x^3/c-1/20*I*b*d*x^4-1/4*b*d*arctan(c*x)/c^4+1/4*d*x^4*(a+b*arctan(c*x))+1/5*I*c*d*x^5*(a+b*arctan(c*x))-1/10*I*b*d*ln(c^2*x^2+1)/c^4,1],
[x^2*(d+I*c*d*x)*(a+b*arctan(c*x)),x,7,1/4*I*b*d*x/c^2-1/6*b*d*x^2/c-1/12*I*b*d*x^3-1/4*I*b*d*arctan(c*x)/c^3+1/3*d*x^3*(a+b*arctan(c*x))+1/4*I*c*d*x^4*(a+b*arctan(c*x))+1/6*b*d*ln(c^2*x^2+1)/c^3,1],
[x*(d+I*c*d*x)*(a+b*arctan(c*x)),x,7,-1/2*b*d*x/c-1/6*I*b*d*x^2+1/2*b*d*arctan(c*x)/c^2+1/2*d*x^2*(a+b*arctan(c*x))+1/3*I*c*d*x^3*(a+b*arctan(c*x))+1/6*I*b*d*ln(c^2*x^2+1)/c^2,1],
[(d+I*c*d*x)*(a+b*arctan(c*x)),x,4,-1/2*I*b*d*x-1/2*I*d*(1+I*c*x)^2*(a+b*arctan(c*x))/c-b*d*ln(I+c*x)/c,1],
[(d+I*c*d*x)*(a+b*arctan(c*x))/x,x,8,I*a*c*d*x+I*b*c*d*x*arctan(c*x)+a*d*ln(x)-1/2*I*b*d*ln(c^2*x^2+1)+1/2*I*b*d*polylog(2,-I*c*x)-1/2*I*b*d*polylog(2,I*c*x),1],
[(d+I*c*d*x)*(a+b*arctan(c*x))/x^2,x,10,-d*(a+b*arctan(c*x))/x+I*a*c*d*ln(x)+b*c*d*ln(x)-1/2*b*c*d*ln(c^2*x^2+1)-1/2*b*c*d*polylog(2,-I*c*x)+1/2*b*c*d*polylog(2,I*c*x),1],
[(d+I*c*d*x)*(a+b*arctan(c*x))/x^3,x,4,-1/2*b*c*d/x-1/2*d*(1+I*c*x)^2*(a+b*arctan(c*x))/x^2+I*b*c^2*d*ln(x)-I*b*c^2*d*ln(I+c*x),1],
[(d+I*c*d*x)*(a+b*arctan(c*x))/x^4,x,4,-1/6*b*c*d/x^2-1/2*I*b*c^2*d/x-1/3*d*(a+b*arctan(c*x))/x^3-1/2*I*c*d*(a+b*arctan(c*x))/x^2-1/3*b*c^3*d*ln(x)-1/12*b*c^3*d*ln(I-c*x)+5/12*b*c^3*d*ln(I+c*x),1],
[(d+I*c*d*x)*(a+b*arctan(c*x))/x^5,x,4,-1/12*b*c*d/x^3-1/6*I*b*c^2*d/x^2+1/4*b*c^3*d/x-1/4*d*(a+b*arctan(c*x))/x^4-1/3*I*c*d*(a+b*arctan(c*x))/x^3-1/3*I*b*c^4*d*ln(x)+1/24*I*b*c^4*d*ln(I-c*x)+7/24*I*b*c^4*d*ln(I+c*x),1],
[x^3*(d+I*c*d*x)^2*(a+b*arctan(c*x)),x,7,5/12*b*d^2*x/c^3+1/5*I*b*d^2*x^2/c^2-5/36*b*d^2*x^3/c-1/10*I*b*d^2*x^4+1/30*b*c*d^2*x^5-5/12*b*d^2*arctan(c*x)/c^4+1/4*d^2*x^4*(a+b*arctan(c*x))+2/5*I*c*d^2*x^5*(a+b*arctan(c*x))-1/6*c^2*d^2*x^6*(a+b*arctan(c*x))-1/5*I*b*d^2*ln(c^2*x^2+1)/c^4,1],
[x^2*(d+I*c*d*x)^2*(a+b*arctan(c*x)),x,7,1/2*I*b*d^2*x/c^2-4/15*b*d^2*x^2/c-1/6*I*b*d^2*x^3+1/20*b*c*d^2*x^4-1/2*I*b*d^2*arctan(c*x)/c^3+1/3*d^2*x^3*(a+b*arctan(c*x))+1/2*I*c*d^2*x^4*(a+b*arctan(c*x))-1/5*c^2*d^2*x^5*(a+b*arctan(c*x))+4/15*b*d^2*ln(c^2*x^2+1)/c^3,1],
[x*(d+I*c*d*x)^2*(a+b*arctan(c*x)),x,7,-3/4*b*d^2*x/c-1/3*I*b*d^2*x^2+1/12*b*c*d^2*x^3+3/4*b*d^2*arctan(c*x)/c^2+1/2*d^2*x^2*(a+b*arctan(c*x))+2/3*I*c*d^2*x^3*(a+b*arctan(c*x))-1/4*c^2*d^2*x^4*(a+b*arctan(c*x))+1/3*I*b*d^2*ln(c^2*x^2+1)/c^2,1],
[(d+I*c*d*x)^2*(a+b*arctan(c*x)),x,4,-2/3*I*b*d^2*x-1/6*b*d^2*(1+I*c*x)^2/c-1/3*I*d^2*(1+I*c*x)^3*(a+b*arctan(c*x))/c-4/3*b*d^2*ln(1-I*c*x)/c,1],
[(d+I*c*d*x)^2*(a+b*arctan(c*x))/x,x,11,2*I*a*c*d^2*x+1/2*b*c*d^2*x-1/2*b*d^2*arctan(c*x)+2*I*b*c*d^2*x*arctan(c*x)-1/2*c^2*d^2*x^2*(a+b*arctan(c*x))+a*d^2*ln(x)-I*b*d^2*ln(c^2*x^2+1)+1/2*I*b*d^2*polylog(2,-I*c*x)-1/2*I*b*d^2*polylog(2,I*c*x),1],
[(d+I*c*d*x)^2*(a+b*arctan(c*x))/x^2,x,13,-a*c^2*d^2*x-b*c^2*d^2*x*arctan(c*x)-d^2*(a+b*arctan(c*x))/x+2*I*a*c*d^2*ln(x)+b*c*d^2*ln(x)-b*c*d^2*polylog(2,-I*c*x)+b*c*d^2*polylog(2,I*c*x),1],
[(d+I*c*d*x)^2*(a+b*arctan(c*x))/x^3,x,13,-1/2*b*c*d^2/x-1/2*b*c^2*d^2*arctan(c*x)-1/2*d^2*(a+b*arctan(c*x))/x^2-2*I*c*d^2*(a+b*arctan(c*x))/x-a*c^2*d^2*ln(x)+2*I*b*c^2*d^2*ln(x)-I*b*c^2*d^2*ln(c^2*x^2+1)-1/2*I*b*c^2*d^2*polylog(2,-I*c*x)+1/2*I*b*c^2*d^2*polylog(2,I*c*x),1],
[(d+I*c*d*x)^2*(a+b*arctan(c*x))/x^4,x,4,-1/6*b*c*d^2/x^2-I*b*c^2*d^2/x-1/3*d^2*(1+I*c*x)^3*(a+b*arctan(c*x))/x^3-4/3*b*c^3*d^2*ln(x)+4/3*b*c^3*d^2*ln(I+c*x),1],
[(d+I*c*d*x)^2*(a+b*arctan(c*x))/x^5,x,4,-1/12*b*c*d^2/x^3-1/3*I*b*c^2*d^2/x^2+3/4*b*c^3*d^2/x-1/4*d^2*(a+b*arctan(c*x))/x^4-2/3*I*c*d^2*(a+b*arctan(c*x))/x^3+1/2*c^2*d^2*(a+b*arctan(c*x))/x^2-2/3*I*b*c^4*d^2*ln(x)-1/24*I*b*c^4*d^2*ln(I-c*x)+17/24*I*b*c^4*d^2*ln(I+c*x),1],
[(d+I*c*d*x)^2*(a+b*arctan(c*x))/x^6,x,4,-1/20*b*c*d^2/x^4-1/6*I*b*c^2*d^2/x^3+4/15*b*c^3*d^2/x^2+1/2*I*b*c^4*d^2/x-1/5*d^2*(a+b*arctan(c*x))/x^5-1/2*I*c*d^2*(a+b*arctan(c*x))/x^4+1/3*c^2*d^2*(a+b*arctan(c*x))/x^3+8/15*b*c^5*d^2*ln(x)-1/60*b*c^5*d^2*ln(I-c*x)-31/60*b*c^5*d^2*ln(I+c*x),1],
[x^3*(d+I*c*d*x)^3*(a+b*arctan(c*x)),x,7,3/4*b*d^3*x/c^3+13/35*I*b*d^3*x^2/c^2-1/4*b*d^3*x^3/c-13/70*I*b*d^3*x^4+1/10*b*c*d^3*x^5+1/42*I*b*c^2*d^3*x^6-3/4*b*d^3*arctan(c*x)/c^4+1/4*d^3*x^4*(a+b*arctan(c*x))+3/5*I*c*d^3*x^5*(a+b*arctan(c*x))-1/2*c^2*d^3*x^6*(a+b*arctan(c*x))-1/7*I*c^3*d^3*x^7*(a+b*arctan(c*x))-13/35*I*b*d^3*ln(c^2*x^2+1)/c^4,1],
[x^2*(d+I*c*d*x)^3*(a+b*arctan(c*x)),x,7,11/12*I*b*d^3*x/c^2-7/15*b*d^3*x^2/c-11/36*I*b*d^3*x^3+3/20*b*c*d^3*x^4+1/30*I*b*c^2*d^3*x^5-11/12*I*b*d^3*arctan(c*x)/c^3+1/3*d^3*x^3*(a+b*arctan(c*x))+3/4*I*c*d^3*x^4*(a+b*arctan(c*x))-3/5*c^2*d^3*x^5*(a+b*arctan(c*x))-1/6*I*c^3*d^3*x^6*(a+b*arctan(c*x))+7/15*b*d^3*ln(c^2*x^2+1)/c^3,1],
[x*(d+I*c*d*x)^3*(a+b*arctan(c*x)),x,4,-3/5*b*d^3*x/c-3/20*I*b*d^3*(I-c*x)^2/c^2-1/20*b*d^3*(I-c*x)^3/c^2+1/20*I*b*d^3*(I-c*x)^4/c^2+1/4*d^3*(1+I*c*x)^4*(a+b*arctan(c*x))/c^2-1/5*d^3*(1+I*c*x)^5*(a+b*arctan(c*x))/c^2+6/5*I*b*d^3*ln(I+c*x)/c^2,1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x)),x,4,-I*b*d^3*x-1/4*b*d^3*(1+I*c*x)^2/c-1/12*b*d^3*(1+I*c*x)^3/c-1/4*I*d^3*(1+I*c*x)^4*(a+b*arctan(c*x))/c-2*b*d^3*ln(1-I*c*x)/c,1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))/x,x,15,3*I*a*c*d^3*x+3/2*b*c*d^3*x+1/6*I*b*c^2*d^3*x^2-3/2*b*d^3*arctan(c*x)+3*I*b*c*d^3*x*arctan(c*x)-3/2*c^2*d^3*x^2*(a+b*arctan(c*x))-1/3*I*c^3*d^3*x^3*(a+b*arctan(c*x))+a*d^3*ln(x)-5/3*I*b*d^3*ln(c^2*x^2+1)+1/2*I*b*d^3*polylog(2,-I*c*x)-1/2*I*b*d^3*polylog(2,I*c*x),1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))/x^2,x,16,-3*a*c^2*d^3*x+1/2*I*b*c^2*d^3*x-1/2*I*b*c*d^3*arctan(c*x)-3*b*c^2*d^3*x*arctan(c*x)-d^3*(a+b*arctan(c*x))/x-1/2*I*c^3*d^3*x^2*(a+b*arctan(c*x))+3*I*a*c*d^3*ln(x)+b*c*d^3*ln(x)+b*c*d^3*ln(c^2*x^2+1)-3/2*b*c*d^3*polylog(2,-I*c*x)+3/2*b*c*d^3*polylog(2,I*c*x),1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))/x^3,x,16,-1/2*b*c*d^3/x-I*a*c^3*d^3*x-1/2*b*c^2*d^3*arctan(c*x)-I*b*c^3*d^3*x*arctan(c*x)-1/2*d^3*(a+b*arctan(c*x))/x^2-3*I*c*d^3*(a+b*arctan(c*x))/x-3*a*c^2*d^3*ln(x)+3*I*b*c^2*d^3*ln(x)-I*b*c^2*d^3*ln(c^2*x^2+1)-3/2*I*b*c^2*d^3*polylog(2,-I*c*x)+3/2*I*b*c^2*d^3*polylog(2,I*c*x),1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))/x^4,x,17,-1/6*b*c*d^3/x^2-3/2*I*b*c^2*d^3/x-3/2*I*b*c^3*d^3*arctan(c*x)-1/3*d^3*(a+b*arctan(c*x))/x^3-3/2*I*c*d^3*(a+b*arctan(c*x))/x^2+3*c^2*d^3*(a+b*arctan(c*x))/x-I*a*c^3*d^3*ln(x)-10/3*b*c^3*d^3*ln(x)+5/3*b*c^3*d^3*ln(c^2*x^2+1)+1/2*b*c^3*d^3*polylog(2,-I*c*x)-1/2*b*c^3*d^3*polylog(2,I*c*x),1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))/x^5,x,4,-1/12*b*c*d^3/x^3-1/2*I*b*c^2*d^3/x^2+7/4*b*c^3*d^3/x-1/4*d^3*(1+I*c*x)^4*(a+b*arctan(c*x))/x^4-2*I*b*c^4*d^3*ln(x)+2*I*b*c^4*d^3*ln(I+c*x),1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))/x^6,x,4,-1/20*b*c*d^3/x^4-1/4*I*b*c^2*d^3/x^3+3/5*b*c^3*d^3/x^2+5/4*I*b*c^4*d^3/x-1/5*d^3*(1+I*c*x)^4*(a+b*arctan(c*x))/x^5+1/20*I*c*d^3*(1+I*c*x)^4*(a+b*arctan(c*x))/x^4+6/5*b*c^5*d^3*ln(x)-6/5*b*c^5*d^3*ln(I+c*x),1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))/x^7,x,7,-1/30*b*c*d^3/x^5-3/20*I*b*c^2*d^3/x^4+11/36*b*c^3*d^3/x^3+7/15*I*b*c^4*d^3/x^2-11/12*b*c^5*d^3/x-11/12*b*c^6*d^3*arctan(c*x)-1/6*d^3*(a+b*arctan(c*x))/x^6-3/5*I*c*d^3*(a+b*arctan(c*x))/x^5+3/4*c^2*d^3*(a+b*arctan(c*x))/x^4+1/3*I*c^3*d^3*(a+b*arctan(c*x))/x^3+14/15*I*b*c^6*d^3*ln(x)-7/15*I*b*c^6*d^3*ln(c^2*x^2+1),1],
[x^3*(d+I*c*d*x)^4*(a+b*arctan(c*x)),x,7,11/8*b*d^4*x/c^3+24/35*I*b*d^4*x^2/c^2-11/24*b*d^4*x^3/c-12/35*I*b*d^4*x^4+9/40*b*c*d^4*x^5+2/21*I*b*c^2*d^4*x^6-1/56*b*c^3*d^4*x^7-11/8*b*d^4*arctan(c*x)/c^4+1/4*d^4*x^4*(a+b*arctan(c*x))+4/5*I*c*d^4*x^5*(a+b*arctan(c*x))-c^2*d^4*x^6*(a+b*arctan(c*x))-4/7*I*c^3*d^4*x^7*(a+b*arctan(c*x))+1/8*c^4*d^4*x^8*(a+b*arctan(c*x))-24/35*I*b*d^4*ln(c^2*x^2+1)/c^4,1],
[x^2*(d+I*c*d*x)^4*(a+b*arctan(c*x)),x,4,5/3*I*b*d^4*x/c^2-88/105*b*d^4*x^2/c-5/9*I*b*d^4*x^3+47/140*b*c*d^4*x^4+2/15*I*b*c^2*d^4*x^5-1/42*b*c^3*d^4*x^6+1/5*I*d^4*(1+I*c*x)^5*(a+b*arctan(c*x))/c^3-1/3*I*d^4*(1+I*c*x)^6*(a+b*arctan(c*x))/c^3+1/7*I*d^4*(1+I*c*x)^7*(a+b*arctan(c*x))/c^3+176/105*b*d^4*ln(I+c*x)/c^3,1],
[x*(d+I*c*d*x)^4*(a+b*arctan(c*x)),x,4,-16/15*b*d^4*x/c-4/15*I*b*d^4*(I-c*x)^2/c^2-4/45*b*d^4*(I-c*x)^3/c^2+1/30*I*b*d^4*(I-c*x)^4/c^2+1/30*b*d^4*(I-c*x)^5/c^2+1/5*d^4*(1+I*c*x)^5*(a+b*arctan(c*x))/c^2-1/6*d^4*(1+I*c*x)^6*(a+b*arctan(c*x))/c^2+32/15*I*b*d^4*ln(I+c*x)/c^2,1],
[(d+I*c*d*x)^4*(a+b*arctan(c*x)),x,4,-8/5*I*b*d^4*x-2/5*b*d^4*(1+I*c*x)^2/c-2/15*b*d^4*(1+I*c*x)^3/c-1/20*b*d^4*(1+I*c*x)^4/c-1/5*I*d^4*(1+I*c*x)^5*(a+b*arctan(c*x))/c-16/5*b*d^4*ln(1-I*c*x)/c,1],
[(d+I*c*d*x)^4*(a+b*arctan(c*x))/x,x,19,4*I*a*c*d^4*x+13/4*b*c*d^4*x+2/3*I*b*c^2*d^4*x^2-1/12*b*c^3*d^4*x^3-13/4*b*d^4*arctan(c*x)+4*I*b*c*d^4*x*arctan(c*x)-3*c^2*d^4*x^2*(a+b*arctan(c*x))-4/3*I*c^3*d^4*x^3*(a+b*arctan(c*x))+1/4*c^4*d^4*x^4*(a+b*arctan(c*x))+a*d^4*ln(x)-8/3*I*b*d^4*ln(c^2*x^2+1)+1/2*I*b*d^4*polylog(2,-I*c*x)-1/2*I*b*d^4*polylog(2,I*c*x),1],
[(d+I*c*d*x)^4*(a+b*arctan(c*x))/x^2,x,20,-6*a*c^2*d^4*x+2*I*b*c^2*d^4*x-1/6*b*c^3*d^4*x^2-2*I*b*c*d^4*arctan(c*x)-6*b*c^2*d^4*x*arctan(c*x)-d^4*(a+b*arctan(c*x))/x-2*I*c^3*d^4*x^2*(a+b*arctan(c*x))+1/3*c^4*d^4*x^3*(a+b*arctan(c*x))+4*I*a*c*d^4*ln(x)+b*c*d^4*ln(x)+8/3*b*c*d^4*ln(c^2*x^2+1)-2*b*c*d^4*polylog(2,-I*c*x)+2*b*c*d^4*polylog(2,I*c*x),1],
[(d+I*c*d*x)^4*(a+b*arctan(c*x))/x^3,x,19,-1/2*b*c*d^4/x-4*I*a*c^3*d^4*x-1/2*b*c^3*d^4*x-4*I*b*c^3*d^4*x*arctan(c*x)-1/2*d^4*(a+b*arctan(c*x))/x^2-4*I*c*d^4*(a+b*arctan(c*x))/x+1/2*c^4*d^4*x^2*(a+b*arctan(c*x))-6*a*c^2*d^4*ln(x)+4*I*b*c^2*d^4*ln(x)-3*I*b*c^2*d^4*polylog(2,-I*c*x)+3*I*b*c^2*d^4*polylog(2,I*c*x),1],
[(d+I*c*d*x)^4*(a+b*arctan(c*x))/x^4,x,20,-1/6*b*c*d^4/x^2-2*I*b*c^2*d^4/x+a*c^4*d^4*x-2*I*b*c^3*d^4*arctan(c*x)+b*c^4*d^4*x*arctan(c*x)-1/3*d^4*(a+b*arctan(c*x))/x^3-2*I*c*d^4*(a+b*arctan(c*x))/x^2+6*c^2*d^4*(a+b*arctan(c*x))/x-4*I*a*c^3*d^4*ln(x)-19/3*b*c^3*d^4*ln(x)+8/3*b*c^3*d^4*ln(c^2*x^2+1)+2*b*c^3*d^4*polylog(2,-I*c*x)-2*b*c^3*d^4*polylog(2,I*c*x),1],
[(d+I*c*d*x)^4*(a+b*arctan(c*x))/x^5,x,21,-1/12*b*c*d^4/x^3-2/3*I*b*c^2*d^4/x^2+13/4*b*c^3*d^4/x+13/4*b*c^4*d^4*arctan(c*x)-1/4*d^4*(a+b*arctan(c*x))/x^4-4/3*I*c*d^4*(a+b*arctan(c*x))/x^3+3*c^2*d^4*(a+b*arctan(c*x))/x^2+4*I*c^3*d^4*(a+b*arctan(c*x))/x+a*c^4*d^4*ln(x)-16/3*I*b*c^4*d^4*ln(x)+8/3*I*b*c^4*d^4*ln(c^2*x^2+1)+1/2*I*b*c^4*d^4*polylog(2,-I*c*x)-1/2*I*b*c^4*d^4*polylog(2,I*c*x),1],
[(d+I*c*d*x)^4*(a+b*arctan(c*x))/x^6,x,4,-1/20*b*c*d^4/x^4-1/3*I*b*c^2*d^4/x^3+11/10*b*c^3*d^4/x^2+3*I*b*c^4*d^4/x-1/5*d^4*(1+I*c*x)^5*(a+b*arctan(c*x))/x^5+16/5*b*c^5*d^4*ln(x)-16/5*b*c^5*d^4*ln(I+c*x),1],
[(d+I*c*d*x)^4*(a+b*arctan(c*x))/x^7,x,4,-1/30*b*c*d^4/x^5-1/5*I*b*c^2*d^4/x^4+5/9*b*c^3*d^4/x^3+16/15*I*b*c^4*d^4/x^2-13/6*b*c^5*d^4/x-1/6*d^4*(1+I*c*x)^5*(a+b*arctan(c*x))/x^6+1/30*I*c*d^4*(1+I*c*x)^5*(a+b*arctan(c*x))/x^5+32/15*I*b*c^6*d^4*ln(x)-32/15*I*b*c^6*d^4*ln(I+c*x),1],
[(d+I*c*d*x)^4*(a+b*arctan(c*x))/x^8,x,7,-1/42*b*c*d^4/x^6-2/15*I*b*c^2*d^4/x^5+47/140*b*c^3*d^4/x^4+5/9*I*b*c^4*d^4/x^3-88/105*b*c^5*d^4/x^2-5/3*I*b*c^6*d^4/x-5/3*I*b*c^7*d^4*arctan(c*x)-1/7*d^4*(a+b*arctan(c*x))/x^7-2/3*I*c*d^4*(a+b*arctan(c*x))/x^6+6/5*c^2*d^4*(a+b*arctan(c*x))/x^5+I*c^3*d^4*(a+b*arctan(c*x))/x^4-1/3*c^4*d^4*(a+b*arctan(c*x))/x^3-176/105*b*c^7*d^4*ln(x)+88/105*b*c^7*d^4*ln(c^2*x^2+1),1],
[x^3*(a+b*arctan(c*x))/(d+I*c*d*x),x,16,I*a*x/c^3/d-1/2*b*x/c^3/d+1/6*I*b*x^2/c^2/d+1/2*b*arctan(c*x)/c^4/d+I*b*x*arctan(c*x)/c^3/d+1/2*x^2*(a+b*arctan(c*x))/c^2/d-1/3*I*x^3*(a+b*arctan(c*x))/c/d+(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^4/d-2/3*I*b*ln(c^2*x^2+1)/c^4/d+1/2*I*b*polylog(2,1-2/(1+I*c*x))/c^4/d,1],
[x^2*(a+b*arctan(c*x))/(d+I*c*d*x),x,11,a*x/c^2/d+1/2*I*b*x/c^2/d-1/2*I*b*arctan(c*x)/c^3/d+b*x*arctan(c*x)/c^2/d-1/2*I*x^2*(a+b*arctan(c*x))/c/d-I*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3/d-1/2*b*ln(c^2*x^2+1)/c^3/d+1/2*b*polylog(2,1-2/(1+I*c*x))/c^3/d,1],
[x*(a+b*arctan(c*x))/(d+I*c*d*x),x,7,-I*a*x/c/d-I*b*x*arctan(c*x)/c/d-(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^2/d+1/2*I*b*ln(c^2*x^2+1)/c^2/d-1/2*I*b*polylog(2,1-2/(1+I*c*x))/c^2/d,1],
[(a+b*arctan(c*x))/(d+I*c*d*x),x,3,I*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c/d-1/2*b*polylog(2,1-2/(1+I*c*x))/c/d,1],
[(a+b*arctan(c*x))/x/(d+I*c*d*x),x,2,(a+b*arctan(c*x))*ln(2-2/(1+I*c*x))/d+1/2*I*b*polylog(2,-1+2/(1+I*c*x))/d,1],
[(a+b*arctan(c*x))/x^2/(d+I*c*d*x),x,8,-(a+b*arctan(c*x))/d/x+b*c*ln(x)/d-1/2*b*c*ln(c^2*x^2+1)/d-I*c*(a+b*arctan(c*x))*ln(2-2/(1+I*c*x))/d+1/2*b*c*polylog(2,-1+2/(1+I*c*x))/d,1],
[(a+b*arctan(c*x))/x^3/(d+I*c*d*x),x,12,-1/2*b*c/d/x-1/2*b*c^2*arctan(c*x)/d-1/2*(a+b*arctan(c*x))/d/x^2+I*c*(a+b*arctan(c*x))/d/x-I*b*c^2*ln(x)/d+1/2*I*b*c^2*ln(c^2*x^2+1)/d-c^2*(a+b*arctan(c*x))*ln(2-2/(1+I*c*x))/d-1/2*I*b*c^2*polylog(2,-1+2/(1+I*c*x))/d,1],
[(a+b*arctan(c*x))/x^4/(d+I*c*d*x),x,17,-1/6*b*c/d/x^2+1/2*I*b*c^2/d/x+1/2*I*b*c^3*arctan(c*x)/d-1/3*(a+b*arctan(c*x))/d/x^3+1/2*I*c*(a+b*arctan(c*x))/d/x^2+c^2*(a+b*arctan(c*x))/d/x-4/3*b*c^3*ln(x)/d+2/3*b*c^3*ln(c^2*x^2+1)/d+I*c^3*(a+b*arctan(c*x))*ln(2-2/(1+I*c*x))/d-1/2*b*c^3*polylog(2,-1+2/(1+I*c*x))/d,1],
[x^3*(a+b*arctan(c*x))/(d+I*c*d*x)^2,x,16,-2*I*a*x/c^3/d^2+1/2*b*x/c^3/d^2+1/2*b/c^4/d^2/(I-c*x)-b*arctan(c*x)/c^4/d^2-2*I*b*x*arctan(c*x)/c^3/d^2-1/2*x^2*(a+b*arctan(c*x))/c^2/d^2+I*(a+b*arctan(c*x))/c^4/d^2/(I-c*x)-3*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^4/d^2+I*b*ln(c^2*x^2+1)/c^4/d^2-3/2*I*b*polylog(2,1-2/(1+I*c*x))/c^4/d^2,1],
[x^2*(a+b*arctan(c*x))/(d+I*c*d*x)^2,x,13,-a*x/c^2/d^2-1/2*I*b/c^3/d^2/(I-c*x)+1/2*I*b*arctan(c*x)/c^3/d^2-b*x*arctan(c*x)/c^2/d^2+(a+b*arctan(c*x))/c^3/d^2/(I-c*x)+2*I*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3/d^2+1/2*b*ln(c^2*x^2+1)/c^3/d^2-b*polylog(2,1-2/(1+I*c*x))/c^3/d^2,1],
[x*(a+b*arctan(c*x))/(d+I*c*d*x)^2,x,10,-1/2*b/c^2/d^2/(I-c*x)+1/2*b*arctan(c*x)/c^2/d^2-I*(a+b*arctan(c*x))/c^2/d^2/(I-c*x)+(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^2/d^2+1/2*I*b*polylog(2,1-2/(1+I*c*x))/c^2/d^2,1],
[(a+b*arctan(c*x))/(d+I*c*d*x)^2,x,5,1/2*I*b/c/d^2/(I-c*x)-1/2*I*b*arctan(c*x)/c/d^2+I*(a+b*arctan(c*x))/c/d^2/(1+I*c*x),1],
[(a+b*arctan(c*x))/x/(d+I*c*d*x)^2,x,13,1/2*b/d^2/(I-c*x)-1/2*b*arctan(c*x)/d^2+I*(a+b*arctan(c*x))/d^2/(I-c*x)+a*ln(x)/d^2+(a+b*arctan(c*x))*ln(2/(1+I*c*x))/d^2+1/2*I*b*polylog(2,-I*c*x)/d^2-1/2*I*b*polylog(2,I*c*x)/d^2+1/2*I*b*polylog(2,1-2/(1+I*c*x))/d^2,1],
[(a+b*arctan(c*x))/x^2/(d+I*c*d*x)^2,x,18,-1/2*I*b*c/d^2/(I-c*x)+1/2*I*b*c*arctan(c*x)/d^2-(a+b*arctan(c*x))/d^2/x+c*(a+b*arctan(c*x))/d^2/(I-c*x)-2*I*a*c*ln(x)/d^2+b*c*ln(x)/d^2-2*I*c*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/d^2-1/2*b*c*ln(c^2*x^2+1)/d^2+b*c*polylog(2,-I*c*x)/d^2-b*c*polylog(2,I*c*x)/d^2+b*c*polylog(2,1-2/(1+I*c*x))/d^2,1],
[(a+b*arctan(c*x))/x^3/(d+I*c*d*x)^2,x,21,-1/2*b*c/d^2/x-1/2*b*c^2/d^2/(I-c*x)-1/2*(a+b*arctan(c*x))/d^2/x^2+2*I*c*(a+b*arctan(c*x))/d^2/x-I*c^2*(a+b*arctan(c*x))/d^2/(I-c*x)-3*a*c^2*ln(x)/d^2-2*I*b*c^2*ln(x)/d^2-3*c^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/d^2+I*b*c^2*ln(c^2*x^2+1)/d^2-3/2*I*b*c^2*polylog(2,-I*c*x)/d^2+3/2*I*b*c^2*polylog(2,I*c*x)/d^2-3/2*I*b*c^2*polylog(2,1-2/(1+I*c*x))/d^2,1],
[x^4*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x,21,-3*a*x/c^4/d^3-1/2*I*b*x/c^4/d^3-1/8*b/c^5/d^3/(I-c*x)^2-15/8*I*b/c^5/d^3/(I-c*x)+19/8*I*b*arctan(c*x)/c^5/d^3-3*b*x*arctan(c*x)/c^4/d^3+1/2*I*x^2*(a+b*arctan(c*x))/c^3/d^3-1/2*I*(a+b*arctan(c*x))/c^5/d^3/(I-c*x)^2+4*(a+b*arctan(c*x))/c^5/d^3/(I-c*x)+6*I*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^5/d^3+3/2*b*ln(c^2*x^2+1)/c^5/d^3-3*b*polylog(2,1-2/(1+I*c*x))/c^5/d^3,1],
[x^3*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x,18,I*a*x/c^3/d^3+1/8*I*b/c^4/d^3/(I-c*x)^2-11/8*b/c^4/d^3/(I-c*x)+11/8*b*arctan(c*x)/c^4/d^3+I*b*x*arctan(c*x)/c^3/d^3-1/2*(a+b*arctan(c*x))/c^4/d^3/(I-c*x)^2-3*I*(a+b*arctan(c*x))/c^4/d^3/(I-c*x)+3*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^4/d^3-1/2*I*b*ln(c^2*x^2+1)/c^4/d^3+3/2*I*b*polylog(2,1-2/(1+I*c*x))/c^4/d^3,1],
[x^2*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x,15,1/8*b/c^3/d^3/(I-c*x)^2+7/8*I*b/c^3/d^3/(I-c*x)-7/8*I*b*arctan(c*x)/c^3/d^3+1/2*I*(a+b*arctan(c*x))/c^3/d^3/(I-c*x)^2-2*(a+b*arctan(c*x))/c^3/d^3/(I-c*x)-I*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3/d^3+1/2*b*polylog(2,1-2/(1+I*c*x))/c^3/d^3,1],
[x*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x,5,-1/8*I*b/c^2/d^3/(I-c*x)^2+3/8*b/c^2/d^3/(I-c*x)+1/8*b*arctan(c*x)/c^2/d^3+1/2*x^2*(a+b*arctan(c*x))/d^3/(1+I*c*x)^2,1],
[(a+b*arctan(c*x))/(d+I*c*d*x)^3,x,5,-1/8*b/c/d^3/(I-c*x)^2+1/8*I*b/c/d^3/(I-c*x)-1/8*I*b*arctan(c*x)/c/d^3+1/2*I*(a+b*arctan(c*x))/c/d^3/(1+I*c*x)^2,1],
[(a+b*arctan(c*x))/x/(d+I*c*d*x)^3,x,18,1/8*I*b/d^3/(I-c*x)^2+5/8*b/d^3/(I-c*x)-5/8*b*arctan(c*x)/d^3-1/2*(a+b*arctan(c*x))/d^3/(I-c*x)^2+I*(a+b*arctan(c*x))/d^3/(I-c*x)+a*ln(x)/d^3+(a+b*arctan(c*x))*ln(2/(1+I*c*x))/d^3+1/2*I*b*polylog(2,-I*c*x)/d^3-1/2*I*b*polylog(2,I*c*x)/d^3+1/2*I*b*polylog(2,1-2/(1+I*c*x))/d^3,1],
[(a+b*arctan(c*x))/x^2/(d+I*c*d*x)^3,x,23,1/8*b*c/d^3/(I-c*x)^2-9/8*I*b*c/d^3/(I-c*x)+9/8*I*b*c*arctan(c*x)/d^3-(a+b*arctan(c*x))/d^3/x+1/2*I*c*(a+b*arctan(c*x))/d^3/(I-c*x)^2+2*c*(a+b*arctan(c*x))/d^3/(I-c*x)-3*I*a*c*ln(x)/d^3+b*c*ln(x)/d^3-3*I*c*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/d^3-1/2*b*c*ln(c^2*x^2+1)/d^3+3/2*b*c*polylog(2,-I*c*x)/d^3-3/2*b*c*polylog(2,I*c*x)/d^3+3/2*b*c*polylog(2,1-2/(1+I*c*x))/d^3,1],
[(a+b*arctan(c*x))/x^3/(d+I*c*d*x)^3,x,26,-1/2*b*c/d^3/x-1/8*I*b*c^2/d^3/(I-c*x)^2-13/8*b*c^2/d^3/(I-c*x)+9/8*b*c^2*arctan(c*x)/d^3-1/2*(a+b*arctan(c*x))/d^3/x^2+3*I*c*(a+b*arctan(c*x))/d^3/x+1/2*c^2*(a+b*arctan(c*x))/d^3/(I-c*x)^2-3*I*c^2*(a+b*arctan(c*x))/d^3/(I-c*x)-6*a*c^2*ln(x)/d^3-3*I*b*c^2*ln(x)/d^3-6*c^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/d^3+3/2*I*b*c^2*ln(c^2*x^2+1)/d^3-3*I*b*c^2*polylog(2,-I*c*x)/d^3+3*I*b*c^2*polylog(2,I*c*x)/d^3-3*I*b*c^2*polylog(2,1-2/(1+I*c*x))/d^3,1],
[(a+b*arctan(c*x))/(1+I*c*x)^4,x,5,-1/18*I*b/c/(I-c*x)^3-1/24*b/c/(I-c*x)^2+1/24*I*b/c/(I-c*x)-1/24*I*b*arctan(c*x)/c+1/3*I*(a+b*arctan(c*x))/c/(1+I*c*x)^3,1],
[arctan(a*x)/(c*x+I*a*c*x^2),x,3,arctan(a*x)*ln(2-2/(1+I*a*x))/c+1/2*I*polylog(2,-1+2/(1+I*a*x))/c,1],
[x^3*(d+I*c*d*x)*(a+b*arctan(c*x))^2,x,27,1/2*a*b*d*x/c^3-3/10*I*b^2*d*x/c^3+1/12*b^2*d*x^2/c^2+1/30*I*b^2*d*x^3/c+3/10*I*b^2*d*arctan(c*x)/c^4+1/2*b^2*d*x*arctan(c*x)/c^3+1/5*I*b*d*x^2*(a+b*arctan(c*x))/c^2-1/6*b*d*x^3*(a+b*arctan(c*x))/c-1/10*I*b*d*x^4*(a+b*arctan(c*x))-9/20*d*(a+b*arctan(c*x))^2/c^4+1/4*d*x^4*(a+b*arctan(c*x))^2+1/5*I*c*d*x^5*(a+b*arctan(c*x))^2+2/5*I*b*d*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^4-1/3*b^2*d*ln(c^2*x^2+1)/c^4-1/5*b^2*d*polylog(2,1-2/(1+I*c*x))/c^4,1],
[x^2*(d+I*c*d*x)*(a+b*arctan(c*x))^2,x,22,1/2*I*a*b*d*x/c^2+1/3*b^2*d*x/c^2+1/12*I*b^2*d*x^2/c-1/3*b^2*d*arctan(c*x)/c^3+1/2*I*b^2*d*x*arctan(c*x)/c^2-1/3*b*d*x^2*(a+b*arctan(c*x))/c-1/6*I*b*d*x^3*(a+b*arctan(c*x))-7/12*I*d*(a+b*arctan(c*x))^2/c^3+1/3*d*x^3*(a+b*arctan(c*x))^2+1/4*I*c*d*x^4*(a+b*arctan(c*x))^2-2/3*b*d*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3-1/3*I*b^2*d*ln(c^2*x^2+1)/c^3-1/3*I*b^2*d*polylog(2,1-2/(1+I*c*x))/c^3,1],
[x*(d+I*c*d*x)*(a+b*arctan(c*x))^2,x,17,-a*b*d*x/c+1/3*I*b^2*d*x/c-1/3*I*b^2*d*arctan(c*x)/c^2-b^2*d*x*arctan(c*x)/c-1/3*I*b*d*x^2*(a+b*arctan(c*x))+5/6*d*(a+b*arctan(c*x))^2/c^2+1/2*d*x^2*(a+b*arctan(c*x))^2+1/3*I*c*d*x^3*(a+b*arctan(c*x))^2-2/3*I*b*d*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^2+1/2*b^2*d*ln(c^2*x^2+1)/c^2+1/3*b^2*d*polylog(2,1-2/(1+I*c*x))/c^2,1],
[(d+I*c*d*x)*(a+b*arctan(c*x))^2,x,9,-I*a*b*d*x-I*b^2*d*x*arctan(c*x)-1/2*I*d*(1+I*c*x)^2*(a+b*arctan(c*x))^2/c+2*b*d*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/c+1/2*I*b^2*d*ln(c^2*x^2+1)/c-I*b^2*d*polylog(2,1-2/(1-I*c*x))/c,1],
[(d+I*c*d*x)*(a+b*arctan(c*x))^2/x,x,13,-d*(a+b*arctan(c*x))^2+I*c*d*x*(a+b*arctan(c*x))^2+2*d*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))+2*I*b*d*(a+b*arctan(c*x))*ln(2/(1+I*c*x))-b^2*d*polylog(2,1-2/(1+I*c*x))-I*b*d*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))+I*b*d*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))-1/2*b^2*d*polylog(3,1-2/(1+I*c*x))+1/2*b^2*d*polylog(3,-1+2/(1+I*c*x)),1],
[(d+I*c*d*x)*(a+b*arctan(c*x))^2/x^2,x,12,-I*c*d*(a+b*arctan(c*x))^2-d*(a+b*arctan(c*x))^2/x+2*I*c*d*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))+2*b*c*d*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))-I*b^2*c*d*polylog(2,-1+2/(1-I*c*x))+b*c*d*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))-b*c*d*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))-1/2*I*b^2*c*d*polylog(3,1-2/(1+I*c*x))+1/2*I*b^2*c*d*polylog(3,-1+2/(1+I*c*x)),1],
[(d+I*c*d*x)*(a+b*arctan(c*x))^2/x^3,x,14,-b*c*d*(a+b*arctan(c*x))/x+1/2*c^2*d*(a+b*arctan(c*x))^2-1/2*d*(a+b*arctan(c*x))^2/x^2-I*c*d*(a+b*arctan(c*x))^2/x+b^2*c^2*d*ln(x)-1/2*b^2*c^2*d*ln(c^2*x^2+1)+2*I*b*c^2*d*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))+b^2*c^2*d*polylog(2,-1+2/(1-I*c*x)),1],
[(d+I*c*d*x)*(a+b*arctan(c*x))^2/x^4,x,18,-1/3*b^2*c^2*d/x-1/3*b^2*c^3*d*arctan(c*x)-1/3*b*c*d*(a+b*arctan(c*x))/x^2-I*b*c^2*d*(a+b*arctan(c*x))/x-1/6*I*c^3*d*(a+b*arctan(c*x))^2-1/3*d*(a+b*arctan(c*x))^2/x^3-1/2*I*c*d*(a+b*arctan(c*x))^2/x^2+I*b^2*c^3*d*ln(x)-1/2*I*b^2*c^3*d*ln(c^2*x^2+1)-2/3*b*c^3*d*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))+1/3*I*b^2*c^3*d*polylog(2,-1+2/(1-I*c*x)),1],
[x^3*(d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x,43,5/6*a*b*d^2*x/c^3+2/5*I*c*d^2*x^5*(a+b*arctan(c*x))^2+31/180*b^2*d^2*x^2/c^2+3/5*I*b^2*d^2*arctan(c*x)/c^4-1/60*b^2*d^2*x^4+2/5*I*b*d^2*x^2*(a+b*arctan(c*x))/c^2+5/6*b^2*d^2*x*arctan(c*x)/c^3-1/5*I*b*d^2*x^4*(a+b*arctan(c*x))-5/18*b*d^2*x^3*(a+b*arctan(c*x))/c-3/5*I*b^2*d^2*x/c^3+1/15*b*c*d^2*x^5*(a+b*arctan(c*x))-49/60*d^2*(a+b*arctan(c*x))^2/c^4+1/4*d^2*x^4*(a+b*arctan(c*x))^2+4/5*I*b*d^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^4-1/6*c^2*d^2*x^6*(a+b*arctan(c*x))^2+1/15*I*b^2*d^2*x^3/c-53/90*b^2*d^2*ln(c^2*x^2+1)/c^4-2/5*b^2*d^2*polylog(2,1-2/(1+I*c*x))/c^4,1],
[x^2*(d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x,36,I*b^2*d^2*x*arctan(c*x)/c^2+19/30*b^2*d^2*x/c^2-8/15*I*b^2*d^2*polylog(2,1-2/(1+I*c*x))/c^3-1/30*b^2*d^2*x^3-19/30*b^2*d^2*arctan(c*x)/c^3+I*a*b*d^2*x/c^2-8/15*b*d^2*x^2*(a+b*arctan(c*x))/c-1/3*I*b*d^2*x^3*(a+b*arctan(c*x))+1/10*b*c*d^2*x^4*(a+b*arctan(c*x))-31/30*I*d^2*(a+b*arctan(c*x))^2/c^3+1/3*d^2*x^3*(a+b*arctan(c*x))^2+1/6*I*b^2*d^2*x^2/c-1/5*c^2*d^2*x^5*(a+b*arctan(c*x))^2-16/15*b*d^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3+1/2*I*c*d^2*x^4*(a+b*arctan(c*x))^2-2/3*I*b^2*d^2*ln(c^2*x^2+1)/c^3,1],
[x*(d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x,28,-3/2*a*b*d^2*x/c+2/3*I*b^2*d^2*x/c-1/12*b^2*d^2*x^2-2/3*I*b^2*d^2*arctan(c*x)/c^2-3/2*b^2*d^2*x*arctan(c*x)/c-2/3*I*b*d^2*x^2*(a+b*arctan(c*x))+1/6*b*c*d^2*x^3*(a+b*arctan(c*x))+17/12*d^2*(a+b*arctan(c*x))^2/c^2+1/2*d^2*x^2*(a+b*arctan(c*x))^2+2/3*I*c*d^2*x^3*(a+b*arctan(c*x))^2-1/4*c^2*d^2*x^4*(a+b*arctan(c*x))^2-4/3*I*b*d^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^2+5/6*b^2*d^2*ln(c^2*x^2+1)/c^2+2/3*b^2*d^2*polylog(2,1-2/(1+I*c*x))/c^2,1],
[(d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x,12,-2*I*a*b*d^2*x-1/3*b^2*d^2*x+1/3*b^2*d^2*arctan(c*x)/c-2*I*b^2*d^2*x*arctan(c*x)+1/3*b*c*d^2*x^2*(a+b*arctan(c*x))-1/3*I*d^2*(1+I*c*x)^3*(a+b*arctan(c*x))^2/c+8/3*b*d^2*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/c+I*b^2*d^2*ln(c^2*x^2+1)/c-4/3*I*b^2*d^2*polylog(2,1-2/(1-I*c*x))/c,1],
[(d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x,x,19,a*b*c*d^2*x+b^2*c*d^2*x*arctan(c*x)-5/2*d^2*(a+b*arctan(c*x))^2+2*I*c*d^2*x*(a+b*arctan(c*x))^2-1/2*c^2*d^2*x^2*(a+b*arctan(c*x))^2+2*d^2*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))+4*I*b*d^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))-1/2*b^2*d^2*ln(c^2*x^2+1)-2*b^2*d^2*polylog(2,1-2/(1+I*c*x))-I*b*d^2*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))+I*b*d^2*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))-1/2*b^2*d^2*polylog(3,1-2/(1+I*c*x))+1/2*b^2*d^2*polylog(3,-1+2/(1+I*c*x)),1],
[(d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x^2,x,17,-2*I*c*d^2*(a+b*arctan(c*x))^2-d^2*(a+b*arctan(c*x))^2/x-c^2*d^2*x*(a+b*arctan(c*x))^2+4*I*c*d^2*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))-2*b*c*d^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))+2*b*c*d^2*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))-I*b^2*c*d^2*polylog(2,-1+2/(1-I*c*x))-I*b^2*c*d^2*polylog(2,1-2/(1+I*c*x))+2*b*c*d^2*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))-2*b*c*d^2*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))-I*b^2*c*d^2*polylog(3,1-2/(1+I*c*x))+I*b^2*c*d^2*polylog(3,-1+2/(1+I*c*x)),1],
[(d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x^3,x,20,-b*c*d^2*(a+b*arctan(c*x))/x+3/2*c^2*d^2*(a+b*arctan(c*x))^2-1/2*d^2*(a+b*arctan(c*x))^2/x^2-2*I*c*d^2*(a+b*arctan(c*x))^2/x-2*c^2*d^2*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))+b^2*c^2*d^2*ln(x)-1/2*b^2*c^2*d^2*ln(c^2*x^2+1)+4*I*b*c^2*d^2*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))+2*b^2*c^2*d^2*polylog(2,-1+2/(1-I*c*x))+I*b*c^2*d^2*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))-I*b*c^2*d^2*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))+1/2*b^2*c^2*d^2*polylog(3,1-2/(1+I*c*x))-1/2*b^2*c^2*d^2*polylog(3,-1+2/(1+I*c*x)),1],
[(d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x^4,x,18,-1/3*b^2*c^2*d^2/x-1/3*b^2*c^3*d^2*arctan(c*x)-1/3*b*c*d^2*(a+b*arctan(c*x))/x^2-2*I*b*c^2*d^2*(a+b*arctan(c*x))/x-1/3*d^2*(1+I*c*x)^3*(a+b*arctan(c*x))^2/x^3-8/3*a*b*c^3*d^2*ln(x)+2*I*b^2*c^3*d^2*ln(x)-8/3*b*c^3*d^2*(a+b*arctan(c*x))*ln(2/(1-I*c*x))-I*b^2*c^3*d^2*ln(c^2*x^2+1)-4/3*I*b^2*c^3*d^2*polylog(2,-I*c*x)+4/3*I*b^2*c^3*d^2*polylog(2,I*c*x)+4/3*I*b^2*c^3*d^2*polylog(2,1-2/(1-I*c*x)),1],
[x^3*(d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x,62,3/2*a*b*d^3*x/c^3-1/7*I*c^3*d^3*x^7*(a+b*arctan(c*x))^2+7/20*b^2*d^3*x^2/c^2+26/35*I*b*d^3*x^2*(a+b*arctan(c*x))/c^2-1/20*b^2*d^3*x^4+44/315*I*b^2*d^3*x^3/c+1/21*I*b*c^2*d^3*x^6*(a+b*arctan(c*x))+3/2*b^2*d^3*x*arctan(c*x)/c^3-122/105*I*b^2*d^3*x/c^3-1/2*b*d^3*x^3*(a+b*arctan(c*x))/c+3/5*I*c*d^3*x^5*(a+b*arctan(c*x))^2+1/5*b*c*d^3*x^5*(a+b*arctan(c*x))-1/105*I*b^2*c*d^3*x^5-209/140*d^3*(a+b*arctan(c*x))^2/c^4+1/4*d^3*x^4*(a+b*arctan(c*x))^2+52/35*I*b*d^3*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^4-1/2*c^2*d^3*x^6*(a+b*arctan(c*x))^2-13/35*I*b*d^3*x^4*(a+b*arctan(c*x))+122/105*I*b^2*d^3*arctan(c*x)/c^4-11/10*b^2*d^3*ln(c^2*x^2+1)/c^4-26/35*b^2*d^3*polylog(2,1-2/(1+I*c*x))/c^4,1],
[x^2*(d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x,52,1/15*I*b*c^2*d^3*x^5*(a+b*arctan(c*x))+37/30*b^2*d^3*x/c^2-1/6*I*c^3*d^3*x^6*(a+b*arctan(c*x))^2-1/10*b^2*d^3*x^3-11/18*I*b*d^3*x^3*(a+b*arctan(c*x))-37/30*b^2*d^3*arctan(c*x)/c^3-113/90*I*b^2*d^3*ln(c^2*x^2+1)/c^3-14/15*b*d^3*x^2*(a+b*arctan(c*x))/c-37/20*I*d^3*(a+b*arctan(c*x))^2/c^3+3/10*b*c*d^3*x^4*(a+b*arctan(c*x))+3/4*I*c*d^3*x^4*(a+b*arctan(c*x))^2+11/6*I*a*b*d^3*x/c^2+1/3*d^3*x^3*(a+b*arctan(c*x))^2-14/15*I*b^2*d^3*polylog(2,1-2/(1+I*c*x))/c^3-3/5*c^2*d^3*x^5*(a+b*arctan(c*x))^2-1/60*I*b^2*c*d^3*x^4-28/15*b*d^3*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3+61/180*I*b^2*d^3*x^2/c+11/6*I*b^2*d^3*x*arctan(c*x)/c^2,1],
[x*(d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x,38,-5/2*a*b*d^3*x/c+13/10*I*b^2*d^3*x/c-1/4*b^2*d^3*x^2-1/30*I*b^2*c*d^3*x^3-13/10*I*b^2*d^3*arctan(c*x)/c^2-5/2*b^2*d^3*x*arctan(c*x)/c-6/5*I*b*d^3*x^2*(a+b*arctan(c*x))+1/2*b*c*d^3*x^3*(a+b*arctan(c*x))+1/10*I*b*c^2*d^3*x^4*(a+b*arctan(c*x))+1/4*d^3*(1+I*c*x)^4*(a+b*arctan(c*x))^2/c^2-1/5*d^3*(1+I*c*x)^5*(a+b*arctan(c*x))^2/c^2-12/5*I*b*d^3*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/c^2+3/2*b^2*d^3*ln(c^2*x^2+1)/c^2-6/5*b^2*d^3*polylog(2,1-2/(1-I*c*x))/c^2,1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x,16,-7/2*I*a*b*d^3*x-b^2*d^3*x-1/12*I*b^2*c*d^3*x^2+b^2*d^3*arctan(c*x)/c-7/2*I*b^2*d^3*x*arctan(c*x)+b*c*d^3*x^2*(a+b*arctan(c*x))+1/6*I*b*c^2*d^3*x^3*(a+b*arctan(c*x))-1/4*I*d^3*(1+I*c*x)^4*(a+b*arctan(c*x))^2/c+4*b*d^3*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/c+11/6*I*b^2*d^3*ln(c^2*x^2+1)/c-2*I*b^2*d^3*polylog(2,1-2/(1-I*c*x))/c,1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x,x,28,3*a*b*c*d^3*x-1/3*I*c^3*d^3*x^3*(a+b*arctan(c*x))^2+20/3*I*b*d^3*(a+b*arctan(c*x))*ln(2/(1+I*c*x))+3*b^2*c*d^3*x*arctan(c*x)+3*I*c*d^3*x*(a+b*arctan(c*x))^2-29/6*d^3*(a+b*arctan(c*x))^2+I*b*d^3*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))-3/2*c^2*d^3*x^2*(a+b*arctan(c*x))^2-1/3*I*b^2*c*d^3*x+2*d^3*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))-I*b*d^3*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))-3/2*b^2*d^3*ln(c^2*x^2+1)-10/3*b^2*d^3*polylog(2,1-2/(1+I*c*x))+1/3*I*b^2*d^3*arctan(c*x)+1/3*I*b*c^2*d^3*x^2*(a+b*arctan(c*x))-1/2*b^2*d^3*polylog(3,1-2/(1+I*c*x))+1/2*b^2*d^3*polylog(3,-1+2/(1+I*c*x)),1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^2,x,23,3/2*I*b^2*c*d^3*polylog(3,-1+2/(1+I*c*x))-1/2*I*c^3*d^3*x^2*(a+b*arctan(c*x))^2-1/2*I*b^2*c*d^3*ln(c^2*x^2+1)-d^3*(a+b*arctan(c*x))^2/x-3*c^2*d^3*x*(a+b*arctan(c*x))^2-9/2*I*c*d^3*(a+b*arctan(c*x))^2-3/2*I*b^2*c*d^3*polylog(3,1-2/(1+I*c*x))-6*b*c*d^3*(a+b*arctan(c*x))*ln(2/(1+I*c*x))-I*b^2*c*d^3*polylog(2,-1+2/(1-I*c*x))+2*b*c*d^3*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))+I*a*b*c^2*d^3*x+6*I*c*d^3*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))+3*b*c*d^3*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))-3*b*c*d^3*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))+I*b^2*c^2*d^3*x*arctan(c*x)-3*I*b^2*c*d^3*polylog(2,1-2/(1+I*c*x)),1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^3,x,25,-b*c*d^3*(a+b*arctan(c*x))/x+7/2*c^2*d^3*(a+b*arctan(c*x))^2-1/2*d^3*(a+b*arctan(c*x))^2/x^2-3*I*b*c^2*d^3*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))-3*I*c*d^3*(a+b*arctan(c*x))^2/x-6*c^2*d^3*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))+b^2*c^2*d^3*ln(x)+6*I*b*c^2*d^3*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))-1/2*b^2*c^2*d^3*ln(c^2*x^2+1)-2*I*b*c^2*d^3*(a+b*arctan(c*x))*ln(2/(1+I*c*x))+3*b^2*c^2*d^3*polylog(2,-1+2/(1-I*c*x))+b^2*c^2*d^3*polylog(2,1-2/(1+I*c*x))-I*c^3*d^3*x*(a+b*arctan(c*x))^2+3*I*b*c^2*d^3*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))+3/2*b^2*c^2*d^3*polylog(3,1-2/(1+I*c*x))-3/2*b^2*c^2*d^3*polylog(3,-1+2/(1+I*c*x)),1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^4,x,28,-1/3*b^2*c^2*d^3/x-1/3*b^2*c^3*d^3*arctan(c*x)-1/3*b*c*d^3*(a+b*arctan(c*x))/x^2-3/2*I*b^2*c^3*d^3*ln(c^2*x^2+1)+11/6*I*c^3*d^3*(a+b*arctan(c*x))^2-1/3*d^3*(a+b*arctan(c*x))^2/x^3+3*I*b^2*c^3*d^3*ln(x)+3*c^2*d^3*(a+b*arctan(c*x))^2/x-1/2*I*b^2*c^3*d^3*polylog(3,-1+2/(1+I*c*x))-2*I*c^3*d^3*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))+1/2*I*b^2*c^3*d^3*polylog(3,1-2/(1+I*c*x))-20/3*b*c^3*d^3*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))-3/2*I*c*d^3*(a+b*arctan(c*x))^2/x^2-b*c^3*d^3*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))+b*c^3*d^3*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))+10/3*I*b^2*c^3*d^3*polylog(2,-1+2/(1-I*c*x))-3*I*b*c^2*d^3*(a+b*arctan(c*x))/x,1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^5,x,22,-1/12*b^2*c^2*d^3/x^2-I*b^2*c^3*d^3/x-I*b^2*c^4*d^3*arctan(c*x)-1/6*b*c*d^3*(a+b*arctan(c*x))/x^3-I*b*c^2*d^3*(a+b*arctan(c*x))/x^2+7/2*b*c^3*d^3*(a+b*arctan(c*x))/x-1/4*d^3*(1+I*c*x)^4*(a+b*arctan(c*x))^2/x^4-4*I*a*b*c^4*d^3*ln(x)-11/3*b^2*c^4*d^3*ln(x)-4*I*b*c^4*d^3*(a+b*arctan(c*x))*ln(2/(1-I*c*x))+11/6*b^2*c^4*d^3*ln(c^2*x^2+1)+2*b^2*c^4*d^3*polylog(2,-I*c*x)-2*b^2*c^4*d^3*polylog(2,I*c*x)-2*b^2*c^4*d^3*polylog(2,1-2/(1-I*c*x)),1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^6,x,26,-1/30*b^2*c^2*d^3/x^3+1/20*I*c*d^3*(1+I*c*x)^4*(a+b*arctan(c*x))^2/x^4+13/10*b^2*c^4*d^3/x+13/10*b^2*c^5*d^3*arctan(c*x)-1/10*b*c*d^3*(a+b*arctan(c*x))/x^4-3*I*b^2*c^5*d^3*ln(x)+6/5*b*c^3*d^3*(a+b*arctan(c*x))/x^2-1/4*I*b^2*c^3*d^3/x^2-1/5*d^3*(1+I*c*x)^4*(a+b*arctan(c*x))^2/x^5-6/5*I*b^2*c^5*d^3*polylog(2,I*c*x)+12/5*a*b*c^5*d^3*ln(x)+5/2*I*b*c^4*d^3*(a+b*arctan(c*x))/x+12/5*b*c^5*d^3*(a+b*arctan(c*x))*ln(2/(1-I*c*x))+6/5*I*b^2*c^5*d^3*polylog(2,-I*c*x)-6/5*I*b^2*c^5*d^3*polylog(2,1-2/(1-I*c*x))+3/2*I*b^2*c^5*d^3*ln(c^2*x^2+1)-1/2*I*b*c^2*d^3*(a+b*arctan(c*x))/x^3,1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^7,x,33,-1/60*b^2*c^2*d^3/x^4+37/30*I*b^2*c^5*d^3/x+61/180*b^2*c^4*d^3/x^2+1/3*I*c^3*d^3*(a+b*arctan(c*x))^2/x^3+1/60*I*b*c^6*d^3*(a+b*arctan(c*x))*ln(2/(1+I*c*x))-1/15*b*c*d^3*(a+b*arctan(c*x))/x^5+37/30*I*b^2*c^6*d^3*arctan(c*x)+11/18*b*c^3*d^3*(a+b*arctan(c*x))/x^3+37/20*I*b*c^6*d^3*(a+b*arctan(c*x))*ln(2/(1-I*c*x))-11/6*b*c^5*d^3*(a+b*arctan(c*x))/x-1/6*d^3*(a+b*arctan(c*x))^2/x^6-1/10*I*b^2*c^3*d^3/x^3+3/4*c^2*d^3*(a+b*arctan(c*x))^2/x^4+14/15*I*b*c^4*d^3*(a+b*arctan(c*x))/x^2-3/5*I*c*d^3*(a+b*arctan(c*x))^2/x^5+113/45*b^2*c^6*d^3*ln(x)+28/15*I*a*b*c^6*d^3*ln(x)-3/10*I*b*c^2*d^3*(a+b*arctan(c*x))/x^4-113/90*b^2*c^6*d^3*ln(c^2*x^2+1)-14/15*b^2*c^6*d^3*polylog(2,-I*c*x)+14/15*b^2*c^6*d^3*polylog(2,I*c*x)+37/40*b^2*c^6*d^3*polylog(2,1-2/(1-I*c*x))-1/120*b^2*c^6*d^3*polylog(2,1-2/(1+I*c*x)),1],
[x^3*(a+b*arctan(c*x))^2/(d+I*c*d*x),x,26,-a*b*x/c^3/d-1/3*I*b^2*x/c^3/d+1/3*I*b^2*arctan(c*x)/c^4/d-b^2*x*arctan(c*x)/c^3/d+1/3*I*b*x^2*(a+b*arctan(c*x))/c^2/d-5/6*(a+b*arctan(c*x))^2/c^4/d+I*x*(a+b*arctan(c*x))^2/c^3/d+1/2*x^2*(a+b*arctan(c*x))^2/c^2/d-1/3*I*x^3*(a+b*arctan(c*x))^2/c/d+8/3*I*b*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^4/d+(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/c^4/d+1/2*b^2*ln(c^2*x^2+1)/c^4/d-4/3*b^2*polylog(2,1-2/(1+I*c*x))/c^4/d+I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/c^4/d+1/2*b^2*polylog(3,1-2/(1+I*c*x))/c^4/d,1],
[x^2*(a+b*arctan(c*x))^2/(d+I*c*d*x),x,16,I*a*b*x/c^2/d+I*b^2*x*arctan(c*x)/c^2/d+1/2*I*(a+b*arctan(c*x))^2/c^3/d+x*(a+b*arctan(c*x))^2/c^2/d-1/2*I*x^2*(a+b*arctan(c*x))^2/c/d+2*b*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3/d-I*(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/c^3/d-1/2*I*b^2*ln(c^2*x^2+1)/c^3/d+I*b^2*polylog(2,1-2/(1+I*c*x))/c^3/d+b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/c^3/d-1/2*I*b^2*polylog(3,1-2/(1+I*c*x))/c^3/d,1],
[x*(a+b*arctan(c*x))^2/(d+I*c*d*x),x,9,(a+b*arctan(c*x))^2/c^2/d-I*x*(a+b*arctan(c*x))^2/c/d-2*I*b*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^2/d-(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/c^2/d+b^2*polylog(2,1-2/(1+I*c*x))/c^2/d-I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/c^2/d-1/2*b^2*polylog(3,1-2/(1+I*c*x))/c^2/d,1],
[(a+b*arctan(c*x))^2/(d+I*c*d*x),x,3,I*(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/c/d-b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/c/d+1/2*I*b^2*polylog(3,1-2/(1+I*c*x))/c/d,1],
[(a+b*arctan(c*x))^2/x/(d+I*c*d*x),x,3,(a+b*arctan(c*x))^2*ln(2-2/(1+I*c*x))/d+I*b*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d+1/2*b^2*polylog(3,-1+2/(1+I*c*x))/d,1],
[(a+b*arctan(c*x))^2/x^2/(d+I*c*d*x),x,8,-I*c*(a+b*arctan(c*x))^2/d-(a+b*arctan(c*x))^2/d/x+2*b*c*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))/d-I*c*(a+b*arctan(c*x))^2*ln(2-2/(1+I*c*x))/d-I*b^2*c*polylog(2,-1+2/(1-I*c*x))/d+b*c*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d-1/2*I*b^2*c*polylog(3,-1+2/(1+I*c*x))/d,1],
[(a+b*arctan(c*x))^2/x^3/(d+I*c*d*x),x,17,-b*c*(a+b*arctan(c*x))/d/x-3/2*c^2*(a+b*arctan(c*x))^2/d-1/2*(a+b*arctan(c*x))^2/d/x^2+I*c*(a+b*arctan(c*x))^2/d/x+b^2*c^2*ln(x)/d-1/2*b^2*c^2*ln(c^2*x^2+1)/d-2*I*b*c^2*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))/d-c^2*(a+b*arctan(c*x))^2*ln(2-2/(1+I*c*x))/d-b^2*c^2*polylog(2,-1+2/(1-I*c*x))/d-I*b*c^2*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d-1/2*b^2*c^2*polylog(3,-1+2/(1+I*c*x))/d,1],
[(a+b*arctan(c*x))^2/x^4/(d+I*c*d*x),x,26,-1/3*b^2*c^2/d/x-1/3*b^2*c^3*arctan(c*x)/d-1/3*b*c*(a+b*arctan(c*x))/d/x^2+I*b*c^2*(a+b*arctan(c*x))/d/x+11/6*I*c^3*(a+b*arctan(c*x))^2/d-1/3*(a+b*arctan(c*x))^2/d/x^3+1/2*I*c*(a+b*arctan(c*x))^2/d/x^2+c^2*(a+b*arctan(c*x))^2/d/x-I*b^2*c^3*ln(x)/d+1/2*I*b^2*c^3*ln(c^2*x^2+1)/d-8/3*b*c^3*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))/d+I*c^3*(a+b*arctan(c*x))^2*ln(2-2/(1+I*c*x))/d+4/3*I*b^2*c^3*polylog(2,-1+2/(1-I*c*x))/d-b*c^3*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d+1/2*I*b^2*c^3*polylog(3,-1+2/(1+I*c*x))/d,1],
[x^4*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x,33,10/3*I*b^2*polylog(2,1-2/(1+I*c*x))/c^5/d^2-1/3*b^2*x/c^4/d^2+1/2*b^2/c^5/d^2/(I-c*x)-1/6*b^2*arctan(c*x)/c^5/d^2-I*b^2*ln(c^2*x^2+1)/c^5/d^2+1/3*b*x^2*(a+b*arctan(c*x))/c^3/d^2-2*I*b^2*polylog(3,1-2/(1+I*c*x))/c^5/d^2+2*I*b^2*x*arctan(c*x)/c^4/d^2+3*x*(a+b*arctan(c*x))^2/c^4/d^2+I*b*(a+b*arctan(c*x))/c^5/d^2/(I-c*x)-1/3*x^3*(a+b*arctan(c*x))^2/c^2/d^2-(a+b*arctan(c*x))^2/c^5/d^2/(I-c*x)+20/3*b*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^5/d^2+2*I*a*b*x/c^4/d^2+11/6*I*(a+b*arctan(c*x))^2/c^5/d^2-4*I*(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/c^5/d^2+4*b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/c^5/d^2-I*x^2*(a+b*arctan(c*x))^2/c^3/d^2,1],
[x^3*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x,24,a*b*x/c^3/d^2-1/2*I*b^2/c^4/d^2/(I-c*x)+1/2*I*b^2*arctan(c*x)/c^4/d^2+b^2*x*arctan(c*x)/c^3/d^2+b*(a+b*arctan(c*x))/c^4/d^2/(I-c*x)+(a+b*arctan(c*x))^2/c^4/d^2-2*I*x*(a+b*arctan(c*x))^2/c^3/d^2-1/2*x^2*(a+b*arctan(c*x))^2/c^2/d^2+I*(a+b*arctan(c*x))^2/c^4/d^2/(I-c*x)-4*I*b*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^4/d^2-3*(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/c^4/d^2-1/2*b^2*ln(c^2*x^2+1)/c^4/d^2+2*b^2*polylog(2,1-2/(1+I*c*x))/c^4/d^2-3*I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/c^4/d^2-3/2*b^2*polylog(3,1-2/(1+I*c*x))/c^4/d^2,1],
[x^2*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x,18,-1/2*b^2/c^3/d^2/(I-c*x)+1/2*b^2*arctan(c*x)/c^3/d^2-I*b*(a+b*arctan(c*x))/c^3/d^2/(I-c*x)-1/2*I*(a+b*arctan(c*x))^2/c^3/d^2-x*(a+b*arctan(c*x))^2/c^2/d^2+(a+b*arctan(c*x))^2/c^3/d^2/(I-c*x)-2*b*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3/d^2+2*I*(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/c^3/d^2-I*b^2*polylog(2,1-2/(1+I*c*x))/c^3/d^2-2*b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/c^3/d^2+I*b^2*polylog(3,1-2/(1+I*c*x))/c^3/d^2,1],
[x*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x,13,1/2*I*b^2/c^2/d^2/(I-c*x)-1/2*I*b^2*arctan(c*x)/c^2/d^2-b*(a+b*arctan(c*x))/c^2/d^2/(I-c*x)+1/2*(a+b*arctan(c*x))^2/c^2/d^2-I*(a+b*arctan(c*x))^2/c^2/d^2/(I-c*x)+(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/c^2/d^2+I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/c^2/d^2+1/2*b^2*polylog(3,1-2/(1+I*c*x))/c^2/d^2,1],
[(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x,8,1/2*b^2/c/d^2/(I-c*x)-1/2*b^2*arctan(c*x)/c/d^2+I*b*(a+b*arctan(c*x))/c/d^2/(I-c*x)-1/2*I*(a+b*arctan(c*x))^2/c/d^2+I*(a+b*arctan(c*x))^2/c/d^2/(1+I*c*x),1],
[(a+b*arctan(c*x))^2/x/(d+I*c*d*x)^2,x,19,-1/2*I*b^2/d^2/(I-c*x)+1/2*I*b^2*arctan(c*x)/d^2+b*(a+b*arctan(c*x))/d^2/(I-c*x)-1/2*(a+b*arctan(c*x))^2/d^2+I*(a+b*arctan(c*x))^2/d^2/(I-c*x)+2*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))/d^2+(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/d^2+I*b*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d^2+1/2*b^2*polylog(3,-1+2/(1+I*c*x))/d^2,1],
[(a+b*arctan(c*x))^2/x^2/(d+I*c*d*x)^2,x,23,-1/2*b^2*c/d^2/(I-c*x)+1/2*b^2*c*arctan(c*x)/d^2-I*b*c*(a+b*arctan(c*x))/d^2/(I-c*x)-1/2*I*c*(a+b*arctan(c*x))^2/d^2-(a+b*arctan(c*x))^2/d^2/x+c*(a+b*arctan(c*x))^2/d^2/(I-c*x)-4*I*c*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))/d^2-2*I*c*(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/d^2+2*b*c*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))/d^2-I*b^2*c*polylog(2,-1+2/(1-I*c*x))/d^2+2*b*c*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d^2-I*b^2*c*polylog(3,-1+2/(1+I*c*x))/d^2,1],
[(a+b*arctan(c*x))^2/x^3/(d+I*c*d*x)^2,x,31,1/2*I*b^2*c^2/d^2/(I-c*x)-I*c^2*(a+b*arctan(c*x))^2/d^2/(I-c*x)-b*c*(a+b*arctan(c*x))/d^2/x-b*c^2*(a+b*arctan(c*x))/d^2/(I-c*x)-2*c^2*(a+b*arctan(c*x))^2/d^2-1/2*(a+b*arctan(c*x))^2/d^2/x^2-3*I*b*c^2*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d^2-1/2*I*b^2*c^2*arctan(c*x)/d^2-6*c^2*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))/d^2+b^2*c^2*ln(x)/d^2-3*c^2*(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/d^2-1/2*b^2*c^2*ln(c^2*x^2+1)/d^2+2*I*c*(a+b*arctan(c*x))^2/d^2/x-2*b^2*c^2*polylog(2,-1+2/(1-I*c*x))/d^2-4*I*b*c^2*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))/d^2-3/2*b^2*c^2*polylog(3,-1+2/(1+I*c*x))/d^2,1],
[x^4*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x,37,6*I*(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/c^5/d^3+1/2*I*x^2*(a+b*arctan(c*x))^2/c^3/d^3-29/16*b^2/c^5/d^3/(I-c*x)+29/16*b^2*arctan(c*x)/c^5/d^3-1/2*I*(a+b*arctan(c*x))^2/c^5/d^3/(I-c*x)^2-1/4*b*(a+b*arctan(c*x))/c^5/d^3/(I-c*x)^2-3*I*b^2*polylog(2,1-2/(1+I*c*x))/c^5/d^3+1/16*I*b^2/c^5/d^3/(I-c*x)^2-3*x*(a+b*arctan(c*x))^2/c^4/d^3+3*I*b^2*polylog(3,1-2/(1+I*c*x))/c^5/d^3-15/4*I*b*(a+b*arctan(c*x))/c^5/d^3/(I-c*x)+4*(a+b*arctan(c*x))^2/c^5/d^3/(I-c*x)-6*b*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^5/d^3-I*a*b*x/c^4/d^3-I*b^2*x*arctan(c*x)/c^4/d^3-5/8*I*(a+b*arctan(c*x))^2/c^5/d^3-6*b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/c^5/d^3+1/2*I*b^2*ln(c^2*x^2+1)/c^5/d^3,1],
[x^3*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x,31,1/16*b^2/c^4/d^3/(I-c*x)^2+21/16*I*b^2/c^4/d^3/(I-c*x)-21/16*I*b^2*arctan(c*x)/c^4/d^3+1/4*I*b*(a+b*arctan(c*x))/c^4/d^3/(I-c*x)^2-11/4*b*(a+b*arctan(c*x))/c^4/d^3/(I-c*x)+3/8*(a+b*arctan(c*x))^2/c^4/d^3+I*x*(a+b*arctan(c*x))^2/c^3/d^3-1/2*(a+b*arctan(c*x))^2/c^4/d^3/(I-c*x)^2-3*I*(a+b*arctan(c*x))^2/c^4/d^3/(I-c*x)+2*I*b*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^4/d^3+3*(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/c^4/d^3-b^2*polylog(2,1-2/(1+I*c*x))/c^4/d^3+3*I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/c^4/d^3+3/2*b^2*polylog(3,1-2/(1+I*c*x))/c^4/d^3,1],
[x^2*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x,26,-1/16*I*b^2/c^3/d^3/(I-c*x)^2+13/16*b^2/c^3/d^3/(I-c*x)-13/16*b^2*arctan(c*x)/c^3/d^3+1/4*b*(a+b*arctan(c*x))/c^3/d^3/(I-c*x)^2+7/4*I*b*(a+b*arctan(c*x))/c^3/d^3/(I-c*x)-7/8*I*(a+b*arctan(c*x))^2/c^3/d^3+1/2*I*(a+b*arctan(c*x))^2/c^3/d^3/(I-c*x)^2-2*(a+b*arctan(c*x))^2/c^3/d^3/(I-c*x)-I*(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/c^3/d^3+b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/c^3/d^3-1/2*I*b^2*polylog(3,1-2/(1+I*c*x))/c^3/d^3,1],
[x*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x,15,-1/16*b^2/c^2/d^3/(I-c*x)^2-5/16*I*b^2/c^2/d^3/(I-c*x)+5/16*I*b^2*arctan(c*x)/c^2/d^3-1/4*I*b*(a+b*arctan(c*x))/c^2/d^3/(I-c*x)^2+3/4*b*(a+b*arctan(c*x))/c^2/d^3/(I-c*x)+1/8*(a+b*arctan(c*x))^2/c^2/d^3+1/2*x^2*(a+b*arctan(c*x))^2/d^3/(1+I*c*x)^2,1],
[(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x,13,1/16*I*b^2/c/d^3/(I-c*x)^2+3/16*b^2/c/d^3/(I-c*x)-3/16*b^2*arctan(c*x)/c/d^3-1/4*b*(a+b*arctan(c*x))/c/d^3/(I-c*x)^2+1/4*I*b*(a+b*arctan(c*x))/c/d^3/(I-c*x)-1/8*I*(a+b*arctan(c*x))^2/c/d^3+1/2*I*(a+b*arctan(c*x))^2/c/d^3/(1+I*c*x)^2,1],
[(a+b*arctan(c*x))^2/x/(d+I*c*d*x)^3,x,32,1/16*b^2/d^3/(I-c*x)^2-11/16*I*b^2/d^3/(I-c*x)+11/16*I*b^2*arctan(c*x)/d^3+1/4*I*b*(a+b*arctan(c*x))/d^3/(I-c*x)^2+5/4*b*(a+b*arctan(c*x))/d^3/(I-c*x)-5/8*(a+b*arctan(c*x))^2/d^3-1/2*(a+b*arctan(c*x))^2/d^3/(I-c*x)^2+I*(a+b*arctan(c*x))^2/d^3/(I-c*x)+2*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))/d^3+(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/d^3+I*b*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d^3+1/2*b^2*polylog(3,-1+2/(1+I*c*x))/d^3,1],
[(a+b*arctan(c*x))^2/x^2/(d+I*c*d*x)^3,x,36,-1/16*I*b^2*c/d^3/(I-c*x)^2-19/16*b^2*c/d^3/(I-c*x)+19/16*b^2*c*arctan(c*x)/d^3+1/4*b*c*(a+b*arctan(c*x))/d^3/(I-c*x)^2-9/4*I*b*c*(a+b*arctan(c*x))/d^3/(I-c*x)+1/8*I*c*(a+b*arctan(c*x))^2/d^3-(a+b*arctan(c*x))^2/d^3/x+1/2*I*c*(a+b*arctan(c*x))^2/d^3/(I-c*x)^2+2*c*(a+b*arctan(c*x))^2/d^3/(I-c*x)-6*I*c*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))/d^3-3*I*c*(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/d^3+2*b*c*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))/d^3-I*b^2*c*polylog(2,-1+2/(1-I*c*x))/d^3+3*b*c*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d^3-3/2*I*b^2*c*polylog(3,-1+2/(1+I*c*x))/d^3,1],
[(a+b*arctan(c*x))^2/(1+I*c*x)^4,x,18,-1/54*b^2/c/(I-c*x)^3+5/144*I*b^2/c/(I-c*x)^2+11/144*b^2/c/(I-c*x)-11/144*b^2*arctan(c*x)/c-1/9*I*b*(a+b*arctan(c*x))/c/(I-c*x)^3-1/12*b*(a+b*arctan(c*x))/c/(I-c*x)^2+1/12*I*b*(a+b*arctan(c*x))/c/(I-c*x)-1/24*I*(a+b*arctan(c*x))^2/c+1/3*I*(a+b*arctan(c*x))^2/c/(1+I*c*x)^3,1],
[arctan(a*x)^2/(c*x-I*a*c*x^2),x,4,arctan(a*x)^2*ln(2-2/(1-I*a*x))/c-I*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))/c+1/2*polylog(3,-1+2/(1-I*a*x))/c,1],
[(d+I*c*d*x)^3*(a+b*arctan(c*x))^3,x,26,-3*a*b^2*d^3*x-11*I*b^2*d^3*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c-1/4*I*d^3*(1+I*c*x)^4*(a+b*arctan(c*x))^3/c-3*b^3*d^3*x*arctan(c*x)-21/4*I*b*d^3*x*(a+b*arctan(c*x))^2+7*b*d^3*(a+b*arctan(c*x))^2/c+1/4*I*b^3*d^3*x+3/2*b*c*d^3*x^2*(a+b*arctan(c*x))^2-6*I*b^2*d^3*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/c-1/4*I*b^2*c*d^3*x^2*(a+b*arctan(c*x))+6*b*d^3*(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/c-1/4*I*b^3*d^3*arctan(c*x)/c+3/2*b^3*d^3*ln(c^2*x^2+1)/c+1/4*I*b*c^2*d^3*x^3*(a+b*arctan(c*x))^2+11/2*b^3*d^3*polylog(2,1-2/(1+I*c*x))/c+3*b^3*d^3*polylog(3,1-2/(1-I*c*x))/c,1],
[(d+I*c*d*x)^2*(a+b*arctan(c*x))^3,x,17,-a*b^2*d^2*x-b^3*d^2*x*arctan(c*x)+7/2*b*d^2*(a+b*arctan(c*x))^2/c-3*I*b*d^2*x*(a+b*arctan(c*x))^2+1/2*b*c*d^2*x^2*(a+b*arctan(c*x))^2-1/3*I*d^2*(1+I*c*x)^3*(a+b*arctan(c*x))^3/c+4*b*d^2*(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/c-6*I*b^2*d^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c+1/2*b^3*d^2*ln(c^2*x^2+1)/c-4*I*b^2*d^2*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/c+3*b^3*d^2*polylog(2,1-2/(1+I*c*x))/c+2*b^3*d^2*polylog(3,1-2/(1-I*c*x))/c,1],
[(d+I*c*d*x)*(a+b*arctan(c*x))^3,x,11,3/2*b*d*(a+b*arctan(c*x))^2/c-3/2*I*b*d*x*(a+b*arctan(c*x))^2-1/2*I*d*(1+I*c*x)^2*(a+b*arctan(c*x))^3/c+3*b*d*(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/c-3*I*b^2*d*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c-3*I*b^2*d*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/c+3/2*b^3*d*polylog(2,1-2/(1+I*c*x))/c+3/2*b^3*d*polylog(3,1-2/(1-I*c*x))/c,1],
[(a+b*arctan(c*x))^3/(d+I*c*d*x),x,4,I*(a+b*arctan(c*x))^3*ln(2/(1+I*c*x))/c/d-3/2*b*(a+b*arctan(c*x))^2*polylog(2,1-2/(1+I*c*x))/c/d+3/2*I*b^2*(a+b*arctan(c*x))*polylog(3,1-2/(1+I*c*x))/c/d+3/4*b^3*polylog(4,1-2/(1+I*c*x))/c/d,1],
[(a+b*arctan(c*x))^3/(d+I*c*d*x)^2,x,11,-3/4*I*b^3/c/d^2/(I-c*x)+3/4*I*b^3*arctan(c*x)/c/d^2+3/2*b^2*(a+b*arctan(c*x))/c/d^2/(I-c*x)-3/4*b*(a+b*arctan(c*x))^2/c/d^2+3/2*I*b*(a+b*arctan(c*x))^2/c/d^2/(I-c*x)-1/2*I*(a+b*arctan(c*x))^3/c/d^2+I*(a+b*arctan(c*x))^3/c/d^2/(1+I*c*x),1],
[(a+b*arctan(c*x))^3/(d+I*c*d*x)^3,x,24,3/64*b^3/c/d^3/(I-c*x)^2-21/64*I*b^3/c/d^3/(I-c*x)+21/64*I*b^3*arctan(c*x)/c/d^3+3/16*I*b^2*(a+b*arctan(c*x))/c/d^3/(I-c*x)^2+9/16*b^2*(a+b*arctan(c*x))/c/d^3/(I-c*x)-9/32*b*(a+b*arctan(c*x))^2/c/d^3-3/8*b*(a+b*arctan(c*x))^2/c/d^3/(I-c*x)^2+3/8*I*b*(a+b*arctan(c*x))^2/c/d^3/(I-c*x)-1/8*I*(a+b*arctan(c*x))^3/c/d^3+1/2*I*(a+b*arctan(c*x))^3/c/d^3/(1+I*c*x)^2,1],
[(a+b*arctan(c*x))^3/(d+I*c*d*x)^4,x,42,1/108*I*b^3/c/d^4/(I-c*x)^3+19/576*b^3/c/d^4/(I-c*x)^2-85/576*I*b^3/c/d^4/(I-c*x)+85/576*I*b^3*arctan(c*x)/c/d^4-1/18*b^2*(a+b*arctan(c*x))/c/d^4/(I-c*x)^3+5/48*I*b^2*(a+b*arctan(c*x))/c/d^4/(I-c*x)^2+11/48*b^2*(a+b*arctan(c*x))/c/d^4/(I-c*x)-11/96*b*(a+b*arctan(c*x))^2/c/d^4-1/6*I*b*(a+b*arctan(c*x))^2/c/d^4/(I-c*x)^3-1/8*b*(a+b*arctan(c*x))^2/c/d^4/(I-c*x)^2+1/8*I*b*(a+b*arctan(c*x))^2/c/d^4/(I-c*x)-1/24*I*(a+b*arctan(c*x))^3/c/d^4+1/3*I*(a+b*arctan(c*x))^3/c/d^4/(1+I*c*x)^3,1],
[x^2*(a+b*arctan(c*x))^3/(d+I*c*d*x),x,19,-3/2*b*(a+b*arctan(c*x))^2/c^3/d+3/2*I*b*x*(a+b*arctan(c*x))^2/c^2/d+1/2*I*(a+b*arctan(c*x))^3/c^3/d+x*(a+b*arctan(c*x))^3/c^2/d-1/2*I*x^2*(a+b*arctan(c*x))^3/c/d+3*I*b^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3/d+3*b*(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/c^3/d-I*(a+b*arctan(c*x))^3*ln(2/(1+I*c*x))/c^3/d-3/2*b^3*polylog(2,1-2/(1+I*c*x))/c^3/d+3*I*b^2*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/c^3/d+3/2*b*(a+b*arctan(c*x))^2*polylog(2,1-2/(1+I*c*x))/c^3/d+3/2*b^3*polylog(3,1-2/(1+I*c*x))/c^3/d-3/2*I*b^2*(a+b*arctan(c*x))*polylog(3,1-2/(1+I*c*x))/c^3/d-3/4*b^3*polylog(4,1-2/(1+I*c*x))/c^3/d,1],
[x*(a+b*arctan(c*x))^3/(d+I*c*d*x),x,10,(a+b*arctan(c*x))^3/c^2/d-I*x*(a+b*arctan(c*x))^3/c/d-3*I*b*(a+b*arctan(c*x))^2*ln(2/(1+I*c*x))/c^2/d-(a+b*arctan(c*x))^3*ln(2/(1+I*c*x))/c^2/d+3*b^2*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/c^2/d-3/2*I*b*(a+b*arctan(c*x))^2*polylog(2,1-2/(1+I*c*x))/c^2/d-3/2*I*b^3*polylog(3,1-2/(1+I*c*x))/c^2/d-3/2*b^2*(a+b*arctan(c*x))*polylog(3,1-2/(1+I*c*x))/c^2/d+3/4*I*b^3*polylog(4,1-2/(1+I*c*x))/c^2/d,1],
[(a+b*arctan(c*x))^3/(d+I*c*d*x),x,4,I*(a+b*arctan(c*x))^3*ln(2/(1+I*c*x))/c/d-3/2*b*(a+b*arctan(c*x))^2*polylog(2,1-2/(1+I*c*x))/c/d+3/2*I*b^2*(a+b*arctan(c*x))*polylog(3,1-2/(1+I*c*x))/c/d+3/4*b^3*polylog(4,1-2/(1+I*c*x))/c/d,1],
[(a+b*arctan(c*x))^3/x/(d+I*c*d*x),x,4,(a+b*arctan(c*x))^3*ln(2-2/(1+I*c*x))/d+3/2*I*b*(a+b*arctan(c*x))^2*polylog(2,-1+2/(1+I*c*x))/d+3/2*b^2*(a+b*arctan(c*x))*polylog(3,-1+2/(1+I*c*x))/d-3/4*I*b^3*polylog(4,-1+2/(1+I*c*x))/d,1],
[(a+b*arctan(c*x))^3/x^2/(d+I*c*d*x),x,10,-I*c*(a+b*arctan(c*x))^3/d-(a+b*arctan(c*x))^3/d/x+3*b*c*(a+b*arctan(c*x))^2*ln(2-2/(1-I*c*x))/d-I*c*(a+b*arctan(c*x))^3*ln(2-2/(1+I*c*x))/d-3*I*b^2*c*(a+b*arctan(c*x))*polylog(2,-1+2/(1-I*c*x))/d+3/2*b*c*(a+b*arctan(c*x))^2*polylog(2,-1+2/(1+I*c*x))/d+3/2*b^3*c*polylog(3,-1+2/(1-I*c*x))/d-3/2*I*b^2*c*(a+b*arctan(c*x))*polylog(3,-1+2/(1+I*c*x))/d-3/4*b^3*c*polylog(4,-1+2/(1+I*c*x))/d,1],
[(a+b*arctan(c*x))^3/x^3/(d+I*c*d*x),x,18,-3/2*I*b*c^2*(a+b*arctan(c*x))^2/d-3/2*b*c*(a+b*arctan(c*x))^2/d/x-3/2*c^2*(a+b*arctan(c*x))^3/d-1/2*(a+b*arctan(c*x))^3/d/x^2+I*c*(a+b*arctan(c*x))^3/d/x+3*b^2*c^2*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))/d-3*I*b*c^2*(a+b*arctan(c*x))^2*ln(2-2/(1-I*c*x))/d-c^2*(a+b*arctan(c*x))^3*ln(2-2/(1+I*c*x))/d-3/2*I*b^3*c^2*polylog(2,-1+2/(1-I*c*x))/d-3*b^2*c^2*(a+b*arctan(c*x))*polylog(2,-1+2/(1-I*c*x))/d-3/2*I*b*c^2*(a+b*arctan(c*x))^2*polylog(2,-1+2/(1+I*c*x))/d-3/2*I*b^3*c^2*polylog(3,-1+2/(1-I*c*x))/d-3/2*b^2*c^2*(a+b*arctan(c*x))*polylog(3,-1+2/(1+I*c*x))/d+3/4*I*b^3*c^2*polylog(4,-1+2/(1+I*c*x))/d,1],
[1/(d+I*c*d*x)/(a+b*arctan(c*x)),x,0,Defer(Int)(1/(d+I*c*d*x)/(a+b*arctan(c*x)),x),0],
[x^3*(a+b*arctan(c*x))/(e*x+d),x,16,a*d^2*x/e^3+1/2*b*d*x/c/e^2-1/6*b*x^2/c/e-1/2*b*d*arctan(c*x)/c^2/e^2+b*d^2*x*arctan(c*x)/e^3-1/2*d*x^2*(a+b*arctan(c*x))/e^2+1/3*x^3*(a+b*arctan(c*x))/e+d^3*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/e^4-d^3*(a+b*arctan(c*x))*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^4-1/2*b*d^2*ln(c^2*x^2+1)/c/e^3+1/6*b*ln(c^2*x^2+1)/c^3/e-1/2*I*b*d^3*polylog(2,1-2/(1-I*c*x))/e^4+1/2*I*b*d^3*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^4,1],
[x^2*(a+b*arctan(c*x))/(e*x+d),x,12,-a*d*x/e^2-1/2*b*x/c/e+1/2*b*arctan(c*x)/c^2/e-b*d*x*arctan(c*x)/e^2+1/2*x^2*(a+b*arctan(c*x))/e-d^2*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/e^3+d^2*(a+b*arctan(c*x))*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^3+1/2*b*d*ln(c^2*x^2+1)/c/e^2+1/2*I*b*d^2*polylog(2,1-2/(1-I*c*x))/e^3-1/2*I*b*d^2*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^3,1],
[x*(a+b*arctan(c*x))/(e*x+d),x,9,a*x/e+b*x*arctan(c*x)/e+d*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/e^2-d*(a+b*arctan(c*x))*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^2-1/2*b*ln(c^2*x^2+1)/c/e-1/2*I*b*d*polylog(2,1-2/(1-I*c*x))/e^2+1/2*I*b*d*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^2,1],
[(a+b*arctan(c*x))/(e*x+d),x,4,-(a+b*arctan(c*x))*ln(2/(1-I*c*x))/e+(a+b*arctan(c*x))*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e+1/2*I*b*polylog(2,1-2/(1-I*c*x))/e-1/2*I*b*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e,1],
[(a+b*arctan(c*x))/x/(e*x+d),x,9,a*ln(x)/d+(a+b*arctan(c*x))*ln(2/(1-I*c*x))/d-(a+b*arctan(c*x))*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d+1/2*I*b*polylog(2,-I*c*x)/d-1/2*I*b*polylog(2,I*c*x)/d-1/2*I*b*polylog(2,1-2/(1-I*c*x))/d+1/2*I*b*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d,1],
[(a+b*arctan(c*x))/x^2/(e*x+d),x,14,-(a+b*arctan(c*x))/d/x+b*c*ln(x)/d-a*e*ln(x)/d^2-e*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/d^2+e*(a+b*arctan(c*x))*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d^2-1/2*b*c*ln(c^2*x^2+1)/d-1/2*I*b*e*polylog(2,-I*c*x)/d^2+1/2*I*b*e*polylog(2,I*c*x)/d^2+1/2*I*b*e*polylog(2,1-2/(1-I*c*x))/d^2-1/2*I*b*e*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d^2,1],
[(a+b*arctan(c*x))/x^3/(e*x+d),x,17,-1/2*b*c/d/x-1/2*b*c^2*arctan(c*x)/d-1/2*(a+b*arctan(c*x))/d/x^2+e*(a+b*arctan(c*x))/d^2/x-b*c*e*ln(x)/d^2+a*e^2*ln(x)/d^3+e^2*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/d^3-e^2*(a+b*arctan(c*x))*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d^3+1/2*b*c*e*ln(c^2*x^2+1)/d^2+1/2*I*b*e^2*polylog(2,-I*c*x)/d^3-1/2*I*b*e^2*polylog(2,I*c*x)/d^3-1/2*I*b*e^2*polylog(2,1-2/(1-I*c*x))/d^3+1/2*I*b*e^2*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d^3,1],
[x^3*(a+b*arctan(c*x))^2/(e*x+d),x,23,a*b*d*x/c/e^2+1/3*b^2*x/c^2/e-1/3*b^2*arctan(c*x)/c^3/e+b^2*d*x*arctan(c*x)/c/e^2-1/3*b*x^2*(a+b*arctan(c*x))/c/e+I*b^2*d^2*polylog(2,1-2/(1+I*c*x))/c/e^3-1/2*d*(a+b*arctan(c*x))^2/c^2/e^2-I*b*d^3*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/e^4+d^2*x*(a+b*arctan(c*x))^2/e^3-1/2*d*x^2*(a+b*arctan(c*x))^2/e^2+1/3*x^3*(a+b*arctan(c*x))^2/e+d^3*(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/e^4+2*b*d^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c/e^3-2/3*b*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3/e-d^3*(a+b*arctan(c*x))^2*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^4-1/2*b^2*d*ln(c^2*x^2+1)/c^2/e^2+I*d^2*(a+b*arctan(c*x))^2/c/e^3-1/3*I*(a+b*arctan(c*x))^2/c^3/e-1/3*I*b^2*polylog(2,1-2/(1+I*c*x))/c^3/e+I*b*d^3*(a+b*arctan(c*x))*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^4+1/2*b^2*d^3*polylog(3,1-2/(1-I*c*x))/e^4-1/2*b^2*d^3*polylog(3,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^4,1],
[x^2*(a+b*arctan(c*x))^2/(e*x+d),x,14,-a*b*x/c/e-b^2*x*arctan(c*x)/c/e-I*d*(a+b*arctan(c*x))^2/c/e^2+1/2*(a+b*arctan(c*x))^2/c^2/e-d*x*(a+b*arctan(c*x))^2/e^2+1/2*x^2*(a+b*arctan(c*x))^2/e-d^2*(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/e^3-2*b*d*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c/e^2+d^2*(a+b*arctan(c*x))^2*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^3+1/2*b^2*ln(c^2*x^2+1)/c^2/e+I*b*d^2*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/e^3-I*b^2*d*polylog(2,1-2/(1+I*c*x))/c/e^2-I*b*d^2*(a+b*arctan(c*x))*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^3-1/2*b^2*d^2*polylog(3,1-2/(1-I*c*x))/e^3+1/2*b^2*d^2*polylog(3,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^3,1],
[x*(a+b*arctan(c*x))^2/(e*x+d),x,8,I*(a+b*arctan(c*x))^2/c/e+x*(a+b*arctan(c*x))^2/e+d*(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/e^2+2*b*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c/e-d*(a+b*arctan(c*x))^2*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^2-I*b*d*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/e^2+I*b^2*polylog(2,1-2/(1+I*c*x))/c/e+I*b*d*(a+b*arctan(c*x))*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^2+1/2*b^2*d*polylog(3,1-2/(1-I*c*x))/e^2-1/2*b^2*d*polylog(3,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e^2,1],
[(a+b*arctan(c*x))^2/(e*x+d),x,1,-(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/e+(a+b*arctan(c*x))^2*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e+I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/e-I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e-1/2*b^2*polylog(3,1-2/(1-I*c*x))/e+1/2*b^2*polylog(3,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/e,1],
[(a+b*arctan(c*x))^2/x/(e*x+d),x,9,2*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))/d+(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/d-(a+b*arctan(c*x))^2*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d-I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/d-I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/d+I*b*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d+I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d+1/2*b^2*polylog(3,1-2/(1-I*c*x))/d-1/2*b^2*polylog(3,1-2/(1+I*c*x))/d+1/2*b^2*polylog(3,-1+2/(1+I*c*x))/d-1/2*b^2*polylog(3,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d,1],
[(a+b*arctan(c*x))^2/x^2/(e*x+d),x,13,-I*c*(a+b*arctan(c*x))^2/d-(a+b*arctan(c*x))^2/d/x-2*e*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))/d^2-e*(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/d^2+e*(a+b*arctan(c*x))^2*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d^2+2*b*c*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))/d+I*b*e*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/d^2-I*b^2*c*polylog(2,-1+2/(1-I*c*x))/d+I*b*e*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/d^2-I*b*e*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d^2-I*b*e*(a+b*arctan(c*x))*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d^2-1/2*b^2*e*polylog(3,1-2/(1-I*c*x))/d^2+1/2*b^2*e*polylog(3,1-2/(1+I*c*x))/d^2-1/2*b^2*e*polylog(3,-1+2/(1+I*c*x))/d^2+1/2*b^2*e*polylog(3,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d^2,1],
[(a+b*arctan(c*x))^2/x^3/(e*x+d),x,21,-b*c*(a+b*arctan(c*x))/d/x-1/2*c^2*(a+b*arctan(c*x))^2/d+I*b*e^2*(a+b*arctan(c*x))*polylog(2,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d^3-1/2*(a+b*arctan(c*x))^2/d/x^2+e*(a+b*arctan(c*x))^2/d^2/x+2*e^2*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))/d^3+b^2*c^2*ln(x)/d+e^2*(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/d^3-e^2*(a+b*arctan(c*x))^2*ln(2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d^3-1/2*b^2*c^2*ln(c^2*x^2+1)/d-2*b*c*e*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))/d^2+I*b^2*c*e*polylog(2,-1+2/(1-I*c*x))/d^2+I*b*e^2*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d^3-I*b*e^2*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/d^3-I*b*e^2*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/d^3+I*c*e*(a+b*arctan(c*x))^2/d^2+1/2*b^2*e^2*polylog(3,1-2/(1-I*c*x))/d^3-1/2*b^2*e^2*polylog(3,1-2/(1+I*c*x))/d^3+1/2*b^2*e^2*polylog(3,-1+2/(1+I*c*x))/d^3-1/2*b^2*e^2*polylog(3,1-2*c*(e*x+d)/(c*d+I*e)/(1-I*c*x))/d^3,1],
[1/(e*x+d)/(a+b*arctan(c*x)),x,0,Defer(Int)(1/(e*x+d)/(a+b*arctan(c*x)),x),0],
[x^3*(a^2*c*x^2+c)*arctan(a*x),x,9,1/12*c*x/a^3-1/36*c*x^3/a-1/30*a*c*x^5-1/12*c*arctan(a*x)/a^4+1/4*c*x^4*arctan(a*x)+1/6*a^2*c*x^6*arctan(a*x),1],
[x^2*(a^2*c*x^2+c)*arctan(a*x),x,9,-1/15*c*x^2/a-1/20*a*c*x^4+1/3*c*x^3*arctan(a*x)+1/5*a^2*c*x^5*arctan(a*x)+1/15*c*ln(a^2*x^2+1)/a^3,1],
[x*(a^2*c*x^2+c)*arctan(a*x),x,2,-1/4*c*x/a-1/12*a*c*x^3+1/4*c*(a^2*x^2+1)^2*arctan(a*x)/a^2,1],
[(a^2*c*x^2+c)*arctan(a*x),x,3,-1/6*a*c*x^2+c*x*arctan(a*x)+1/3*a^2*c*x^3*arctan(a*x)-1/3*c*ln(a^2*x^2+1)/a,1],
[(a^2*c*x^2+c)*arctan(a*x)/x,x,7,-1/2*a*c*x+1/2*c*arctan(a*x)+1/2*a^2*c*x^2*arctan(a*x)+1/2*I*c*polylog(2,-I*a*x)-1/2*I*c*polylog(2,I*a*x),1],
[(a^2*c*x^2+c)*arctan(a*x)/x^2,x,8,-c*arctan(a*x)/x+a^2*c*x*arctan(a*x)+a*c*ln(x)-a*c*ln(a^2*x^2+1),1],
[(a^2*c*x^2+c)*arctan(a*x)/x^3,x,7,-1/2*a*c/x-1/2*a^2*c*arctan(a*x)-1/2*c*arctan(a*x)/x^2+1/2*I*a^2*c*polylog(2,-I*a*x)-1/2*I*a^2*c*polylog(2,I*a*x),1],
[(a^2*c*x^2+c)*arctan(a*x)/x^4,x,10,-1/6*a*c/x^2-1/3*c*arctan(a*x)/x^3-a^2*c*arctan(a*x)/x+2/3*a^3*c*ln(x)-1/3*a^3*c*ln(a^2*x^2+1),1],
[x^3*(a^2*c*x^2+c)^2*arctan(a*x),x,14,1/24*c^2*x/a^3-1/72*c^2*x^3/a-1/24*a*c^2*x^5-1/56*a^3*c^2*x^7-1/24*c^2*arctan(a*x)/a^4+1/4*c^2*x^4*arctan(a*x)+1/3*a^2*c^2*x^6*arctan(a*x)+1/8*a^4*c^2*x^8*arctan(a*x),1],
[x^2*(a^2*c*x^2+c)^2*arctan(a*x),x,14,-4/105*c^2*x^2/a-9/140*a*c^2*x^4-1/42*a^3*c^2*x^6+1/3*c^2*x^3*arctan(a*x)+2/5*a^2*c^2*x^5*arctan(a*x)+1/7*a^4*c^2*x^7*arctan(a*x)+4/105*c^2*ln(a^2*x^2+1)/a^3,1],
[x*(a^2*c*x^2+c)^2*arctan(a*x),x,3,-1/6*c^2*x/a-1/9*a*c^2*x^3-1/30*a^3*c^2*x^5+1/6*c^2*(a^2*x^2+1)^3*arctan(a*x)/a^2,1],
[(a^2*c*x^2+c)^2*arctan(a*x),x,4,-2/15*c^2*(a^2*x^2+1)/a-1/20*c^2*(a^2*x^2+1)^2/a+8/15*c^2*x*arctan(a*x)+4/15*c^2*x*(a^2*x^2+1)*arctan(a*x)+1/5*c^2*x*(a^2*x^2+1)^2*arctan(a*x)-4/15*c^2*ln(a^2*x^2+1)/a,1],
[(a^2*c*x^2+c)^2*arctan(a*x)/x,x,12,-3/4*a*c^2*x-1/12*a^3*c^2*x^3+3/4*c^2*arctan(a*x)+a^2*c^2*x^2*arctan(a*x)+1/4*a^4*c^2*x^4*arctan(a*x)+1/2*I*c^2*polylog(2,-I*a*x)-1/2*I*c^2*polylog(2,I*a*x),1],
[(a^2*c*x^2+c)^2*arctan(a*x)/x^2,x,13,-1/6*a^3*c^2*x^2-c^2*arctan(a*x)/x+2*a^2*c^2*x*arctan(a*x)+1/3*a^4*c^2*x^3*arctan(a*x)+a*c^2*ln(x)-4/3*a*c^2*ln(a^2*x^2+1),1],
[(a^2*c*x^2+c)^2*arctan(a*x)/x^3,x,11,-1/2*a*c^2/x-1/2*a^3*c^2*x-1/2*c^2*arctan(a*x)/x^2+1/2*a^4*c^2*x^2*arctan(a*x)+I*a^2*c^2*polylog(2,-I*a*x)-I*a^2*c^2*polylog(2,I*a*x),1],
[(a^2*c*x^2+c)^2*arctan(a*x)/x^4,x,13,-1/6*a*c^2/x^2-1/3*c^2*arctan(a*x)/x^3-2*a^2*c^2*arctan(a*x)/x+a^4*c^2*x*arctan(a*x)+5/3*a^3*c^2*ln(x)-4/3*a^3*c^2*ln(a^2*x^2+1),1],
[x^3*(a^2*c*x^2+c)^3*arctan(a*x),x,18,1/40*c^3*x/a^3-1/120*c^3*x^3/a-9/200*a*c^3*x^5-11/280*a^3*c^3*x^7-1/90*a^5*c^3*x^9-1/40*c^3*arctan(a*x)/a^4+1/4*c^3*x^4*arctan(a*x)+1/2*a^2*c^3*x^6*arctan(a*x)+3/8*a^4*c^3*x^8*arctan(a*x)+1/10*a^6*c^3*x^10*arctan(a*x),1],
[x^2*(a^2*c*x^2+c)^3*arctan(a*x),x,18,-8/315*c^3*x^2/a-89/1260*a*c^3*x^4-10/189*a^3*c^3*x^6-1/72*a^5*c^3*x^8+1/3*c^3*x^3*arctan(a*x)+3/5*a^2*c^3*x^5*arctan(a*x)+3/7*a^4*c^3*x^7*arctan(a*x)+1/9*a^6*c^3*x^9*arctan(a*x)+8/315*c^3*ln(a^2*x^2+1)/a^3,1],
[x*(a^2*c*x^2+c)^3*arctan(a*x),x,3,-1/8*c^3*x/a-1/8*a*c^3*x^3-3/40*a^3*c^3*x^5-1/56*a^5*c^3*x^7+1/8*c^3*(a^2*x^2+1)^4*arctan(a*x)/a^2,1],
[(a^2*c*x^2+c)^3*arctan(a*x),x,5,-4/35*c^3*(a^2*x^2+1)/a-3/70*c^3*(a^2*x^2+1)^2/a-1/42*c^3*(a^2*x^2+1)^3/a+16/35*c^3*x*arctan(a*x)+8/35*c^3*x*(a^2*x^2+1)*arctan(a*x)+6/35*c^3*x*(a^2*x^2+1)^2*arctan(a*x)+1/7*c^3*x*(a^2*x^2+1)^3*arctan(a*x)-8/35*c^3*ln(a^2*x^2+1)/a,1],
[(a^2*c*x^2+c)^3*arctan(a*x)/x,x,16,-11/12*a*c^3*x-7/36*a^3*c^3*x^3-1/30*a^5*c^3*x^5+11/12*c^3*arctan(a*x)+3/2*a^2*c^3*x^2*arctan(a*x)+3/4*a^4*c^3*x^4*arctan(a*x)+1/6*a^6*c^3*x^6*arctan(a*x)+1/2*I*c^3*polylog(2,-I*a*x)-1/2*I*c^3*polylog(2,I*a*x),1],
[(a^2*c*x^2+c)^3*arctan(a*x)/x^2,x,17,-2/5*a^3*c^3*x^2-1/20*a^5*c^3*x^4-c^3*arctan(a*x)/x+3*a^2*c^3*x*arctan(a*x)+a^4*c^3*x^3*arctan(a*x)+1/5*a^6*c^3*x^5*arctan(a*x)+a*c^3*ln(x)-8/5*a*c^3*ln(a^2*x^2+1),1],
[(a^2*c*x^2+c)^3*arctan(a*x)/x^3,x,15,-1/2*a*c^3/x-5/4*a^3*c^3*x-1/12*a^5*c^3*x^3+3/4*a^2*c^3*arctan(a*x)-1/2*c^3*arctan(a*x)/x^2+3/2*a^4*c^3*x^2*arctan(a*x)+1/4*a^6*c^3*x^4*arctan(a*x)+3/2*I*a^2*c^3*polylog(2,-I*a*x)-3/2*I*a^2*c^3*polylog(2,I*a*x),1],
[(a^2*c*x^2+c)^3*arctan(a*x)/x^4,x,17,-1/6*a*c^3/x^2-1/6*a^5*c^3*x^2-1/3*c^3*arctan(a*x)/x^3-3*a^2*c^3*arctan(a*x)/x+3*a^4*c^3*x*arctan(a*x)+1/3*a^6*c^3*x^3*arctan(a*x)+8/3*a^3*c^3*ln(x)-8/3*a^3*c^3*ln(a^2*x^2+1),1],
[x^4*arctan(a*x)/(a^2*c*x^2+c),x,9,-1/6*x^2/a^3/c-x*arctan(a*x)/a^4/c+1/3*x^3*arctan(a*x)/a^2/c+1/2*arctan(a*x)^2/a^5/c+2/3*ln(a^2*x^2+1)/a^5/c,1],
[x^3*arctan(a*x)/(a^2*c*x^2+c),x,8,-1/2*x/a^3/c+1/2*arctan(a*x)/a^4/c+1/2*x^2*arctan(a*x)/a^2/c+1/2*I*arctan(a*x)^2/a^4/c+arctan(a*x)*ln(2/(1+I*a*x))/a^4/c+1/2*I*polylog(2,1-2/(1+I*a*x))/a^4/c,1],
[x^2*arctan(a*x)/(a^2*c*x^2+c),x,4,x*arctan(a*x)/a^2/c-1/2*arctan(a*x)^2/a^3/c-1/2*ln(a^2*x^2+1)/a^3/c,1],
[x*arctan(a*x)/(a^2*c*x^2+c),x,4,-1/2*I*arctan(a*x)^2/a^2/c-arctan(a*x)*ln(2/(1+I*a*x))/a^2/c-1/2*I*polylog(2,1-2/(1+I*a*x))/a^2/c,1],
[arctan(a*x)/(a^2*c*x^2+c),x,1,1/2*arctan(a*x)^2/a/c,1],
[arctan(a*x)/x/(a^2*c*x^2+c),x,3,-1/2*I*arctan(a*x)^2/c+arctan(a*x)*ln(2-2/(1-I*a*x))/c-1/2*I*polylog(2,-1+2/(1-I*a*x))/c,1],
[arctan(a*x)/x^2/(a^2*c*x^2+c),x,7,-arctan(a*x)/c/x-1/2*a*arctan(a*x)^2/c+a*ln(x)/c-1/2*a*ln(a^2*x^2+1)/c,1],
[arctan(a*x)/x^3/(a^2*c*x^2+c),x,7,-1/2*a/c/x-1/2*a^2*arctan(a*x)/c-1/2*arctan(a*x)/c/x^2+1/2*I*a^2*arctan(a*x)^2/c-a^2*arctan(a*x)*ln(2-2/(1-I*a*x))/c+1/2*I*a^2*polylog(2,-1+2/(1-I*a*x))/c,1],
[arctan(a*x)/x^4/(a^2*c*x^2+c),x,12,-1/6*a/c/x^2-1/3*arctan(a*x)/c/x^3+a^2*arctan(a*x)/c/x+1/2*a^3*arctan(a*x)^2/c-4/3*a^3*ln(x)/c+2/3*a^3*ln(a^2*x^2+1)/c,1],
[x^5*arctan(a*x)/(a^2*c*x^2+c)^2,x,17,-1/2*x/a^5/c^2+1/4*x/a^5/c^2/(a^2*x^2+1)+3/4*arctan(a*x)/a^6/c^2+1/2*x^2*arctan(a*x)/a^4/c^2-1/2*arctan(a*x)/a^6/c^2/(a^2*x^2+1)+I*arctan(a*x)^2/a^6/c^2+2*arctan(a*x)*ln(2/(1+I*a*x))/a^6/c^2+I*polylog(2,1-2/(1+I*a*x))/a^6/c^2,1],
[x^4*arctan(a*x)/(a^2*c*x^2+c)^2,x,7,1/4/a^5/c^2/(a^2*x^2+1)+x*arctan(a*x)/a^4/c^2+1/2*x*arctan(a*x)/a^4/c^2/(a^2*x^2+1)-3/4*arctan(a*x)^2/a^5/c^2-1/2*ln(a^2*x^2+1)/a^5/c^2,1],
[x^3*arctan(a*x)/(a^2*c*x^2+c)^2,x,8,-1/4*x/a^3/c^2/(a^2*x^2+1)-1/4*arctan(a*x)/a^4/c^2+1/2*arctan(a*x)/a^4/c^2/(a^2*x^2+1)-1/2*I*arctan(a*x)^2/a^4/c^2-arctan(a*x)*ln(2/(1+I*a*x))/a^4/c^2-1/2*I*polylog(2,1-2/(1+I*a*x))/a^4/c^2,1],
[x^2*arctan(a*x)/(a^2*c*x^2+c)^2,x,2,-1/4/a^3/c^2/(a^2*x^2+1)-1/2*x*arctan(a*x)/a^2/c^2/(a^2*x^2+1)+1/4*arctan(a*x)^2/a^3/c^2,1],
[x*arctan(a*x)/(a^2*c*x^2+c)^2,x,3,1/4*x/a/c^2/(a^2*x^2+1)+1/4*arctan(a*x)/a^2/c^2-1/2*arctan(a*x)/a^2/c^2/(a^2*x^2+1),1],
[arctan(a*x)/(a^2*c*x^2+c)^2,x,2,1/4/a/c^2/(a^2*x^2+1)+1/2*x*arctan(a*x)/c^2/(a^2*x^2+1)+1/4*arctan(a*x)^2/a/c^2,1],
[arctan(a*x)/x/(a^2*c*x^2+c)^2,x,7,-1/4*a*x/c^2/(a^2*x^2+1)-1/4*arctan(a*x)/c^2+1/2*arctan(a*x)/c^2/(a^2*x^2+1)-1/2*I*arctan(a*x)^2/c^2+arctan(a*x)*ln(2-2/(1-I*a*x))/c^2-1/2*I*polylog(2,-1+2/(1-I*a*x))/c^2,1],
[arctan(a*x)/x^2/(a^2*c*x^2+c)^2,x,10,-1/4*a/c^2/(a^2*x^2+1)-arctan(a*x)/c^2/x-1/2*a^2*x*arctan(a*x)/c^2/(a^2*x^2+1)-3/4*a*arctan(a*x)^2/c^2+a*ln(x)/c^2-1/2*a*ln(a^2*x^2+1)/c^2,1],
[arctan(a*x)/x^3/(a^2*c*x^2+c)^2,x,15,-1/2*a/c^2/x+1/4*a^3*x/c^2/(a^2*x^2+1)-1/4*a^2*arctan(a*x)/c^2-1/2*arctan(a*x)/c^2/x^2-1/2*a^2*arctan(a*x)/c^2/(a^2*x^2+1)+I*a^2*arctan(a*x)^2/c^2-2*a^2*arctan(a*x)*ln(2-2/(1-I*a*x))/c^2+I*a^2*polylog(2,-1+2/(1-I*a*x))/c^2,1],
[arctan(a*x)/x^4/(a^2*c*x^2+c)^2,x,23,-1/6*a/c^2/x^2+1/4*a^3/c^2/(a^2*x^2+1)-1/3*arctan(a*x)/c^2/x^3+2*a^2*arctan(a*x)/c^2/x+1/2*a^4*x*arctan(a*x)/c^2/(a^2*x^2+1)+5/4*a^3*arctan(a*x)^2/c^2-7/3*a^3*ln(x)/c^2+7/6*a^3*ln(a^2*x^2+1)/c^2,1],
[x^3*arctan(a*x)/(a^2*c*x^2+c)^3,x,4,1/16*x^3/a/c^3/(a^2*x^2+1)^2+3/32*x/a^3/c^3/(a^2*x^2+1)-3/32*arctan(a*x)/a^4/c^3+1/4*x^4*arctan(a*x)/c^3/(a^2*x^2+1)^2,1],
[x^2*arctan(a*x)/(a^2*c*x^2+c)^3,x,3,-1/16/a^3/c^3/(a^2*x^2+1)^2+1/16/a^3/c^3/(a^2*x^2+1)-1/4*x*arctan(a*x)/a^2/c^3/(a^2*x^2+1)^2+1/8*x*arctan(a*x)/a^2/c^3/(a^2*x^2+1)+1/16*arctan(a*x)^2/a^3/c^3,1],
[x*arctan(a*x)/(a^2*c*x^2+c)^3,x,4,1/16*x/a/c^3/(a^2*x^2+1)^2+3/32*x/a/c^3/(a^2*x^2+1)+3/32*arctan(a*x)/a^2/c^3-1/4*arctan(a*x)/a^2/c^3/(a^2*x^2+1)^2,1],
[arctan(a*x)/(a^2*c*x^2+c)^3,x,3,1/16/a/c^3/(a^2*x^2+1)^2+3/16/a/c^3/(a^2*x^2+1)+1/4*x*arctan(a*x)/c^3/(a^2*x^2+1)^2+3/8*x*arctan(a*x)/c^3/(a^2*x^2+1)+3/16*arctan(a*x)^2/a/c^3,1],
[arctan(a*x)/x/(a^2*c*x^2+c)^3,x,12,-1/16*a*x/c^3/(a^2*x^2+1)^2-11/32*a*x/c^3/(a^2*x^2+1)-11/32*arctan(a*x)/c^3+1/4*arctan(a*x)/c^3/(a^2*x^2+1)^2+1/2*arctan(a*x)/c^3/(a^2*x^2+1)-1/2*I*arctan(a*x)^2/c^3+arctan(a*x)*ln(2-2/(1-I*a*x))/c^3-1/2*I*polylog(2,-1+2/(1-I*a*x))/c^3,1],
[arctan(a*x)/x^2/(a^2*c*x^2+c)^3,x,14,-1/16*a/c^3/(a^2*x^2+1)^2-7/16*a/c^3/(a^2*x^2+1)-arctan(a*x)/c^3/x-1/4*a^2*x*arctan(a*x)/c^3/(a^2*x^2+1)^2-7/8*a^2*x*arctan(a*x)/c^3/(a^2*x^2+1)-15/16*a*arctan(a*x)^2/c^3+a*ln(x)/c^3-1/2*a*ln(a^2*x^2+1)/c^3,1],
[arctan(a*x)/x^3/(a^2*c*x^2+c)^3,x,28,-1/2*a/c^3/x+1/16*a^3*x/c^3/(a^2*x^2+1)^2+19/32*a^3*x/c^3/(a^2*x^2+1)+3/32*a^2*arctan(a*x)/c^3-1/2*arctan(a*x)/c^3/x^2-1/4*a^2*arctan(a*x)/c^3/(a^2*x^2+1)^2-a^2*arctan(a*x)/c^3/(a^2*x^2+1)+3/2*I*a^2*arctan(a*x)^2/c^3-3*a^2*arctan(a*x)*ln(2-2/(1-I*a*x))/c^3+3/2*I*a^2*polylog(2,-1+2/(1-I*a*x))/c^3,1],
[arctan(a*x)/x^4/(a^2*c*x^2+c)^3,x,38,-1/6*a/c^3/x^2+1/16*a^3/c^3/(a^2*x^2+1)^2+11/16*a^3/c^3/(a^2*x^2+1)-1/3*arctan(a*x)/c^3/x^3+3*a^2*arctan(a*x)/c^3/x+1/4*a^4*x*arctan(a*x)/c^3/(a^2*x^2+1)^2+11/8*a^4*x*arctan(a*x)/c^3/(a^2*x^2+1)+35/16*a^3*arctan(a*x)^2/c^3-10/3*a^3*ln(x)/c^3+5/3*a^3*ln(a^2*x^2+1)/c^3,1],
[x^3*sqrt(a^2*c*x^2+c)*arctan(a*x),x,12,1/24*x*sqrt(a^2*c*x^2+c)/a^3-1/20*x^3*sqrt(a^2*c*x^2+c)/a-2/15*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^4+1/15*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2+1/5*x^4*sqrt(a^2*c*x^2+c)*arctan(a*x)+11/120*sqrt(c)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^4,1],
[x^2*sqrt(a^2*c*x^2+c)*arctan(a*x),x,8,1/8*sqrt(a^2*c*x^2+c)/a^3-1/12*(a^2*c*x^2+c)^(3/2)/a^3/c+1/8*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2+1/4*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/4*I*c*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)-1/8*I*c*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)+1/8*I*c*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c),1],
[x*sqrt(a^2*c*x^2+c)*arctan(a*x),x,4,-1/6*x*sqrt(a^2*c*x^2+c)/a+1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)/a^2/c-1/6*sqrt(c)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^2,1],
[sqrt(a^2*c*x^2+c)*arctan(a*x),x,3,-1/2*sqrt(a^2*c*x^2+c)/a+1/2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)-I*c*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)+1/2*I*c*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)-1/2*I*c*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)/x,x,5,sqrt(a^2*c*x^2+c)*arctan(a*x)-2*c*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-sqrt(c)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))+I*c*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-I*c*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)/x^2,x,7,-sqrt(a^2*c*x^2+c)*arctan(a*x)/x-2*I*a*c*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-a*sqrt(c)*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))+I*a*c*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-I*a*c*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)/x^3,x,6,-1/2*a*sqrt(a^2*c*x^2+c)/x-1/2*sqrt(a^2*c*x^2+c)*arctan(a*x)/x^2-a^2*c*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+1/2*I*a^2*c*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-1/2*I*a^2*c*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)/x^4,x,5,-1/6*a*sqrt(a^2*c*x^2+c)/x^2-1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)/c/x^3-1/6*a^3*sqrt(c)*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c)),1],
[x^3*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x,31,3/112*c*x*sqrt(a^2*c*x^2+c)/a^3-23/840*c*x^3*sqrt(a^2*c*x^2+c)/a-1/42*a*c*x^5*sqrt(a^2*c*x^2+c)-2/35*c*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^4+1/35*c*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2+8/35*c*x^4*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/7*a^2*c*x^6*sqrt(a^2*c*x^2+c)*arctan(a*x)+17/560*c^(3/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^4,1],
[x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x,21,1/16*c*sqrt(a^2*c*x^2+c)/a^3+1/72*(a^2*c*x^2+c)^(3/2)/a^3-1/30*(a^2*c*x^2+c)^(5/2)/a^3/c+1/16*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2+7/24*c*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/6*a^2*c*x^5*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/8*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)-1/16*I*c^2*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)+1/16*I*c^2*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c),1],
[x*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x,5,-3/40*c*x*sqrt(a^2*c*x^2+c)/a-1/20*x*(a^2*c*x^2+c)^(3/2)/a+1/5*(a^2*c*x^2+c)^(5/2)*arctan(a*x)/a^2/c-3/40*c^(3/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^2,1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x),x,4,-3/8*c*sqrt(a^2*c*x^2+c)/a-1/12*(a^2*c*x^2+c)^(3/2)/a+3/8*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/4*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)-3/4*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)+3/8*I*c^2*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)-3/8*I*c^2*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)/x,x,10,-1/6*a*c*x*sqrt(a^2*c*x^2+c)+c*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)-2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-7/6*c^(3/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))+I*c^2*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-I*c^2*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^2,x,11,-1/2*a*c*sqrt(a^2*c*x^2+c)-c*sqrt(a^2*c*x^2+c)*arctan(a*x)/x+1/2*a^2*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)-3*I*a*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-a*c^(3/2)*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))+3/2*I*a*c^2*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-3/2*I*a*c^2*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^3,x,12,-1/2*a*c*sqrt(a^2*c*x^2+c)/x+a^2*c*sqrt(a^2*c*x^2+c)*arctan(a*x)-1/2*c*sqrt(a^2*c*x^2+c)*arctan(a*x)/x^2-3*a^2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-a^2*c^(3/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))+3/2*I*a^2*c^2*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-3/2*I*a^2*c^2*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^4,x,13,-1/6*a*c*sqrt(a^2*c*x^2+c)/x^2-a^2*c*sqrt(a^2*c*x^2+c)*arctan(a*x)/x-1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^3-2*I*a^3*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-7/6*a^3*c^(3/2)*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))+I*a^3*c^2*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-I*a^3*c^2*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[x^3*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x,76,47/2688*c^2*x*sqrt(a^2*c*x^2+c)/a^3-205/12096*c^2*x^3*sqrt(a^2*c*x^2+c)/a-103/3024*a*c^2*x^5*sqrt(a^2*c*x^2+c)-1/72*a^3*c^2*x^7*sqrt(a^2*c*x^2+c)-2/63*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^4+1/63*c^2*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2+5/21*c^2*x^4*sqrt(a^2*c*x^2+c)*arctan(a*x)+19/63*a^2*c^2*x^6*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/9*a^4*c^2*x^8*sqrt(a^2*c*x^2+c)*arctan(a*x)+115/8064*c^(5/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^4,1],
[x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x,51,5/128*c^2*sqrt(a^2*c*x^2+c)/a^3+5/576*c*(a^2*c*x^2+c)^(3/2)/a^3+1/240*(a^2*c*x^2+c)^(5/2)/a^3-1/56*(a^2*c*x^2+c)^(7/2)/a^3/c+5/128*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2+59/192*c^2*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)+17/48*a^2*c^2*x^5*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/8*a^4*c^2*x^7*sqrt(a^2*c*x^2+c)*arctan(a*x)+5/64*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)-5/128*I*c^3*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)+5/128*I*c^3*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c),1],
[x*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x,6,-5/112*c^2*x*sqrt(a^2*c*x^2+c)/a-5/168*c*x*(a^2*c*x^2+c)^(3/2)/a-1/42*x*(a^2*c*x^2+c)^(5/2)/a+1/7*(a^2*c*x^2+c)^(7/2)*arctan(a*x)/a^2/c-5/112*c^(5/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^2,1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x),x,5,-5/16*c^2*sqrt(a^2*c*x^2+c)/a-5/72*c*(a^2*c*x^2+c)^(3/2)/a-1/30*(a^2*c*x^2+c)^(5/2)/a+5/16*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)+5/24*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)+1/6*x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)-5/8*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)+5/16*I*c^3*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)-5/16*I*c^3*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)/x,x,16,-29/120*a*c^2*x*sqrt(a^2*c*x^2+c)-1/20*a*c*x*(a^2*c*x^2+c)^(3/2)+c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/3*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)+1/5*(a^2*c*x^2+c)^(5/2)*arctan(a*x)-2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-149/120*c^(5/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))+I*c^3*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-I*c^3*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)/x^2,x,16,-7/8*a*c^2*sqrt(a^2*c*x^2+c)-1/12*a*c*(a^2*c*x^2+c)^(3/2)-c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/x+7/8*a^2*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/4*a^2*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)-15/4*I*a*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-a*c^(5/2)*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))+15/8*I*a*c^3*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-15/8*I*a*c^3*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)/x^3,x,23,-1/2*a*c^2*sqrt(a^2*c*x^2+c)/x-1/6*a^3*c^2*x*sqrt(a^2*c*x^2+c)+2*a^2*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)-1/2*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/x^2+1/3*a^2*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)-5*a^2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-13/6*a^2*c^(5/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))+5/2*I*a^2*c^3*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-5/2*I*a^2*c^3*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)/x^4,x,25,-1/2*a^3*c^2*sqrt(a^2*c*x^2+c)-1/6*a*c^2*sqrt(a^2*c*x^2+c)/x^2-2*a^2*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/x+1/2*a^4*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)-1/3*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^3-5*I*a^3*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-13/6*a^3*c^(5/2)*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))+5/2*I*a^3*c^3*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-5/2*I*a^3*c^3*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[x^3*arctan(a*x)/sqrt(a^2*c*x^2+c),x,7,-1/6*x*sqrt(a^2*c*x^2+c)/a^3/c-2/3*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^4/c+1/3*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2/c+5/6*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^4/sqrt(c),1],
[x^2*arctan(a*x)/sqrt(a^2*c*x^2+c),x,4,-1/2*sqrt(a^2*c*x^2+c)/a^3/c+1/2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2/c+I*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)-1/2*I*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)+1/2*I*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c),1],
[x*arctan(a*x)/sqrt(a^2*c*x^2+c),x,3,sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2/c-arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^2/sqrt(c),1],
[arctan(a*x)/sqrt(a^2*c*x^2+c),x,2,-2*I*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)+I*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)-I*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)/x/sqrt(a^2*c*x^2+c),x,2,-2*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+I*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-I*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)/x^2/sqrt(a^2*c*x^2+c),x,4,-sqrt(a^2*c*x^2+c)*arctan(a*x)/c/x-a*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))/sqrt(c),1],
[arctan(a*x)/x^3/sqrt(a^2*c*x^2+c),x,4,-1/2*a*sqrt(a^2*c*x^2+c)/c/x-1/2*sqrt(a^2*c*x^2+c)*arctan(a*x)/c/x^2+a^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-1/2*I*a^2*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+1/2*I*a^2*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)/x^4/sqrt(a^2*c*x^2+c),x,9,-1/6*a*sqrt(a^2*c*x^2+c)/c/x^2-1/3*sqrt(a^2*c*x^2+c)*arctan(a*x)/c/x^3+2/3*a^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/c/x+5/6*a^3*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))/sqrt(c),1],
[x^3*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x,6,-x/a^3/c/sqrt(a^2*c*x^2+c)+arctan(a*x)/a^4/c/sqrt(a^2*c*x^2+c)+sqrt(a^2*c*x^2+c)*arctan(a*x)/a^4/c^2-arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^4/c^(3/2),1],
[x^2*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x,3,-1/a^3/c/sqrt(a^2*c*x^2+c)-x*arctan(a*x)/a^2/c/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/c/sqrt(a^2*c*x^2+c)+I*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/c/sqrt(a^2*c*x^2+c)-I*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/c/sqrt(a^2*c*x^2+c),1],
[x*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x,2,x/a/c/sqrt(a^2*c*x^2+c)-arctan(a*x)/a^2/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)/(a^2*c*x^2+c)^(3/2),x,1,1/a/c/sqrt(a^2*c*x^2+c)+x*arctan(a*x)/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)/x/(a^2*c*x^2+c)^(3/2),x,5,-a*x/c/sqrt(a^2*c*x^2+c)+arctan(a*x)/c/sqrt(a^2*c*x^2+c)-2*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/c/sqrt(a^2*c*x^2+c)+I*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/c/sqrt(a^2*c*x^2+c)-I*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)/x^2/(a^2*c*x^2+c)^(3/2),x,6,-a/c/sqrt(a^2*c*x^2+c)-a^2*x*arctan(a*x)/c/sqrt(a^2*c*x^2+c)-sqrt(a^2*c*x^2+c)*arctan(a*x)/c^2/x-a*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))/c^(3/2),1],
[arctan(a*x)/x^3/(a^2*c*x^2+c)^(3/2),x,10,a^3*x/c/sqrt(a^2*c*x^2+c)-1/2*a*sqrt(a^2*c*x^2+c)/c^2/x-a^2*arctan(a*x)/c/sqrt(a^2*c*x^2+c)-1/2*sqrt(a^2*c*x^2+c)*arctan(a*x)/c^2/x^2+3*a^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/c/sqrt(a^2*c*x^2+c)-3/2*I*a^2*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/c/sqrt(a^2*c*x^2+c)+3/2*I*a^2*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)/x^4/(a^2*c*x^2+c)^(3/2),x,16,a^3/c/sqrt(a^2*c*x^2+c)-1/6*a*sqrt(a^2*c*x^2+c)/c^2/x^2+a^4*x*arctan(a*x)/c/sqrt(a^2*c*x^2+c)-1/3*sqrt(a^2*c*x^2+c)*arctan(a*x)/c^2/x^3+5/3*a^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/c^2/x+11/6*a^3*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))/c^(3/2),1],
[x^5*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x,10,-1/9*x^3/a^3/c/(a^2*c*x^2+c)^(3/2)-5/3*x/a^5/c^2/sqrt(a^2*c*x^2+c)+1/3*x^2*arctan(a*x)/a^4/c/(a^2*c*x^2+c)^(3/2)+5/3*arctan(a*x)/a^6/c^2/sqrt(a^2*c*x^2+c)+sqrt(a^2*c*x^2+c)*arctan(a*x)/a^6/c^3-arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^6/c^(5/2),1],
[x^4*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x,8,1/9/a^5/c/(a^2*c*x^2+c)^(3/2)-4/3/a^5/c^2/sqrt(a^2*c*x^2+c)-1/3*x^3*arctan(a*x)/a^2/c/(a^2*c*x^2+c)^(3/2)-x*arctan(a*x)/a^4/c^2/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^5/c^2/sqrt(a^2*c*x^2+c)+I*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^5/c^2/sqrt(a^2*c*x^2+c)-I*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^5/c^2/sqrt(a^2*c*x^2+c),1],
[x^3*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x,3,1/9*x^3/a/c/(a^2*c*x^2+c)^(3/2)+2/3*x/a^3/c^2/sqrt(a^2*c*x^2+c)-1/3*x^2*arctan(a*x)/a^2/c/(a^2*c*x^2+c)^(3/2)-2/3*arctan(a*x)/a^4/c^2/sqrt(a^2*c*x^2+c),1],
[x^2*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x,4,-1/9/a^3/c/(a^2*c*x^2+c)^(3/2)+1/3/a^3/c^2/sqrt(a^2*c*x^2+c)+1/3*x^3*arctan(a*x)/c/(a^2*c*x^2+c)^(3/2),1],
[x*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x,3,1/9*x/a/c/(a^2*c*x^2+c)^(3/2)+2/9*x/a/c^2/sqrt(a^2*c*x^2+c)-1/3*arctan(a*x)/a^2/c/(a^2*c*x^2+c)^(3/2),1],
[arctan(a*x)/(a^2*c*x^2+c)^(5/2),x,2,1/9/a/c/(a^2*c*x^2+c)^(3/2)+2/3/a/c^2/sqrt(a^2*c*x^2+c)+1/3*x*arctan(a*x)/c/(a^2*c*x^2+c)^(3/2)+2/3*x*arctan(a*x)/c^2/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)/x/(a^2*c*x^2+c)^(5/2),x,9,-1/9*a*x/c/(a^2*c*x^2+c)^(3/2)-11/9*a*x/c^2/sqrt(a^2*c*x^2+c)+1/3*arctan(a*x)/c/(a^2*c*x^2+c)^(3/2)+arctan(a*x)/c^2/sqrt(a^2*c*x^2+c)-2*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/c^2/sqrt(a^2*c*x^2+c)+I*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/c^2/sqrt(a^2*c*x^2+c)-I*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/c^2/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)/x^2/(a^2*c*x^2+c)^(5/2),x,9,-1/9*a/c/(a^2*c*x^2+c)^(3/2)-5/3*a/c^2/sqrt(a^2*c*x^2+c)-1/3*a^2*x*arctan(a*x)/c/(a^2*c*x^2+c)^(3/2)-5/3*a^2*x*arctan(a*x)/c^2/sqrt(a^2*c*x^2+c)-sqrt(a^2*c*x^2+c)*arctan(a*x)/c^3/x-a*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))/c^(5/2),1],
[x^m*(a^2*c*x^2+c)^3*arctan(a*x),x,10,c^3*x^(1+m)*arctan(a*x)/(1+m)+3*a^2*c^3*x^(3+m)*arctan(a*x)/(3+m)+3*a^4*c^3*x^(5+m)*arctan(a*x)/(5+m)+a^6*c^3*x^(7+m)*arctan(a*x)/(7+m)-a*c^3*x^(2+m)*hypergeom([1, 1+1/2*m],[2+1/2*m],-a^2*x^2)/(m^2+3*m+2)-3*a^3*c^3*x^(4+m)*hypergeom([1, 2+1/2*m],[3+1/2*m],-a^2*x^2)/(m^2+7*m+12)-3*a^5*c^3*x^(6+m)*hypergeom([1, 3+1/2*m],[4+1/2*m],-a^2*x^2)/(5+m)/(6+m)-a^7*c^3*x^(8+m)*hypergeom([1, 4+1/2*m],[5+1/2*m],-a^2*x^2)/(7+m)/(8+m),1],
[x^m*(a^2*c*x^2+c)^2*arctan(a*x),x,8,c^2*x^(1+m)*arctan(a*x)/(1+m)+2*a^2*c^2*x^(3+m)*arctan(a*x)/(3+m)+a^4*c^2*x^(5+m)*arctan(a*x)/(5+m)-a*c^2*x^(2+m)*hypergeom([1, 1+1/2*m],[2+1/2*m],-a^2*x^2)/(m^2+3*m+2)-2*a^3*c^2*x^(4+m)*hypergeom([1, 2+1/2*m],[3+1/2*m],-a^2*x^2)/(m^2+7*m+12)-a^5*c^2*x^(6+m)*hypergeom([1, 3+1/2*m],[4+1/2*m],-a^2*x^2)/(5+m)/(6+m),1],
[x^m*(a^2*c*x^2+c)*arctan(a*x),x,5,c*x^(1+m)*arctan(a*x)/(1+m)+a^2*c*x^(3+m)*arctan(a*x)/(3+m)-a*c*x^(2+m)*hypergeom([1, 1+1/2*m],[2+1/2*m],-a^2*x^2)/(m^2+3*m+2)-a^3*c*x^(4+m)*hypergeom([1, 2+1/2*m],[3+1/2*m],-a^2*x^2)/(m^2+7*m+12),1],
[x^m*arctan(a*x)/(a^2*c*x^2+c),x,0,Defer(Int)(x^m*arctan(a*x)/(a^2*c*x^2+c),x),0],
[x^m*arctan(a*x)/(a^2*c*x^2+c)^2,x,0,Defer(Int)(x^m*arctan(a*x)/(a^2*c*x^2+c)^2,x),0],
[x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x),0],
[x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x),0],
[x^m*sqrt(a^2*c*x^2+c)*arctan(a*x),x,3,x^(1+m)*sqrt(a^2*c*x^2+c)*arctan(a*x)/(2+m)-a*x^(2+m)*sqrt(a^2*c*x^2+c)*hypergeom([1, 3/2+1/2*m],[2+1/2*m],-a^2*x^2)/(2+m)^2+c*Defer(Int)(x^m*arctan(a*x)/sqrt(a^2*c*x^2+c),x)/(2+m),0],
[x^m*arctan(a*x)/sqrt(a^2*c*x^2+c),x,0,Defer(Int)(x^m*arctan(a*x)/sqrt(a^2*c*x^2+c),x),0],
[x^m*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(x^m*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x),0],
[x^3*(a^2*c*x^2+c)*arctan(a*x)^2,x,26,-1/180*c*x^2/a^2+1/60*c*x^4+1/6*c*x*arctan(a*x)/a^3-1/18*c*x^3*arctan(a*x)/a-1/15*a*c*x^5*arctan(a*x)-1/12*c*arctan(a*x)^2/a^4+1/4*c*x^4*arctan(a*x)^2+1/6*a^2*c*x^6*arctan(a*x)^2-7/90*c*ln(a^2*x^2+1)/a^4,1],
[x^2*(a^2*c*x^2+c)*arctan(a*x)^2,x,24,1/30*c*x/a^2+1/30*c*x^3-1/30*c*arctan(a*x)/a^3-2/15*c*x^2*arctan(a*x)/a-1/10*a*c*x^4*arctan(a*x)-2/15*I*c*arctan(a*x)^2/a^3+1/3*c*x^3*arctan(a*x)^2+1/5*a^2*c*x^5*arctan(a*x)^2-4/15*c*arctan(a*x)*ln(2/(1+I*a*x))/a^3-2/15*I*c*polylog(2,1-2/(1+I*a*x))/a^3,1],
[x*(a^2*c*x^2+c)*arctan(a*x)^2,x,4,1/12*c*(a^2*x^2+1)/a^2-1/3*c*x*arctan(a*x)/a-1/6*c*x*(a^2*x^2+1)*arctan(a*x)/a+1/4*c*(a^2*x^2+1)^2*arctan(a*x)^2/a^2+1/6*c*ln(a^2*x^2+1)/a^2,1],
[(a^2*c*x^2+c)*arctan(a*x)^2,x,7,1/3*c*x-1/3*c*(a^2*x^2+1)*arctan(a*x)/a+2/3*I*c*arctan(a*x)^2/a+2/3*c*x*arctan(a*x)^2+1/3*c*x*(a^2*x^2+1)*arctan(a*x)^2+4/3*c*arctan(a*x)*ln(2/(1+I*a*x))/a+2/3*I*c*polylog(2,1-2/(1+I*a*x))/a,1],
[(a^2*c*x^2+c)*arctan(a*x)^2/x,x,12,-a*c*x*arctan(a*x)+1/2*c*arctan(a*x)^2+1/2*a^2*c*x^2*arctan(a*x)^2+2*c*arctan(a*x)^2*arctanh(1-2/(1+I*a*x))+1/2*c*ln(a^2*x^2+1)-I*c*arctan(a*x)*polylog(2,1-2/(1+I*a*x))+I*c*arctan(a*x)*polylog(2,-1+2/(1+I*a*x))-1/2*c*polylog(3,1-2/(1+I*a*x))+1/2*c*polylog(3,-1+2/(1+I*a*x)),1],
[(a^2*c*x^2+c)*arctan(a*x)^2/x^2,x,10,-c*arctan(a*x)^2/x+a^2*c*x*arctan(a*x)^2+2*a*c*arctan(a*x)*ln(2/(1+I*a*x))+2*a*c*arctan(a*x)*ln(2-2/(1-I*a*x))-I*a*c*polylog(2,-1+2/(1-I*a*x))+I*a*c*polylog(2,1-2/(1+I*a*x)),1],
[(a^2*c*x^2+c)*arctan(a*x)^2/x^3,x,15,-a*c*arctan(a*x)/x-1/2*a^2*c*arctan(a*x)^2-1/2*c*arctan(a*x)^2/x^2+2*a^2*c*arctan(a*x)^2*arctanh(1-2/(1+I*a*x))+a^2*c*ln(x)-1/2*a^2*c*ln(a^2*x^2+1)-I*a^2*c*arctan(a*x)*polylog(2,1-2/(1+I*a*x))+I*a^2*c*arctan(a*x)*polylog(2,-1+2/(1+I*a*x))-1/2*a^2*c*polylog(3,1-2/(1+I*a*x))+1/2*a^2*c*polylog(3,-1+2/(1+I*a*x)),1],
[(a^2*c*x^2+c)*arctan(a*x)^2/x^4,x,13,-1/3*a^2*c/x-1/3*a^3*c*arctan(a*x)-1/3*a*c*arctan(a*x)/x^2-2/3*I*a^3*c*arctan(a*x)^2-1/3*c*arctan(a*x)^2/x^3-a^2*c*arctan(a*x)^2/x+4/3*a^3*c*arctan(a*x)*ln(2-2/(1-I*a*x))-2/3*I*a^3*c*polylog(2,-1+2/(1-I*a*x)),1],
[x^3*(a^2*c*x^2+c)^2*arctan(a*x)^2,x,47,-5/504*c^2*x^2/a^2+1/84*c^2*x^4+1/168*a^2*c^2*x^6+1/12*c^2*x*arctan(a*x)/a^3-1/36*c^2*x^3*arctan(a*x)/a-1/12*a*c^2*x^5*arctan(a*x)-1/28*a^3*c^2*x^7*arctan(a*x)-1/24*c^2*arctan(a*x)^2/a^4+1/4*c^2*x^4*arctan(a*x)^2+1/3*a^2*c^2*x^6*arctan(a*x)^2+1/8*a^4*c^2*x^8*arctan(a*x)^2-2/63*c^2*ln(a^2*x^2+1)/a^4,1],
[x^2*(a^2*c*x^2+c)^2*arctan(a*x)^2,x,44,-1/210*c^2*x/a^2+17/630*c^2*x^3+1/105*a^2*c^2*x^5+1/210*c^2*arctan(a*x)/a^3-8/105*c^2*x^2*arctan(a*x)/a-9/70*a*c^2*x^4*arctan(a*x)-1/21*a^3*c^2*x^6*arctan(a*x)-8/105*I*c^2*arctan(a*x)^2/a^3+1/3*c^2*x^3*arctan(a*x)^2+2/5*a^2*c^2*x^5*arctan(a*x)^2+1/7*a^4*c^2*x^7*arctan(a*x)^2-16/105*c^2*arctan(a*x)*ln(2/(1+I*a*x))/a^3-8/105*I*c^2*polylog(2,1-2/(1+I*a*x))/a^3,1],
[x*(a^2*c*x^2+c)^2*arctan(a*x)^2,x,5,2/45*c^2*(a^2*x^2+1)/a^2+1/60*c^2*(a^2*x^2+1)^2/a^2-8/45*c^2*x*arctan(a*x)/a-4/45*c^2*x*(a^2*x^2+1)*arctan(a*x)/a-1/15*c^2*x*(a^2*x^2+1)^2*arctan(a*x)/a+1/6*c^2*(a^2*x^2+1)^3*arctan(a*x)^2/a^2+4/45*c^2*ln(a^2*x^2+1)/a^2,1],
[(a^2*c*x^2+c)^2*arctan(a*x)^2,x,9,11/30*c^2*x+1/30*a^2*c^2*x^3-4/15*c^2*(a^2*x^2+1)*arctan(a*x)/a-1/10*c^2*(a^2*x^2+1)^2*arctan(a*x)/a+8/15*I*c^2*arctan(a*x)^2/a+8/15*c^2*x*arctan(a*x)^2+4/15*c^2*x*(a^2*x^2+1)*arctan(a*x)^2+1/5*c^2*x*(a^2*x^2+1)^2*arctan(a*x)^2+16/15*c^2*arctan(a*x)*ln(2/(1+I*a*x))/a+8/15*I*c^2*polylog(2,1-2/(1+I*a*x))/a,1],
[(a^2*c*x^2+c)^2*arctan(a*x)^2/x,x,23,1/12*a^2*c^2*x^2-3/2*a*c^2*x*arctan(a*x)-1/6*a^3*c^2*x^3*arctan(a*x)+3/4*c^2*arctan(a*x)^2+a^2*c^2*x^2*arctan(a*x)^2+1/4*a^4*c^2*x^4*arctan(a*x)^2+2*c^2*arctan(a*x)^2*arctanh(1-2/(1+I*a*x))+2/3*c^2*ln(a^2*x^2+1)-I*c^2*arctan(a*x)*polylog(2,1-2/(1+I*a*x))+I*c^2*arctan(a*x)*polylog(2,-1+2/(1+I*a*x))-1/2*c^2*polylog(3,1-2/(1+I*a*x))+1/2*c^2*polylog(3,-1+2/(1+I*a*x)),1],
[(a^2*c*x^2+c)^2*arctan(a*x)^2/x^2,x,20,1/3*a^2*c^2*x-1/3*a*c^2*arctan(a*x)-1/3*a^3*c^2*x^2*arctan(a*x)+2/3*I*a*c^2*arctan(a*x)^2-c^2*arctan(a*x)^2/x+2*a^2*c^2*x*arctan(a*x)^2+1/3*a^4*c^2*x^3*arctan(a*x)^2+10/3*a*c^2*arctan(a*x)*ln(2/(1+I*a*x))+2*a*c^2*arctan(a*x)*ln(2-2/(1-I*a*x))-I*a*c^2*polylog(2,-1+2/(1-I*a*x))+5/3*I*a*c^2*polylog(2,1-2/(1+I*a*x)),1],
[(a^2*c*x^2+c)^2*arctan(a*x)^2/x^3,x,21,-a*c^2*arctan(a*x)/x-a^3*c^2*x*arctan(a*x)-1/2*c^2*arctan(a*x)^2/x^2+1/2*a^4*c^2*x^2*arctan(a*x)^2+4*a^2*c^2*arctan(a*x)^2*arctanh(1-2/(1+I*a*x))+a^2*c^2*ln(x)-2*I*a^2*c^2*arctan(a*x)*polylog(2,1-2/(1+I*a*x))+2*I*a^2*c^2*arctan(a*x)*polylog(2,-1+2/(1+I*a*x))-a^2*c^2*polylog(3,1-2/(1+I*a*x))+a^2*c^2*polylog(3,-1+2/(1+I*a*x)),1],
[(a^2*c*x^2+c)^2*arctan(a*x)^2/x^4,x,19,-1/3*a^2*c^2/x-1/3*a^3*c^2*arctan(a*x)-1/3*a*c^2*arctan(a*x)/x^2-2/3*I*a^3*c^2*arctan(a*x)^2-1/3*c^2*arctan(a*x)^2/x^3-2*a^2*c^2*arctan(a*x)^2/x+a^4*c^2*x*arctan(a*x)^2+2*a^3*c^2*arctan(a*x)*ln(2/(1+I*a*x))+10/3*a^3*c^2*arctan(a*x)*ln(2-2/(1-I*a*x))-5/3*I*a^3*c^2*polylog(2,-1+2/(1-I*a*x))+I*a^3*c^2*polylog(2,1-2/(1+I*a*x)),1],
[x^3*(a^2*c*x^2+c)^3*arctan(a*x)^2,x,72,-107/12600*c^3*x^2/a^2+53/6300*c^3*x^4+71/7560*a^2*c^3*x^6+1/360*a^4*c^3*x^8+1/20*c^3*x*arctan(a*x)/a^3-1/60*c^3*x^3*arctan(a*x)/a-9/100*a*c^3*x^5*arctan(a*x)-11/140*a^3*c^3*x^7*arctan(a*x)-1/45*a^5*c^3*x^9*arctan(a*x)-1/40*c^3*arctan(a*x)^2/a^4+1/4*c^3*x^4*arctan(a*x)^2+1/2*a^2*c^3*x^6*arctan(a*x)^2+3/8*a^4*c^3*x^8*arctan(a*x)^2+1/10*a^6*c^3*x^10*arctan(a*x)^2-26/1575*c^3*ln(a^2*x^2+1)/a^4,1],
[x^2*(a^2*c*x^2+c)^3*arctan(a*x)^2,x,68,-47/3780*c^3*x/a^2+239/11340*c^3*x^3+59/3780*a^2*c^3*x^5+1/252*a^4*c^3*x^7+47/3780*c^3*arctan(a*x)/a^3-16/315*c^3*x^2*arctan(a*x)/a-89/630*a*c^3*x^4*arctan(a*x)-20/189*a^3*c^3*x^6*arctan(a*x)-1/36*a^5*c^3*x^8*arctan(a*x)-16/315*I*c^3*polylog(2,1-2/(1+I*a*x))/a^3+1/3*c^3*x^3*arctan(a*x)^2+3/5*a^2*c^3*x^5*arctan(a*x)^2+3/7*a^4*c^3*x^7*arctan(a*x)^2+1/9*a^6*c^3*x^9*arctan(a*x)^2-32/315*c^3*arctan(a*x)*ln(2/(1+I*a*x))/a^3-16/315*I*c^3*arctan(a*x)^2/a^3,1],
[x*(a^2*c*x^2+c)^3*arctan(a*x)^2,x,6,1/35*c^3*(a^2*x^2+1)/a^2+3/280*c^3*(a^2*x^2+1)^2/a^2+1/168*c^3*(a^2*x^2+1)^3/a^2-4/35*c^3*x*arctan(a*x)/a-2/35*c^3*x*(a^2*x^2+1)*arctan(a*x)/a-3/70*c^3*x*(a^2*x^2+1)^2*arctan(a*x)/a-1/28*c^3*x*(a^2*x^2+1)^3*arctan(a*x)/a+1/8*c^3*(a^2*x^2+1)^4*arctan(a*x)^2/a^2+2/35*c^3*ln(a^2*x^2+1)/a^2,1],
[(a^2*c*x^2+c)^3*arctan(a*x)^2,x,12,38/105*c^3*x+19/315*a^2*c^3*x^3+1/105*a^4*c^3*x^5-8/35*c^3*(a^2*x^2+1)*arctan(a*x)/a-3/35*c^3*(a^2*x^2+1)^2*arctan(a*x)/a-1/21*c^3*(a^2*x^2+1)^3*arctan(a*x)/a+16/35*I*c^3*arctan(a*x)^2/a+16/35*c^3*x*arctan(a*x)^2+8/35*c^3*x*(a^2*x^2+1)*arctan(a*x)^2+6/35*c^3*x*(a^2*x^2+1)^2*arctan(a*x)^2+1/7*c^3*x*(a^2*x^2+1)^3*arctan(a*x)^2+32/35*c^3*arctan(a*x)*ln(2/(1+I*a*x))/a+16/35*I*c^3*polylog(2,1-2/(1+I*a*x))/a,1],
[(a^2*c*x^2+c)^3*arctan(a*x)^2/x,x,38,29/180*a^2*c^3*x^2+1/60*a^4*c^3*x^4-11/6*a*c^3*x*arctan(a*x)-7/18*a^3*c^3*x^3*arctan(a*x)-1/15*a^5*c^3*x^5*arctan(a*x)+11/12*c^3*arctan(a*x)^2+3/2*a^2*c^3*x^2*arctan(a*x)^2+3/4*a^4*c^3*x^4*arctan(a*x)^2+1/6*a^6*c^3*x^6*arctan(a*x)^2+2*c^3*arctan(a*x)^2*arctanh(1-2/(1+I*a*x))+34/45*c^3*ln(a^2*x^2+1)-I*c^3*arctan(a*x)*polylog(2,1-2/(1+I*a*x))+I*c^3*arctan(a*x)*polylog(2,-1+2/(1+I*a*x))-1/2*c^3*polylog(3,1-2/(1+I*a*x))+1/2*c^3*polylog(3,-1+2/(1+I*a*x)),1],
[(a^2*c*x^2+c)^3*arctan(a*x)^2/x^2,x,34,7/10*a^2*c^3*x+1/30*a^4*c^3*x^3-7/10*a*c^3*arctan(a*x)-4/5*a^3*c^3*x^2*arctan(a*x)-1/10*a^5*c^3*x^4*arctan(a*x)+6/5*I*a*c^3*arctan(a*x)^2-c^3*arctan(a*x)^2/x+3*a^2*c^3*x*arctan(a*x)^2+a^4*c^3*x^3*arctan(a*x)^2+1/5*a^6*c^3*x^5*arctan(a*x)^2+22/5*a*c^3*arctan(a*x)*ln(2/(1+I*a*x))+2*a*c^3*arctan(a*x)*ln(2-2/(1-I*a*x))-I*a*c^3*polylog(2,-1+2/(1-I*a*x))+11/5*I*a*c^3*polylog(2,1-2/(1+I*a*x)),1],
[(a^2*c*x^2+c)^3*arctan(a*x)^2/x^3,x,31,1/12*a^4*c^3*x^2-a*c^3*arctan(a*x)/x-5/2*a^3*c^3*x*arctan(a*x)-1/6*a^5*c^3*x^3*arctan(a*x)+3/4*a^2*c^3*arctan(a*x)^2-1/2*c^3*arctan(a*x)^2/x^2+3/2*a^4*c^3*x^2*arctan(a*x)^2+1/4*a^6*c^3*x^4*arctan(a*x)^2+6*a^2*c^3*arctan(a*x)^2*arctanh(1-2/(1+I*a*x))+a^2*c^3*ln(x)+2/3*a^2*c^3*ln(a^2*x^2+1)-3*I*a^2*c^3*arctan(a*x)*polylog(2,1-2/(1+I*a*x))+3*I*a^2*c^3*arctan(a*x)*polylog(2,-1+2/(1+I*a*x))-3/2*a^2*c^3*polylog(3,1-2/(1+I*a*x))+3/2*a^2*c^3*polylog(3,-1+2/(1+I*a*x)),1],
[(a^2*c*x^2+c)^3*arctan(a*x)^2/x^4,x,28,-1/3*a^2*c^3/x+1/3*a^4*c^3*x-2/3*a^3*c^3*arctan(a*x)-1/3*a*c^3*arctan(a*x)/x^2-1/3*a^5*c^3*x^2*arctan(a*x)-1/3*c^3*arctan(a*x)^2/x^3-3*a^2*c^3*arctan(a*x)^2/x+3*a^4*c^3*x*arctan(a*x)^2+1/3*a^6*c^3*x^3*arctan(a*x)^2+16/3*a^3*c^3*arctan(a*x)*ln(2/(1+I*a*x))+16/3*a^3*c^3*arctan(a*x)*ln(2-2/(1-I*a*x))-8/3*I*a^3*c^3*polylog(2,-1+2/(1-I*a*x))+8/3*I*a^3*c^3*polylog(2,1-2/(1+I*a*x)),1],
[x^4*arctan(a*x)^2/(a^2*c*x^2+c),x,17,1/3*x/a^4/c-1/3*arctan(a*x)/a^5/c-1/3*x^2*arctan(a*x)/a^3/c-4/3*I*arctan(a*x)^2/a^5/c-x*arctan(a*x)^2/a^4/c+1/3*x^3*arctan(a*x)^2/a^2/c+1/3*arctan(a*x)^3/a^5/c-8/3*arctan(a*x)*ln(2/(1+I*a*x))/a^5/c-4/3*I*polylog(2,1-2/(1+I*a*x))/a^5/c,1],
[x^3*arctan(a*x)^2/(a^2*c*x^2+c),x,10,-x*arctan(a*x)/a^3/c+1/2*arctan(a*x)^2/a^4/c+1/2*x^2*arctan(a*x)^2/a^2/c+1/3*I*arctan(a*x)^3/a^4/c+arctan(a*x)^2*ln(2/(1+I*a*x))/a^4/c+1/2*ln(a^2*x^2+1)/a^4/c+I*arctan(a*x)*polylog(2,1-2/(1+I*a*x))/a^4/c+1/2*polylog(3,1-2/(1+I*a*x))/a^4/c,1],
[x^2*arctan(a*x)^2/(a^2*c*x^2+c),x,7,I*arctan(a*x)^2/a^3/c+x*arctan(a*x)^2/a^2/c-1/3*arctan(a*x)^3/a^3/c+2*arctan(a*x)*ln(2/(1+I*a*x))/a^3/c+I*polylog(2,1-2/(1+I*a*x))/a^3/c,1],
[x*arctan(a*x)^2/(a^2*c*x^2+c),x,4,-1/3*I*arctan(a*x)^3/a^2/c-arctan(a*x)^2*ln(2/(1+I*a*x))/a^2/c-I*arctan(a*x)*polylog(2,1-2/(1+I*a*x))/a^2/c-1/2*polylog(3,1-2/(1+I*a*x))/a^2/c,1],
[arctan(a*x)^2/(a^2*c*x^2+c),x,1,1/3*arctan(a*x)^3/a/c,1],
[arctan(a*x)^2/x/(a^2*c*x^2+c),x,4,-1/3*I*arctan(a*x)^3/c+arctan(a*x)^2*ln(2-2/(1-I*a*x))/c-I*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))/c+1/2*polylog(3,-1+2/(1-I*a*x))/c,1],
[arctan(a*x)^2/x^2/(a^2*c*x^2+c),x,6,-I*a*arctan(a*x)^2/c-arctan(a*x)^2/c/x-1/3*a*arctan(a*x)^3/c+2*a*arctan(a*x)*ln(2-2/(1-I*a*x))/c-I*a*polylog(2,-1+2/(1-I*a*x))/c,1],
[arctan(a*x)^2/x^3/(a^2*c*x^2+c),x,13,-a*arctan(a*x)/c/x-1/2*a^2*arctan(a*x)^2/c-1/2*arctan(a*x)^2/c/x^2+1/3*I*a^2*arctan(a*x)^3/c+a^2*ln(x)/c-1/2*a^2*ln(a^2*x^2+1)/c-a^2*arctan(a*x)^2*ln(2-2/(1-I*a*x))/c+I*a^2*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))/c-1/2*a^2*polylog(3,-1+2/(1-I*a*x))/c,1],
[arctan(a*x)^2/x^4/(a^2*c*x^2+c),x,15,-1/3*a^2/c/x-1/3*a^3*arctan(a*x)/c-1/3*a*arctan(a*x)/c/x^2+4/3*I*a^3*arctan(a*x)^2/c-1/3*arctan(a*x)^2/c/x^3+a^2*arctan(a*x)^2/c/x+1/3*a^3*arctan(a*x)^3/c-8/3*a^3*arctan(a*x)*ln(2-2/(1-I*a*x))/c+4/3*I*a^3*polylog(2,-1+2/(1-I*a*x))/c,1],
[x^3*arctan(a*x)^2/(a^2*c*x^2+c)^2,x,8,-1/4/a^4/c^2/(a^2*x^2+1)-1/2*x*arctan(a*x)/a^3/c^2/(a^2*x^2+1)-1/4*arctan(a*x)^2/a^4/c^2+1/2*arctan(a*x)^2/a^4/c^2/(a^2*x^2+1)-1/3*I*arctan(a*x)^3/a^4/c^2-arctan(a*x)^2*ln(2/(1+I*a*x))/a^4/c^2-I*arctan(a*x)*polylog(2,1-2/(1+I*a*x))/a^4/c^2-1/2*polylog(3,1-2/(1+I*a*x))/a^4/c^2,1],
[x^2*arctan(a*x)^2/(a^2*c*x^2+c)^2,x,4,1/4*x/a^2/c^2/(a^2*x^2+1)+1/4*arctan(a*x)/a^3/c^2-1/2*arctan(a*x)/a^3/c^2/(a^2*x^2+1)-1/2*x*arctan(a*x)^2/a^2/c^2/(a^2*x^2+1)+1/6*arctan(a*x)^3/a^3/c^2,1],
[x*arctan(a*x)^2/(a^2*c*x^2+c)^2,x,3,1/4/a^2/c^2/(a^2*x^2+1)+1/2*x*arctan(a*x)/a/c^2/(a^2*x^2+1)+1/4*arctan(a*x)^2/a^2/c^2-1/2*arctan(a*x)^2/a^2/c^2/(a^2*x^2+1),1],
[arctan(a*x)^2/(a^2*c*x^2+c)^2,x,4,-1/4*x/c^2/(a^2*x^2+1)-1/4*arctan(a*x)/a/c^2+1/2*arctan(a*x)/a/c^2/(a^2*x^2+1)+1/2*x*arctan(a*x)^2/c^2/(a^2*x^2+1)+1/6*arctan(a*x)^3/a/c^2,1],
[arctan(a*x)^2/x/(a^2*c*x^2+c)^2,x,8,-1/4/c^2/(a^2*x^2+1)-1/2*a*x*arctan(a*x)/c^2/(a^2*x^2+1)-1/4*arctan(a*x)^2/c^2+1/2*arctan(a*x)^2/c^2/(a^2*x^2+1)-1/3*I*arctan(a*x)^3/c^2+arctan(a*x)^2*ln(2-2/(1-I*a*x))/c^2-I*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))/c^2+1/2*polylog(3,-1+2/(1-I*a*x))/c^2,1],
[arctan(a*x)^2/x^2/(a^2*c*x^2+c)^2,x,11,1/4*a^2*x/c^2/(a^2*x^2+1)+1/4*a*arctan(a*x)/c^2-1/2*a*arctan(a*x)/c^2/(a^2*x^2+1)-I*a*arctan(a*x)^2/c^2-arctan(a*x)^2/c^2/x-1/2*a^2*x*arctan(a*x)^2/c^2/(a^2*x^2+1)-1/2*a*arctan(a*x)^3/c^2+2*a*arctan(a*x)*ln(2-2/(1-I*a*x))/c^2-I*a*polylog(2,-1+2/(1-I*a*x))/c^2,1],
[arctan(a*x)^2/x^3/(a^2*c*x^2+c)^2,x,22,1/4*a^2/c^2/(a^2*x^2+1)-a*arctan(a*x)/c^2/x+1/2*a^3*x*arctan(a*x)/c^2/(a^2*x^2+1)-1/4*a^2*arctan(a*x)^2/c^2-1/2*arctan(a*x)^2/c^2/x^2-1/2*a^2*arctan(a*x)^2/c^2/(a^2*x^2+1)+2/3*I*a^2*arctan(a*x)^3/c^2+a^2*ln(x)/c^2-1/2*a^2*ln(a^2*x^2+1)/c^2-2*a^2*arctan(a*x)^2*ln(2-2/(1-I*a*x))/c^2+2*I*a^2*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))/c^2-a^2*polylog(3,-1+2/(1-I*a*x))/c^2,1],
[arctan(a*x)^2/x^4/(a^2*c*x^2+c)^2,x,27,-1/3*a^2/c^2/x-1/4*a^4*x/c^2/(a^2*x^2+1)-7/12*a^3*arctan(a*x)/c^2-1/3*a*arctan(a*x)/c^2/x^2+1/2*a^3*arctan(a*x)/c^2/(a^2*x^2+1)+7/3*I*a^3*arctan(a*x)^2/c^2-1/3*arctan(a*x)^2/c^2/x^3+2*a^2*arctan(a*x)^2/c^2/x+1/2*a^4*x*arctan(a*x)^2/c^2/(a^2*x^2+1)+5/6*a^3*arctan(a*x)^3/c^2-14/3*a^3*arctan(a*x)*ln(2-2/(1-I*a*x))/c^2+7/3*I*a^3*polylog(2,-1+2/(1-I*a*x))/c^2,1],
[x^3*arctan(a*x)^2/(a^2*c*x^2+c)^3,x,4,-1/32*x^4/c^3/(a^2*x^2+1)^2+3/32/a^4/c^3/(a^2*x^2+1)+1/8*x^3*arctan(a*x)/a/c^3/(a^2*x^2+1)^2+3/16*x*arctan(a*x)/a^3/c^3/(a^2*x^2+1)-3/32*arctan(a*x)^2/a^4/c^3+1/4*x^4*arctan(a*x)^2/c^3/(a^2*x^2+1)^2,1],
[x^2*arctan(a*x)^2/(a^2*c*x^2+c)^3,x,13,1/32*x/a^2/c^3/(a^2*x^2+1)^2-1/64*x/a^2/c^3/(a^2*x^2+1)-1/64*arctan(a*x)/a^3/c^3-1/8*arctan(a*x)/a^3/c^3/(a^2*x^2+1)^2+1/8*arctan(a*x)/a^3/c^3/(a^2*x^2+1)-1/4*x*arctan(a*x)^2/a^2/c^3/(a^2*x^2+1)^2+1/8*x*arctan(a*x)^2/a^2/c^3/(a^2*x^2+1)+1/24*arctan(a*x)^3/a^3/c^3,1],
[x*arctan(a*x)^2/(a^2*c*x^2+c)^3,x,4,1/32/a^2/c^3/(a^2*x^2+1)^2+3/32/a^2/c^3/(a^2*x^2+1)+1/8*x*arctan(a*x)/a/c^3/(a^2*x^2+1)^2+3/16*x*arctan(a*x)/a/c^3/(a^2*x^2+1)+3/32*arctan(a*x)^2/a^2/c^3-1/4*arctan(a*x)^2/a^2/c^3/(a^2*x^2+1)^2,1],
[arctan(a*x)^2/(a^2*c*x^2+c)^3,x,8,-1/32*x/c^3/(a^2*x^2+1)^2-15/64*x/c^3/(a^2*x^2+1)-15/64*arctan(a*x)/a/c^3+1/8*arctan(a*x)/a/c^3/(a^2*x^2+1)^2+3/8*arctan(a*x)/a/c^3/(a^2*x^2+1)+1/4*x*arctan(a*x)^2/c^3/(a^2*x^2+1)^2+3/8*x*arctan(a*x)^2/c^3/(a^2*x^2+1)+1/8*arctan(a*x)^3/a/c^3,1],
[arctan(a*x)^2/x/(a^2*c*x^2+c)^3,x,13,-1/32/c^3/(a^2*x^2+1)^2-11/32/c^3/(a^2*x^2+1)-1/8*a*x*arctan(a*x)/c^3/(a^2*x^2+1)^2-11/16*a*x*arctan(a*x)/c^3/(a^2*x^2+1)-11/32*arctan(a*x)^2/c^3+1/4*arctan(a*x)^2/c^3/(a^2*x^2+1)^2+1/2*arctan(a*x)^2/c^3/(a^2*x^2+1)-1/3*I*arctan(a*x)^3/c^3+arctan(a*x)^2*ln(2-2/(1-I*a*x))/c^3-I*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))/c^3+1/2*polylog(3,-1+2/(1-I*a*x))/c^3,1],
[arctan(a*x)^2/x^2/(a^2*c*x^2+c)^3,x,20,1/32*a^2*x/c^3/(a^2*x^2+1)^2+31/64*a^2*x/c^3/(a^2*x^2+1)+31/64*a*arctan(a*x)/c^3-1/8*a*arctan(a*x)/c^3/(a^2*x^2+1)^2-7/8*a*arctan(a*x)/c^3/(a^2*x^2+1)-I*a*arctan(a*x)^2/c^3-arctan(a*x)^2/c^3/x-1/4*a^2*x*arctan(a*x)^2/c^3/(a^2*x^2+1)^2-7/8*a^2*x*arctan(a*x)^2/c^3/(a^2*x^2+1)-5/8*a*arctan(a*x)^3/c^3+2*a*arctan(a*x)*ln(2-2/(1-I*a*x))/c^3-I*a*polylog(2,-1+2/(1-I*a*x))/c^3,1],
[arctan(a*x)^2/x^3/(a^2*c*x^2+c)^3,x,36,1/32*a^2/c^3/(a^2*x^2+1)^2+19/32*a^2/c^3/(a^2*x^2+1)-a*arctan(a*x)/c^3/x+1/8*a^3*x*arctan(a*x)/c^3/(a^2*x^2+1)^2+19/16*a^3*x*arctan(a*x)/c^3/(a^2*x^2+1)+3/32*a^2*arctan(a*x)^2/c^3-1/2*arctan(a*x)^2/c^3/x^2-1/4*a^2*arctan(a*x)^2/c^3/(a^2*x^2+1)^2-a^2*arctan(a*x)^2/c^3/(a^2*x^2+1)+I*a^2*arctan(a*x)^3/c^3+a^2*ln(x)/c^3-1/2*a^2*ln(a^2*x^2+1)/c^3-3*a^2*arctan(a*x)^2*ln(2-2/(1-I*a*x))/c^3+3*I*a^2*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))/c^3-3/2*a^2*polylog(3,-1+2/(1-I*a*x))/c^3,1],
[arctan(a*x)^2/x^4/(a^2*c*x^2+c)^3,x,48,-1/3*a^2/c^3/x-1/32*a^4*x/c^3/(a^2*x^2+1)^2-47/64*a^4*x/c^3/(a^2*x^2+1)-205/192*a^3*arctan(a*x)/c^3-1/3*a*arctan(a*x)/c^3/x^2+1/8*a^3*arctan(a*x)/c^3/(a^2*x^2+1)^2+11/8*a^3*arctan(a*x)/c^3/(a^2*x^2+1)+10/3*I*a^3*arctan(a*x)^2/c^3-1/3*arctan(a*x)^2/c^3/x^3+3*a^2*arctan(a*x)^2/c^3/x+1/4*a^4*x*arctan(a*x)^2/c^3/(a^2*x^2+1)^2+11/8*a^4*x*arctan(a*x)^2/c^3/(a^2*x^2+1)+35/24*a^3*arctan(a*x)^3/c^3-20/3*a^3*arctan(a*x)*ln(2-2/(1-I*a*x))/c^3+10/3*I*a^3*polylog(2,-1+2/(1-I*a*x))/c^3,1],
[x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)^2,x,26,-11/60*sqrt(a^2*c*x^2+c)/a^4+1/30*(a^2*c*x^2+c)^(3/2)/a^4/c+1/12*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^3-1/10*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)/a-2/15*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^4+1/15*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^2+1/5*x^4*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-11/30*I*c*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/sqrt(a^2*c*x^2+c)+11/60*I*c*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/sqrt(a^2*c*x^2+c)-11/60*I*c*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/sqrt(a^2*c*x^2+c),1],
[x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2,x,35,1/12*x*sqrt(a^2*c*x^2+c)/a^2+1/12*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^3-1/6*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/a+1/8*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^2+1/4*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+1/4*I*c*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^3/sqrt(a^2*c*x^2+c)-1/6*sqrt(c)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^3-1/4*I*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+1/4*I*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+1/4*c*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-1/4*c*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c),1],
[x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2,x,4,1/3*sqrt(a^2*c*x^2+c)/a^2-1/3*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a+1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/a^2/c+2/3*I*c*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^2/sqrt(a^2*c*x^2+c)-1/3*I*c*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^2/sqrt(a^2*c*x^2+c)+1/3*I*c*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^2/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^2,x,12,-sqrt(a^2*c*x^2+c)*arctan(a*x)/a+1/2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-I*c*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a/sqrt(a^2*c*x^2+c)+sqrt(c)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a+I*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-I*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-c*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+c*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x,x,13,sqrt(a^2*c*x^2+c)*arctan(a*x)^2+4*I*c*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-2*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*I*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-2*I*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-2*I*c*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+2*I*c*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-2*c*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*c*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x^2,x,13,-sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x-2*I*a*c*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/sqrt(a^2*c*x^2+c)-4*a*c*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+2*I*a*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-2*I*a*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*I*a*c*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-2*I*a*c*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-2*a*c*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*a*c*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x^3,x,24,-a*sqrt(a^2*c*x^2+c)*arctan(a*x)/x-1/2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x^2-a^2*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-a^2*sqrt(c)*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))+I*a^2*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-I*a^2*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-a^2*c*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+a^2*c*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x^4,x,7,-1/3*a^2*sqrt(a^2*c*x^2+c)/x-1/3*a*sqrt(a^2*c*x^2+c)*arctan(a*x)/x^2-1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/c/x^3-2/3*a^3*c*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+1/3*I*a^3*c*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-1/3*I*a^3*c*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[x^3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x,75,-17/280*c*sqrt(a^2*c*x^2+c)/a^4-17/1260*(a^2*c*x^2+c)^(3/2)/a^4+1/105*(a^2*c*x^2+c)^(5/2)/a^4/c+3/56*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^3-23/420*c*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)/a-1/21*a*c*x^5*sqrt(a^2*c*x^2+c)*arctan(a*x)-2/35*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^4+1/35*c*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^2+8/35*c*x^4*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+1/7*a^2*c*x^6*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-17/140*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/sqrt(a^2*c*x^2+c)+17/280*I*c^2*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/sqrt(a^2*c*x^2+c)-17/280*I*c^2*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/sqrt(a^2*c*x^2+c),1],
[x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x,92,1/36*c*x*sqrt(a^2*c*x^2+c)/a^2+1/60*c*x^3*sqrt(a^2*c*x^2+c)+31/360*c*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^3-19/180*c*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/a-1/15*a*c*x^4*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/16*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^2+7/24*c*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+1/6*a^2*c*x^5*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+1/8*I*c^2*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^3/sqrt(a^2*c*x^2+c)-41/360*c^(3/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^3-1/8*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+1/8*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+1/8*c^2*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-1/8*c^2*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c),1],
[x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x,5,3/20*c*sqrt(a^2*c*x^2+c)/a^2+1/30*(a^2*c*x^2+c)^(3/2)/a^2-3/20*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a-1/10*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)/a+1/5*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/a^2/c+3/10*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^2/sqrt(a^2*c*x^2+c)-3/20*I*c^2*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^2/sqrt(a^2*c*x^2+c)+3/20*I*c^2*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^2/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x,16,1/12*c*x*sqrt(a^2*c*x^2+c)-3/4*c*sqrt(a^2*c*x^2+c)*arctan(a*x)/a-1/6*(a^2*c*x^2+c)^(3/2)*arctan(a*x)/a+3/8*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+1/4*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2-3/4*I*c^2*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a/sqrt(a^2*c*x^2+c)+5/6*c^(3/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a+3/4*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-3/4*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-3/4*c^2*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+3/4*c^2*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x,x,18,1/3*c*sqrt(a^2*c*x^2+c)-1/3*a*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)+c*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2+14/3*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-2*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-7/3*I*c^2*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+7/3*I*c^2*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-2*c^2*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*c^2*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^2,x,26,-a*c*sqrt(a^2*c*x^2+c)*arctan(a*x)-c*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x+1/2*a^2*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-3*I*a*c^2*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/sqrt(a^2*c*x^2+c)-4*a*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+a*c^(3/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))+3*I*a*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*I*a*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*I*a*c^2*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-2*I*a*c^2*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-3*a*c^2*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*a*c^2*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^3,x,38,-a*c*sqrt(a^2*c*x^2+c)*arctan(a*x)/x+a^2*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-1/2*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x^2+4*I*a^2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-3*a^2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-a^2*c^(3/2)*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))+3*I*a^2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*I*a^2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-2*I*a^2*c^2*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+2*I*a^2*c^2*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-3*a^2*c^2*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*a^2*c^2*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^4,x,21,-1/3*a^2*c*sqrt(a^2*c*x^2+c)/x-1/3*a*c*sqrt(a^2*c*x^2+c)*arctan(a*x)/x^2-a^2*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x-1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^3-2*I*a^3*c^2*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/sqrt(a^2*c*x^2+c)-14/3*a^3*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+2*I*a^3*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-2*I*a^3*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+7/3*I*a^3*c^2*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-7/3*I*a^3*c^2*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-2*a^3*c^2*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*a^3*c^2*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[x^3*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x,203,-115/4032*c^2*sqrt(a^2*c*x^2+c)/a^4-115/18144*c*(a^2*c*x^2+c)^(3/2)/a^4-23/7560*(a^2*c*x^2+c)^(5/2)/a^4+1/252*(a^2*c*x^2+c)^(7/2)/a^4/c+47/1344*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^3-205/6048*c^2*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)/a-103/1512*a*c^2*x^5*sqrt(a^2*c*x^2+c)*arctan(a*x)-1/36*a^3*c^2*x^7*sqrt(a^2*c*x^2+c)*arctan(a*x)-2/63*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^4+1/63*c^2*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^2+5/21*c^2*x^4*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+19/63*a^2*c^2*x^6*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+1/9*a^4*c^2*x^8*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+115/4032*I*c^3*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/sqrt(a^2*c*x^2+c)-115/4032*I*c^3*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/sqrt(a^2*c*x^2+c)-115/2016*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/sqrt(a^2*c*x^2+c),1],
[x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x,238,43/4032*c^2*x*sqrt(a^2*c*x^2+c)/a^2+29/1680*c^2*x^3*sqrt(a^2*c*x^2+c)+1/168*a^2*c^2*x^5*sqrt(a^2*c*x^2+c)+1373/20160*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^3-737/10080*c^2*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/a-83/840*a*c^2*x^4*sqrt(a^2*c*x^2+c)*arctan(a*x)-1/28*a^3*c^2*x^6*sqrt(a^2*c*x^2+c)*arctan(a*x)+5/128*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^2+59/192*c^2*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+17/48*a^2*c^2*x^5*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+1/8*a^4*c^2*x^7*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+5/64*I*c^3*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^3/sqrt(a^2*c*x^2+c)-397/5040*c^(5/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^3+5/64*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-5/64*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+5/64*c^3*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-5/64*c^3*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c),1],
[x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x,6,5/56*c^2*sqrt(a^2*c*x^2+c)/a^2+5/252*c*(a^2*c*x^2+c)^(3/2)/a^2+1/105*(a^2*c*x^2+c)^(5/2)/a^2-5/56*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a-5/84*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)/a-1/21*x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)/a+1/7*(a^2*c*x^2+c)^(7/2)*arctan(a*x)^2/a^2/c+5/28*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^2/sqrt(a^2*c*x^2+c)-5/56*I*c^3*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^2/sqrt(a^2*c*x^2+c)+5/56*I*c^3*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^2/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x,21,17/180*c^2*x*sqrt(a^2*c*x^2+c)+1/60*c*x*(a^2*c*x^2+c)^(3/2)-5/8*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/a-5/36*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)/a-1/15*(a^2*c*x^2+c)^(5/2)*arctan(a*x)/a+5/16*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+5/24*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2+1/6*x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2-5/8*I*c^3*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a/sqrt(a^2*c*x^2+c)+259/360*c^(5/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a+5/8*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-5/8*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-5/8*c^3*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+5/8*c^3*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x,x,24,29/60*c^2*sqrt(a^2*c*x^2+c)+1/30*c*(a^2*c*x^2+c)^(3/2)-29/60*a*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)-1/10*a*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)+c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+1/3*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2+1/5*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2+149/30*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-2*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-149/60*I*c^3*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+149/60*I*c^3*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-2*c^3*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*c^3*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x^2,x,43,1/12*a^2*c^2*x*sqrt(a^2*c*x^2+c)-7/4*a*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)-1/6*a*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)-c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x+7/8*a^2*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+1/4*a^2*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2-15/4*I*a*c^3*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/sqrt(a^2*c*x^2+c)-4*a*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+11/6*a*c^(5/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))+15/4*I*a*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-15/4*I*a*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*I*a*c^3*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-2*I*a*c^3*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-15/4*a*c^3*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+15/4*a*c^3*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x^3,x,57,1/3*a^2*c^2*sqrt(a^2*c*x^2+c)-a*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/x-1/3*a^3*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)+2*a^2*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-1/2*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x^2+1/3*a^2*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2+26/3*I*a^2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-5*a^2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-a^2*c^(5/2)*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))+5*I*a^2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-5*I*a^2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-13/3*I*a^2*c^3*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+13/3*I*a^2*c^3*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-5*a^2*c^3*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+5*a^2*c^3*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x^4,x,48,-1/3*a^2*c^2*sqrt(a^2*c*x^2+c)/x-a^3*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)-1/3*a*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/x^2-2*a^2*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x+1/2*a^4*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-1/3*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^3-5*I*a^3*c^3*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/sqrt(a^2*c*x^2+c)-26/3*a^3*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+a^3*c^(5/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))+5*I*a^3*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-5*I*a^3*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+13/3*I*a^3*c^3*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-13/3*I*a^3*c^3*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-5*a^3*c^3*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+5*a^3*c^3*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[x^3*arctan(a*x)^2/sqrt(a^2*c*x^2+c),x,8,1/3*sqrt(a^2*c*x^2+c)/a^4/c-1/3*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^3/c-2/3*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^4/c+1/3*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^2/c-10/3*I*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/sqrt(a^2*c*x^2+c)+5/3*I*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/sqrt(a^2*c*x^2+c)-5/3*I*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/sqrt(a^2*c*x^2+c),1],
[x^2*arctan(a*x)^2/sqrt(a^2*c*x^2+c),x,13,-sqrt(a^2*c*x^2+c)*arctan(a*x)/a^3/c+1/2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^2/c+I*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^3/sqrt(a^2*c*x^2+c)+arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^3/sqrt(c)-I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c),1],
[x*arctan(a*x)^2/sqrt(a^2*c*x^2+c),x,3,sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^2/c+4*I*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^2/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^2/sqrt(a^2*c*x^2+c)+2*I*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^2/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^2/sqrt(a^2*c*x^2+c),x,9,-2*I*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a/sqrt(a^2*c*x^2+c)+2*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-2*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+2*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^2/x/sqrt(a^2*c*x^2+c),x,9,-2*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-2*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^2/x^2/sqrt(a^2*c*x^2+c),x,3,-sqrt(a^2*c*x^2+c)*arctan(a*x)^2/c/x-4*a*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+2*I*a*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-2*I*a*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^2/x^3/sqrt(a^2*c*x^2+c),x,14,-a*sqrt(a^2*c*x^2+c)*arctan(a*x)/c/x-1/2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/c/x^2+a^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-a^2*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))/sqrt(c)-I*a^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+I*a^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+a^2*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-a^2*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^2/x^4/sqrt(a^2*c*x^2+c),x,8,-1/3*a^2*sqrt(a^2*c*x^2+c)/c/x-1/3*a*sqrt(a^2*c*x^2+c)*arctan(a*x)/c/x^2-1/3*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/c/x^3+2/3*a^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/c/x+10/3*a^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-5/3*I*a^3*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+5/3*I*a^3*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[x^3*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x,6,-2/a^4/c/sqrt(a^2*c*x^2+c)-2*x*arctan(a*x)/a^3/c/sqrt(a^2*c*x^2+c)+arctan(a*x)^2/a^4/c/sqrt(a^2*c*x^2+c)+sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^4/c^2+4*I*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/c/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/c/sqrt(a^2*c*x^2+c)+2*I*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^4/c/sqrt(a^2*c*x^2+c),1],
[x^2*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x,12,2*x/a^2/c/sqrt(a^2*c*x^2+c)-2*arctan(a*x)/a^3/c/sqrt(a^2*c*x^2+c)-x*arctan(a*x)^2/a^2/c/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^3/c/sqrt(a^2*c*x^2+c)+2*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^3/c/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^3/c/sqrt(a^2*c*x^2+c)-2*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^3/c/sqrt(a^2*c*x^2+c)+2*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^3/c/sqrt(a^2*c*x^2+c),1],
[x*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x,2,2/a^2/c/sqrt(a^2*c*x^2+c)+2*x*arctan(a*x)/a/c/sqrt(a^2*c*x^2+c)-arctan(a*x)^2/a^2/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x,2,-2*x/c/sqrt(a^2*c*x^2+c)+2*arctan(a*x)/a/c/sqrt(a^2*c*x^2+c)+x*arctan(a*x)^2/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^2/x/(a^2*c*x^2+c)^(3/2),x,12,-2/c/sqrt(a^2*c*x^2+c)-2*a*x*arctan(a*x)/c/sqrt(a^2*c*x^2+c)+arctan(a*x)^2/c/sqrt(a^2*c*x^2+c)-2*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)+2*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)-2*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)+2*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^2/x^2/(a^2*c*x^2+c)^(3/2),x,6,2*a^2*x/c/sqrt(a^2*c*x^2+c)-2*a*arctan(a*x)/c/sqrt(a^2*c*x^2+c)-a^2*x*arctan(a*x)^2/c/sqrt(a^2*c*x^2+c)-sqrt(a^2*c*x^2+c)*arctan(a*x)^2/c^2/x-4*a*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/c/sqrt(a^2*c*x^2+c)+2*I*a*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/c/sqrt(a^2*c*x^2+c)-2*I*a*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^2/x^3/(a^2*c*x^2+c)^(3/2),x,27,2*a^2/c/sqrt(a^2*c*x^2+c)+2*a^3*x*arctan(a*x)/c/sqrt(a^2*c*x^2+c)-a*sqrt(a^2*c*x^2+c)*arctan(a*x)/c^2/x-a^2*arctan(a*x)^2/c/sqrt(a^2*c*x^2+c)-1/2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/c^2/x^2+3*a^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)-a^2*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))/c^(3/2)-3*I*a^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)+3*I*a^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)+3*a^2*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)-3*a^2*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^2/x^4/(a^2*c*x^2+c)^(3/2),x,15,-2*a^4*x/c/sqrt(a^2*c*x^2+c)-1/3*a^2*sqrt(a^2*c*x^2+c)/c^2/x+2*a^3*arctan(a*x)/c/sqrt(a^2*c*x^2+c)-1/3*a*sqrt(a^2*c*x^2+c)*arctan(a*x)/c^2/x^2+a^4*x*arctan(a*x)^2/c/sqrt(a^2*c*x^2+c)-1/3*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/c^2/x^3+5/3*a^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/c^2/x+22/3*a^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/c/sqrt(a^2*c*x^2+c)-11/3*I*a^3*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/c/sqrt(a^2*c*x^2+c)+11/3*I*a^3*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/c/sqrt(a^2*c*x^2+c),1],
[x^5*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x,13,2/27/a^6/c/(a^2*c*x^2+c)^(3/2)-32/9/a^6/c^2/sqrt(a^2*c*x^2+c)-2/9*x^3*arctan(a*x)/a^3/c/(a^2*c*x^2+c)^(3/2)-10/3*x*arctan(a*x)/a^5/c^2/sqrt(a^2*c*x^2+c)+1/3*x^2*arctan(a*x)^2/a^4/c/(a^2*c*x^2+c)^(3/2)+5/3*arctan(a*x)^2/a^6/c^2/sqrt(a^2*c*x^2+c)+sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^6/c^3+4*I*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^6/c^2/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^6/c^2/sqrt(a^2*c*x^2+c)+2*I*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^6/c^2/sqrt(a^2*c*x^2+c),1],
[x^4*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x,17,2/27*x^3/a^2/c/(a^2*c*x^2+c)^(3/2)+22/9*x/a^4/c^2/sqrt(a^2*c*x^2+c)-2/9*x^2*arctan(a*x)/a^3/c/(a^2*c*x^2+c)^(3/2)-22/9*arctan(a*x)/a^5/c^2/sqrt(a^2*c*x^2+c)-1/3*x^3*arctan(a*x)^2/a^2/c/(a^2*c*x^2+c)^(3/2)-x*arctan(a*x)^2/a^4/c^2/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^5/c^2/sqrt(a^2*c*x^2+c)+2*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^5/c^2/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^5/c^2/sqrt(a^2*c*x^2+c)-2*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^5/c^2/sqrt(a^2*c*x^2+c)+2*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^5/c^2/sqrt(a^2*c*x^2+c),1],
[x^3*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x,6,-2/27/a^4/c/(a^2*c*x^2+c)^(3/2)+14/9/a^4/c^2/sqrt(a^2*c*x^2+c)+2/9*x^3*arctan(a*x)/a/c/(a^2*c*x^2+c)^(3/2)+4/3*x*arctan(a*x)/a^3/c^2/sqrt(a^2*c*x^2+c)-1/3*x^2*arctan(a*x)^2/a^2/c/(a^2*c*x^2+c)^(3/2)-2/3*arctan(a*x)^2/a^4/c^2/sqrt(a^2*c*x^2+c),1],
[x^2*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x,4,-2/27*x^3/c/(a^2*c*x^2+c)^(3/2)-4/9*x/a^2/c^2/sqrt(a^2*c*x^2+c)+2/9*x^2*arctan(a*x)/a/c/(a^2*c*x^2+c)^(3/2)+4/9*arctan(a*x)/a^3/c^2/sqrt(a^2*c*x^2+c)+1/3*x^3*arctan(a*x)^2/c/(a^2*c*x^2+c)^(3/2),1],
[x*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x,3,2/27/a^2/c/(a^2*c*x^2+c)^(3/2)+4/9/a^2/c^2/sqrt(a^2*c*x^2+c)+2/9*x*arctan(a*x)/a/c/(a^2*c*x^2+c)^(3/2)+4/9*x*arctan(a*x)/a/c^2/sqrt(a^2*c*x^2+c)-1/3*arctan(a*x)^2/a^2/c/(a^2*c*x^2+c)^(3/2),1],
[arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x,5,-2/27*x/c/(a^2*c*x^2+c)^(3/2)-40/27*x/c^2/sqrt(a^2*c*x^2+c)+2/9*arctan(a*x)/a/c/(a^2*c*x^2+c)^(3/2)+4/3*arctan(a*x)/a/c^2/sqrt(a^2*c*x^2+c)+1/3*x*arctan(a*x)^2/c/(a^2*c*x^2+c)^(3/2)+2/3*x*arctan(a*x)^2/c^2/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^2/x/(a^2*c*x^2+c)^(5/2),x,16,-2/27/c/(a^2*c*x^2+c)^(3/2)-22/9/c^2/sqrt(a^2*c*x^2+c)-2/9*a*x*arctan(a*x)/c/(a^2*c*x^2+c)^(3/2)-22/9*a*x*arctan(a*x)/c^2/sqrt(a^2*c*x^2+c)+1/3*arctan(a*x)^2/c/(a^2*c*x^2+c)^(3/2)+arctan(a*x)^2/c^2/sqrt(a^2*c*x^2+c)-2*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)+2*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)-2*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)+2*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^2/x^2/(a^2*c*x^2+c)^(5/2),x,12,2/27*a^2*x/c/(a^2*c*x^2+c)^(3/2)+94/27*a^2*x/c^2/sqrt(a^2*c*x^2+c)-2/9*a*arctan(a*x)/c/(a^2*c*x^2+c)^(3/2)-10/3*a*arctan(a*x)/c^2/sqrt(a^2*c*x^2+c)-1/3*a^2*x*arctan(a*x)^2/c/(a^2*c*x^2+c)^(3/2)-5/3*a^2*x*arctan(a*x)^2/c^2/sqrt(a^2*c*x^2+c)-sqrt(a^2*c*x^2+c)*arctan(a*x)^2/c^3/x-4*a*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/c^2/sqrt(a^2*c*x^2+c)+2*I*a*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/c^2/sqrt(a^2*c*x^2+c)-2*I*a*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/c^2/sqrt(a^2*c*x^2+c),1],
[x^m*(a^2*c*x^2+c)^2*arctan(a*x)^2,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^2,x),0],
[x^m*(a^2*c*x^2+c)*arctan(a*x)^2,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)*arctan(a*x)^2,x),0],
[x^m*arctan(a*x)^2/(a^2*c*x^2+c),x,0,Defer(Int)(x^m*arctan(a*x)^2/(a^2*c*x^2+c),x),0],
[x^m*arctan(a*x)^2/(a^2*c*x^2+c)^2,x,0,Defer(Int)(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^2,x),0],
[x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x),0],
[x^m*sqrt(a^2*c*x^2+c)*arctan(a*x)^2,x,0,Defer(Int)(x^m*sqrt(a^2*c*x^2+c)*arctan(a*x)^2,x),0],
[x^m*arctan(a*x)^2/sqrt(a^2*c*x^2+c),x,0,Defer(Int)(x^m*arctan(a*x)^2/sqrt(a^2*c*x^2+c),x),0],
[x^m*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x),0],
[x^3*(a^2*c*x^2+c)*arctan(a*x)^3,x,52,1/15*c*x/a^3-1/60*c*x^3/a-1/15*c*arctan(a*x)/a^4-1/60*c*x^2*arctan(a*x)/a^2+1/20*c*x^4*arctan(a*x)+7/30*I*c*arctan(a*x)^2/a^4+1/4*c*x*arctan(a*x)^2/a^3-1/12*c*x^3*arctan(a*x)^2/a-1/10*a*c*x^5*arctan(a*x)^2-1/12*c*arctan(a*x)^3/a^4+1/4*c*x^4*arctan(a*x)^3+1/6*a^2*c*x^6*arctan(a*x)^3+7/15*c*arctan(a*x)*ln(2/(1+I*a*x))/a^4+7/30*I*c*polylog(2,1-2/(1+I*a*x))/a^4,1],
[x^2*(a^2*c*x^2+c)*arctan(a*x)^3,x,34,-1/20*c*x^2/a+1/10*c*x*arctan(a*x)/a^2+1/10*c*x^3*arctan(a*x)-1/20*c*arctan(a*x)^2/a^3-1/5*c*x^2*arctan(a*x)^2/a-3/20*a*c*x^4*arctan(a*x)^2-2/15*I*c*arctan(a*x)^3/a^3+1/3*c*x^3*arctan(a*x)^3+1/5*a^2*c*x^5*arctan(a*x)^3-2/5*c*arctan(a*x)^2*ln(2/(1+I*a*x))/a^3-2/5*I*c*arctan(a*x)*polylog(2,1-2/(1+I*a*x))/a^3-1/5*c*polylog(3,1-2/(1+I*a*x))/a^3,1],
[x*(a^2*c*x^2+c)*arctan(a*x)^3,x,8,-1/4*c*x/a+1/4*c*(a^2*x^2+1)*arctan(a*x)/a^2-1/2*I*c*arctan(a*x)^2/a^2-1/2*c*x*arctan(a*x)^2/a-1/4*c*x*(a^2*x^2+1)*arctan(a*x)^2/a+1/4*c*(a^2*x^2+1)^2*arctan(a*x)^3/a^2-c*arctan(a*x)*ln(2/(1+I*a*x))/a^2-1/2*I*c*polylog(2,1-2/(1+I*a*x))/a^2,1],
[(a^2*c*x^2+c)*arctan(a*x)^3,x,8,c*x*arctan(a*x)-1/2*c*(a^2*x^2+1)*arctan(a*x)^2/a+2/3*I*c*arctan(a*x)^3/a+2/3*c*x*arctan(a*x)^3+1/3*c*x*(a^2*x^2+1)*arctan(a*x)^3+2*c*arctan(a*x)^2*ln(2/(1+I*a*x))/a-1/2*c*ln(a^2*x^2+1)/a+2*I*c*arctan(a*x)*polylog(2,1-2/(1+I*a*x))/a+c*polylog(3,1-2/(1+I*a*x))/a,1],
[(a^2*c*x^2+c)*arctan(a*x)^3/x,x,17,-3/2*I*c*arctan(a*x)^2-3/2*a*c*x*arctan(a*x)^2+1/2*c*arctan(a*x)^3+1/2*a^2*c*x^2*arctan(a*x)^3+2*c*arctan(a*x)^3*arctanh(1-2/(1+I*a*x))-3*c*arctan(a*x)*ln(2/(1+I*a*x))-3/2*I*c*polylog(2,1-2/(1+I*a*x))-3/2*I*c*arctan(a*x)^2*polylog(2,1-2/(1+I*a*x))+3/2*I*c*arctan(a*x)^2*polylog(2,-1+2/(1+I*a*x))-3/2*c*arctan(a*x)*polylog(3,1-2/(1+I*a*x))+3/2*c*arctan(a*x)*polylog(3,-1+2/(1+I*a*x))+3/4*I*c*polylog(4,1-2/(1+I*a*x))-3/4*I*c*polylog(4,-1+2/(1+I*a*x)),1],
[(a^2*c*x^2+c)*arctan(a*x)^3/x^2,x,11,-c*arctan(a*x)^3/x+a^2*c*x*arctan(a*x)^3+3*a*c*arctan(a*x)^2*ln(2/(1+I*a*x))+3*a*c*arctan(a*x)^2*ln(2-2/(1-I*a*x))-3*I*a*c*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))+3*I*a*c*arctan(a*x)*polylog(2,1-2/(1+I*a*x))+3/2*a*c*polylog(3,-1+2/(1-I*a*x))+3/2*a*c*polylog(3,1-2/(1+I*a*x)),1],
[(a^2*c*x^2+c)*arctan(a*x)^3/x^3,x,16,-3/2*I*a^2*c*arctan(a*x)^2-3/2*a*c*arctan(a*x)^2/x-1/2*a^2*c*arctan(a*x)^3-1/2*c*arctan(a*x)^3/x^2+2*a^2*c*arctan(a*x)^3*arctanh(1-2/(1+I*a*x))+3*a^2*c*arctan(a*x)*ln(2-2/(1-I*a*x))-3/2*I*a^2*c*polylog(2,-1+2/(1-I*a*x))-3/2*I*a^2*c*arctan(a*x)^2*polylog(2,1-2/(1+I*a*x))+3/2*I*a^2*c*arctan(a*x)^2*polylog(2,-1+2/(1+I*a*x))-3/2*a^2*c*arctan(a*x)*polylog(3,1-2/(1+I*a*x))+3/2*a^2*c*arctan(a*x)*polylog(3,-1+2/(1+I*a*x))+3/4*I*a^2*c*polylog(4,1-2/(1+I*a*x))-3/4*I*a^2*c*polylog(4,-1+2/(1+I*a*x)),1],
[(a^2*c*x^2+c)*arctan(a*x)^3/x^4,x,20,-a^2*c*arctan(a*x)/x-1/2*a^3*c*arctan(a*x)^2-1/2*a*c*arctan(a*x)^2/x^2-2/3*I*a^3*c*arctan(a*x)^3-1/3*c*arctan(a*x)^3/x^3-a^2*c*arctan(a*x)^3/x+a^3*c*ln(x)-1/2*a^3*c*ln(a^2*x^2+1)+2*a^3*c*arctan(a*x)^2*ln(2-2/(1-I*a*x))-2*I*a^3*c*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))+a^3*c*polylog(3,-1+2/(1-I*a*x)),1],
[x^3*(a^2*c*x^2+c)^2*arctan(a*x)^3,x,106,1/21*c^2*x/a^3-1/168*c^2*x^3/a-1/280*a*c^2*x^5-1/21*c^2*arctan(a*x)/a^4-5/168*c^2*x^2*arctan(a*x)/a^2+1/28*c^2*x^4*arctan(a*x)+1/56*a^2*c^2*x^6*arctan(a*x)+2/21*I*c^2*arctan(a*x)^2/a^4+1/8*c^2*x*arctan(a*x)^2/a^3-1/24*c^2*x^3*arctan(a*x)^2/a-1/8*a*c^2*x^5*arctan(a*x)^2-3/56*a^3*c^2*x^7*arctan(a*x)^2-1/24*c^2*arctan(a*x)^3/a^4+1/4*c^2*x^4*arctan(a*x)^3+1/3*a^2*c^2*x^6*arctan(a*x)^3+1/8*a^4*c^2*x^8*arctan(a*x)^3+4/21*c^2*arctan(a*x)*ln(2/(1+I*a*x))/a^4+2/21*I*c^2*polylog(2,1-2/(1+I*a*x))/a^4,1],
[x^2*(a^2*c*x^2+c)^2*arctan(a*x)^3,x,73,-11/420*c^2*x^2/a-1/140*a*c^2*x^4-1/70*c^2*x*arctan(a*x)/a^2+17/210*c^2*x^3*arctan(a*x)+1/35*a^2*c^2*x^5*arctan(a*x)+1/140*c^2*arctan(a*x)^2/a^3-4/35*c^2*x^2*arctan(a*x)^2/a-27/140*a*c^2*x^4*arctan(a*x)^2-1/14*a^3*c^2*x^6*arctan(a*x)^2-8/105*I*c^2*arctan(a*x)^3/a^3+1/3*c^2*x^3*arctan(a*x)^3+2/5*a^2*c^2*x^5*arctan(a*x)^3+1/7*a^4*c^2*x^7*arctan(a*x)^3-8/35*c^2*arctan(a*x)^2*ln(2/(1+I*a*x))/a^3+1/30*c^2*ln(a^2*x^2+1)/a^3-8/35*I*c^2*arctan(a*x)*polylog(2,1-2/(1+I*a*x))/a^3-4/35*c^2*polylog(3,1-2/(1+I*a*x))/a^3,1],
[x*(a^2*c*x^2+c)^2*arctan(a*x)^3,x,10,-11/60*c^2*x/a-1/60*a*c^2*x^3+2/15*c^2*(a^2*x^2+1)*arctan(a*x)/a^2+1/20*c^2*(a^2*x^2+1)^2*arctan(a*x)/a^2-4/15*I*c^2*arctan(a*x)^2/a^2-4/15*c^2*x*arctan(a*x)^2/a-2/15*c^2*x*(a^2*x^2+1)*arctan(a*x)^2/a-1/10*c^2*x*(a^2*x^2+1)^2*arctan(a*x)^2/a+1/6*c^2*(a^2*x^2+1)^3*arctan(a*x)^3/a^2-8/15*c^2*arctan(a*x)*ln(2/(1+I*a*x))/a^2-4/15*I*c^2*polylog(2,1-2/(1+I*a*x))/a^2,1],
[(a^2*c*x^2+c)^2*arctan(a*x)^3,x,12,-1/20*c^2*(a^2*x^2+1)/a+c^2*x*arctan(a*x)+1/10*c^2*x*(a^2*x^2+1)*arctan(a*x)-2/5*c^2*(a^2*x^2+1)*arctan(a*x)^2/a-3/20*c^2*(a^2*x^2+1)^2*arctan(a*x)^2/a+8/15*I*c^2*arctan(a*x)^3/a+8/15*c^2*x*arctan(a*x)^3+4/15*c^2*x*(a^2*x^2+1)*arctan(a*x)^3+1/5*c^2*x*(a^2*x^2+1)^2*arctan(a*x)^3+8/5*c^2*arctan(a*x)^2*ln(2/(1+I*a*x))/a-1/2*c^2*ln(a^2*x^2+1)/a+8/5*I*c^2*arctan(a*x)*polylog(2,1-2/(1+I*a*x))/a+4/5*c^2*polylog(3,1-2/(1+I*a*x))/a,1],
[(a^2*c*x^2+c)^2*arctan(a*x)^3/x,x,36,-1/4*a*c^2*x+1/4*c^2*arctan(a*x)+1/4*a^2*c^2*x^2*arctan(a*x)-2*I*c^2*arctan(a*x)^2-9/4*a*c^2*x*arctan(a*x)^2-1/4*a^3*c^2*x^3*arctan(a*x)^2+3/4*c^2*arctan(a*x)^3+a^2*c^2*x^2*arctan(a*x)^3+1/4*a^4*c^2*x^4*arctan(a*x)^3+2*c^2*arctan(a*x)^3*arctanh(1-2/(1+I*a*x))-4*c^2*arctan(a*x)*ln(2/(1+I*a*x))-3/4*I*c^2*polylog(4,-1+2/(1+I*a*x))-2*I*c^2*polylog(2,1-2/(1+I*a*x))+3/4*I*c^2*polylog(4,1-2/(1+I*a*x))-3/2*c^2*arctan(a*x)*polylog(3,1-2/(1+I*a*x))+3/2*c^2*arctan(a*x)*polylog(3,-1+2/(1+I*a*x))-3/2*I*c^2*arctan(a*x)^2*polylog(2,1-2/(1+I*a*x))+3/2*I*c^2*arctan(a*x)^2*polylog(2,-1+2/(1+I*a*x)),1],
[(a^2*c*x^2+c)^2*arctan(a*x)^3/x^2,x,23,a^2*c^2*x*arctan(a*x)-1/2*a*c^2*arctan(a*x)^2-1/2*a^3*c^2*x^2*arctan(a*x)^2+2/3*I*a*c^2*arctan(a*x)^3-c^2*arctan(a*x)^3/x+2*a^2*c^2*x*arctan(a*x)^3+1/3*a^4*c^2*x^3*arctan(a*x)^3+5*a*c^2*arctan(a*x)^2*ln(2/(1+I*a*x))-1/2*a*c^2*ln(a^2*x^2+1)+3*a*c^2*arctan(a*x)^2*ln(2-2/(1-I*a*x))-3*I*a*c^2*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))+5*I*a*c^2*arctan(a*x)*polylog(2,1-2/(1+I*a*x))+3/2*a*c^2*polylog(3,-1+2/(1-I*a*x))+5/2*a*c^2*polylog(3,1-2/(1+I*a*x)),1],
[(a^2*c*x^2+c)^2*arctan(a*x)^3/x^3,x,25,-3/2*I*a^2*c^2*polylog(2,1-2/(1+I*a*x))-3/2*a*c^2*arctan(a*x)^2/x-3/2*a^3*c^2*x*arctan(a*x)^2-1/2*c^2*arctan(a*x)^3/x^2+1/2*a^4*c^2*x^2*arctan(a*x)^3+4*a^2*c^2*arctan(a*x)^3*arctanh(1-2/(1+I*a*x))-3*a^2*c^2*arctan(a*x)*ln(2/(1+I*a*x))+3*a^2*c^2*arctan(a*x)*ln(2-2/(1-I*a*x))-3*I*a^2*c^2*arctan(a*x)^2-3*I*a^2*c^2*arctan(a*x)^2*polylog(2,1-2/(1+I*a*x))-3/2*I*a^2*c^2*polylog(4,-1+2/(1+I*a*x))-3/2*I*a^2*c^2*polylog(2,-1+2/(1-I*a*x))-3*a^2*c^2*arctan(a*x)*polylog(3,1-2/(1+I*a*x))+3*a^2*c^2*arctan(a*x)*polylog(3,-1+2/(1+I*a*x))+3*I*a^2*c^2*arctan(a*x)^2*polylog(2,-1+2/(1+I*a*x))+3/2*I*a^2*c^2*polylog(4,1-2/(1+I*a*x)),1],
[(a^2*c*x^2+c)^2*arctan(a*x)^3/x^4,x,26,-a^2*c^2*arctan(a*x)/x-1/2*a^3*c^2*arctan(a*x)^2-1/2*a*c^2*arctan(a*x)^2/x^2-2/3*I*a^3*c^2*arctan(a*x)^3-1/3*c^2*arctan(a*x)^3/x^3-2*a^2*c^2*arctan(a*x)^3/x+a^4*c^2*x*arctan(a*x)^3+a^3*c^2*ln(x)+3*a^3*c^2*arctan(a*x)^2*ln(2/(1+I*a*x))-1/2*a^3*c^2*ln(a^2*x^2+1)+5*a^3*c^2*arctan(a*x)^2*ln(2-2/(1-I*a*x))-5*I*a^3*c^2*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))+3*I*a^3*c^2*arctan(a*x)*polylog(2,1-2/(1+I*a*x))+5/2*a^3*c^2*polylog(3,-1+2/(1-I*a*x))+3/2*a^3*c^2*polylog(3,1-2/(1+I*a*x)),1],
[x^3*(a^2*c*x^2+c)^3*arctan(a*x)^3,x,184,389/12600*c^3*x/a^3-17/9450*c^3*x^3/a-1/252*a*c^3*x^5-1/840*a^3*c^3*x^7-389/12600*c^3*arctan(a*x)/a^4-107/4200*c^3*x^2*arctan(a*x)/a^2+53/2100*c^3*x^4*arctan(a*x)+71/2520*a^2*c^3*x^6*arctan(a*x)+1/120*a^4*c^3*x^8*arctan(a*x)+26/525*I*c^3*arctan(a*x)^2/a^4+3/40*c^3*x*arctan(a*x)^2/a^3-1/40*c^3*x^3*arctan(a*x)^2/a-27/200*a*c^3*x^5*arctan(a*x)^2-33/280*a^3*c^3*x^7*arctan(a*x)^2-1/30*a^5*c^3*x^9*arctan(a*x)^2-1/40*c^3*arctan(a*x)^3/a^4+1/4*c^3*x^4*arctan(a*x)^3+1/2*a^2*c^3*x^6*arctan(a*x)^3+3/8*a^4*c^3*x^8*arctan(a*x)^3+1/10*a^6*c^3*x^10*arctan(a*x)^3+52/525*c^3*arctan(a*x)*ln(2/(1+I*a*x))/a^4+26/525*I*c^3*polylog(2,1-2/(1+I*a*x))/a^4,1],
[x^2*(a^2*c*x^2+c)^3*arctan(a*x)^3,x,132,-107/7560*c^3*x^2/a-11/1260*a*c^3*x^4-1/504*a^3*c^3*x^6-47/1260*c^3*x*arctan(a*x)/a^2+239/3780*c^3*x^3*arctan(a*x)+59/1260*a^2*c^3*x^5*arctan(a*x)+1/84*a^4*c^3*x^7*arctan(a*x)+47/2520*c^3*arctan(a*x)^2/a^3-8/105*c^3*x^2*arctan(a*x)^2/a-89/420*a*c^3*x^4*arctan(a*x)^2-10/63*a^3*c^3*x^6*arctan(a*x)^2-1/24*a^5*c^3*x^8*arctan(a*x)^2-16/315*I*c^3*arctan(a*x)^3/a^3+1/3*c^3*x^3*arctan(a*x)^3+3/5*a^2*c^3*x^5*arctan(a*x)^3+3/7*a^4*c^3*x^7*arctan(a*x)^3+1/9*a^6*c^3*x^9*arctan(a*x)^3-16/105*c^3*arctan(a*x)^2*ln(2/(1+I*a*x))/a^3+31/945*c^3*ln(a^2*x^2+1)/a^3-16/105*I*c^3*arctan(a*x)*polylog(2,1-2/(1+I*a*x))/a^3-8/105*c^3*polylog(3,1-2/(1+I*a*x))/a^3,1],
[x*(a^2*c*x^2+c)^3*arctan(a*x)^3,x,13,-19/140*c^3*x/a-19/840*a*c^3*x^3-1/280*a^3*c^3*x^5+3/35*c^3*(a^2*x^2+1)*arctan(a*x)/a^2+9/280*c^3*(a^2*x^2+1)^2*arctan(a*x)/a^2+1/56*c^3*(a^2*x^2+1)^3*arctan(a*x)/a^2-6/35*I*c^3*arctan(a*x)^2/a^2-6/35*c^3*x*arctan(a*x)^2/a-3/35*c^3*x*(a^2*x^2+1)*arctan(a*x)^2/a-9/140*c^3*x*(a^2*x^2+1)^2*arctan(a*x)^2/a-3/56*c^3*x*(a^2*x^2+1)^3*arctan(a*x)^2/a+1/8*c^3*(a^2*x^2+1)^4*arctan(a*x)^3/a^2-12/35*c^3*arctan(a*x)*ln(2/(1+I*a*x))/a^2-6/35*I*c^3*polylog(2,1-2/(1+I*a*x))/a^2,1],
[(a^2*c*x^2+c)^3*arctan(a*x)^3,x,17,-13/210*c^3*(a^2*x^2+1)/a-1/140*c^3*(a^2*x^2+1)^2/a+14/15*c^3*x*arctan(a*x)+13/105*c^3*x*(a^2*x^2+1)*arctan(a*x)+1/35*c^3*x*(a^2*x^2+1)^2*arctan(a*x)-12/35*c^3*(a^2*x^2+1)*arctan(a*x)^2/a-9/70*c^3*(a^2*x^2+1)^2*arctan(a*x)^2/a-1/14*c^3*(a^2*x^2+1)^3*arctan(a*x)^2/a+48/35*I*c^3*arctan(a*x)*polylog(2,1-2/(1+I*a*x))/a+16/35*c^3*x*arctan(a*x)^3+8/35*c^3*x*(a^2*x^2+1)*arctan(a*x)^3+6/35*c^3*x*(a^2*x^2+1)^2*arctan(a*x)^3+1/7*c^3*x*(a^2*x^2+1)^3*arctan(a*x)^3+48/35*c^3*arctan(a*x)^2*ln(2/(1+I*a*x))/a-7/15*c^3*ln(a^2*x^2+1)/a+16/35*I*c^3*arctan(a*x)^3/a+24/35*c^3*polylog(3,1-2/(1+I*a*x))/a,1],
[(a^2*c*x^2+c)^3*arctan(a*x)^3/x,x,69,-13/30*a*c^3*x-1/60*a^3*c^3*x^3+13/30*c^3*arctan(a*x)+29/60*a^2*c^3*x^2*arctan(a*x)+1/20*a^4*c^3*x^4*arctan(a*x)-3/2*I*c^3*arctan(a*x)^2*polylog(2,1-2/(1+I*a*x))-11/4*a*c^3*x*arctan(a*x)^2-7/12*a^3*c^3*x^3*arctan(a*x)^2-1/10*a^5*c^3*x^5*arctan(a*x)^2+11/12*c^3*arctan(a*x)^3+3/2*a^2*c^3*x^2*arctan(a*x)^3+3/4*a^4*c^3*x^4*arctan(a*x)^3+1/6*a^6*c^3*x^6*arctan(a*x)^3+2*c^3*arctan(a*x)^3*arctanh(1-2/(1+I*a*x))-68/15*c^3*arctan(a*x)*ln(2/(1+I*a*x))+3/2*I*c^3*arctan(a*x)^2*polylog(2,-1+2/(1+I*a*x))-34/15*I*c^3*arctan(a*x)^2+3/4*I*c^3*polylog(4,1-2/(1+I*a*x))-3/2*c^3*arctan(a*x)*polylog(3,1-2/(1+I*a*x))+3/2*c^3*arctan(a*x)*polylog(3,-1+2/(1+I*a*x))-3/4*I*c^3*polylog(4,-1+2/(1+I*a*x))-34/15*I*c^3*polylog(2,1-2/(1+I*a*x)),1],
[(a^2*c*x^2+c)^3*arctan(a*x)^3/x^2,x,45,-1/20*a^3*c^3*x^2+21/10*a^2*c^3*x*arctan(a*x)+1/10*a^4*c^3*x^3*arctan(a*x)-21/20*a*c^3*arctan(a*x)^2-6/5*a^3*c^3*x^2*arctan(a*x)^2-3/20*a^5*c^3*x^4*arctan(a*x)^2+33/5*I*a*c^3*arctan(a*x)*polylog(2,1-2/(1+I*a*x))-c^3*arctan(a*x)^3/x+3*a^2*c^3*x*arctan(a*x)^3+a^4*c^3*x^3*arctan(a*x)^3+1/5*a^6*c^3*x^5*arctan(a*x)^3+33/5*a*c^3*arctan(a*x)^2*ln(2/(1+I*a*x))-a*c^3*ln(a^2*x^2+1)+3*a*c^3*arctan(a*x)^2*ln(2-2/(1-I*a*x))+6/5*I*a*c^3*arctan(a*x)^3-3*I*a*c^3*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))+3/2*a*c^3*polylog(3,-1+2/(1-I*a*x))+33/10*a*c^3*polylog(3,1-2/(1+I*a*x)),1],
[(a^2*c*x^2+c)^3*arctan(a*x)^3/x^3,x,43,-1/4*a^3*c^3*x+1/4*a^2*c^3*arctan(a*x)+1/4*a^4*c^3*x^2*arctan(a*x)-9/4*I*a^2*c^3*polylog(4,-1+2/(1+I*a*x))-3/2*a*c^3*arctan(a*x)^2/x-15/4*a^3*c^3*x*arctan(a*x)^2-1/4*a^5*c^3*x^3*arctan(a*x)^2+3/4*a^2*c^3*arctan(a*x)^3-1/2*c^3*arctan(a*x)^3/x^2+3/2*a^4*c^3*x^2*arctan(a*x)^3+1/4*a^6*c^3*x^4*arctan(a*x)^3+6*a^2*c^3*arctan(a*x)^3*arctanh(1-2/(1+I*a*x))-7*a^2*c^3*arctan(a*x)*ln(2/(1+I*a*x))+3*a^2*c^3*arctan(a*x)*ln(2-2/(1-I*a*x))+9/4*I*a^2*c^3*polylog(4,1-2/(1+I*a*x))-7/2*I*a^2*c^3*polylog(2,1-2/(1+I*a*x))-3/2*I*a^2*c^3*polylog(2,-1+2/(1-I*a*x))-5*I*a^2*c^3*arctan(a*x)^2-9/2*a^2*c^3*arctan(a*x)*polylog(3,1-2/(1+I*a*x))+9/2*a^2*c^3*arctan(a*x)*polylog(3,-1+2/(1+I*a*x))+9/2*I*a^2*c^3*arctan(a*x)^2*polylog(2,-1+2/(1+I*a*x))-9/2*I*a^2*c^3*arctan(a*x)^2*polylog(2,1-2/(1+I*a*x)),1],
[(a^2*c*x^2+c)^3*arctan(a*x)^3/x^4,x,37,-a^2*c^3*arctan(a*x)/x+a^4*c^3*x*arctan(a*x)-a^3*c^3*arctan(a*x)^2-1/2*a*c^3*arctan(a*x)^2/x^2-1/2*a^5*c^3*x^2*arctan(a*x)^2-1/3*c^3*arctan(a*x)^3/x^3-3*a^2*c^3*arctan(a*x)^3/x+3*a^4*c^3*x*arctan(a*x)^3+1/3*a^6*c^3*x^3*arctan(a*x)^3+a^3*c^3*ln(x)+8*a^3*c^3*arctan(a*x)^2*ln(2/(1+I*a*x))-a^3*c^3*ln(a^2*x^2+1)+8*a^3*c^3*arctan(a*x)^2*ln(2-2/(1-I*a*x))+8*I*a^3*c^3*arctan(a*x)*polylog(2,1-2/(1+I*a*x))-8*I*a^3*c^3*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))+4*a^3*c^3*polylog(3,-1+2/(1-I*a*x))+4*a^3*c^3*polylog(3,1-2/(1+I*a*x)),1],
[x^4*arctan(a*x)^3/(a^2*c*x^2+c),x,19,x*arctan(a*x)/a^4/c-1/2*arctan(a*x)^2/a^5/c-1/2*x^2*arctan(a*x)^2/a^3/c-4/3*I*arctan(a*x)^3/a^5/c-x*arctan(a*x)^3/a^4/c+1/3*x^3*arctan(a*x)^3/a^2/c+1/4*arctan(a*x)^4/a^5/c-4*arctan(a*x)^2*ln(2/(1+I*a*x))/a^5/c-1/2*ln(a^2*x^2+1)/a^5/c-4*I*arctan(a*x)*polylog(2,1-2/(1+I*a*x))/a^5/c-2*polylog(3,1-2/(1+I*a*x))/a^5/c,1],
[x^3*arctan(a*x)^3/(a^2*c*x^2+c),x,14,-3/2*I*arctan(a*x)^2/a^4/c-3/2*x*arctan(a*x)^2/a^3/c+1/2*arctan(a*x)^3/a^4/c+1/2*x^2*arctan(a*x)^3/a^2/c+1/4*I*arctan(a*x)^4/a^4/c-3*arctan(a*x)*ln(2/(1+I*a*x))/a^4/c+arctan(a*x)^3*ln(2/(1+I*a*x))/a^4/c-3/2*I*polylog(2,1-2/(1+I*a*x))/a^4/c+3/2*I*arctan(a*x)^2*polylog(2,1-2/(1+I*a*x))/a^4/c+3/2*arctan(a*x)*polylog(3,1-2/(1+I*a*x))/a^4/c-3/4*I*polylog(4,1-2/(1+I*a*x))/a^4/c,1],
[x^2*arctan(a*x)^3/(a^2*c*x^2+c),x,7,I*arctan(a*x)^3/a^3/c+x*arctan(a*x)^3/a^2/c-1/4*arctan(a*x)^4/a^3/c+3*arctan(a*x)^2*ln(2/(1+I*a*x))/a^3/c+3*I*arctan(a*x)*polylog(2,1-2/(1+I*a*x))/a^3/c+3/2*polylog(3,1-2/(1+I*a*x))/a^3/c,1],
[x*arctan(a*x)^3/(a^2*c*x^2+c),x,5,-1/4*I*arctan(a*x)^4/a^2/c-arctan(a*x)^3*ln(2/(1+I*a*x))/a^2/c-3/2*I*arctan(a*x)^2*polylog(2,1-2/(1+I*a*x))/a^2/c-3/2*arctan(a*x)*polylog(3,1-2/(1+I*a*x))/a^2/c+3/4*I*polylog(4,1-2/(1+I*a*x))/a^2/c,1],
[arctan(a*x)^3/(a^2*c*x^2+c),x,1,1/4*arctan(a*x)^4/a/c,1],
[arctan(a*x)^3/x/(a^2*c*x^2+c),x,5,-1/4*I*arctan(a*x)^4/c+arctan(a*x)^3*ln(2-2/(1-I*a*x))/c-3/2*I*arctan(a*x)^2*polylog(2,-1+2/(1-I*a*x))/c+3/2*arctan(a*x)*polylog(3,-1+2/(1-I*a*x))/c+3/4*I*polylog(4,-1+2/(1-I*a*x))/c,1],
[arctan(a*x)^3/x^2/(a^2*c*x^2+c),x,7,-I*a*arctan(a*x)^3/c-arctan(a*x)^3/c/x-1/4*a*arctan(a*x)^4/c+3*a*arctan(a*x)^2*ln(2-2/(1-I*a*x))/c-3*I*a*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))/c+3/2*a*polylog(3,-1+2/(1-I*a*x))/c,1],
[arctan(a*x)^3/x^3/(a^2*c*x^2+c),x,13,-3/2*I*a^2*arctan(a*x)^2/c-3/2*a*arctan(a*x)^2/c/x-1/2*a^2*arctan(a*x)^3/c-1/2*arctan(a*x)^3/c/x^2+1/4*I*a^2*arctan(a*x)^4/c+3*a^2*arctan(a*x)*ln(2-2/(1-I*a*x))/c-a^2*arctan(a*x)^3*ln(2-2/(1-I*a*x))/c-3/2*I*a^2*polylog(2,-1+2/(1-I*a*x))/c+3/2*I*a^2*arctan(a*x)^2*polylog(2,-1+2/(1-I*a*x))/c-3/2*a^2*arctan(a*x)*polylog(3,-1+2/(1-I*a*x))/c-3/4*I*a^2*polylog(4,-1+2/(1-I*a*x))/c,1],
[arctan(a*x)^3/x^4/(a^2*c*x^2+c),x,22,-a^2*arctan(a*x)/c/x-1/2*a^3*arctan(a*x)^2/c-1/2*a*arctan(a*x)^2/c/x^2+4/3*I*a^3*arctan(a*x)^3/c-1/3*arctan(a*x)^3/c/x^3+a^2*arctan(a*x)^3/c/x+1/4*a^3*arctan(a*x)^4/c+a^3*ln(x)/c-1/2*a^3*ln(a^2*x^2+1)/c-4*a^3*arctan(a*x)^2*ln(2-2/(1-I*a*x))/c+4*I*a^3*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))/c-2*a^3*polylog(3,-1+2/(1-I*a*x))/c,1],
[x^3*arctan(a*x)^3/(a^2*c*x^2+c)^2,x,11,3/8*x/a^3/c^2/(a^2*x^2+1)+3/8*arctan(a*x)/a^4/c^2-3/4*arctan(a*x)/a^4/c^2/(a^2*x^2+1)-3/4*x*arctan(a*x)^2/a^3/c^2/(a^2*x^2+1)-1/4*arctan(a*x)^3/a^4/c^2+1/2*arctan(a*x)^3/a^4/c^2/(a^2*x^2+1)-1/4*I*arctan(a*x)^4/a^4/c^2-arctan(a*x)^3*ln(2/(1+I*a*x))/a^4/c^2-3/2*I*arctan(a*x)^2*polylog(2,1-2/(1+I*a*x))/a^4/c^2-3/2*arctan(a*x)*polylog(3,1-2/(1+I*a*x))/a^4/c^2+3/4*I*polylog(4,1-2/(1+I*a*x))/a^4/c^2,1],
[x^2*arctan(a*x)^3/(a^2*c*x^2+c)^2,x,4,3/8/a^3/c^2/(a^2*x^2+1)+3/4*x*arctan(a*x)/a^2/c^2/(a^2*x^2+1)+3/8*arctan(a*x)^2/a^3/c^2-3/4*arctan(a*x)^2/a^3/c^2/(a^2*x^2+1)-1/2*x*arctan(a*x)^3/a^2/c^2/(a^2*x^2+1)+1/8*arctan(a*x)^4/a^3/c^2,1],
[x*arctan(a*x)^3/(a^2*c*x^2+c)^2,x,5,-3/8*x/a/c^2/(a^2*x^2+1)-3/8*arctan(a*x)/a^2/c^2+3/4*arctan(a*x)/a^2/c^2/(a^2*x^2+1)+3/4*x*arctan(a*x)^2/a/c^2/(a^2*x^2+1)+1/4*arctan(a*x)^3/a^2/c^2-1/2*arctan(a*x)^3/a^2/c^2/(a^2*x^2+1),1],
[arctan(a*x)^3/(a^2*c*x^2+c)^2,x,4,-3/8/a/c^2/(a^2*x^2+1)-3/4*x*arctan(a*x)/c^2/(a^2*x^2+1)-3/8*arctan(a*x)^2/a/c^2+3/4*arctan(a*x)^2/a/c^2/(a^2*x^2+1)+1/2*x*arctan(a*x)^3/c^2/(a^2*x^2+1)+1/8*arctan(a*x)^4/a/c^2,1],
[arctan(a*x)^3/x/(a^2*c*x^2+c)^2,x,11,3/8*a*x/c^2/(a^2*x^2+1)+3/8*arctan(a*x)/c^2-3/4*arctan(a*x)/c^2/(a^2*x^2+1)-3/4*a*x*arctan(a*x)^2/c^2/(a^2*x^2+1)-1/4*arctan(a*x)^3/c^2+1/2*arctan(a*x)^3/c^2/(a^2*x^2+1)-1/4*I*arctan(a*x)^4/c^2+arctan(a*x)^3*ln(2-2/(1-I*a*x))/c^2-3/2*I*arctan(a*x)^2*polylog(2,-1+2/(1-I*a*x))/c^2+3/2*arctan(a*x)*polylog(3,-1+2/(1-I*a*x))/c^2+3/4*I*polylog(4,-1+2/(1-I*a*x))/c^2,1],
[arctan(a*x)^3/x^2/(a^2*c*x^2+c)^2,x,12,3/8*a/c^2/(a^2*x^2+1)+3/4*a^2*x*arctan(a*x)/c^2/(a^2*x^2+1)+3/8*a*arctan(a*x)^2/c^2-3/4*a*arctan(a*x)^2/c^2/(a^2*x^2+1)-I*a*arctan(a*x)^3/c^2-arctan(a*x)^3/c^2/x-1/2*a^2*x*arctan(a*x)^3/c^2/(a^2*x^2+1)-3/8*a*arctan(a*x)^4/c^2+3*a*arctan(a*x)^2*ln(2-2/(1-I*a*x))/c^2-3*I*a*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))/c^2+3/2*a*polylog(3,-1+2/(1-I*a*x))/c^2,1],
[arctan(a*x)^3/x^3/(a^2*c*x^2+c)^2,x,25,-3/8*a^3*x/c^2/(a^2*x^2+1)-3/8*a^2*arctan(a*x)/c^2+3/4*a^2*arctan(a*x)/c^2/(a^2*x^2+1)+3*I*a^2*arctan(a*x)^2*polylog(2,-1+2/(1-I*a*x))/c^2-3/2*a*arctan(a*x)^2/c^2/x+3/4*a^3*x*arctan(a*x)^2/c^2/(a^2*x^2+1)-1/4*a^2*arctan(a*x)^3/c^2-1/2*arctan(a*x)^3/c^2/x^2-1/2*a^2*arctan(a*x)^3/c^2/(a^2*x^2+1)+1/2*I*a^2*arctan(a*x)^4/c^2+3*a^2*arctan(a*x)*ln(2-2/(1-I*a*x))/c^2-2*a^2*arctan(a*x)^3*ln(2-2/(1-I*a*x))/c^2-3/2*I*a^2*polylog(2,-1+2/(1-I*a*x))/c^2-3/2*I*a^2*arctan(a*x)^2/c^2-3*a^2*arctan(a*x)*polylog(3,-1+2/(1-I*a*x))/c^2-3/2*I*a^2*polylog(4,-1+2/(1-I*a*x))/c^2,1],
[arctan(a*x)^3/x^4/(a^2*c*x^2+c)^2,x,35,-3/8*a^3/c^2/(a^2*x^2+1)-a^2*arctan(a*x)/c^2/x-3/4*a^4*x*arctan(a*x)/c^2/(a^2*x^2+1)-7/8*a^3*arctan(a*x)^2/c^2-1/2*a*arctan(a*x)^2/c^2/x^2+3/4*a^3*arctan(a*x)^2/c^2/(a^2*x^2+1)+7*I*a^3*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))/c^2-1/3*arctan(a*x)^3/c^2/x^3+2*a^2*arctan(a*x)^3/c^2/x+1/2*a^4*x*arctan(a*x)^3/c^2/(a^2*x^2+1)+5/8*a^3*arctan(a*x)^4/c^2+a^3*ln(x)/c^2-1/2*a^3*ln(a^2*x^2+1)/c^2-7*a^3*arctan(a*x)^2*ln(2-2/(1-I*a*x))/c^2+7/3*I*a^3*arctan(a*x)^3/c^2-7/2*a^3*polylog(3,-1+2/(1-I*a*x))/c^2,1],
[x^3*arctan(a*x)^3/(a^2*c*x^2+c)^3,x,9,-3/128*x^3/a/c^3/(a^2*x^2+1)^2-45/256*x/a^3/c^3/(a^2*x^2+1)-27/256*arctan(a*x)/a^4/c^3-3/32*x^4*arctan(a*x)/c^3/(a^2*x^2+1)^2+9/32*arctan(a*x)/a^4/c^3/(a^2*x^2+1)+3/16*x^3*arctan(a*x)^2/a/c^3/(a^2*x^2+1)^2+9/32*x*arctan(a*x)^2/a^3/c^3/(a^2*x^2+1)-3/32*arctan(a*x)^3/a^4/c^3+1/4*x^4*arctan(a*x)^3/c^3/(a^2*x^2+1)^2,1],
[x^2*arctan(a*x)^3/(a^2*c*x^2+c)^3,x,13,3/128/a^3/c^3/(a^2*x^2+1)^2-3/128/a^3/c^3/(a^2*x^2+1)+3/32*x*arctan(a*x)/a^2/c^3/(a^2*x^2+1)^2-3/64*x*arctan(a*x)/a^2/c^3/(a^2*x^2+1)-3/128*arctan(a*x)^2/a^3/c^3-3/16*arctan(a*x)^2/a^3/c^3/(a^2*x^2+1)^2+3/16*arctan(a*x)^2/a^3/c^3/(a^2*x^2+1)-1/4*x*arctan(a*x)^3/a^2/c^3/(a^2*x^2+1)^2+1/8*x*arctan(a*x)^3/a^2/c^3/(a^2*x^2+1)+1/32*arctan(a*x)^4/a^3/c^3,1],
[x*arctan(a*x)^3/(a^2*c*x^2+c)^3,x,9,-3/128*x/a/c^3/(a^2*x^2+1)^2-45/256*x/a/c^3/(a^2*x^2+1)-45/256*arctan(a*x)/a^2/c^3+3/32*arctan(a*x)/a^2/c^3/(a^2*x^2+1)^2+9/32*arctan(a*x)/a^2/c^3/(a^2*x^2+1)+3/16*x*arctan(a*x)^2/a/c^3/(a^2*x^2+1)^2+9/32*x*arctan(a*x)^2/a/c^3/(a^2*x^2+1)+3/32*arctan(a*x)^3/a^2/c^3-1/4*arctan(a*x)^3/a^2/c^3/(a^2*x^2+1)^2,1],
[arctan(a*x)^3/(a^2*c*x^2+c)^3,x,8,-3/128/a/c^3/(a^2*x^2+1)^2-45/128/a/c^3/(a^2*x^2+1)-3/32*x*arctan(a*x)/c^3/(a^2*x^2+1)^2-45/64*x*arctan(a*x)/c^3/(a^2*x^2+1)-45/128*arctan(a*x)^2/a/c^3+3/16*arctan(a*x)^2/a/c^3/(a^2*x^2+1)^2+9/16*arctan(a*x)^2/a/c^3/(a^2*x^2+1)+1/4*x*arctan(a*x)^3/c^3/(a^2*x^2+1)^2+3/8*x*arctan(a*x)^3/c^3/(a^2*x^2+1)+3/32*arctan(a*x)^4/a/c^3,1],
[arctan(a*x)^3/x/(a^2*c*x^2+c)^3,x,21,3/128*a*x/c^3/(a^2*x^2+1)^2+141/256*a*x/c^3/(a^2*x^2+1)+141/256*arctan(a*x)/c^3-3/32*arctan(a*x)/c^3/(a^2*x^2+1)^2-33/32*arctan(a*x)/c^3/(a^2*x^2+1)-3/16*a*x*arctan(a*x)^2/c^3/(a^2*x^2+1)^2-33/32*a*x*arctan(a*x)^2/c^3/(a^2*x^2+1)-11/32*arctan(a*x)^3/c^3+1/4*arctan(a*x)^3/c^3/(a^2*x^2+1)^2+1/2*arctan(a*x)^3/c^3/(a^2*x^2+1)-1/4*I*arctan(a*x)^4/c^3+arctan(a*x)^3*ln(2-2/(1-I*a*x))/c^3-3/2*I*arctan(a*x)^2*polylog(2,-1+2/(1-I*a*x))/c^3+3/2*arctan(a*x)*polylog(3,-1+2/(1-I*a*x))/c^3+3/4*I*polylog(4,-1+2/(1-I*a*x))/c^3,1],
[arctan(a*x)^3/x^2/(a^2*c*x^2+c)^3,x,21,3/128*a/c^3/(a^2*x^2+1)^2+93/128*a/c^3/(a^2*x^2+1)+3/32*a^2*x*arctan(a*x)/c^3/(a^2*x^2+1)^2+93/64*a^2*x*arctan(a*x)/c^3/(a^2*x^2+1)+93/128*a*arctan(a*x)^2/c^3-3/16*a*arctan(a*x)^2/c^3/(a^2*x^2+1)^2-21/16*a*arctan(a*x)^2/c^3/(a^2*x^2+1)-I*a*arctan(a*x)^3/c^3-arctan(a*x)^3/c^3/x-1/4*a^2*x*arctan(a*x)^3/c^3/(a^2*x^2+1)^2-7/8*a^2*x*arctan(a*x)^3/c^3/(a^2*x^2+1)-15/32*a*arctan(a*x)^4/c^3+3*a*arctan(a*x)^2*ln(2-2/(1-I*a*x))/c^3-3*I*a*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))/c^3+3/2*a*polylog(3,-1+2/(1-I*a*x))/c^3,1],
[arctan(a*x)^3/x^3/(a^2*c*x^2+c)^3,x,47,-3/128*a^3*x/c^3/(a^2*x^2+1)^2-237/256*a^3*x/c^3/(a^2*x^2+1)-237/256*a^2*arctan(a*x)/c^3+3/32*a^2*arctan(a*x)/c^3/(a^2*x^2+1)^2+57/32*a^2*arctan(a*x)/c^3/(a^2*x^2+1)+9/2*I*a^2*arctan(a*x)^2*polylog(2,-1+2/(1-I*a*x))/c^3-3/2*a*arctan(a*x)^2/c^3/x+3/16*a^3*x*arctan(a*x)^2/c^3/(a^2*x^2+1)^2+57/32*a^3*x*arctan(a*x)^2/c^3/(a^2*x^2+1)+3/32*a^2*arctan(a*x)^3/c^3-1/2*arctan(a*x)^3/c^3/x^2-1/4*a^2*arctan(a*x)^3/c^3/(a^2*x^2+1)^2-a^2*arctan(a*x)^3/c^3/(a^2*x^2+1)-3/2*I*a^2*polylog(2,-1+2/(1-I*a*x))/c^3+3*a^2*arctan(a*x)*ln(2-2/(1-I*a*x))/c^3-3*a^2*arctan(a*x)^3*ln(2-2/(1-I*a*x))/c^3-3/2*I*a^2*arctan(a*x)^2/c^3-9/4*I*a^2*polylog(4,-1+2/(1-I*a*x))/c^3-9/2*a^2*arctan(a*x)*polylog(3,-1+2/(1-I*a*x))/c^3+3/4*I*a^2*arctan(a*x)^4/c^3,1],
[arctan(a*x)^3/x^4/(a^2*c*x^2+c)^3,x,57,-3/128*a^3/c^3/(a^2*x^2+1)^2-141/128*a^3/c^3/(a^2*x^2+1)-a^2*arctan(a*x)/c^3/x-3/32*a^4*x*arctan(a*x)/c^3/(a^2*x^2+1)^2-141/64*a^4*x*arctan(a*x)/c^3/(a^2*x^2+1)-205/128*a^3*arctan(a*x)^2/c^3-1/2*a*arctan(a*x)^2/c^3/x^2+3/16*a^3*arctan(a*x)^2/c^3/(a^2*x^2+1)^2+33/16*a^3*arctan(a*x)^2/c^3/(a^2*x^2+1)+10*I*a^3*arctan(a*x)*polylog(2,-1+2/(1-I*a*x))/c^3-1/3*arctan(a*x)^3/c^3/x^3+3*a^2*arctan(a*x)^3/c^3/x+1/4*a^4*x*arctan(a*x)^3/c^3/(a^2*x^2+1)^2+11/8*a^4*x*arctan(a*x)^3/c^3/(a^2*x^2+1)+35/32*a^3*arctan(a*x)^4/c^3+a^3*ln(x)/c^3-1/2*a^3*ln(a^2*x^2+1)/c^3-10*a^3*arctan(a*x)^2*ln(2-2/(1-I*a*x))/c^3+10/3*I*a^3*arctan(a*x)^3/c^3-5*a^3*polylog(3,-1+2/(1-I*a*x))/c^3,1],
[x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)^3,x,71,-1/20*x*sqrt(a^2*c*x^2+c)/a^3-9/20*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^4+1/10*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2+1/8*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^3-3/20*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a-11/20*I*c*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^4/sqrt(a^2*c*x^2+c)-2/15*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/a^4+1/15*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/a^2+1/5*x^4*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+1/2*sqrt(c)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^4+11/20*I*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^4/sqrt(a^2*c*x^2+c)-11/20*I*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^4/sqrt(a^2*c*x^2+c)-11/20*c*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^4/sqrt(a^2*c*x^2+c)+11/20*c*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^4/sqrt(a^2*c*x^2+c),1],
[x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^3,x,40,-1/4*sqrt(a^2*c*x^2+c)/a^3+1/4*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2+1/8*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^3-1/4*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a+1/8*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/a^2+1/4*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)^3-1/2*I*c*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)+1/4*I*c*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/a^3/sqrt(a^2*c*x^2+c)-3/8*I*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-3/4*I*c*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+I*c*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)+1/2*I*c*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)+3/4*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-3/4*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+3/4*I*c*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+3/8*I*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c),1],
[x*sqrt(a^2*c*x^2+c)*arctan(a*x)^3,x,13,sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2-1/2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a+I*c*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^2/sqrt(a^2*c*x^2+c)+1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/a^2/c-sqrt(c)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^2-I*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c)+I*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c)+c*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c)-c*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^3,x,14,-3/2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a+1/2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^3-I*c*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/a/sqrt(a^2*c*x^2+c)-6*I*c*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)+3/2*I*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-3/2*I*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+3*I*c*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)-3*I*c*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)-3*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+3*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-3*I*c*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+3*I*c*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^3/x,x,22,6*I*c*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/sqrt(a^2*c*x^2+c)+sqrt(a^2*c*x^2+c)*arctan(a*x)^3-2*c*sqrt(a^2*x^2+1)*arctan(a*x)^3*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*I*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*I*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*I*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*I*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*c*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*c*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*I*c*sqrt(a^2*x^2+1)*polylog(4,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*I*c*sqrt(a^2*x^2+1)*polylog(4,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^3/x^2,x,22,-sqrt(a^2*c*x^2+c)*arctan(a*x)^3/x-2*I*a*c*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/sqrt(a^2*c*x^2+c)-6*a*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*I*a*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*I*a*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*I*a*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*I*a*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*a*c*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*a*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*a*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*a*c*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*I*a*c*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*I*a*c*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^3/x^3,x,27,-3/2*a*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x-1/2*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/x^2-a^2*c*sqrt(a^2*x^2+1)*arctan(a*x)^3*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*a^2*c*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+3/2*I*a^2*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3/2*I*a^2*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*I*a^2*c*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-3*I*a^2*c*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-3*a^2*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*a^2*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*I*a^2*c*sqrt(a^2*x^2+1)*polylog(4,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*I*a^2*c*sqrt(a^2*x^2+1)*polylog(4,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^3/x^4,x,25,-a^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/x-1/2*a*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x^2-1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/c/x^3-a^3*c*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-a^3*sqrt(c)*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))+I*a^3*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-I*a^3*c*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-a^3*c*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+a^3*c*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[x^3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x,200,1/420*c*x*sqrt(a^2*c*x^2+c)/a^3-1/140*c*x^3*sqrt(a^2*c*x^2+c)/a-163/840*c*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^4+1/60*c*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2+1/35*c*x^4*sqrt(a^2*c*x^2+c)*arctan(a*x)+9/112*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^3-23/280*c*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a-1/14*a*c*x^5*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-51/280*I*c^2*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^4/sqrt(a^2*c*x^2+c)-2/35*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/a^4+1/35*c*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/a^2+8/35*c*x^4*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+1/7*a^2*c*x^6*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+23/120*c^(3/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^4-51/280*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^4/sqrt(a^2*c*x^2+c)+51/280*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^4/sqrt(a^2*c*x^2+c)-51/280*c^2*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^4/sqrt(a^2*c*x^2+c)+51/280*c^2*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^4/sqrt(a^2*c*x^2+c),1],
[x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x,108,-1/30*c*sqrt(a^2*c*x^2+c)/a^3-1/60*(a^2*c*x^2+c)^(3/2)/a^3+1/12*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2+1/20*c*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)+31/240*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^3-19/120*c*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a-1/10*a*c*x^4*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+1/16*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/a^2+7/24*c*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+1/6*a^2*c*x^5*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+1/8*I*c^2*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/a^3/sqrt(a^2*c*x^2+c)+3/16*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-3/16*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+41/60*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)+41/120*I*c^2*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)+3/8*I*c^2*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+3/8*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-3/8*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-3/8*I*c^2*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-41/120*I*c^2*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c),1],
[x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x,17,-1/20*c*x*sqrt(a^2*c*x^2+c)/a+9/20*c*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2+1/10*(a^2*c*x^2+c)^(3/2)*arctan(a*x)/a^2-9/40*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a-3/20*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/a+9/20*I*c^2*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^2/sqrt(a^2*c*x^2+c)+1/5*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/a^2/c-1/2*c^(3/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^2-9/20*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c)+9/20*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c)+9/20*c^2*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c)-9/20*c^2*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x,18,-1/4*c*sqrt(a^2*c*x^2+c)/a+1/4*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)-9/8*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a-1/4*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/a+3/8*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+1/4*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3-5/2*I*c^2*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)-9/4*I*c^2*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+5/2*I*c^2*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)-3/4*I*c^2*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/a/sqrt(a^2*c*x^2+c)+9/4*I*c^2*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-9/8*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-9/4*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+9/4*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+9/8*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-5*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x,x,36,c*sqrt(a^2*c*x^2+c)*arctan(a*x)-1/2*a*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-6*I*c^2*sqrt(a^2*x^2+1)*polylog(4,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+c*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3-2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^3*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-c^(3/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))+7*I*c^2*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/sqrt(a^2*c*x^2+c)+7*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+7*c^2*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-7*c^2*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*I*c^2*sqrt(a^2*x^2+1)*polylog(4,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-7*I*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^2,x,37,-3/2*a*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-c*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/x+1/2*a^2*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+9*I*a*c^2*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-9/2*I*a*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*a*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*I*a*c^2*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-6*I*a*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+9/2*I*a*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*I*a*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+3*I*a*c^2*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+6*I*a*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*a*c^2*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-9*a*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+9*a*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*a*c^2*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-9*I*a*c^2*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*I*a*c^2*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^3,x,50,-3/2*a*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x-6*I*a^2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+a^2*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^3-1/2*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/x^2-3*a^2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^3*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*a^2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+9/2*I*a^2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*I*a^2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*I*a^2*c^2*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+9*I*a^2*c^2*sqrt(a^2*x^2+1)*polylog(4,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-9*I*a^2*c^2*sqrt(a^2*x^2+1)*polylog(4,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*I*a^2*c^2*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-9*a^2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*a^2*c^2*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*a^2*c^2*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+9*a^2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-9/2*I*a^2*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*I*a^2*c^2*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^4,x,48,-a^2*c*sqrt(a^2*c*x^2+c)*arctan(a*x)/x-1/2*a*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x^2-a^2*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/x-1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^3+6*I*a^3*c^2*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-7*a^3*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-a^3*c^(3/2)*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))-3*I*a^3*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*I*a^3*c^2*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-7*I*a^3*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-2*I*a^3*c^2*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/sqrt(a^2*c*x^2+c)-7*a^3*c^2*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*a^3*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*a^3*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+7*a^3*c^2*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+7*I*a^3*c^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*I*a^3*c^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x,293,13/6720*c^2*sqrt(a^2*c*x^2+c)/a^3-3/560*c*(a^2*c*x^2+c)^(3/2)/a^3-1/280*(a^2*c*x^2+c)^(5/2)/a^3+43/1344*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2+29/560*c^2*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/56*a^2*c^2*x^5*sqrt(a^2*c*x^2+c)*arctan(a*x)+1373/13440*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^3-737/6720*c^2*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a-83/560*a*c^2*x^4*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-3/56*a^3*c^2*x^6*sqrt(a^2*c*x^2+c)*arctan(a*x)^2+5/128*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/a^2+59/192*c^2*x^3*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+17/48*a^2*c^2*x^5*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+1/8*a^4*c^2*x^7*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+15/64*I*c^3*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+15/128*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+397/1680*I*c^3*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)-397/1680*I*c^3*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)-15/128*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-15/64*I*c^3*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+15/64*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-15/64*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+5/64*I*c^3*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/a^3/sqrt(a^2*c*x^2+c)+397/840*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c),1],
[x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x,22,-17/420*c^2*x*sqrt(a^2*c*x^2+c)/a-1/140*c*x*(a^2*c*x^2+c)^(3/2)/a+15/56*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/a^2+5/84*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)/a^2+1/35*(a^2*c*x^2+c)^(5/2)*arctan(a*x)/a^2-15/112*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a-5/56*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/a-1/14*x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/a+15/56*I*c^3*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^2/sqrt(a^2*c*x^2+c)+1/7*(a^2*c*x^2+c)^(7/2)*arctan(a*x)^3/a^2/c-37/120*c^(5/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^2-15/56*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c)+15/56*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c)+15/56*c^3*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c)-15/56*c^3*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x,23,-17/60*c^2*sqrt(a^2*c*x^2+c)/a-1/60*c*(a^2*c*x^2+c)^(3/2)/a+17/60*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/20*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)-15/16*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a-5/24*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/a-1/10*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/a+5/16*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+5/24*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3+1/6*x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3-15/8*I*c^3*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-259/120*I*c^3*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)-5/8*I*c^3*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/a/sqrt(a^2*c*x^2+c)-15/16*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+15/8*I*c^3*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+259/120*I*c^3*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c)-15/8*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+15/8*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+15/16*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-259/60*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x,x,54,-1/20*a*c^2*x*sqrt(a^2*c*x^2+c)+29/20*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)+1/10*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)-29/40*a*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-3/20*a*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2+149/20*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+1/3*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3+1/5*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3-2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^3*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3/2*c^(5/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))+3*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-149/20*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*I*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*I*c^3*sqrt(a^2*x^2+1)*polylog(4,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+149/20*c^3*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-149/20*c^3*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*I*c^3*sqrt(a^2*x^2+1)*polylog(4,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+149/20*I*c^3*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x^2,x,56,-1/4*a*c^2*sqrt(a^2*c*x^2+c)+1/4*a^2*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)-21/8*a*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-1/4*a*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2-c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/x+7/8*a^2*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^3+1/4*a^2*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3+6*I*a*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*I*a*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*a*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+45/4*I*a*c^3*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-11*I*a*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+45/8*I*a*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-45/8*I*a*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-11/2*I*a*c^3*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-15/4*I*a*c^3*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/sqrt(a^2*c*x^2+c)-6*a*c^3*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-45/4*a*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+45/4*a*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*a*c^3*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-45/4*I*a*c^3*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+11/2*I*a*c^3*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x^3,x,87,a^2*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)-3/2*a*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x-1/2*a^3*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-15/2*I*a^2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+2*a^2*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^3-1/2*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/x^2+1/3*a^2*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3-5*a^2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^3*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*a^2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-a^2*c^(5/2)*arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))+3*I*a^2*c^3*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-3*I*a^2*c^3*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-15*I*a^2*c^3*sqrt(a^2*x^2+1)*polylog(4,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+13*I*a^2*c^3*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/sqrt(a^2*c*x^2+c)+15/2*I*a^2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-13*I*a^2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-15*a^2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+13*a^2*c^3*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-13*a^2*c^3*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+15*a^2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+13*I*a^2*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+15*I*a^2*c^3*sqrt(a^2*x^2+1)*polylog(4,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x^4,x,86,-a^2*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/x-3/2*a^3*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2-1/2*a*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/x^2-2*a^2*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/x+1/2*a^4*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^3-1/3*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^3-5*I*a^3*c^3*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/sqrt(a^2*c*x^2+c)-13*I*a^3*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-13*a^3*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-a^3*c^(5/2)*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))-15*I*a^3*c^3*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+15*I*a^3*c^3*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*I*a^3*c^3*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-6*I*a^3*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-15/2*I*a^3*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+13*I*a^3*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-13*a^3*c^3*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-15*a^3*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+15*a^3*c^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+13*a^3*c^3*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*I*a^3*c^3*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+15/2*I*a^3*c^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[x^3*arctan(a*x)^3/sqrt(a^2*c*x^2+c),x,24,sqrt(a^2*c*x^2+c)*arctan(a*x)/a^4/c-1/2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^3/c-5*I*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^4/sqrt(a^2*c*x^2+c)-2/3*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/a^4/c+1/3*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/a^2/c-arctanh(a*sqrt(c)*x/sqrt(a^2*c*x^2+c))/a^4/sqrt(c)+5*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^4/sqrt(a^2*c*x^2+c)-5*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^4/sqrt(a^2*c*x^2+c)-5*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^4/sqrt(a^2*c*x^2+c)+5*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^4/sqrt(a^2*c*x^2+c),1],
[x^2*arctan(a*x)^3/sqrt(a^2*c*x^2+c),x,15,-3/2*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/a^3/c+1/2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/a^2/c+I*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/a^3/sqrt(a^2*c*x^2+c)-6*I*sqrt(a^2*x^2+1)*arctan(a*x)*arctan(sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)-3/2*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+3/2*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+3*I*sqrt(a^2*x^2+1)*polylog(2,-I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)-3*I*sqrt(a^2*x^2+1)*polylog(2,I*sqrt(1+I*a*x)/sqrt(1-I*a*x))/a^3/sqrt(a^2*c*x^2+c)+3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)+3*I*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c)-3*I*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/a^3/sqrt(a^2*c*x^2+c),1],
[x*arctan(a*x)^3/sqrt(a^2*c*x^2+c),x,10,6*I*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^2/sqrt(a^2*c*x^2+c)+sqrt(a^2*c*x^2+c)*arctan(a*x)^3/a^2/c-6*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c)+6*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c)+6*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c)-6*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^2/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^3/sqrt(a^2*c*x^2+c),x,11,-2*I*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/a/sqrt(a^2*c*x^2+c)+3*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-3*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-6*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+6*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)-6*I*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c)+6*I*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/a/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^3/x/sqrt(a^2*c*x^2+c),x,11,-2*sqrt(a^2*x^2+1)*arctan(a*x)^3*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*I*sqrt(a^2*x^2+1)*polylog(4,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*I*sqrt(a^2*x^2+1)*polylog(4,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^3/x^2/sqrt(a^2*c*x^2+c),x,10,-sqrt(a^2*c*x^2+c)*arctan(a*x)^3/c/x-6*a*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*I*a*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*I*a*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*a*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+6*a*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^3/x^3/sqrt(a^2*c*x^2+c),x,15,-3/2*a*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/c/x-1/2*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/c/x^2+a^2*sqrt(a^2*x^2+1)*arctan(a*x)^3*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-6*a^2*sqrt(a^2*x^2+1)*arctan(a*x)*arctanh(sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-3/2*I*a^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3/2*I*a^2*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*I*a^2*sqrt(a^2*x^2+1)*polylog(2,-sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)-3*I*a^2*sqrt(a^2*x^2+1)*polylog(2,sqrt(1+I*a*x)/sqrt(1-I*a*x))/sqrt(a^2*c*x^2+c)+3*a^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*a^2*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+3*I*a^2*sqrt(a^2*x^2+1)*polylog(4,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-3*I*a^2*sqrt(a^2*x^2+1)*polylog(4,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^3/x^4/sqrt(a^2*c*x^2+c),x,25,-a^2*sqrt(a^2*c*x^2+c)*arctan(a*x)/c/x-1/2*a*sqrt(a^2*c*x^2+c)*arctan(a*x)^2/c/x^2-1/3*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/c/x^3+2/3*a^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^3/c/x+5*a^3*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-a^3*arctanh(sqrt(a^2*c*x^2+c)/sqrt(c))/sqrt(c)-5*I*a^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+5*I*a^3*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)+5*a^3*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c)-5*a^3*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/sqrt(a^2*c*x^2+c),1],
[x^3*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x,14,6*x/a^3/c/sqrt(a^2*c*x^2+c)-6*arctan(a*x)/a^4/c/sqrt(a^2*c*x^2+c)-3*x*arctan(a*x)^2/a^3/c/sqrt(a^2*c*x^2+c)+6*I*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^4/c/sqrt(a^2*c*x^2+c)+arctan(a*x)^3/a^4/c/sqrt(a^2*c*x^2+c)+sqrt(a^2*c*x^2+c)*arctan(a*x)^3/a^4/c^2-6*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^4/c/sqrt(a^2*c*x^2+c)+6*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^4/c/sqrt(a^2*c*x^2+c)+6*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^4/c/sqrt(a^2*c*x^2+c)-6*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^4/c/sqrt(a^2*c*x^2+c),1],
[x^2*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x,14,6/a^3/c/sqrt(a^2*c*x^2+c)+6*x*arctan(a*x)/a^2/c/sqrt(a^2*c*x^2+c)-3*arctan(a*x)^2/a^3/c/sqrt(a^2*c*x^2+c)-x*arctan(a*x)^3/a^2/c/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/a^3/c/sqrt(a^2*c*x^2+c)+3*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/a^3/c/sqrt(a^2*c*x^2+c)-3*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/a^3/c/sqrt(a^2*c*x^2+c)-6*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/a^3/c/sqrt(a^2*c*x^2+c)+6*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/a^3/c/sqrt(a^2*c*x^2+c)-6*I*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/a^3/c/sqrt(a^2*c*x^2+c)+6*I*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/a^3/c/sqrt(a^2*c*x^2+c),1],
[x*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x,3,-6*x/a/c/sqrt(a^2*c*x^2+c)+6*arctan(a*x)/a^2/c/sqrt(a^2*c*x^2+c)+3*x*arctan(a*x)^2/a/c/sqrt(a^2*c*x^2+c)-arctan(a*x)^3/a^2/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x,2,-6/a/c/sqrt(a^2*c*x^2+c)-6*x*arctan(a*x)/c/sqrt(a^2*c*x^2+c)+3*arctan(a*x)^2/a/c/sqrt(a^2*c*x^2+c)+x*arctan(a*x)^3/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^3/x/(a^2*c*x^2+c)^(3/2),x,15,6*a*x/c/sqrt(a^2*c*x^2+c)-6*arctan(a*x)/c/sqrt(a^2*c*x^2+c)-3*a*x*arctan(a*x)^2/c/sqrt(a^2*c*x^2+c)+arctan(a*x)^3/c/sqrt(a^2*c*x^2+c)-2*sqrt(a^2*x^2+1)*arctan(a*x)^3*arctanh(exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)+3*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)-3*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)-6*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)+6*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)-6*I*sqrt(a^2*x^2+1)*polylog(4,-exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)+6*I*sqrt(a^2*x^2+1)*polylog(4,exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^3/x^2/(a^2*c*x^2+c)^(3/2),x,13,6*a/c/sqrt(a^2*c*x^2+c)+6*a^2*x*arctan(a*x)/c/sqrt(a^2*c*x^2+c)-3*a*arctan(a*x)^2/c/sqrt(a^2*c*x^2+c)-a^2*x*arctan(a*x)^3/c/sqrt(a^2*c*x^2+c)-sqrt(a^2*c*x^2+c)*arctan(a*x)^3/c^2/x-6*a*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)+6*I*a*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)-6*I*a*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)-6*a*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c)+6*a*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/c/sqrt(a^2*c*x^2+c),1],
[x^5*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x,22,2/27*x^3/a^3/c/(a^2*c*x^2+c)^(3/2)+94/9*x/a^5/c^2/sqrt(a^2*c*x^2+c)-2/9*x^2*arctan(a*x)/a^4/c/(a^2*c*x^2+c)^(3/2)-94/9*arctan(a*x)/a^6/c^2/sqrt(a^2*c*x^2+c)-1/3*x^3*arctan(a*x)^2/a^3/c/(a^2*c*x^2+c)^(3/2)-5*x*arctan(a*x)^2/a^5/c^2/sqrt(a^2*c*x^2+c)+6*I*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^2/a^6/c^2/sqrt(a^2*c*x^2+c)+1/3*x^2*arctan(a*x)^3/a^4/c/(a^2*c*x^2+c)^(3/2)+5/3*arctan(a*x)^3/a^6/c^2/sqrt(a^2*c*x^2+c)+sqrt(a^2*c*x^2+c)*arctan(a*x)^3/a^6/c^3-6*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-I*exp(I*arctan(a*x)))/a^6/c^2/sqrt(a^2*c*x^2+c)+6*I*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,I*exp(I*arctan(a*x)))/a^6/c^2/sqrt(a^2*c*x^2+c)+6*sqrt(a^2*x^2+1)*polylog(3,-I*exp(I*arctan(a*x)))/a^6/c^2/sqrt(a^2*c*x^2+c)-6*sqrt(a^2*x^2+1)*polylog(3,I*exp(I*arctan(a*x)))/a^6/c^2/sqrt(a^2*c*x^2+c),1],
[x^4*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x,22,-2/27/a^5/c/(a^2*c*x^2+c)^(3/2)+68/9/a^5/c^2/sqrt(a^2*c*x^2+c)+2/9*x^3*arctan(a*x)/a^2/c/(a^2*c*x^2+c)^(3/2)+22/3*x*arctan(a*x)/a^4/c^2/sqrt(a^2*c*x^2+c)-1/3*x^2*arctan(a*x)^2/a^3/c/(a^2*c*x^2+c)^(3/2)-11/3*arctan(a*x)^2/a^5/c^2/sqrt(a^2*c*x^2+c)-1/3*x^3*arctan(a*x)^3/a^2/c/(a^2*c*x^2+c)^(3/2)-x*arctan(a*x)^3/a^4/c^2/sqrt(a^2*c*x^2+c)-2*I*sqrt(a^2*x^2+1)*arctan(exp(I*arctan(a*x)))*arctan(a*x)^3/a^5/c^2/sqrt(a^2*c*x^2+c)+3*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-I*exp(I*arctan(a*x)))/a^5/c^2/sqrt(a^2*c*x^2+c)-3*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,I*exp(I*arctan(a*x)))/a^5/c^2/sqrt(a^2*c*x^2+c)-6*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-I*exp(I*arctan(a*x)))/a^5/c^2/sqrt(a^2*c*x^2+c)+6*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,I*exp(I*arctan(a*x)))/a^5/c^2/sqrt(a^2*c*x^2+c)-6*I*sqrt(a^2*x^2+1)*polylog(4,-I*exp(I*arctan(a*x)))/a^5/c^2/sqrt(a^2*c*x^2+c)+6*I*sqrt(a^2*x^2+1)*polylog(4,I*exp(I*arctan(a*x)))/a^5/c^2/sqrt(a^2*c*x^2+c),1],
[x^3*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x,7,-2/27*x^3/a/c/(a^2*c*x^2+c)^(3/2)-40/9*x/a^3/c^2/sqrt(a^2*c*x^2+c)+2/9*x^2*arctan(a*x)/a^2/c/(a^2*c*x^2+c)^(3/2)+40/9*arctan(a*x)/a^4/c^2/sqrt(a^2*c*x^2+c)+1/3*x^3*arctan(a*x)^2/a/c/(a^2*c*x^2+c)^(3/2)+2*x*arctan(a*x)^2/a^3/c^2/sqrt(a^2*c*x^2+c)-1/3*x^2*arctan(a*x)^3/a^2/c/(a^2*c*x^2+c)^(3/2)-2/3*arctan(a*x)^3/a^4/c^2/sqrt(a^2*c*x^2+c),1],
[x^2*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x,7,2/27/a^3/c/(a^2*c*x^2+c)^(3/2)-14/9/a^3/c^2/sqrt(a^2*c*x^2+c)-2/9*x^3*arctan(a*x)/c/(a^2*c*x^2+c)^(3/2)-4/3*x*arctan(a*x)/a^2/c^2/sqrt(a^2*c*x^2+c)+1/3*x^2*arctan(a*x)^2/a/c/(a^2*c*x^2+c)^(3/2)+2/3*arctan(a*x)^2/a^3/c^2/sqrt(a^2*c*x^2+c)+1/3*x^3*arctan(a*x)^3/c/(a^2*c*x^2+c)^(3/2),1],
[x*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x,6,-2/27*x/a/c/(a^2*c*x^2+c)^(3/2)-40/27*x/a/c^2/sqrt(a^2*c*x^2+c)+2/9*arctan(a*x)/a^2/c/(a^2*c*x^2+c)^(3/2)+4/3*arctan(a*x)/a^2/c^2/sqrt(a^2*c*x^2+c)+1/3*x*arctan(a*x)^2/a/c/(a^2*c*x^2+c)^(3/2)+2/3*x*arctan(a*x)^2/a/c^2/sqrt(a^2*c*x^2+c)-1/3*arctan(a*x)^3/a^2/c/(a^2*c*x^2+c)^(3/2),1],
[arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x,5,-2/27/a/c/(a^2*c*x^2+c)^(3/2)-40/9/a/c^2/sqrt(a^2*c*x^2+c)-2/9*x*arctan(a*x)/c/(a^2*c*x^2+c)^(3/2)-40/9*x*arctan(a*x)/c^2/sqrt(a^2*c*x^2+c)+1/3*arctan(a*x)^2/a/c/(a^2*c*x^2+c)^(3/2)+2*arctan(a*x)^2/a/c^2/sqrt(a^2*c*x^2+c)+1/3*x*arctan(a*x)^3/c/(a^2*c*x^2+c)^(3/2)+2/3*x*arctan(a*x)^3/c^2/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^3/x/(a^2*c*x^2+c)^(5/2),x,22,2/27*a*x/c/(a^2*c*x^2+c)^(3/2)+202/27*a*x/c^2/sqrt(a^2*c*x^2+c)-2/9*arctan(a*x)/c/(a^2*c*x^2+c)^(3/2)-22/3*arctan(a*x)/c^2/sqrt(a^2*c*x^2+c)-1/3*a*x*arctan(a*x)^2/c/(a^2*c*x^2+c)^(3/2)-11/3*a*x*arctan(a*x)^2/c^2/sqrt(a^2*c*x^2+c)+1/3*arctan(a*x)^3/c/(a^2*c*x^2+c)^(3/2)+arctan(a*x)^3/c^2/sqrt(a^2*c*x^2+c)-2*sqrt(a^2*x^2+1)*arctan(a*x)^3*arctanh(exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)+3*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,-exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)-3*I*sqrt(a^2*x^2+1)*arctan(a*x)^2*polylog(2,exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)-6*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,-exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)+6*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(3,exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)-6*I*sqrt(a^2*x^2+1)*polylog(4,-exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)+6*I*sqrt(a^2*x^2+1)*polylog(4,exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^3/x^2/(a^2*c*x^2+c)^(5/2),x,19,2/27*a/c/(a^2*c*x^2+c)^(3/2)+94/9*a/c^2/sqrt(a^2*c*x^2+c)+2/9*a^2*x*arctan(a*x)/c/(a^2*c*x^2+c)^(3/2)+94/9*a^2*x*arctan(a*x)/c^2/sqrt(a^2*c*x^2+c)-1/3*a*arctan(a*x)^2/c/(a^2*c*x^2+c)^(3/2)-5*a*arctan(a*x)^2/c^2/sqrt(a^2*c*x^2+c)-1/3*a^2*x*arctan(a*x)^3/c/(a^2*c*x^2+c)^(3/2)-5/3*a^2*x*arctan(a*x)^3/c^2/sqrt(a^2*c*x^2+c)-sqrt(a^2*c*x^2+c)*arctan(a*x)^3/c^3/x-6*a*sqrt(a^2*x^2+1)*arctan(a*x)^2*arctanh(exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)+6*I*a*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,-exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)-6*I*a*sqrt(a^2*x^2+1)*arctan(a*x)*polylog(2,exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)-6*a*sqrt(a^2*x^2+1)*polylog(3,-exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)+6*a*sqrt(a^2*x^2+1)*polylog(3,exp(I*arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c),1],
[x^m*(a^2*c*x^2+c)^2*arctan(a*x)^3,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^3,x),0],
[x^m*(a^2*c*x^2+c)*arctan(a*x)^3,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)*arctan(a*x)^3,x),0],
[x^m*arctan(a*x)^3/(a^2*c*x^2+c),x,0,Defer(Int)(x^m*arctan(a*x)^3/(a^2*c*x^2+c),x),0],
[x^m*arctan(a*x)^3/(a^2*c*x^2+c)^2,x,0,Defer(Int)(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^2,x),0],
[x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x),0],
[x^m*sqrt(a^2*c*x^2+c)*arctan(a*x)^3,x,0,Defer(Int)(x^m*sqrt(a^2*c*x^2+c)*arctan(a*x)^3,x),0],
[x^m*arctan(a*x)^3/sqrt(a^2*c*x^2+c),x,0,Defer(Int)(x^m*arctan(a*x)^3/sqrt(a^2*c*x^2+c),x),0],
[x^m*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x),0],
[x*(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(x*(a^2*c*x^2+c)/arctan(a*x),x),0],
[(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)((a^2*c*x^2+c)/arctan(a*x),x),0],
[(a^2*c*x^2+c)/x/arctan(a*x),x,0,Defer(Int)((a^2*c*x^2+c)/x/arctan(a*x),x),0],
[x*(a^2*c*x^2+c)^2/arctan(a*x),x,0,Defer(Int)(x*(a^2*c*x^2+c)^2/arctan(a*x),x),0],
[(a^2*c*x^2+c)^2/arctan(a*x),x,0,Defer(Int)((a^2*c*x^2+c)^2/arctan(a*x),x),0],
[(a^2*c*x^2+c)^2/x/arctan(a*x),x,0,Defer(Int)((a^2*c*x^2+c)^2/x/arctan(a*x),x),0],
[x*(a^2*c*x^2+c)^3/arctan(a*x),x,0,Defer(Int)(x*(a^2*c*x^2+c)^3/arctan(a*x),x),0],
[(a^2*c*x^2+c)^3/arctan(a*x),x,0,Defer(Int)((a^2*c*x^2+c)^3/arctan(a*x),x),0],
[(a^2*c*x^2+c)^3/x/arctan(a*x),x,0,Defer(Int)((a^2*c*x^2+c)^3/x/arctan(a*x),x),0],
[x^2/(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(x^2/(a^2*c*x^2+c)/arctan(a*x),x),0],
[x/(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(x/(a^2*c*x^2+c)/arctan(a*x),x),0],
[1/(a^2*c*x^2+c)/arctan(a*x),x,1,ln(arctan(a*x))/a/c,1],
[1/x/(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(1/x/(a^2*c*x^2+c)/arctan(a*x),x),0],
[1/x^2/(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(1/x^2/(a^2*c*x^2+c)/arctan(a*x),x),0],
[x^4/(a^2*c*x^2+c)^2/arctan(a*x),x,0,Defer(Int)(x^4/(a^2*c*x^2+c)^2/arctan(a*x),x),0],
[x^3/(a^2*c*x^2+c)^2/arctan(a*x),x,0,Defer(Int)(x^3/(a^2*c*x^2+c)^2/arctan(a*x),x),0],
[x^2/(a^2*c*x^2+c)^2/arctan(a*x),x,4,-1/2*Ci(2*arctan(a*x))/a^3/c^2+1/2*ln(arctan(a*x))/a^3/c^2,1],
[x/(a^2*c*x^2+c)^2/arctan(a*x),x,4,1/2*Si(2*arctan(a*x))/a^2/c^2,1],
[1/(a^2*c*x^2+c)^2/arctan(a*x),x,4,1/2*Ci(2*arctan(a*x))/a/c^2+1/2*ln(arctan(a*x))/a/c^2,1],
[1/x/(a^2*c*x^2+c)^2/arctan(a*x),x,0,Defer(Int)(1/x/(a^2*c*x^2+c)^2/arctan(a*x),x),0],
[1/x^2/(a^2*c*x^2+c)^2/arctan(a*x),x,0,Defer(Int)(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x),x),0],
[x^6/(a^2*c*x^2+c)^3/arctan(a*x),x,0,Defer(Int)(x^6/(a^2*c*x^2+c)^3/arctan(a*x),x),0],
[x^5/(a^2*c*x^2+c)^3/arctan(a*x),x,0,Defer(Int)(x^5/(a^2*c*x^2+c)^3/arctan(a*x),x),0],
[x^4/(a^2*c*x^2+c)^3/arctan(a*x),x,5,-1/2*Ci(2*arctan(a*x))/a^5/c^3+1/8*Ci(4*arctan(a*x))/a^5/c^3+3/8*ln(arctan(a*x))/a^5/c^3,1],
[x^3/(a^2*c*x^2+c)^3/arctan(a*x),x,5,1/4*Si(2*arctan(a*x))/a^4/c^3-1/8*Si(4*arctan(a*x))/a^4/c^3,1],
[x^2/(a^2*c*x^2+c)^3/arctan(a*x),x,4,-1/8*Ci(4*arctan(a*x))/a^3/c^3+1/8*ln(arctan(a*x))/a^3/c^3,1],
[x/(a^2*c*x^2+c)^3/arctan(a*x),x,5,1/4*Si(2*arctan(a*x))/a^2/c^3+1/8*Si(4*arctan(a*x))/a^2/c^3,1],
[1/(a^2*c*x^2+c)^3/arctan(a*x),x,5,1/2*Ci(2*arctan(a*x))/a/c^3+1/8*Ci(4*arctan(a*x))/a/c^3+3/8*ln(arctan(a*x))/a/c^3,1],
[1/x/(a^2*c*x^2+c)^3/arctan(a*x),x,0,Defer(Int)(1/x/(a^2*c*x^2+c)^3/arctan(a*x),x),0],
[1/x^2/(a^2*c*x^2+c)^3/arctan(a*x),x,0,Defer(Int)(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x),x),0],
[x*sqrt(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(x*sqrt(a^2*c*x^2+c)/arctan(a*x),x),0],
[sqrt(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(sqrt(a^2*c*x^2+c)/arctan(a*x),x),0],
[sqrt(a^2*c*x^2+c)/x/arctan(a*x),x,0,Defer(Int)(sqrt(a^2*c*x^2+c)/x/arctan(a*x),x),0],
[x*(a^2*c*x^2+c)^(3/2)/arctan(a*x),x,0,Defer(Int)(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x),x),0],
[(a^2*c*x^2+c)^(3/2)/arctan(a*x),x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)/arctan(a*x),x),0],
[(a^2*c*x^2+c)^(3/2)/x/arctan(a*x),x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)/x/arctan(a*x),x),0],
[x*(a^2*c*x^2+c)^(5/2)/arctan(a*x),x,0,Defer(Int)(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x),x),0],
[(a^2*c*x^2+c)^(5/2)/arctan(a*x),x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)/arctan(a*x),x),0],
[(a^2*c*x^2+c)^(5/2)/x/arctan(a*x),x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)/x/arctan(a*x),x),0],
[x/sqrt(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(x/sqrt(a^2*c*x^2+c)/arctan(a*x),x),0],
[1/sqrt(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(1/sqrt(a^2*c*x^2+c)/arctan(a*x),x),0],
[1/x/sqrt(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(1/x/sqrt(a^2*c*x^2+c)/arctan(a*x),x),0],
[x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x,0,Defer(Int)(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x),0],
[x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x,0,Defer(Int)(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x),0],
[x/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x,3,sqrt(a^2*x^2+1)*Si(arctan(a*x))/a^2/c/sqrt(a^2*c*x^2+c),1],
[1/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x,3,sqrt(a^2*x^2+1)*Ci(arctan(a*x))/a/c/sqrt(a^2*c*x^2+c),1],
[1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x,0,Defer(Int)(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x),0],
[1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x,0,Defer(Int)(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x),0],
[x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x,0,Defer(Int)(x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x),0],
[x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x,0,Defer(Int)(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x),0],
[x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x,6,3/4*sqrt(a^2*x^2+1)*Si(arctan(a*x))/a^4/c^2/sqrt(a^2*c*x^2+c)-1/4*sqrt(a^2*x^2+1)*Si(3*arctan(a*x))/a^4/c^2/sqrt(a^2*c*x^2+c),1],
[x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x,6,1/4*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/a^3/c^2/sqrt(a^2*c*x^2+c)-1/4*sqrt(a^2*x^2+1)*Ci(3*arctan(a*x))/a^3/c^2/sqrt(a^2*c*x^2+c),1],
[x/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x,6,1/4*sqrt(a^2*x^2+1)*Si(arctan(a*x))/a^2/c^2/sqrt(a^2*c*x^2+c)+1/4*sqrt(a^2*x^2+1)*Si(3*arctan(a*x))/a^2/c^2/sqrt(a^2*c*x^2+c),1],
[1/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x,6,3/4*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/a/c^2/sqrt(a^2*c*x^2+c)+1/4*sqrt(a^2*x^2+1)*Ci(3*arctan(a*x))/a/c^2/sqrt(a^2*c*x^2+c),1],
[1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x,0,Defer(Int)(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x),0],
[1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x,0,Defer(Int)(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x),0],
[x^m*(a^2*c*x^2+c)^3/arctan(a*x),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^3/arctan(a*x),x),0],
[x^m*(a^2*c*x^2+c)^2/arctan(a*x),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^2/arctan(a*x),x),0],
[x^m*(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)/arctan(a*x),x),0],
[x^m/(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)/arctan(a*x),x),0],
[x^m/(a^2*c*x^2+c)^2/arctan(a*x),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^2/arctan(a*x),x),0],
[x^m/(a^2*c*x^2+c)^3/arctan(a*x),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^3/arctan(a*x),x),0],
[x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x),x),0],
[x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x),x),0],
[x^m*sqrt(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(x^m*sqrt(a^2*c*x^2+c)/arctan(a*x),x),0],
[x^m/sqrt(a^2*c*x^2+c)/arctan(a*x),x,0,Defer(Int)(x^m/sqrt(a^2*c*x^2+c)/arctan(a*x),x),0],
[x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x),0],
[x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x),0],
[x*(a^2*c*x^2+c)/arctan(a*x)^2,x,0,Defer(Int)(x*(a^2*c*x^2+c)/arctan(a*x)^2,x),0],
[(a^2*c*x^2+c)/arctan(a*x)^2,x,0,Defer(Int)((a^2*c*x^2+c)/arctan(a*x)^2,x),0],
[(a^2*c*x^2+c)/x/arctan(a*x)^2,x,0,Defer(Int)((a^2*c*x^2+c)/x/arctan(a*x)^2,x),0],
[x*(a^2*c*x^2+c)^2/arctan(a*x)^2,x,0,Defer(Int)(x*(a^2*c*x^2+c)^2/arctan(a*x)^2,x),0],
[(a^2*c*x^2+c)^2/arctan(a*x)^2,x,0,Defer(Int)((a^2*c*x^2+c)^2/arctan(a*x)^2,x),0],
[(a^2*c*x^2+c)^2/x/arctan(a*x)^2,x,0,Defer(Int)((a^2*c*x^2+c)^2/x/arctan(a*x)^2,x),0],
[x*(a^2*c*x^2+c)^3/arctan(a*x)^2,x,0,Defer(Int)(x*(a^2*c*x^2+c)^3/arctan(a*x)^2,x),0],
[(a^2*c*x^2+c)^3/arctan(a*x)^2,x,0,Defer(Int)((a^2*c*x^2+c)^3/arctan(a*x)^2,x),0],
[(a^2*c*x^2+c)^3/x/arctan(a*x)^2,x,0,Defer(Int)((a^2*c*x^2+c)^3/x/arctan(a*x)^2,x),0],
[x^3/(a^2*c*x^2+c)/arctan(a*x)^2,x,1,-x^3/a/c/arctan(a*x)+3*Defer(Int)(x^2/arctan(a*x),x)/a/c,0],
[x^2/(a^2*c*x^2+c)/arctan(a*x)^2,x,1,-x^2/a/c/arctan(a*x)+2*Defer(Int)(x/arctan(a*x),x)/a/c,0],
[x/(a^2*c*x^2+c)/arctan(a*x)^2,x,1,-x/a/c/arctan(a*x)+Defer(Int)(1/arctan(a*x),x)/a/c,0],
[1/(a^2*c*x^2+c)/arctan(a*x)^2,x,1,-1/a/c/arctan(a*x),1],
[1/x/(a^2*c*x^2+c)/arctan(a*x)^2,x,1,-1/a/c/x/arctan(a*x)-Defer(Int)(1/x^2/arctan(a*x),x)/a/c,0],
[1/x^2/(a^2*c*x^2+c)/arctan(a*x)^2,x,1,-1/a/c/x^2/arctan(a*x)-2*Defer(Int)(1/x^3/arctan(a*x),x)/a/c,0],
[1/x^3/(a^2*c*x^2+c)/arctan(a*x)^2,x,1,-1/a/c/x^3/arctan(a*x)-3*Defer(Int)(1/x^4/arctan(a*x),x)/a/c,0],
[1/x^4/(a^2*c*x^2+c)/arctan(a*x)^2,x,1,-1/a/c/x^4/arctan(a*x)-4*Defer(Int)(1/x^5/arctan(a*x),x)/a/c,0],
[x^3/(a^2*c*x^2+c)^2/arctan(a*x)^2,x,11,-x/a^3/c^2/arctan(a*x)+x/a^3/c^2/(a^2*x^2+1)/arctan(a*x)-Ci(2*arctan(a*x))/a^4/c^2+Defer(Int)(1/arctan(a*x),x)/a^3/c^2,0],
[x^2/(a^2*c*x^2+c)^2/arctan(a*x)^2,x,5,-x^2/a/c^2/(a^2*x^2+1)/arctan(a*x)+Si(2*arctan(a*x))/a^3/c^2,1],
[x/(a^2*c*x^2+c)^2/arctan(a*x)^2,x,9,-x/a/c^2/(a^2*x^2+1)/arctan(a*x)+Ci(2*arctan(a*x))/a^2/c^2,1],
[1/(a^2*c*x^2+c)^2/arctan(a*x)^2,x,5,-1/a/c^2/(a^2*x^2+1)/arctan(a*x)-Si(2*arctan(a*x))/a/c^2,1],
[1/x/(a^2*c*x^2+c)^2/arctan(a*x)^2,x,11,-1/a/c^2/x/arctan(a*x)+a*x/c^2/(a^2*x^2+1)/arctan(a*x)-Ci(2*arctan(a*x))/c^2-Defer(Int)(1/x^2/arctan(a*x),x)/a/c^2,0],
[1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^2,x,7,-1/a/c^2/x^2/arctan(a*x)+a/c^2/(a^2*x^2+1)/arctan(a*x)+a*Si(2*arctan(a*x))/c^2-2*Defer(Int)(1/x^3/arctan(a*x),x)/a/c^2,0],
[1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^2,x,13,-1/a/c^2/x^3/arctan(a*x)+a/c^2/x/arctan(a*x)-a^3*x/c^2/(a^2*x^2+1)/arctan(a*x)+a^2*Ci(2*arctan(a*x))/c^2-3*Defer(Int)(1/x^4/arctan(a*x),x)/a/c^2+a*Defer(Int)(1/x^2/arctan(a*x),x)/c^2,0],
[1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^2,x,9,-1/a/c^2/x^4/arctan(a*x)+a/c^2/x^2/arctan(a*x)-a^3/c^2/(a^2*x^2+1)/arctan(a*x)-a^3*Si(2*arctan(a*x))/c^2-4*Defer(Int)(1/x^5/arctan(a*x),x)/a/c^2+2*a*Defer(Int)(1/x^3/arctan(a*x),x)/c^2,0],
[x^3/(a^2*c*x^2+c)^3/arctan(a*x)^2,x,20,x/a^3/c^3/(a^2*x^2+1)^2/arctan(a*x)-x/a^3/c^3/(a^2*x^2+1)/arctan(a*x)+1/2*Ci(2*arctan(a*x))/a^4/c^3-1/2*Ci(4*arctan(a*x))/a^4/c^3,1],
[x^2/(a^2*c*x^2+c)^3/arctan(a*x)^2,x,12,1/a^3/c^3/(a^2*x^2+1)^2/arctan(a*x)-1/a^3/c^3/(a^2*x^2+1)/arctan(a*x)+1/2*Si(4*arctan(a*x))/a^3/c^3,1],
[x/(a^2*c*x^2+c)^3/arctan(a*x)^2,x,10,-x/a/c^3/(a^2*x^2+1)^2/arctan(a*x)+1/2*Ci(2*arctan(a*x))/a^2/c^3+1/2*Ci(4*arctan(a*x))/a^2/c^3,1],
[1/(a^2*c*x^2+c)^3/arctan(a*x)^2,x,6,-1/a/c^3/(a^2*x^2+1)^2/arctan(a*x)-Si(2*arctan(a*x))/a/c^3-1/2*Si(4*arctan(a*x))/a/c^3,1],
[1/x/(a^2*c*x^2+c)^3/arctan(a*x)^2,x,22,-1/a/c^3/x/arctan(a*x)+a*x/c^3/(a^2*x^2+1)^2/arctan(a*x)+a*x/c^3/(a^2*x^2+1)/arctan(a*x)-3/2*Ci(2*arctan(a*x))/c^3-1/2*Ci(4*arctan(a*x))/c^3-Defer(Int)(1/x^2/arctan(a*x),x)/a/c^3,0],
[1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^2,x,14,-1/a/c^3/x^2/arctan(a*x)+a/c^3/(a^2*x^2+1)^2/arctan(a*x)+a/c^3/(a^2*x^2+1)/arctan(a*x)+2*a*Si(2*arctan(a*x))/c^3+1/2*a*Si(4*arctan(a*x))/c^3-2*Defer(Int)(1/x^3/arctan(a*x),x)/a/c^3,0],
[1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^2,x,37,-1/a/c^3/x^3/arctan(a*x)+2*a/c^3/x/arctan(a*x)-a^3*x/c^3/(a^2*x^2+1)^2/arctan(a*x)-2*a^3*x/c^3/(a^2*x^2+1)/arctan(a*x)+5/2*a^2*Ci(2*arctan(a*x))/c^3+1/2*a^2*Ci(4*arctan(a*x))/c^3-3*Defer(Int)(1/x^4/arctan(a*x),x)/a/c^3+2*a*Defer(Int)(1/x^2/arctan(a*x),x)/c^3,0],
[1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^2,x,25,-1/a/c^3/x^4/arctan(a*x)+2*a/c^3/x^2/arctan(a*x)-a^3/c^3/(a^2*x^2+1)^2/arctan(a*x)-2*a^3/c^3/(a^2*x^2+1)/arctan(a*x)-3*a^3*Si(2*arctan(a*x))/c^3-1/2*a^3*Si(4*arctan(a*x))/c^3-4*Defer(Int)(1/x^5/arctan(a*x),x)/a/c^3+4*a*Defer(Int)(1/x^3/arctan(a*x),x)/c^3,0],
[x*sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x,0,Defer(Int)(x*sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x),0],
[sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x,0,Defer(Int)(sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x),0],
[sqrt(a^2*c*x^2+c)/x/arctan(a*x)^2,x,0,Defer(Int)(sqrt(a^2*c*x^2+c)/x/arctan(a*x)^2,x),0],
[x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x,0,Defer(Int)(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x),0],
[(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x),0],
[(a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^2,x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^2,x),0],
[x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,0,Defer(Int)(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x),0],
[(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x),0],
[(a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^2,x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^2,x),0],
[x/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x,0,Defer(Int)(x/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x),0],
[1/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x,0,Defer(Int)(1/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x),0],
[1/x/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x,1,-sqrt(a^2*c*x^2+c)/a/c/x/arctan(a*x)-Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x),x)/a,0],
[x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x,5,x/a^3/c/sqrt(a^2*c*x^2+c)/arctan(a*x)-sqrt(a^2*x^2+1)*Ci(arctan(a*x))/a^4/c/sqrt(a^2*c*x^2+c)+Defer(Int)(x/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/a^2/c,0],
[x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x,5,1/a^3/c/sqrt(a^2*c*x^2+c)/arctan(a*x)+sqrt(a^2*x^2+1)*Si(arctan(a*x))/a^3/c/sqrt(a^2*c*x^2+c)+Defer(Int)(1/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/a^2/c,0],
[x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x,4,-x/a/c/sqrt(a^2*c*x^2+c)/arctan(a*x)+sqrt(a^2*x^2+1)*Ci(arctan(a*x))/a^2/c/sqrt(a^2*c*x^2+c),1],
[1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x,4,-1/a/c/sqrt(a^2*c*x^2+c)/arctan(a*x)-sqrt(a^2*x^2+1)*Si(arctan(a*x))/a/c/sqrt(a^2*c*x^2+c),1],
[1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x,6,a*x/c/sqrt(a^2*c*x^2+c)/arctan(a*x)-sqrt(a^2*c*x^2+c)/a/c^2/x/arctan(a*x)-sqrt(a^2*x^2+1)*Ci(arctan(a*x))/c/sqrt(a^2*c*x^2+c)-Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x),x)/a/c,0],
[1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x,5,a/c/sqrt(a^2*c*x^2+c)/arctan(a*x)+a*sqrt(a^2*x^2+1)*Si(arctan(a*x))/c/sqrt(a^2*c*x^2+c)+Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/c,0],
[1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x,7,-a^3*x/c/sqrt(a^2*c*x^2+c)/arctan(a*x)+a*sqrt(a^2*c*x^2+c)/c^2/x/arctan(a*x)+a^2*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/c/sqrt(a^2*c*x^2+c)+Defer(Int)(1/x^3/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/c+a*Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x),x)/c,0],
[1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x,6,-a^3/c/sqrt(a^2*c*x^2+c)/arctan(a*x)-a^3*sqrt(a^2*x^2+1)*Si(arctan(a*x))/c/sqrt(a^2*c*x^2+c)+Defer(Int)(1/x^4/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/c-a^2*Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/c,0],
[x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,13,x^3/a^3/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)+x/a^5/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)-7/4*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/a^6/c^2/sqrt(a^2*c*x^2+c)+3/4*sqrt(a^2*x^2+1)*Ci(3*arctan(a*x))/a^6/c^2/sqrt(a^2*c*x^2+c)+Defer(Int)(x/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/a^4/c^2,0],
[x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,18,-1/a^5/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)+2/a^5/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)+5/4*sqrt(a^2*x^2+1)*Si(arctan(a*x))/a^5/c^2/sqrt(a^2*c*x^2+c)-3/4*sqrt(a^2*x^2+1)*Si(3*arctan(a*x))/a^5/c^2/sqrt(a^2*c*x^2+c)+Defer(Int)(1/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/a^4/c^2,0],
[x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,7,-x^3/a/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)+3/4*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/a^4/c^2/sqrt(a^2*c*x^2+c)-3/4*sqrt(a^2*x^2+1)*Ci(3*arctan(a*x))/a^4/c^2/sqrt(a^2*c*x^2+c),1],
[x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,12,1/a^3/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)-1/a^3/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)-1/4*sqrt(a^2*x^2+1)*Si(arctan(a*x))/a^3/c^2/sqrt(a^2*c*x^2+c)+3/4*sqrt(a^2*x^2+1)*Si(3*arctan(a*x))/a^3/c^2/sqrt(a^2*c*x^2+c),1],
[x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,13,-x/a/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)+1/4*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/a^2/c^2/sqrt(a^2*c*x^2+c)+3/4*sqrt(a^2*x^2+1)*Ci(3*arctan(a*x))/a^2/c^2/sqrt(a^2*c*x^2+c),1],
[1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,7,-1/a/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)-3/4*sqrt(a^2*x^2+1)*Si(arctan(a*x))/a/c^2/sqrt(a^2*c*x^2+c)-3/4*sqrt(a^2*x^2+1)*Si(3*arctan(a*x))/a/c^2/sqrt(a^2*c*x^2+c),1],
[1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,20,a*x/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)+a*x/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)-sqrt(a^2*c*x^2+c)/a/c^3/x/arctan(a*x)-5/4*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)-3/4*sqrt(a^2*x^2+1)*Ci(3*arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)-Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x),x)/a/c^2,0],
[1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,13,a/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)+a/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)+7/4*a*sqrt(a^2*x^2+1)*Si(arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)+3/4*a*sqrt(a^2*x^2+1)*Si(3*arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)+Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/c^2,0],
[1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,29,-a^3*x/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)-2*a^3*x/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)+2*a*sqrt(a^2*c*x^2+c)/c^3/x/arctan(a*x)+9/4*a^2*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)+3/4*a^2*sqrt(a^2*x^2+1)*Ci(3*arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)+Defer(Int)(1/x^3/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/c^2+2*a*Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x),x)/c^2,0],
[1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,21,-a^3/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)-2*a^3/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)-11/4*a^3*sqrt(a^2*x^2+1)*Si(arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)-3/4*a^3*sqrt(a^2*x^2+1)*Si(3*arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)+Defer(Int)(1/x^4/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/c^2-2*a^2*Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/c^2,0],
[sqrt(f*x)/(c^2*d*x^2+d)^2/(a+b*arctan(c*x))^2,x,0,Defer(Int)(sqrt(f*x)/(c^2*d*x^2+d)^2/(a+b*arctan(c*x))^2,x),0],
[x^m*(a^2*c*x^2+c)^3/arctan(a*x)^2,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^2,x),0],
[x^m*(a^2*c*x^2+c)^2/arctan(a*x)^2,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^2,x),0],
[x^m*(a^2*c*x^2+c)/arctan(a*x)^2,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)/arctan(a*x)^2,x),0],
[x^m/(a^2*c*x^2+c)/arctan(a*x)^2,x,1,-x^m/a/c/arctan(a*x)+m*Defer(Int)(x^(-1+m)/arctan(a*x),x)/a/c,0],
[x^m/(a^2*c*x^2+c)^2/arctan(a*x)^2,x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^2,x),0],
[x^m/(a^2*c*x^2+c)^3/arctan(a*x)^2,x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^2,x),0],
[x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x),0],
[x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x),0],
[x^m*sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x,0,Defer(Int)(x^m*sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x),0],
[x^m/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x,0,Defer(Int)(x^m/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x),0],
[x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x),0],
[x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x),0],
[x*(a^2*c*x^2+c)/arctan(a*x)^3,x,0,Defer(Int)(x*(a^2*c*x^2+c)/arctan(a*x)^3,x),0],
[(a^2*c*x^2+c)/arctan(a*x)^3,x,0,Defer(Int)((a^2*c*x^2+c)/arctan(a*x)^3,x),0],
[(a^2*c*x^2+c)/x/arctan(a*x)^3,x,0,Defer(Int)((a^2*c*x^2+c)/x/arctan(a*x)^3,x),0],
[x*(a^2*c*x^2+c)^2/arctan(a*x)^3,x,0,Defer(Int)(x*(a^2*c*x^2+c)^2/arctan(a*x)^3,x),0],
[(a^2*c*x^2+c)^2/arctan(a*x)^3,x,0,Defer(Int)((a^2*c*x^2+c)^2/arctan(a*x)^3,x),0],
[(a^2*c*x^2+c)^2/x/arctan(a*x)^3,x,0,Defer(Int)((a^2*c*x^2+c)^2/x/arctan(a*x)^3,x),0],
[x*(a^2*c*x^2+c)^3/arctan(a*x)^3,x,0,Defer(Int)(x*(a^2*c*x^2+c)^3/arctan(a*x)^3,x),0],
[(a^2*c*x^2+c)^3/arctan(a*x)^3,x,0,Defer(Int)((a^2*c*x^2+c)^3/arctan(a*x)^3,x),0],
[(a^2*c*x^2+c)^3/x/arctan(a*x)^3,x,0,Defer(Int)((a^2*c*x^2+c)^3/x/arctan(a*x)^3,x),0],
[x^3/(a^2*c*x^2+c)/arctan(a*x)^3,x,1,-1/2*x^3/a/c/arctan(a*x)^2+3/2*Defer(Int)(x^2/arctan(a*x)^2,x)/a/c,0],
[x^2/(a^2*c*x^2+c)/arctan(a*x)^3,x,1,-1/2*x^2/a/c/arctan(a*x)^2+Defer(Int)(x/arctan(a*x)^2,x)/a/c,0],
[x/(a^2*c*x^2+c)/arctan(a*x)^3,x,1,-1/2*x/a/c/arctan(a*x)^2+1/2*Defer(Int)(1/arctan(a*x)^2,x)/a/c,0],
[1/(a^2*c*x^2+c)/arctan(a*x)^3,x,1,-1/2/a/c/arctan(a*x)^2,1],
[1/x/(a^2*c*x^2+c)/arctan(a*x)^3,x,1,-1/2/a/c/x/arctan(a*x)^2-1/2*Defer(Int)(1/x^2/arctan(a*x)^2,x)/a/c,0],
[1/x^2/(a^2*c*x^2+c)/arctan(a*x)^3,x,1,-1/2/a/c/x^2/arctan(a*x)^2-Defer(Int)(1/x^3/arctan(a*x)^2,x)/a/c,0],
[1/x^3/(a^2*c*x^2+c)/arctan(a*x)^3,x,1,-1/2/a/c/x^3/arctan(a*x)^2-3/2*Defer(Int)(1/x^4/arctan(a*x)^2,x)/a/c,0],
[1/x^4/(a^2*c*x^2+c)/arctan(a*x)^3,x,1,-1/2/a/c/x^4/arctan(a*x)^2-2*Defer(Int)(1/x^5/arctan(a*x)^2,x)/a/c,0],
[x^3/(a^2*c*x^2+c)^2/arctan(a*x)^3,x,7,-1/2*x/a^3/c^2/arctan(a*x)^2+1/2*x/a^3/c^2/(a^2*x^2+1)/arctan(a*x)^2+1/2*(-a^2*x^2+1)/a^4/c^2/(a^2*x^2+1)/arctan(a*x)+Si(2*arctan(a*x))/a^4/c^2+1/2*Defer(Int)(1/arctan(a*x)^2,x)/a^3/c^2,0],
[x^2/(a^2*c*x^2+c)^2/arctan(a*x)^3,x,10,-1/2*x^2/a/c^2/(a^2*x^2+1)/arctan(a*x)^2-x/a^2/c^2/(a^2*x^2+1)/arctan(a*x)+Ci(2*arctan(a*x))/a^3/c^2,1],
[x/(a^2*c*x^2+c)^2/arctan(a*x)^3,x,5,-1/2*x/a/c^2/(a^2*x^2+1)/arctan(a*x)^2-1/2*(-a^2*x^2+1)/a^2/c^2/(a^2*x^2+1)/arctan(a*x)-Si(2*arctan(a*x))/a^2/c^2,1],
[1/(a^2*c*x^2+c)^2/arctan(a*x)^3,x,10,-1/2/a/c^2/(a^2*x^2+1)/arctan(a*x)^2+x/c^2/(a^2*x^2+1)/arctan(a*x)-Ci(2*arctan(a*x))/a/c^2,1],
[1/x/(a^2*c*x^2+c)^2/arctan(a*x)^3,x,7,-1/2/a/c^2/x/arctan(a*x)^2+1/2*a*x/c^2/(a^2*x^2+1)/arctan(a*x)^2+1/2*(-a^2*x^2+1)/c^2/(a^2*x^2+1)/arctan(a*x)+Si(2*arctan(a*x))/c^2-1/2*Defer(Int)(1/x^2/arctan(a*x)^2,x)/a/c^2,0],
[1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^3,x,12,-1/2/a/c^2/x^2/arctan(a*x)^2+1/2*a/c^2/(a^2*x^2+1)/arctan(a*x)^2-a^2*x/c^2/(a^2*x^2+1)/arctan(a*x)+a*Ci(2*arctan(a*x))/c^2-Defer(Int)(1/x^3/arctan(a*x)^2,x)/a/c^2,0],
[1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^3,x,9,-1/2/a/c^2/x^3/arctan(a*x)^2+1/2*a/c^2/x/arctan(a*x)^2-1/2*a^3*x/c^2/(a^2*x^2+1)/arctan(a*x)^2-1/2*a^2*(-a^2*x^2+1)/c^2/(a^2*x^2+1)/arctan(a*x)-a^2*Si(2*arctan(a*x))/c^2-3/2*Defer(Int)(1/x^4/arctan(a*x)^2,x)/a/c^2+1/2*a*Defer(Int)(1/x^2/arctan(a*x)^2,x)/c^2,0],
[1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^3,x,14,-1/2/a/c^2/x^4/arctan(a*x)^2+1/2*a/c^2/x^2/arctan(a*x)^2-1/2*a^3/c^2/(a^2*x^2+1)/arctan(a*x)^2+a^4*x/c^2/(a^2*x^2+1)/arctan(a*x)-a^3*Ci(2*arctan(a*x))/c^2-2*Defer(Int)(1/x^5/arctan(a*x)^2,x)/a/c^2+a*Defer(Int)(1/x^3/arctan(a*x)^2,x)/c^2,0],
[x^3/(a^2*c*x^2+c)^3/arctan(a*x)^3,x,25,1/2*x/a^3/c^3/(a^2*x^2+1)^2/arctan(a*x)^2-1/2*x/a^3/c^3/(a^2*x^2+1)/arctan(a*x)^2+2/a^4/c^3/(a^2*x^2+1)^2/arctan(a*x)-3/2/a^4/c^3/(a^2*x^2+1)/arctan(a*x)-1/2*(-a^2*x^2+1)/a^4/c^3/(a^2*x^2+1)/arctan(a*x)-1/2*Si(2*arctan(a*x))/a^4/c^3+Si(4*arctan(a*x))/a^4/c^3,1],
[x^2/(a^2*c*x^2+c)^3/arctan(a*x)^3,x,22,1/2/a^3/c^3/(a^2*x^2+1)^2/arctan(a*x)^2-1/2/a^3/c^3/(a^2*x^2+1)/arctan(a*x)^2-2*x/a^2/c^3/(a^2*x^2+1)^2/arctan(a*x)+x/a^2/c^3/(a^2*x^2+1)/arctan(a*x)+Ci(4*arctan(a*x))/a^3/c^3,1],
[x/(a^2*c*x^2+c)^3/arctan(a*x)^3,x,19,-1/2*x/a/c^3/(a^2*x^2+1)^2/arctan(a*x)^2-2/a^2/c^3/(a^2*x^2+1)^2/arctan(a*x)+3/2/a^2/c^3/(a^2*x^2+1)/arctan(a*x)-1/2*Si(2*arctan(a*x))/a^2/c^3-Si(4*arctan(a*x))/a^2/c^3,1],
[1/(a^2*c*x^2+c)^3/arctan(a*x)^3,x,11,-1/2/a/c^3/(a^2*x^2+1)^2/arctan(a*x)^2+2*x/c^3/(a^2*x^2+1)^2/arctan(a*x)-Ci(2*arctan(a*x))/a/c^3-Ci(4*arctan(a*x))/a/c^3,1],
[1/x/(a^2*c*x^2+c)^3/arctan(a*x)^3,x,27,-1/2/a/c^3/x/arctan(a*x)^2+1/2*a*x/c^3/(a^2*x^2+1)^2/arctan(a*x)^2+1/2*a*x/c^3/(a^2*x^2+1)/arctan(a*x)^2+2/c^3/(a^2*x^2+1)^2/arctan(a*x)-3/2/c^3/(a^2*x^2+1)/arctan(a*x)+1/2*(-a^2*x^2+1)/c^3/(a^2*x^2+1)/arctan(a*x)+3/2*Si(2*arctan(a*x))/c^3+Si(4*arctan(a*x))/c^3-1/2*Defer(Int)(1/x^2/arctan(a*x)^2,x)/a/c^3,0],
[1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^3,x,24,-1/2/a/c^3/x^2/arctan(a*x)^2+1/2*a/c^3/(a^2*x^2+1)^2/arctan(a*x)^2+1/2*a/c^3/(a^2*x^2+1)/arctan(a*x)^2-2*a^2*x/c^3/(a^2*x^2+1)^2/arctan(a*x)-a^2*x/c^3/(a^2*x^2+1)/arctan(a*x)+2*a*Ci(2*arctan(a*x))/c^3+a*Ci(4*arctan(a*x))/c^3-Defer(Int)(1/x^3/arctan(a*x)^2,x)/a/c^3,0],
[1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^3,x,38,-1/2/a/c^3/x^3/arctan(a*x)^2+a/c^3/x/arctan(a*x)^2-1/2*a^3*x/c^3/(a^2*x^2+1)^2/arctan(a*x)^2-a^3*x/c^3/(a^2*x^2+1)/arctan(a*x)^2-2*a^2/c^3/(a^2*x^2+1)^2/arctan(a*x)+3/2*a^2/c^3/(a^2*x^2+1)/arctan(a*x)-a^2*(-a^2*x^2+1)/c^3/(a^2*x^2+1)/arctan(a*x)-5/2*a^2*Si(2*arctan(a*x))/c^3-a^2*Si(4*arctan(a*x))/c^3-3/2*Defer(Int)(1/x^4/arctan(a*x)^2,x)/a/c^3+a*Defer(Int)(1/x^2/arctan(a*x)^2,x)/c^3,0],
[1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^3,x,40,-1/2/a/c^3/x^4/arctan(a*x)^2+a/c^3/x^2/arctan(a*x)^2-1/2*a^3/c^3/(a^2*x^2+1)^2/arctan(a*x)^2-a^3/c^3/(a^2*x^2+1)/arctan(a*x)^2+2*a^4*x/c^3/(a^2*x^2+1)^2/arctan(a*x)+2*a^4*x/c^3/(a^2*x^2+1)/arctan(a*x)-3*a^3*Ci(2*arctan(a*x))/c^3-a^3*Ci(4*arctan(a*x))/c^3-2*Defer(Int)(1/x^5/arctan(a*x)^2,x)/a/c^3+2*a*Defer(Int)(1/x^3/arctan(a*x)^2,x)/c^3,0],
[x^3/(a^2*x^2+1)/arctan(a*x)^3-3/2*x^2/a/arctan(a*x)^2,x,4,-1/2*x^3/a/arctan(a*x)^2,1],
[x*sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x,0,Defer(Int)(x*sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x),0],
[sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x,0,Defer(Int)(sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x),0],
[sqrt(a^2*c*x^2+c)/x/arctan(a*x)^3,x,0,Defer(Int)(sqrt(a^2*c*x^2+c)/x/arctan(a*x)^3,x),0],
[x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x,0,Defer(Int)(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x),0],
[(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x),0],
[(a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^3,x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^3,x),0],
[x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x,0,Defer(Int)(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x),0],
[(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x),0],
[(a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^3,x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^3,x),0],
[x/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x,0,Defer(Int)(x/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x),0],
[1/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x,0,Defer(Int)(1/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x),0],
[1/x/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x,1,-1/2*sqrt(a^2*c*x^2+c)/a/c/x/arctan(a*x)^2-1/2*Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/a,0],
[1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x,0,Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x),0],
[1/x^3/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x,0,Defer(Int)(1/x^3/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x),0],
[x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x,6,1/2*x/a^3/c/sqrt(a^2*c*x^2+c)/arctan(a*x)^2+1/2/a^4/c/sqrt(a^2*c*x^2+c)/arctan(a*x)+1/2*sqrt(a^2*x^2+1)*Si(arctan(a*x))/a^4/c/sqrt(a^2*c*x^2+c)+Defer(Int)(x/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x)/a^2/c,0],
[x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x,6,1/2/a^3/c/sqrt(a^2*c*x^2+c)/arctan(a*x)^2-1/2*x/a^2/c/sqrt(a^2*c*x^2+c)/arctan(a*x)+1/2*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/a^3/c/sqrt(a^2*c*x^2+c)+Defer(Int)(1/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x)/a^2/c,0],
[x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x,5,-1/2*x/a/c/sqrt(a^2*c*x^2+c)/arctan(a*x)^2-1/2/a^2/c/sqrt(a^2*c*x^2+c)/arctan(a*x)-1/2*sqrt(a^2*x^2+1)*Si(arctan(a*x))/a^2/c/sqrt(a^2*c*x^2+c),1],
[1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x,5,-1/2/a/c/sqrt(a^2*c*x^2+c)/arctan(a*x)^2+1/2*x/c/sqrt(a^2*c*x^2+c)/arctan(a*x)-1/2*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/a/c/sqrt(a^2*c*x^2+c),1],
[1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x,7,1/2*a*x/c/sqrt(a^2*c*x^2+c)/arctan(a*x)^2-1/2*sqrt(a^2*c*x^2+c)/a/c^2/x/arctan(a*x)^2+1/2/c/sqrt(a^2*c*x^2+c)/arctan(a*x)+1/2*sqrt(a^2*x^2+1)*Si(arctan(a*x))/c/sqrt(a^2*c*x^2+c)-1/2*Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/a/c,0],
[1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x,6,1/2*a/c/sqrt(a^2*c*x^2+c)/arctan(a*x)^2-1/2*a^2*x/c/sqrt(a^2*c*x^2+c)/arctan(a*x)+1/2*a*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/c/sqrt(a^2*c*x^2+c)+Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x)/c,0],
[1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x,8,-1/2*a^3*x/c/sqrt(a^2*c*x^2+c)/arctan(a*x)^2+1/2*a*sqrt(a^2*c*x^2+c)/c^2/x/arctan(a*x)^2-1/2*a^2/c/sqrt(a^2*c*x^2+c)/arctan(a*x)-1/2*a^2*sqrt(a^2*x^2+1)*Si(arctan(a*x))/c/sqrt(a^2*c*x^2+c)+Defer(Int)(1/x^3/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x)/c+1/2*a*Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/c,0],
[1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x,7,-1/2*a^3/c/sqrt(a^2*c*x^2+c)/arctan(a*x)^2+1/2*a^4*x/c/sqrt(a^2*c*x^2+c)/arctan(a*x)-1/2*a^3*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/c/sqrt(a^2*c*x^2+c)+Defer(Int)(1/x^4/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x)/c-a^2*Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x)/c,0],
[x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x,20,1/2*x^3/a^3/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2+1/2*x/a^5/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^2-3/2/a^6/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)+2/a^6/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)+7/8*sqrt(a^2*x^2+1)*Si(arctan(a*x))/a^6/c^2/sqrt(a^2*c*x^2+c)-9/8*sqrt(a^2*x^2+1)*Si(3*arctan(a*x))/a^6/c^2/sqrt(a^2*c*x^2+c)+Defer(Int)(x/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x)/a^4/c^2,0],
[x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x,27,-1/2/a^5/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2+1/a^5/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^2+3/2*x/a^4/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)-x/a^4/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)+5/8*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/a^5/c^2/sqrt(a^2*c*x^2+c)-9/8*sqrt(a^2*x^2+1)*Ci(3*arctan(a*x))/a^5/c^2/sqrt(a^2*c*x^2+c)+Defer(Int)(1/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x)/a^4/c^2,0],
[x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x,13,-1/2*x^3/a/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2+3/2/a^4/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)-3/2/a^4/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)-3/8*sqrt(a^2*x^2+1)*Si(arctan(a*x))/a^4/c^2/sqrt(a^2*c*x^2+c)+9/8*sqrt(a^2*x^2+1)*Si(3*arctan(a*x))/a^4/c^2/sqrt(a^2*c*x^2+c),1],
[x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x,20,1/2/a^3/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2-1/2/a^3/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^2-3/2*x/a^2/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)+1/2*x/a^2/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)-1/8*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/a^3/c^2/sqrt(a^2*c*x^2+c)+9/8*sqrt(a^2*x^2+1)*Ci(3*arctan(a*x))/a^3/c^2/sqrt(a^2*c*x^2+c),1],
[x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x,20,-1/2*x/a/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2-3/2/a^2/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)+1/a^2/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)-1/8*sqrt(a^2*x^2+1)*Si(arctan(a*x))/a^2/c^2/sqrt(a^2*c*x^2+c)-9/8*sqrt(a^2*x^2+1)*Si(3*arctan(a*x))/a^2/c^2/sqrt(a^2*c*x^2+c),1],
[1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x,14,-1/2/a/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2+3/2*x/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)-3/8*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/a/c^2/sqrt(a^2*c*x^2+c)-9/8*sqrt(a^2*x^2+1)*Ci(3*arctan(a*x))/a/c^2/sqrt(a^2*c*x^2+c),1],
[1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x,28,1/2*a*x/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2+1/2*a*x/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^2-1/2*sqrt(a^2*c*x^2+c)/a/c^3/x/arctan(a*x)^2+3/2/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)-1/2/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)+5/8*sqrt(a^2*x^2+1)*Si(arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)+9/8*sqrt(a^2*x^2+1)*Si(3*arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)-1/2*Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^2,x)/a/c^2,0],
[1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x,21,1/2*a/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2+1/2*a/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^2-3/2*a^2*x/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)-1/2*a^2*x/c^2/sqrt(a^2*c*x^2+c)/arctan(a*x)+7/8*a*sqrt(a^2*x^2+1)*Ci(arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)+9/8*a*sqrt(a^2*x^2+1)*Ci(3*arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)+Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x)/c^2,0],
[x^m*(a^2*c*x^2+c)^3/arctan(a*x)^3,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^3,x),0],
[x^m*(a^2*c*x^2+c)^2/arctan(a*x)^3,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^3,x),0],
[x^m*(a^2*c*x^2+c)/arctan(a*x)^3,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)/arctan(a*x)^3,x),0],
[x^m/(a^2*c*x^2+c)/arctan(a*x)^3,x,1,-1/2*x^m/a/c/arctan(a*x)^2+1/2*m*Defer(Int)(x^(-1+m)/arctan(a*x)^2,x)/a/c,0],
[x^m/(a^2*c*x^2+c)^2/arctan(a*x)^3,x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^3,x),0],
[x^m/(a^2*c*x^2+c)^3/arctan(a*x)^3,x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^3,x),0],
[x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x),0],
[x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x),0],
[x^m*sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x,0,Defer(Int)(x^m*sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x),0],
[x^m/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x,0,Defer(Int)(x^m/sqrt(a^2*c*x^2+c)/arctan(a*x)^3,x),0],
[x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x),0],
[x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x),0],
[x^m*(a^2*c*x^2+c)*sqrt(arctan(a*x)),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)*sqrt(arctan(a*x)),x),0],
[x*(a^2*c*x^2+c)*sqrt(arctan(a*x)),x,1,1/4*c*(a^2*x^2+1)^2*sqrt(arctan(a*x))/a^2-1/8*Defer(Int)((a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a,0],
[(a^2*c*x^2+c)*sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)*sqrt(arctan(a*x)),x),0],
[(a^2*c*x^2+c)*sqrt(arctan(a*x))/x,x,0,Defer(Int)((a^2*c*x^2+c)*sqrt(arctan(a*x))/x,x),0],
[x^m*(a^2*c*x^2+c)^2*sqrt(arctan(a*x)),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^2*sqrt(arctan(a*x)),x),0],
[x*(a^2*c*x^2+c)^2*sqrt(arctan(a*x)),x,1,1/6*c^2*(a^2*x^2+1)^3*sqrt(arctan(a*x))/a^2-1/12*Defer(Int)((a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)/a,0],
[(a^2*c*x^2+c)^2*sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)^2*sqrt(arctan(a*x)),x),0],
[(a^2*c*x^2+c)^2*sqrt(arctan(a*x))/x,x,0,Defer(Int)((a^2*c*x^2+c)^2*sqrt(arctan(a*x))/x,x),0],
[x^m*(a^2*c*x^2+c)^3*sqrt(arctan(a*x)),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^3*sqrt(arctan(a*x)),x),0],
[x*(a^2*c*x^2+c)^3*sqrt(arctan(a*x)),x,1,1/8*c^3*(a^2*x^2+1)^4*sqrt(arctan(a*x))/a^2-1/16*Defer(Int)((a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x)/a,0],
[(a^2*c*x^2+c)^3*sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)^3*sqrt(arctan(a*x)),x),0],
[(a^2*c*x^2+c)^3*sqrt(arctan(a*x))/x,x,0,Defer(Int)((a^2*c*x^2+c)^3*sqrt(arctan(a*x))/x,x),0],
[x^m*sqrt(arctan(a*x))/(a^2*c*x^2+c),x,0,Defer(Int)(x^m*sqrt(arctan(a*x))/(a^2*c*x^2+c),x),0],
[x^3*sqrt(arctan(a*x))/(a^2*c*x^2+c),x,2,-2/3*x*arctan(a*x)^(3/2)/a^3/c+Defer(Int)(x*sqrt(arctan(a*x)),x)/a^2/c+2/3*Defer(Int)(arctan(a*x)^(3/2),x)/a^3/c,0],
[x^2*sqrt(arctan(a*x))/(a^2*c*x^2+c),x,2,-2/3*arctan(a*x)^(3/2)/a^3/c+Defer(Int)(sqrt(arctan(a*x)),x)/a^2/c,0],
[x*sqrt(arctan(a*x))/(a^2*c*x^2+c),x,1,2/3*x*arctan(a*x)^(3/2)/a/c-2/3*Defer(Int)(arctan(a*x)^(3/2),x)/a/c,0],
[sqrt(arctan(a*x))/(a^2*c*x^2+c),x,1,2/3*arctan(a*x)^(3/2)/a/c,1],
[sqrt(arctan(a*x))/x/(a^2*c*x^2+c),x,1,-2/3*I*arctan(a*x)^(3/2)/c+I*Defer(Int)(sqrt(arctan(a*x))/x/(I+a*x),x)/c,0],
[sqrt(arctan(a*x))/x^2/(a^2*c*x^2+c),x,2,-2/3*a*arctan(a*x)^(3/2)/c+Defer(Int)(sqrt(arctan(a*x))/x^2,x)/c,0],
[sqrt(arctan(a*x))/x^3/(a^2*c*x^2+c),x,2,2/3*I*a^2*arctan(a*x)^(3/2)/c+Defer(Int)(sqrt(arctan(a*x))/x^3,x)/c-I*a^2*Defer(Int)(sqrt(arctan(a*x))/x/(I+a*x),x)/c,0],
[sqrt(arctan(a*x))/x^4/(a^2*c*x^2+c),x,3,2/3*a^3*arctan(a*x)^(3/2)/c+Defer(Int)(sqrt(arctan(a*x))/x^4,x)/c-a^2*Defer(Int)(sqrt(arctan(a*x))/x^2,x)/c,0],
[x^m*sqrt(arctan(a*x))/(a^2*c*x^2+c)^2,x,0,Defer(Int)(x^m*sqrt(arctan(a*x))/(a^2*c*x^2+c)^2,x),0],
[x^3*sqrt(arctan(a*x))/(a^2*c*x^2+c)^2,x,0,Defer(Int)(x^3*sqrt(arctan(a*x))/(a^2*c*x^2+c)^2,x),0],
[x^2*sqrt(arctan(a*x))/(a^2*c*x^2+c)^2,x,6,-1/2*x*sqrt(arctan(a*x))/a^2/c^2/(a^2*x^2+1)+1/3*arctan(a*x)^(3/2)/a^3/c^2+1/8*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^3/c^2,1],
[x*sqrt(arctan(a*x))/(a^2*c*x^2+c)^2,x,6,1/4*sqrt(arctan(a*x))/a^2/c^2-1/2*sqrt(arctan(a*x))/a^2/c^2/(a^2*x^2+1)+1/8*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^2/c^2,1],
[sqrt(arctan(a*x))/(a^2*c*x^2+c)^2,x,6,1/2*x*sqrt(arctan(a*x))/c^2/(a^2*x^2+1)+1/3*arctan(a*x)^(3/2)/a/c^2-1/8*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a/c^2,1],
[sqrt(arctan(a*x))/x/(a^2*c*x^2+c)^2,x,0,Defer(Int)(sqrt(arctan(a*x))/x/(a^2*c*x^2+c)^2,x),0],
[x^m*sqrt(arctan(a*x))/(a^2*c*x^2+c)^3,x,0,Defer(Int)(x^m*sqrt(arctan(a*x))/(a^2*c*x^2+c)^3,x),0],
[x^5*sqrt(arctan(a*x))/(a^2*c*x^2+c)^3,x,0,Defer(Int)(x^5*sqrt(arctan(a*x))/(a^2*c*x^2+c)^3,x),0],
[x^4*sqrt(arctan(a*x))/(a^2*c*x^2+c)^3,x,9,1/4*arctan(a*x)^(3/2)/a^5/c^3-1/64*sqrt(1/2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^5/c^3+1/8*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^5/c^3-1/4*sqrt(arctan(a*x))*sin(2*arctan(a*x))/a^5/c^3+1/32*sqrt(arctan(a*x))*sin(4*arctan(a*x))/a^5/c^3,1],
[x^3*sqrt(arctan(a*x))/(a^2*c*x^2+c)^3,x,8,-3/32*sqrt(arctan(a*x))/a^4/c^3+1/4*x^4*sqrt(arctan(a*x))/c^3/(a^2*x^2+1)^2-1/64*sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^4/c^3+1/16*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^4/c^3,1],
[x^2*sqrt(arctan(a*x))/(a^2*c*x^2+c)^3,x,6,1/12*arctan(a*x)^(3/2)/a^3/c^3+1/64*sqrt(1/2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c^3-1/32*sqrt(arctan(a*x))*sin(4*arctan(a*x))/a^3/c^3,1],
[x*sqrt(arctan(a*x))/(a^2*c*x^2+c)^3,x,8,3/32*sqrt(arctan(a*x))/a^2/c^3-1/4*sqrt(arctan(a*x))/a^2/c^3/(a^2*x^2+1)^2+1/64*sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c^3+1/16*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^2/c^3,1],
[sqrt(arctan(a*x))/(a^2*c*x^2+c)^3,x,9,1/4*arctan(a*x)^(3/2)/a/c^3-1/64*sqrt(1/2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c^3-1/8*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a/c^3+1/4*sqrt(arctan(a*x))*sin(2*arctan(a*x))/a/c^3+1/32*sqrt(arctan(a*x))*sin(4*arctan(a*x))/a/c^3,1],
[sqrt(arctan(a*x))/x/(a^2*c*x^2+c)^3,x,0,Defer(Int)(sqrt(arctan(a*x))/x/(a^2*c*x^2+c)^3,x),0],
[x^m*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x)),x,0,Defer(Int)(x^m*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x)),x),0],
[x^2*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x)),x,0,Defer(Int)(x^2*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x)),x),0],
[x*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x)),x,1,1/3*(a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x))/a^2/c-1/6*Defer(Int)(sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a,0],
[sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x)),x,0,Defer(Int)(sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x)),x),0],
[x^m*(a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x)),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x)),x),0],
[x^2*(a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x)),x,0,Defer(Int)(x^2*(a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x)),x),0],
[x*(a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x)),x,1,1/5*(a^2*c*x^2+c)^(5/2)*sqrt(arctan(a*x))/a^2/c-1/10*Defer(Int)((a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)/a,0],
[(a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x)),x),0],
[x^m*(a^2*c*x^2+c)^(5/2)*sqrt(arctan(a*x)),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(5/2)*sqrt(arctan(a*x)),x),0],
[x^2*(a^2*c*x^2+c)^(5/2)*sqrt(arctan(a*x)),x,0,Defer(Int)(x^2*(a^2*c*x^2+c)^(5/2)*sqrt(arctan(a*x)),x),0],
[x*(a^2*c*x^2+c)^(5/2)*sqrt(arctan(a*x)),x,1,1/7*(a^2*c*x^2+c)^(7/2)*sqrt(arctan(a*x))/a^2/c-1/14*Defer(Int)((a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x)/a,0],
[(a^2*c*x^2+c)^(5/2)*sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)*sqrt(arctan(a*x)),x),0],
[x^m*sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x,0,Defer(Int)(x^m*sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x),0],
[x^3*sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x,2,-2/3*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/a^4/c+1/3*x^2*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/a^2/c+1/3*Defer(Int)(1/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a^3-1/6*Defer(Int)(x^2/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a,0],
[x^2*sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x,1,1/2*x*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/a^2/c-1/4*Defer(Int)(x/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a-1/2*Defer(Int)(sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x)/a^2,0],
[x*sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x,1,sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/a^2/c-1/2*Defer(Int)(1/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a,0],
[sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x,0,Defer(Int)(sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x),0],
[sqrt(arctan(a*x))/x/sqrt(a^2*c*x^2+c),x,0,Defer(Int)(sqrt(arctan(a*x))/x/sqrt(a^2*c*x^2+c),x),0],
[sqrt(arctan(a*x))/x^2/sqrt(a^2*c*x^2+c),x,1,-sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/c/x+1/2*a*Defer(Int)(1/x/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[sqrt(arctan(a*x))/x^3/sqrt(a^2*c*x^2+c),x,1,-1/2*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/c/x^2+1/4*a*Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)-1/2*a^2*Defer(Int)(sqrt(arctan(a*x))/x/sqrt(a^2*c*x^2+c),x),0],
[sqrt(arctan(a*x))/x^4/sqrt(a^2*c*x^2+c),x,2,-1/3*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/c/x^3+2/3*a^2*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/c/x+1/6*a*Defer(Int)(1/x^3/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)-1/3*a^3*Defer(Int)(1/x/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[x^m*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(x^m*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x),0],
[x^3*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(x^3*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x),0],
[x^2*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(x^2*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x),0],
[x*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x,5,-sqrt(arctan(a*x))/a^2/c/sqrt(a^2*c*x^2+c)+sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c/sqrt(a^2*c*x^2+c),1],
[sqrt(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x,5,x*sqrt(arctan(a*x))/c/sqrt(a^2*c*x^2+c)-sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c/sqrt(a^2*c*x^2+c),1],
[sqrt(arctan(a*x))/x/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(sqrt(arctan(a*x))/x/(a^2*c*x^2+c)^(3/2),x),0],
[sqrt(arctan(a*x))/x^2/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(sqrt(arctan(a*x))/x^2/(a^2*c*x^2+c)^(3/2),x),0],
[x^m*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x,0,Defer(Int)(x^m*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x),0],
[x^4*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x,0,Defer(Int)(x^4*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x),0],
[x^3*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x,10,-3/4*sqrt(arctan(a*x))/a^4/c^2/sqrt(a^2*c*x^2+c)+1/12*sqrt(a^2*x^2+1)*sqrt(arctan(a*x))*cos(3*arctan(a*x))/a^4/c^2/sqrt(a^2*c*x^2+c)+3/4*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^4/c^2/sqrt(a^2*c*x^2+c)-1/12*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^4/c^2/sqrt(a^2*c*x^2+c),1],
[x^2*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x,9,1/3*x^3*sqrt(arctan(a*x))/c/(a^2*c*x^2+c)^(3/2)-1/4*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c)+1/12*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c),1],
[x*sqrt(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x,9,-1/3*sqrt(arctan(a*x))/a^2/c/(a^2*c*x^2+c)^(3/2)+1/4*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c)+1/12*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c),1],
[sqrt(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x,10,3/4*x*sqrt(arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)-3/4*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c^2/sqrt(a^2*c*x^2+c)-1/12*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/a/c^2/sqrt(a^2*c*x^2+c)+1/12*sqrt(a^2*x^2+1)*sqrt(arctan(a*x))*sin(3*arctan(a*x))/a/c^2/sqrt(a^2*c*x^2+c),1],
[sqrt(arctan(a*x))/x/(a^2*c*x^2+c)^(5/2),x,0,Defer(Int)(sqrt(arctan(a*x))/x/(a^2*c*x^2+c)^(5/2),x),0],
[x^m*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x),0],
[x^2*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x,0,Defer(Int)(x^2*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x),0],
[x*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x,1,1/4*c*(a^2*x^2+1)^2*arctan(a*x)^(3/2)/a^2-3/8*Defer(Int)((a^2*c*x^2+c)*sqrt(arctan(a*x)),x)/a,0],
[(a^2*c*x^2+c)*arctan(a*x)^(3/2),x,1,-1/4*c*(a^2*x^2+1)*sqrt(arctan(a*x))/a+1/3*c*x*(a^2*x^2+1)*arctan(a*x)^(3/2)+1/8*c*Defer(Int)(1/sqrt(arctan(a*x)),x)+2/3*c*Defer(Int)(arctan(a*x)^(3/2),x),0],
[(a^2*c*x^2+c)*arctan(a*x)^(3/2)/x,x,0,Defer(Int)((a^2*c*x^2+c)*arctan(a*x)^(3/2)/x,x),0],
[(a^2*c*x^2+c)*arctan(a*x)^(3/2)/x^2,x,0,Defer(Int)((a^2*c*x^2+c)*arctan(a*x)^(3/2)/x^2,x),0],
[x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x),0],
[x^2*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x,0,Defer(Int)(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x),0],
[x*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x,1,1/6*c^2*(a^2*x^2+1)^3*arctan(a*x)^(3/2)/a^2-1/4*Defer(Int)((a^2*c*x^2+c)^2*sqrt(arctan(a*x)),x)/a,0],
[(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x,2,-1/5*c^2*(a^2*x^2+1)*sqrt(arctan(a*x))/a-3/40*c^2*(a^2*x^2+1)^2*sqrt(arctan(a*x))/a+4/15*c^2*x*(a^2*x^2+1)*arctan(a*x)^(3/2)+1/5*c^2*x*(a^2*x^2+1)^2*arctan(a*x)^(3/2)+1/10*c^2*Defer(Int)(1/sqrt(arctan(a*x)),x)+3/80*c*Defer(Int)((a^2*c*x^2+c)/sqrt(arctan(a*x)),x)+8/15*c^2*Defer(Int)(arctan(a*x)^(3/2),x),0],
[(a^2*c*x^2+c)^2*arctan(a*x)^(3/2)/x,x,0,Defer(Int)((a^2*c*x^2+c)^2*arctan(a*x)^(3/2)/x,x),0],
[(a^2*c*x^2+c)^2*arctan(a*x)^(3/2)/x^2,x,0,Defer(Int)((a^2*c*x^2+c)^2*arctan(a*x)^(3/2)/x^2,x),0],
[x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x),0],
[x^2*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x,0,Defer(Int)(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x),0],
[x*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x,1,1/8*c^3*(a^2*x^2+1)^4*arctan(a*x)^(3/2)/a^2-3/16*Defer(Int)((a^2*c*x^2+c)^3*sqrt(arctan(a*x)),x)/a,0],
[(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x,3,-6/35*c^3*(a^2*x^2+1)*sqrt(arctan(a*x))/a-9/140*c^3*(a^2*x^2+1)^2*sqrt(arctan(a*x))/a-1/28*c^3*(a^2*x^2+1)^3*sqrt(arctan(a*x))/a+8/35*c^3*x*(a^2*x^2+1)*arctan(a*x)^(3/2)+6/35*c^3*x*(a^2*x^2+1)^2*arctan(a*x)^(3/2)+1/7*c^3*x*(a^2*x^2+1)^3*arctan(a*x)^(3/2)+3/35*c^3*Defer(Int)(1/sqrt(arctan(a*x)),x)+9/280*c^2*Defer(Int)((a^2*c*x^2+c)/sqrt(arctan(a*x)),x)+1/56*c*Defer(Int)((a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)+16/35*c^3*Defer(Int)(arctan(a*x)^(3/2),x),0],
[(a^2*c*x^2+c)^3*arctan(a*x)^(3/2)/x,x,0,Defer(Int)((a^2*c*x^2+c)^3*arctan(a*x)^(3/2)/x,x),0],
[(a^2*c*x^2+c)^3*arctan(a*x)^(3/2)/x^2,x,0,Defer(Int)((a^2*c*x^2+c)^3*arctan(a*x)^(3/2)/x^2,x),0],
[x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x,0,Defer(Int)(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x),0],
[x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x,2,-2/5*x*arctan(a*x)^(5/2)/a^3/c+Defer(Int)(x*arctan(a*x)^(3/2),x)/a^2/c+2/5*Defer(Int)(arctan(a*x)^(5/2),x)/a^3/c,0],
[x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x,2,-2/5*arctan(a*x)^(5/2)/a^3/c+Defer(Int)(arctan(a*x)^(3/2),x)/a^2/c,0],
[x*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x,1,2/5*x*arctan(a*x)^(5/2)/a/c-2/5*Defer(Int)(arctan(a*x)^(5/2),x)/a/c,0],
[arctan(a*x)^(3/2)/(a^2*c*x^2+c),x,1,2/5*arctan(a*x)^(5/2)/a/c,1],
[arctan(a*x)^(3/2)/x/(a^2*c*x^2+c),x,1,-2/5*I*arctan(a*x)^(5/2)/c+I*Defer(Int)(arctan(a*x)^(3/2)/x/(I+a*x),x)/c,0],
[arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c),x,2,-2/5*a*arctan(a*x)^(5/2)/c+Defer(Int)(arctan(a*x)^(3/2)/x^2,x)/c,0],
[arctan(a*x)^(3/2)/x^3/(a^2*c*x^2+c),x,2,2/5*I*a^2*arctan(a*x)^(5/2)/c+Defer(Int)(arctan(a*x)^(3/2)/x^3,x)/c-I*a^2*Defer(Int)(arctan(a*x)^(3/2)/x/(I+a*x),x)/c,0],
[arctan(a*x)^(3/2)/x^4/(a^2*c*x^2+c),x,3,2/5*a^3*arctan(a*x)^(5/2)/c+Defer(Int)(arctan(a*x)^(3/2)/x^4,x)/c-a^2*Defer(Int)(arctan(a*x)^(3/2)/x^2,x)/c,0],
[x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x,0,Defer(Int)(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x),0],
[x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x,0,Defer(Int)(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x),0],
[x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x,7,3/16*sqrt(arctan(a*x))/a^3/c^2-3/8*sqrt(arctan(a*x))/a^3/c^2/(a^2*x^2+1)-1/2*x*arctan(a*x)^(3/2)/a^2/c^2/(a^2*x^2+1)+1/5*arctan(a*x)^(5/2)/a^3/c^2+3/32*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^3/c^2,1],
[x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x,7,3/8*x*sqrt(arctan(a*x))/a/c^2/(a^2*x^2+1)+1/4*arctan(a*x)^(3/2)/a^2/c^2-1/2*arctan(a*x)^(3/2)/a^2/c^2/(a^2*x^2+1)-3/32*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^2/c^2,1],
[arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x,7,-3/16*sqrt(arctan(a*x))/a/c^2+3/8*sqrt(arctan(a*x))/a/c^2/(a^2*x^2+1)+1/2*x*arctan(a*x)^(3/2)/c^2/(a^2*x^2+1)+1/5*arctan(a*x)^(5/2)/a/c^2-3/32*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a/c^2,1],
[arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^2,x,0,Defer(Int)(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^2,x),0],
[x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x,0,Defer(Int)(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x),0],
[x^5*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x,0,Defer(Int)(x^5*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x),0],
[x^4*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x,15,27/256*sqrt(arctan(a*x))/a^5/c^3+3/32*x^4*sqrt(arctan(a*x))/a/c^3/(a^2*x^2+1)^2-9/32*sqrt(arctan(a*x))/a^5/c^3/(a^2*x^2+1)-1/4*x^3*arctan(a*x)^(3/2)/a^2/c^3/(a^2*x^2+1)^2-3/8*x*arctan(a*x)^(3/2)/a^4/c^3/(a^2*x^2+1)+3/20*arctan(a*x)^(5/2)/a^5/c^3-3/512*sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^5/c^3+3/32*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^5/c^3,1],
[x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x,10,-3/32*arctan(a*x)^(3/2)/a^4/c^3+1/4*x^4*arctan(a*x)^(3/2)/c^3/(a^2*x^2+1)^2+3/512*sqrt(1/2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^4/c^3-3/64*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^4/c^3+3/32*sqrt(arctan(a*x))*sin(2*arctan(a*x))/a^4/c^3-3/256*sqrt(arctan(a*x))*sin(4*arctan(a*x))/a^4/c^3,1],
[x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x,7,1/20*arctan(a*x)^(5/2)/a^3/c^3-3/256*sqrt(arctan(a*x))*cos(4*arctan(a*x))/a^3/c^3+3/512*sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c^3-1/32*arctan(a*x)^(3/2)*sin(4*arctan(a*x))/a^3/c^3,1],
[x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x,10,3/32*arctan(a*x)^(3/2)/a^2/c^3-1/4*arctan(a*x)^(3/2)/a^2/c^3/(a^2*x^2+1)^2-3/512*sqrt(1/2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c^3-3/64*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^2/c^3+3/32*sqrt(arctan(a*x))*sin(2*arctan(a*x))/a^2/c^3+3/256*sqrt(arctan(a*x))*sin(4*arctan(a*x))/a^2/c^3,1],
[arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x,15,-45/256*sqrt(arctan(a*x))/a/c^3+3/32*sqrt(arctan(a*x))/a/c^3/(a^2*x^2+1)^2+9/32*sqrt(arctan(a*x))/a/c^3/(a^2*x^2+1)+1/4*x*arctan(a*x)^(3/2)/c^3/(a^2*x^2+1)^2+3/8*x*arctan(a*x)^(3/2)/c^3/(a^2*x^2+1)+3/20*arctan(a*x)^(5/2)/a/c^3-3/512*sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c^3-3/32*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a/c^3,1],
[arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^3,x,0,Defer(Int)(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^3,x),0],
[x^m*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2),x,0,Defer(Int)(x^m*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2),x),0],
[x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2),x,0,Defer(Int)(x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2),x),0],
[x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2),x,1,1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2)/a^2/c-1/2*Defer(Int)(sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x)),x)/a,0],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2),x,1,-3/4*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/a+1/2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)+3/8*c*Defer(Int)(1/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)+1/2*c*Defer(Int)(arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x),0],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/x,x,0,Defer(Int)(sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/x,x),0],
[x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x),0],
[x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x,0,Defer(Int)(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x),0],
[x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x,1,1/5*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2)/a^2/c-3/10*Defer(Int)((a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x)),x)/a,0],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x,2,-9/16*c*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/a-1/8*(a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x))/a+3/8*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)+1/4*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2)+9/32*c^2*Defer(Int)(1/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)+1/16*c*Defer(Int)(sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)+3/8*c^2*Defer(Int)(arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x),0],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2)/x,x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2)/x,x),0],
[x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x),0],
[x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x,0,Defer(Int)(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x),0],
[x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x,1,1/7*(a^2*c*x^2+c)^(7/2)*arctan(a*x)^(3/2)/a^2/c-3/14*Defer(Int)((a^2*c*x^2+c)^(5/2)*sqrt(arctan(a*x)),x)/a,0],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x,3,-15/32*c^2*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/a-5/48*c*(a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x))/a-1/20*(a^2*c*x^2+c)^(5/2)*sqrt(arctan(a*x))/a+5/16*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)+5/24*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2)+1/6*x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2)+15/64*c^3*Defer(Int)(1/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)+5/96*c^2*Defer(Int)(sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)+1/40*c*Defer(Int)((a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)+5/16*c^3*Defer(Int)(arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x),0],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2)/x,x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2)/x,x),0],
[x^m*arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x,0,Defer(Int)(x^m*arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x),0],
[x^3*arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x,4,-1/4*x*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/a^3/c-2/3*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/a^4/c+1/3*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/a^2/c+1/8*Defer(Int)(x/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a^2+5/4*Defer(Int)(sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x)/a^3,0],
[x^2*arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x,2,-3/4*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/a^3/c+1/2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/a^2/c+3/8*Defer(Int)(1/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a^2-1/2*Defer(Int)(arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x)/a^2,0],
[x*arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x,1,sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/a^2/c-3/2*Defer(Int)(sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x)/a,0],
[arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x,0,Defer(Int)(arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x),0],
[arctan(a*x)^(3/2)/x/sqrt(a^2*c*x^2+c),x,0,Defer(Int)(arctan(a*x)^(3/2)/x/sqrt(a^2*c*x^2+c),x),0],
[arctan(a*x)^(3/2)/x^2/sqrt(a^2*c*x^2+c),x,1,-sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/c/x+3/2*a*Defer(Int)(sqrt(arctan(a*x))/x/sqrt(a^2*c*x^2+c),x),0],
[arctan(a*x)^(3/2)/x^3/sqrt(a^2*c*x^2+c),x,2,-3/4*a*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/c/x-1/2*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/c/x^2+3/8*a^2*Defer(Int)(1/x/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)-1/2*a^2*Defer(Int)(arctan(a*x)^(3/2)/x/sqrt(a^2*c*x^2+c),x),0],
[arctan(a*x)^(3/2)/x^4/sqrt(a^2*c*x^2+c),x,4,-1/4*a*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/c/x^2-1/3*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/c/x^3+2/3*a^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/c/x+1/8*a^2*Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)-5/4*a^3*Defer(Int)(sqrt(arctan(a*x))/x/sqrt(a^2*c*x^2+c),x),0],
[x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x),0],
[x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x),0],
[x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x),0],
[x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x,6,3/2*x*sqrt(arctan(a*x))/a/c/sqrt(a^2*c*x^2+c)-arctan(a*x)^(3/2)/a^2/c/sqrt(a^2*c*x^2+c)-3/2*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x,5,3/2*sqrt(arctan(a*x))/a/c/sqrt(a^2*c*x^2+c)+x*arctan(a*x)^(3/2)/c/sqrt(a^2*c*x^2+c)-3/2*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(3/2),x),0],
[arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(3/2),x),0],
[x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x,0,Defer(Int)(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x),0],
[x^5*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x,0,Defer(Int)(x^5*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x),0],
[x^4*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x,0,Defer(Int)(x^4*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x),0],
[x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x,15,1/6*x^3*sqrt(arctan(a*x))/a/c/(a^2*c*x^2+c)^(3/2)+x*sqrt(arctan(a*x))/a^3/c^2/sqrt(a^2*c*x^2+c)-1/3*x^2*arctan(a*x)^(3/2)/a^2/c/(a^2*c*x^2+c)^(3/2)-2/3*arctan(a*x)^(3/2)/a^4/c^2/sqrt(a^2*c*x^2+c)-9/8*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^4/c^2/sqrt(a^2*c*x^2+c)+1/24*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^4/c^2/sqrt(a^2*c*x^2+c),1],
[x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x,11,3/8*sqrt(arctan(a*x))/a^3/c^2/sqrt(a^2*c*x^2+c)+1/3*x^3*arctan(a*x)^(3/2)/c/(a^2*c*x^2+c)^(3/2)-1/24*sqrt(a^2*x^2+1)*sqrt(arctan(a*x))*cos(3*arctan(a*x))/a^3/c^2/sqrt(a^2*c*x^2+c)-3/8*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c)+1/24*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c),1],
[x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x,11,3/8*x*sqrt(arctan(a*x))/a/c^2/sqrt(a^2*c*x^2+c)-1/3*arctan(a*x)^(3/2)/a^2/c/(a^2*c*x^2+c)^(3/2)-3/8*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c)-1/24*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c)+1/24*sqrt(a^2*x^2+1)*sqrt(arctan(a*x))*sin(3*arctan(a*x))/a^2/c^2/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x,14,1/6*sqrt(arctan(a*x))/a/c/(a^2*c*x^2+c)^(3/2)+sqrt(arctan(a*x))/a/c^2/sqrt(a^2*c*x^2+c)+1/3*x*arctan(a*x)^(3/2)/c/(a^2*c*x^2+c)^(3/2)+2/3*x*arctan(a*x)^(3/2)/c^2/sqrt(a^2*c*x^2+c)-9/8*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c^2/sqrt(a^2*c*x^2+c)-1/24*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/a/c^2/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(5/2),x,0,Defer(Int)(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(5/2),x),0],
[arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(5/2),x,0,Defer(Int)(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(5/2),x),0],
[x^m*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x),0],
[x^2*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x,0,Defer(Int)(x^2*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x),0],
[x*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x,2,5/32*c*(a^2*x^2+1)*sqrt(arctan(a*x))/a^2-5/24*c*x*(a^2*x^2+1)*arctan(a*x)^(3/2)/a+1/4*c*(a^2*x^2+1)^2*arctan(a*x)^(5/2)/a^2-5/64*c*Defer(Int)(1/sqrt(arctan(a*x)),x)/a-5/12*c*Defer(Int)(arctan(a*x)^(3/2),x)/a,0],
[(a^2*c*x^2+c)*arctan(a*x)^(5/2),x,1,-5/12*c*(a^2*x^2+1)*arctan(a*x)^(3/2)/a+1/3*c*x*(a^2*x^2+1)*arctan(a*x)^(5/2)+5/8*c*Defer(Int)(sqrt(arctan(a*x)),x)+2/3*c*Defer(Int)(arctan(a*x)^(5/2),x),0],
[(a^2*c*x^2+c)*arctan(a*x)^(5/2)/x,x,0,Defer(Int)((a^2*c*x^2+c)*arctan(a*x)^(5/2)/x,x),0],
[(a^2*c*x^2+c)*arctan(a*x)^(5/2)/x^2,x,0,Defer(Int)((a^2*c*x^2+c)*arctan(a*x)^(5/2)/x^2,x),0],
[x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x),0],
[x^2*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x,0,Defer(Int)(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x),0],
[x*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x,3,1/12*c^2*(a^2*x^2+1)*sqrt(arctan(a*x))/a^2+1/32*c^2*(a^2*x^2+1)^2*sqrt(arctan(a*x))/a^2-1/9*c^2*x*(a^2*x^2+1)*arctan(a*x)^(3/2)/a-1/12*c^2*x*(a^2*x^2+1)^2*arctan(a*x)^(3/2)/a+1/6*c^2*(a^2*x^2+1)^3*arctan(a*x)^(5/2)/a^2-1/24*c^2*Defer(Int)(1/sqrt(arctan(a*x)),x)/a-1/64*c*Defer(Int)((a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a-2/9*c^2*Defer(Int)(arctan(a*x)^(3/2),x)/a,0],
[(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x,2,-1/3*c^2*(a^2*x^2+1)*arctan(a*x)^(3/2)/a-1/8*c^2*(a^2*x^2+1)^2*arctan(a*x)^(3/2)/a+4/15*c^2*x*(a^2*x^2+1)*arctan(a*x)^(5/2)+1/5*c^2*x*(a^2*x^2+1)^2*arctan(a*x)^(5/2)+1/2*c^2*Defer(Int)(sqrt(arctan(a*x)),x)+3/16*c*Defer(Int)((a^2*c*x^2+c)*sqrt(arctan(a*x)),x)+8/15*c^2*Defer(Int)(arctan(a*x)^(5/2),x),0],
[(a^2*c*x^2+c)^2*arctan(a*x)^(5/2)/x,x,0,Defer(Int)((a^2*c*x^2+c)^2*arctan(a*x)^(5/2)/x,x),0],
[(a^2*c*x^2+c)^2*arctan(a*x)^(5/2)/x^2,x,0,Defer(Int)((a^2*c*x^2+c)^2*arctan(a*x)^(5/2)/x^2,x),0],
[x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x),0],
[x^2*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x,0,Defer(Int)(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x),0],
[x*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x,4,3/56*c^3*(a^2*x^2+1)*sqrt(arctan(a*x))/a^2+9/448*c^3*(a^2*x^2+1)^2*sqrt(arctan(a*x))/a^2+5/448*c^3*(a^2*x^2+1)^3*sqrt(arctan(a*x))/a^2-1/14*c^3*x*(a^2*x^2+1)*arctan(a*x)^(3/2)/a-3/56*c^3*x*(a^2*x^2+1)^2*arctan(a*x)^(3/2)/a-5/112*c^3*x*(a^2*x^2+1)^3*arctan(a*x)^(3/2)/a+1/8*c^3*(a^2*x^2+1)^4*arctan(a*x)^(5/2)/a^2-3/112*c^3*Defer(Int)(1/sqrt(arctan(a*x)),x)/a-9/896*c^2*Defer(Int)((a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a-5/896*c*Defer(Int)((a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)/a-1/7*c^3*Defer(Int)(arctan(a*x)^(3/2),x)/a,0],
[(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x,3,-2/7*c^3*(a^2*x^2+1)*arctan(a*x)^(3/2)/a-3/28*c^3*(a^2*x^2+1)^2*arctan(a*x)^(3/2)/a-5/84*c^3*(a^2*x^2+1)^3*arctan(a*x)^(3/2)/a+8/35*c^3*x*(a^2*x^2+1)*arctan(a*x)^(5/2)+6/35*c^3*x*(a^2*x^2+1)^2*arctan(a*x)^(5/2)+1/7*c^3*x*(a^2*x^2+1)^3*arctan(a*x)^(5/2)+3/7*c^3*Defer(Int)(sqrt(arctan(a*x)),x)+9/56*c^2*Defer(Int)((a^2*c*x^2+c)*sqrt(arctan(a*x)),x)+5/56*c*Defer(Int)((a^2*c*x^2+c)^2*sqrt(arctan(a*x)),x)+16/35*c^3*Defer(Int)(arctan(a*x)^(5/2),x),0],
[(a^2*c*x^2+c)^3*arctan(a*x)^(5/2)/x,x,0,Defer(Int)((a^2*c*x^2+c)^3*arctan(a*x)^(5/2)/x,x),0],
[(a^2*c*x^2+c)^3*arctan(a*x)^(5/2)/x^2,x,0,Defer(Int)((a^2*c*x^2+c)^3*arctan(a*x)^(5/2)/x^2,x),0],
[x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x,0,Defer(Int)(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x),0],
[x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x,2,-2/7*x*arctan(a*x)^(7/2)/a^3/c+Defer(Int)(x*arctan(a*x)^(5/2),x)/a^2/c+2/7*Defer(Int)(arctan(a*x)^(7/2),x)/a^3/c,0],
[x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x,2,-2/7*arctan(a*x)^(7/2)/a^3/c+Defer(Int)(arctan(a*x)^(5/2),x)/a^2/c,0],
[x*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x,1,2/7*x*arctan(a*x)^(7/2)/a/c-2/7*Defer(Int)(arctan(a*x)^(7/2),x)/a/c,0],
[arctan(a*x)^(5/2)/(a^2*c*x^2+c),x,1,2/7*arctan(a*x)^(7/2)/a/c,1],
[arctan(a*x)^(5/2)/x/(a^2*c*x^2+c),x,1,-2/7*I*arctan(a*x)^(7/2)/c+I*Defer(Int)(arctan(a*x)^(5/2)/x/(I+a*x),x)/c,0],
[arctan(a*x)^(5/2)/x^2/(a^2*c*x^2+c),x,2,-2/7*a*arctan(a*x)^(7/2)/c+Defer(Int)(arctan(a*x)^(5/2)/x^2,x)/c,0],
[arctan(a*x)^(5/2)/x^3/(a^2*c*x^2+c),x,2,2/7*I*a^2*arctan(a*x)^(7/2)/c+Defer(Int)(arctan(a*x)^(5/2)/x^3,x)/c-I*a^2*Defer(Int)(arctan(a*x)^(5/2)/x/(I+a*x),x)/c,0],
[arctan(a*x)^(5/2)/x^4/(a^2*c*x^2+c),x,3,2/7*a^3*arctan(a*x)^(7/2)/c+Defer(Int)(arctan(a*x)^(5/2)/x^4,x)/c-a^2*Defer(Int)(arctan(a*x)^(5/2)/x^2,x)/c,0],
[x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x,0,Defer(Int)(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x),0],
[x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x,0,Defer(Int)(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x),0],
[x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x,8,15/32*x*sqrt(arctan(a*x))/a^2/c^2/(a^2*x^2+1)+5/16*arctan(a*x)^(3/2)/a^3/c^2-5/8*arctan(a*x)^(3/2)/a^3/c^2/(a^2*x^2+1)-1/2*x*arctan(a*x)^(5/2)/a^2/c^2/(a^2*x^2+1)+1/7*arctan(a*x)^(7/2)/a^3/c^2-15/128*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^3/c^2,1],
[x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x,8,-15/64*sqrt(arctan(a*x))/a^2/c^2+15/32*sqrt(arctan(a*x))/a^2/c^2/(a^2*x^2+1)+5/8*x*arctan(a*x)^(3/2)/a/c^2/(a^2*x^2+1)+1/4*arctan(a*x)^(5/2)/a^2/c^2-1/2*arctan(a*x)^(5/2)/a^2/c^2/(a^2*x^2+1)-15/128*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^2/c^2,1],
[arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x,8,-15/32*x*sqrt(arctan(a*x))/c^2/(a^2*x^2+1)-5/16*arctan(a*x)^(3/2)/a/c^2+5/8*arctan(a*x)^(3/2)/a/c^2/(a^2*x^2+1)+1/2*x*arctan(a*x)^(5/2)/c^2/(a^2*x^2+1)+1/7*arctan(a*x)^(7/2)/a/c^2+15/128*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a/c^2,1],
[arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^2,x,0,Defer(Int)(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^2,x),0],
[x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x,0,Defer(Int)(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x),0],
[x^5*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x,0,Defer(Int)(x^5*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x),0],
[x^4*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x,18,45/128*x*sqrt(arctan(a*x))/a^4/c^3/(a^2*x^2+1)+45/256*arctan(a*x)^(3/2)/a^5/c^3+5/32*x^4*arctan(a*x)^(3/2)/a/c^3/(a^2*x^2+1)^2-15/32*arctan(a*x)^(3/2)/a^5/c^3/(a^2*x^2+1)-1/4*x^3*arctan(a*x)^(5/2)/a^2/c^3/(a^2*x^2+1)^2-3/8*x*arctan(a*x)^(5/2)/a^4/c^3/(a^2*x^2+1)+3/28*arctan(a*x)^(7/2)/a^5/c^3+15/4096*sqrt(1/2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^5/c^3-15/128*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^5/c^3+15/256*sqrt(arctan(a*x))*sin(2*arctan(a*x))/a^5/c^3-15/2048*sqrt(arctan(a*x))*sin(4*arctan(a*x))/a^5/c^3,1],
[x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x,16,-135/2048*sqrt(arctan(a*x))/a^4/c^3-15/256*x^4*sqrt(arctan(a*x))/c^3/(a^2*x^2+1)^2+45/256*sqrt(arctan(a*x))/a^4/c^3/(a^2*x^2+1)+5/32*x^3*arctan(a*x)^(3/2)/a/c^3/(a^2*x^2+1)^2+15/64*x*arctan(a*x)^(3/2)/a^3/c^3/(a^2*x^2+1)-3/32*arctan(a*x)^(5/2)/a^4/c^3+1/4*x^4*arctan(a*x)^(5/2)/c^3/(a^2*x^2+1)^2+15/4096*sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^4/c^3-15/256*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^4/c^3,1],
[x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x,8,1/28*arctan(a*x)^(7/2)/a^3/c^3-5/256*arctan(a*x)^(3/2)*cos(4*arctan(a*x))/a^3/c^3-15/4096*sqrt(1/2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c^3+15/2048*sqrt(arctan(a*x))*sin(4*arctan(a*x))/a^3/c^3-1/32*arctan(a*x)^(5/2)*sin(4*arctan(a*x))/a^3/c^3,1],
[x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x,16,-225/2048*sqrt(arctan(a*x))/a^2/c^3+15/256*sqrt(arctan(a*x))/a^2/c^3/(a^2*x^2+1)^2+45/256*sqrt(arctan(a*x))/a^2/c^3/(a^2*x^2+1)+5/32*x*arctan(a*x)^(3/2)/a/c^3/(a^2*x^2+1)^2+15/64*x*arctan(a*x)^(3/2)/a/c^3/(a^2*x^2+1)+3/32*arctan(a*x)^(5/2)/a^2/c^3-1/4*arctan(a*x)^(5/2)/a^2/c^3/(a^2*x^2+1)^2-15/4096*sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c^3-15/256*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^2/c^3,1],
[arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x,18,-45/128*x*sqrt(arctan(a*x))/c^3/(a^2*x^2+1)-75/256*arctan(a*x)^(3/2)/a/c^3+5/32*arctan(a*x)^(3/2)/a/c^3/(a^2*x^2+1)^2+15/32*arctan(a*x)^(3/2)/a/c^3/(a^2*x^2+1)+1/4*x*arctan(a*x)^(5/2)/c^3/(a^2*x^2+1)^2+3/8*x*arctan(a*x)^(5/2)/c^3/(a^2*x^2+1)+3/28*arctan(a*x)^(7/2)/a/c^3+15/4096*sqrt(1/2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c^3+15/128*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a/c^3-15/256*sqrt(arctan(a*x))*sin(2*arctan(a*x))/a/c^3-15/2048*sqrt(arctan(a*x))*sin(4*arctan(a*x))/a/c^3,1],
[arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^3,x,0,Defer(Int)(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^3,x),0],
[x^m*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2),x,0,Defer(Int)(x^m*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2),x),0],
[x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2),x,0,Defer(Int)(x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2),x),0],
[x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2),x,2,5/8*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/a^2-5/12*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/a+1/3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2)/a^2/c-5/16*c*Defer(Int)(1/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a-5/12*c*Defer(Int)(arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x)/a,0],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2),x,1,-5/4*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/a+1/2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2)+15/8*c*Defer(Int)(sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x)+1/2*c*Defer(Int)(arctan(a*x)^(5/2)/sqrt(a^2*c*x^2+c),x),0],
[sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2)/x,x,0,Defer(Int)(sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2)/x,x),0],
[x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x),0],
[x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x,0,Defer(Int)(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x),0],
[x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x,3,9/32*c*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/a^2+1/16*(a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x))/a^2-3/16*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/a-1/8*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2)/a+1/5*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2)/a^2/c-9/64*c^2*Defer(Int)(1/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a-1/32*c*Defer(Int)(sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a-3/16*c^2*Defer(Int)(arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x)/a,0],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x,2,-15/16*c*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/a-5/24*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2)/a+3/8*c*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2)+1/4*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2)+45/32*c^2*Defer(Int)(sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x)+5/16*c*Defer(Int)(sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x)),x)+3/8*c^2*Defer(Int)(arctan(a*x)^(5/2)/sqrt(a^2*c*x^2+c),x),0],
[(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2)/x,x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2)/x,x),0],
[x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x),0],
[x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x,0,Defer(Int)(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x),0],
[x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x,4,75/448*c^2*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/a^2+25/672*c*(a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x))/a^2+1/56*(a^2*c*x^2+c)^(5/2)*sqrt(arctan(a*x))/a^2-25/224*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/a-25/336*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2)/a-5/84*x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2)/a+1/7*(a^2*c*x^2+c)^(7/2)*arctan(a*x)^(5/2)/a^2/c-75/896*c^3*Defer(Int)(1/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a-25/1344*c^2*Defer(Int)(sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a-1/112*c*Defer(Int)((a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)/a-25/224*c^3*Defer(Int)(arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x)/a,0],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x,3,-25/32*c^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/a-25/144*c*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2)/a-1/12*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2)/a+5/16*c^2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2)+5/24*c*x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2)+1/6*x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2)+75/64*c^3*Defer(Int)(sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x)+25/96*c^2*Defer(Int)(sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x)),x)+1/8*c*Defer(Int)((a^2*c*x^2+c)^(3/2)*sqrt(arctan(a*x)),x)+5/16*c^3*Defer(Int)(arctan(a*x)^(5/2)/sqrt(a^2*c*x^2+c),x),0],
[(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2)/x,x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2)/x,x),0],
[x^m*arctan(a*x)^(5/2)/sqrt(a^2*c*x^2+c),x,0,Defer(Int)(x^m*arctan(a*x)^(5/2)/sqrt(a^2*c*x^2+c),x),0],
[x^3*arctan(a*x)^(5/2)/sqrt(a^2*c*x^2+c),x,5,5/8*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/a^4/c-5/12*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/a^3/c-2/3*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2)/a^4/c+1/3*x^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2)/a^2/c-5/16*Defer(Int)(1/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a^3+25/12*Defer(Int)(arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x)/a^3,0],
[x^2*arctan(a*x)^(5/2)/sqrt(a^2*c*x^2+c),x,2,-5/4*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/a^3/c+1/2*x*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2)/a^2/c+15/8*Defer(Int)(sqrt(arctan(a*x))/sqrt(a^2*c*x^2+c),x)/a^2-1/2*Defer(Int)(arctan(a*x)^(5/2)/sqrt(a^2*c*x^2+c),x)/a^2,0],
[x*arctan(a*x)^(5/2)/sqrt(a^2*c*x^2+c),x,1,sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2)/a^2/c-5/2*Defer(Int)(arctan(a*x)^(3/2)/sqrt(a^2*c*x^2+c),x)/a,0],
[arctan(a*x)^(5/2)/sqrt(a^2*c*x^2+c),x,0,Defer(Int)(arctan(a*x)^(5/2)/sqrt(a^2*c*x^2+c),x),0],
[arctan(a*x)^(5/2)/x/sqrt(a^2*c*x^2+c),x,0,Defer(Int)(arctan(a*x)^(5/2)/x/sqrt(a^2*c*x^2+c),x),0],
[arctan(a*x)^(5/2)/x^2/sqrt(a^2*c*x^2+c),x,1,-sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2)/c/x+5/2*a*Defer(Int)(arctan(a*x)^(3/2)/x/sqrt(a^2*c*x^2+c),x),0],
[arctan(a*x)^(5/2)/x^3/sqrt(a^2*c*x^2+c),x,2,-5/4*a*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/c/x-1/2*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2)/c/x^2+15/8*a^2*Defer(Int)(sqrt(arctan(a*x))/x/sqrt(a^2*c*x^2+c),x)-1/2*a^2*Defer(Int)(arctan(a*x)^(5/2)/x/sqrt(a^2*c*x^2+c),x),0],
[arctan(a*x)^(5/2)/x^4/sqrt(a^2*c*x^2+c),x,5,-5/8*a^2*sqrt(a^2*c*x^2+c)*sqrt(arctan(a*x))/c/x-5/12*a*sqrt(a^2*c*x^2+c)*arctan(a*x)^(3/2)/c/x^2-1/3*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2)/c/x^3+2/3*a^2*sqrt(a^2*c*x^2+c)*arctan(a*x)^(5/2)/c/x+5/16*a^3*Defer(Int)(1/x/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)-25/12*a^3*Defer(Int)(arctan(a*x)^(3/2)/x/sqrt(a^2*c*x^2+c),x),0],
[x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x),0],
[x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x),0],
[x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x,6,15/4*sqrt(arctan(a*x))/a^2/c/sqrt(a^2*c*x^2+c)+5/2*x*arctan(a*x)^(3/2)/a/c/sqrt(a^2*c*x^2+c)-arctan(a*x)^(5/2)/a^2/c/sqrt(a^2*c*x^2+c)-15/4*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x,6,-15/4*x*sqrt(arctan(a*x))/c/sqrt(a^2*c*x^2+c)+5/2*arctan(a*x)^(3/2)/a/c/sqrt(a^2*c*x^2+c)+x*arctan(a*x)^(5/2)/c/sqrt(a^2*c*x^2+c)+15/4*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(3/2),x,0,Defer(Int)(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(3/2),x),0],
[x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x,0,Defer(Int)(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x),0],
[x^4*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x,0,Defer(Int)(x^4*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x),0],
[x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x,17,45/16*sqrt(arctan(a*x))/a^4/c^2/sqrt(a^2*c*x^2+c)+5/18*x^3*arctan(a*x)^(3/2)/a/c/(a^2*c*x^2+c)^(3/2)+5/3*x*arctan(a*x)^(3/2)/a^3/c^2/sqrt(a^2*c*x^2+c)-1/3*x^2*arctan(a*x)^(5/2)/a^2/c/(a^2*c*x^2+c)^(3/2)-2/3*arctan(a*x)^(5/2)/a^4/c^2/sqrt(a^2*c*x^2+c)-5/144*sqrt(a^2*x^2+1)*sqrt(arctan(a*x))*cos(3*arctan(a*x))/a^4/c^2/sqrt(a^2*c*x^2+c)-45/16*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^4/c^2/sqrt(a^2*c*x^2+c)+5/144*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^4/c^2/sqrt(a^2*c*x^2+c),1],
[x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x,16,-5/36*x^3*sqrt(arctan(a*x))/c/(a^2*c*x^2+c)^(3/2)-5/6*x*sqrt(arctan(a*x))/a^2/c^2/sqrt(a^2*c*x^2+c)+5/18*x^2*arctan(a*x)^(3/2)/a/c/(a^2*c*x^2+c)^(3/2)+5/9*arctan(a*x)^(3/2)/a^3/c^2/sqrt(a^2*c*x^2+c)+1/3*x^3*arctan(a*x)^(5/2)/c/(a^2*c*x^2+c)^(3/2)+15/16*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c)-5/144*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c),1],
[x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x,15,5/36*sqrt(arctan(a*x))/a^2/c/(a^2*c*x^2+c)^(3/2)+5/6*sqrt(arctan(a*x))/a^2/c^2/sqrt(a^2*c*x^2+c)+5/18*x*arctan(a*x)^(3/2)/a/c/(a^2*c*x^2+c)^(3/2)+5/9*x*arctan(a*x)^(3/2)/a/c^2/sqrt(a^2*c*x^2+c)-1/3*arctan(a*x)^(5/2)/a^2/c/(a^2*c*x^2+c)^(3/2)-15/16*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c)-5/144*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x,17,-45/16*x*sqrt(arctan(a*x))/c^2/sqrt(a^2*c*x^2+c)+5/18*arctan(a*x)^(3/2)/a/c/(a^2*c*x^2+c)^(3/2)+5/3*arctan(a*x)^(3/2)/a/c^2/sqrt(a^2*c*x^2+c)+1/3*x*arctan(a*x)^(5/2)/c/(a^2*c*x^2+c)^(3/2)+2/3*x*arctan(a*x)^(5/2)/c^2/sqrt(a^2*c*x^2+c)+45/16*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c^2/sqrt(a^2*c*x^2+c)+5/144*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/a/c^2/sqrt(a^2*c*x^2+c)-5/144*sqrt(a^2*x^2+1)*sqrt(arctan(a*x))*sin(3*arctan(a*x))/a/c^2/sqrt(a^2*c*x^2+c),1],
[arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(5/2),x,0,Defer(Int)(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(5/2),x),0],
[x^m*(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[x*(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,0,Defer(Int)(x*(a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[(a^2*c*x^2+c)/x/sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)/x/sqrt(arctan(a*x)),x),0],
[x^m*(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[x*(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x,0,Defer(Int)(x*(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[(a^2*c*x^2+c)^2/x/sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)^2/x/sqrt(arctan(a*x)),x),0],
[x^m*(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x),0],
[x*(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x,0,Defer(Int)(x*(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x),0],
[(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x),0],
[(a^2*c*x^2+c)^3/x/sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)^3/x/sqrt(arctan(a*x)),x),0],
[x^m/(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[x/(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,1,2*x*sqrt(arctan(a*x))/a/c-2*Defer(Int)(sqrt(arctan(a*x)),x)/a/c,0],
[1/(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,1,2*sqrt(arctan(a*x))/a/c,1],
[1/x/(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,0,Defer(Int)(1/x/(a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[x^m/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[x^3/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x,0,Defer(Int)(x^3/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[x^2/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x,5,sqrt(arctan(a*x))/a^3/c^2-1/2*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^3/c^2,1],
[x/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x,5,1/2*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^2/c^2,1],
[1/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x,5,sqrt(arctan(a*x))/a/c^2+1/2*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a/c^2,1],
[1/x/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x,0,Defer(Int)(1/x/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[x^m/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x),0],
[x^5/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x,0,Defer(Int)(x^5/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x),0],
[x^4/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x,7,3/4*sqrt(arctan(a*x))/a^5/c^3+1/8*sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^5/c^3-1/2*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^5/c^3,1],
[x^3/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x,7,-1/8*sqrt(1/2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^4/c^3+1/4*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^4/c^3,1],
[x^2/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x,5,1/4*sqrt(arctan(a*x))/a^3/c^3-1/8*sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c^3,1],
[x/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x,7,1/8*sqrt(1/2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c^3+1/4*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^2/c^3,1],
[1/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x,7,3/4*sqrt(arctan(a*x))/a/c^3+1/8*sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c^3+1/2*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a/c^3,1],
[1/x/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x,0,Defer(Int)(1/x/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x),0],
[x^m*sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,0,Defer(Int)(x^m*sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[x*sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,0,Defer(Int)(x*sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,0,Defer(Int)(sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[sqrt(a^2*c*x^2+c)/x/sqrt(arctan(a*x)),x,0,Defer(Int)(sqrt(a^2*c*x^2+c)/x/sqrt(arctan(a*x)),x),0],
[x^m*(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[x*(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x,0,Defer(Int)(x*(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[(a^2*c*x^2+c)^(3/2)/x/sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)/x/sqrt(arctan(a*x)),x),0],
[x^m*(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x),0],
[x*(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x,0,Defer(Int)(x*(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x),0],
[(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x),0],
[(a^2*c*x^2+c)^(5/2)/x/sqrt(arctan(a*x)),x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)/x/sqrt(arctan(a*x)),x),0],
[x^m/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,0,Defer(Int)(x^m/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[x/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,0,Defer(Int)(x/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[1/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,0,Defer(Int)(1/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[1/x/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x,0,Defer(Int)(1/x/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x),0],
[x^m/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[x^2/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x,0,Defer(Int)(x^2/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[x/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x,4,sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c/sqrt(a^2*c*x^2+c),1],
[1/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x,4,sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c/sqrt(a^2*c*x^2+c),1],
[1/x/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x,0,Defer(Int)(1/x/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[x^m/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x),0],
[x^4/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x,0,Defer(Int)(x^4/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x),0],
[x^3/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x,8,3/2*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^4/c^2/sqrt(a^2*c*x^2+c)-1/2*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^4/c^2/sqrt(a^2*c*x^2+c),1],
[x^2/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x,8,1/2*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c)-1/2*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c),1],
[x/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x,8,1/2*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c)+1/2*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c),1],
[1/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x,8,3/2*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c^2/sqrt(a^2*c*x^2+c)+1/2*sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/a/c^2/sqrt(a^2*c*x^2+c),1],
[1/x/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x,0,Defer(Int)(1/x/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x),0],
[x^m*(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)/arctan(a*x)^(3/2),x),0],
[x*(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,0,Defer(Int)(x*(a^2*c*x^2+c)/arctan(a*x)^(3/2),x),0],
[(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,0,Defer(Int)((a^2*c*x^2+c)/arctan(a*x)^(3/2),x),0],
[(a^2*c*x^2+c)/x/arctan(a*x)^(3/2),x,0,Defer(Int)((a^2*c*x^2+c)/x/arctan(a*x)^(3/2),x),0],
[x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x),0],
[x*(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x,0,Defer(Int)(x*(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x),0],
[(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x,0,Defer(Int)((a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x),0],
[(a^2*c*x^2+c)^2/x/arctan(a*x)^(3/2),x,0,Defer(Int)((a^2*c*x^2+c)^2/x/arctan(a*x)^(3/2),x),0],
[x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x),0],
[x*(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x,0,Defer(Int)(x*(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x),0],
[(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x,0,Defer(Int)((a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x),0],
[(a^2*c*x^2+c)^3/x/arctan(a*x)^(3/2),x,0,Defer(Int)((a^2*c*x^2+c)^3/x/arctan(a*x)^(3/2),x),0],
[x^m/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,1,-2*x^m/a/c/sqrt(arctan(a*x))+2*m*Defer(Int)(x^(-1+m)/sqrt(arctan(a*x)),x)/a/c,0],
[x/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,1,-2*x/a/c/sqrt(arctan(a*x))+2*Defer(Int)(1/sqrt(arctan(a*x)),x)/a/c,0],
[1/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,1,-2/a/c/sqrt(arctan(a*x)),1],
[1/x/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,1,-2/a/c/x/sqrt(arctan(a*x))-2*Defer(Int)(1/x^2/sqrt(arctan(a*x)),x)/a/c,0],
[x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x),0],
[x^4/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x,1,-2*x^4/a/c^2/(a^2*x^2+1)/sqrt(arctan(a*x))+8*Defer(Int)(x^3/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)/a+4*a*Defer(Int)(x^5/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x,6,-2*x^3/a/c^2/(a^2*x^2+1)/sqrt(arctan(a*x))+6*sqrt(arctan(a*x))/a^4/c^2-3*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^4/c^2+2*a*Defer(Int)(x^4/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x,6,-2*x^2/a/c^2/(a^2*x^2+1)/sqrt(arctan(a*x))+2*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^3/c^2,1],
[x/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x,7,-2*x/a/c^2/(a^2*x^2+1)/sqrt(arctan(a*x))+4*sqrt(arctan(a*x))/a^2/c^2-8*sqrt(arctan(a*x))/a^2/c^2/(a^2*x^2+1)+4*(-a^2*x^2+1)*sqrt(arctan(a*x))/a^2/c^2/(a^2*x^2+1)+2*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^2/c^2,1],
[1/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x,6,-2/a/c^2/(a^2*x^2+1)/sqrt(arctan(a*x))-2*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a/c^2,1],
[1/x/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x,6,-2/a/c^2/x/(a^2*x^2+1)/sqrt(arctan(a*x))-6*sqrt(arctan(a*x))/c^2-3*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/c^2-2*Defer(Int)(1/x^2/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)/a,0],
[1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x,1,-2/a/c^2/x^2/(a^2*x^2+1)/sqrt(arctan(a*x))-4*Defer(Int)(1/x^3/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)/a-8*a*Defer(Int)(1/x/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x,1,-2/a/c^2/x^3/(a^2*x^2+1)/sqrt(arctan(a*x))-6*Defer(Int)(1/x^4/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)/a-10*a*Defer(Int)(1/x^2/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x,1,-2/a/c^2/x^4/(a^2*x^2+1)/sqrt(arctan(a*x))-8*Defer(Int)(1/x^5/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)/a-12*a*Defer(Int)(1/x^3/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x),0],
[x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x,13,-2*x^3/a/c^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))-sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^4/c^3+sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^4/c^3,1],
[x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x,15,-2*x^2/a/c^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))+sqrt(1/2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c^3,1],
[x/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x,13,-2*x/a/c^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))+sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c^3+sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^2/c^3,1],
[1/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x,8,-2/a/c^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))-sqrt(1/2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c^3-2*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a/c^3,1],
[1/x/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x,8,-2/a/c^3/x/(a^2*x^2+1)^2/sqrt(arctan(a*x))-15/2*sqrt(arctan(a*x))/c^3-5/4*sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/c^3-5*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/c^3-2*Defer(Int)(1/x^2/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x)/a,0],
[1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x,1,-2/a/c^3/x^2/(a^2*x^2+1)^2/sqrt(arctan(a*x))-4*Defer(Int)(1/x^3/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x)/a-12*a*Defer(Int)(1/x/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x),0],
[1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x,1,-2/a/c^3/x^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))-6*Defer(Int)(1/x^4/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x)/a-14*a*Defer(Int)(1/x^2/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x),0],
[1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x,1,-2/a/c^3/x^4/(a^2*x^2+1)^2/sqrt(arctan(a*x))-8*Defer(Int)(1/x^5/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x)/a-16*a*Defer(Int)(1/x^3/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x),0],
[x^m*sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,0,Defer(Int)(x^m*sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x),0],
[x*sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,0,Defer(Int)(x*sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x),0],
[sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,0,Defer(Int)(sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x),0],
[sqrt(a^2*c*x^2+c)/x/arctan(a*x)^(3/2),x,0,Defer(Int)(sqrt(a^2*c*x^2+c)/x/arctan(a*x)^(3/2),x),0],
[x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x),0],
[x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x,0,Defer(Int)(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x),0],
[(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x),0],
[(a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(3/2),x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(3/2),x),0],
[x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x),0],
[x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x,0,Defer(Int)(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x),0],
[(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x),0],
[(a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(3/2),x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(3/2),x),0],
[x^m/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,0,Defer(Int)(x^m/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x),0],
[x/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,0,Defer(Int)(x/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x),0],
[1/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,0,Defer(Int)(1/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x),0],
[1/x/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,1,-2*sqrt(a^2*c*x^2+c)/a/c/x/sqrt(arctan(a*x))-2*Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x)),x)/a,0],
[1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x,0,Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x),0],
[x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x),0],
[x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x,1,-2*x^3/a/c/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))+6*Defer(Int)(x^2/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)/a+4*a*Defer(Int)(x^4/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x,5,-2*x^2/a/c/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))+4*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c/sqrt(a^2*c*x^2+c)+2*a*Defer(Int)(x^3/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x,5,-2*x/a/c/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))+2*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c/sqrt(a^2*c*x^2+c),1],
[1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x,5,-2/a/c/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))-2*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c/sqrt(a^2*c*x^2+c),1],
[1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x,5,-2/a/c/x/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))-4*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/c/sqrt(a^2*c*x^2+c)-2*Defer(Int)(1/x^2/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)/a,0],
[1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x,1,-2/a/c/x^2/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))-4*Defer(Int)(1/x^3/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)/a-6*a*Defer(Int)(1/x/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x,1,-2/a/c/x^3/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))-6*Defer(Int)(1/x^4/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)/a-8*a*Defer(Int)(1/x^2/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x,1,-2/a/c/x^4/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))-8*Defer(Int)(1/x^5/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)/a-10*a*Defer(Int)(1/x^3/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x),0],
[x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x,9,-2*x^3/a/c/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))+3*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^4/c^2/sqrt(a^2*c*x^2+c)-sqrt(3/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^4/c^2/sqrt(a^2*c*x^2+c),1],
[x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x,17,-2*x^2/a/c/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))-3*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c)+sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c)+sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c)+sqrt(2/3*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c),1],
[x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x,17,-2*x/a/c/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))+3*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c)-sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c)+sqrt(1/6*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c)+sqrt(2/3*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c),1],
[1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x,9,-2/a/c/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))-3*sqrt(1/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c^2/sqrt(a^2*c*x^2+c)-sqrt(3/2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/a/c^2/sqrt(a^2*c*x^2+c),1],
[1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x,9,-2/a/c/x/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))-6*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)-2*sqrt(2/3*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)-2*Defer(Int)(1/x^2/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x)/a,0],
[1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x,1,-2/a/c/x^2/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))-4*Defer(Int)(1/x^3/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x)/a-10*a*Defer(Int)(1/x/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x),0],
[1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x,1,-2/a/c/x^3/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))-6*Defer(Int)(1/x^4/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x)/a-12*a*Defer(Int)(1/x^2/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x),0],
[1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x,1,-2/a/c/x^4/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))-8*Defer(Int)(1/x^5/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x)/a-14*a*Defer(Int)(1/x^3/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x),0],
[x^m*(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)/arctan(a*x)^(5/2),x),0],
[x*(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,0,Defer(Int)(x*(a^2*c*x^2+c)/arctan(a*x)^(5/2),x),0],
[(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,0,Defer(Int)((a^2*c*x^2+c)/arctan(a*x)^(5/2),x),0],
[(a^2*c*x^2+c)/x/arctan(a*x)^(5/2),x,0,Defer(Int)((a^2*c*x^2+c)/x/arctan(a*x)^(5/2),x),0],
[x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x),0],
[x*(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x,0,Defer(Int)(x*(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x),0],
[(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x,0,Defer(Int)((a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x),0],
[(a^2*c*x^2+c)^2/x/arctan(a*x)^(5/2),x,0,Defer(Int)((a^2*c*x^2+c)^2/x/arctan(a*x)^(5/2),x),0],
[x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x),0],
[x*(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x,0,Defer(Int)(x*(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x),0],
[(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x,0,Defer(Int)((a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x),0],
[(a^2*c*x^2+c)^3/x/arctan(a*x)^(5/2),x,0,Defer(Int)((a^2*c*x^2+c)^3/x/arctan(a*x)^(5/2),x),0],
[x^m/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,1,-2/3*x^m/a/c/arctan(a*x)^(3/2)+2/3*m*Defer(Int)(x^(-1+m)/arctan(a*x)^(3/2),x)/a/c,0],
[x/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,1,-2/3*x/a/c/arctan(a*x)^(3/2)+2/3*Defer(Int)(1/arctan(a*x)^(3/2),x)/a/c,0],
[1/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,1,-2/3/a/c/arctan(a*x)^(3/2),1],
[1/x/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,1,-2/3/a/c/x/arctan(a*x)^(3/2)-2/3*Defer(Int)(1/x^2/arctan(a*x)^(3/2),x)/a/c,0],
[x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x),0],
[x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x,8,-2/3*x^3/a/c^2/(a^2*x^2+1)/arctan(a*x)^(3/2)-4*x^2/a^2/c^2/(a^2*x^2+1)/sqrt(arctan(a*x))-4/3*x^4/c^2/(a^2*x^2+1)/sqrt(arctan(a*x))+4*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^4/c^2+16/3*Defer(Int)(x^3/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)+8/3*a^2*Defer(Int)(x^5/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x,8,-2/3*x^2/a/c^2/(a^2*x^2+1)/arctan(a*x)^(3/2)-8/3*x/a^2/c^2/(a^2*x^2+1)/sqrt(arctan(a*x))+16/3*sqrt(arctan(a*x))/a^3/c^2-32/3*sqrt(arctan(a*x))/a^3/c^2/(a^2*x^2+1)+16/3*(-a^2*x^2+1)*sqrt(arctan(a*x))/a^3/c^2/(a^2*x^2+1)+8/3*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a^3/c^2,1],
[x/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x,6,-2/3*x/a/c^2/(a^2*x^2+1)/arctan(a*x)^(3/2)-4/3*(-a^2*x^2+1)/a^2/c^2/(a^2*x^2+1)/sqrt(arctan(a*x))-8/3*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^2/c^2,1],
[1/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x,8,-2/3/a/c^2/(a^2*x^2+1)/arctan(a*x)^(3/2)+8/3*x/c^2/(a^2*x^2+1)/sqrt(arctan(a*x))-16/3*sqrt(arctan(a*x))/a/c^2+32/3*sqrt(arctan(a*x))/a/c^2/(a^2*x^2+1)-16/3*(-a^2*x^2+1)*sqrt(arctan(a*x))/a/c^2/(a^2*x^2+1)-8/3*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a/c^2,1],
[1/x/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x,8,-2/3/a/c^2/x/(a^2*x^2+1)/arctan(a*x)^(3/2)+4/c^2/(a^2*x^2+1)/sqrt(arctan(a*x))+4/3/a^2/c^2/x^2/(a^2*x^2+1)/sqrt(arctan(a*x))+4*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/c^2+8/3*Defer(Int)(1/x^3/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)/a^2+16/3*Defer(Int)(1/x/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x,9,-2/3/a/c^2/x^2/(a^2*x^2+1)/arctan(a*x)^(3/2)+8/3/a^2/c^2/x^3/(a^2*x^2+1)/sqrt(arctan(a*x))+16/3/c^2/x/(a^2*x^2+1)/sqrt(arctan(a*x))+16*a*sqrt(arctan(a*x))/c^2+8*a*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/c^2+8*Defer(Int)(1/x^4/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)/a^2+56/3*Defer(Int)(1/x^2/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x,4,-2/3/a/c^2/x^3/(a^2*x^2+1)/arctan(a*x)^(3/2)+4/a^2/c^2/x^4/(a^2*x^2+1)/sqrt(arctan(a*x))+20/3/c^2/x^2/(a^2*x^2+1)/sqrt(arctan(a*x))+16*Defer(Int)(1/x^5/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)/a^2+112/3*Defer(Int)(1/x^3/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)+80/3*a^2*Defer(Int)(1/x/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x,4,-2/3/a/c^2/x^4/(a^2*x^2+1)/arctan(a*x)^(3/2)+16/3/a^2/c^2/x^5/(a^2*x^2+1)/sqrt(arctan(a*x))+8/c^2/x^3/(a^2*x^2+1)/sqrt(arctan(a*x))+80/3*Defer(Int)(1/x^6/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)/a^2+184/3*Defer(Int)(1/x^4/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x)+40*a^2*Defer(Int)(1/x^2/(a^2*c*x^2+c)^2/sqrt(arctan(a*x)),x),0],
[x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x),0],
[x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x,24,-2/3*x^3/a/c^3/(a^2*x^2+1)^2/arctan(a*x)^(3/2)-4*x^2/a^2/c^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))+4/3*x^4/c^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))+4/3*sqrt(2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^4/c^3-4/3*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^4/c^3,1],
[x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x,27,-2/3*x^2/a/c^3/(a^2*x^2+1)^2/arctan(a*x)^(3/2)-8/3*x/a^2/c^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))+8/3*x^3/c^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))+4/3*sqrt(2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c^3,1],
[x/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x,24,-2/3*x/a/c^3/(a^2*x^2+1)^2/arctan(a*x)^(3/2)-4/3/a^2/c^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))+4*x^2/c^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))-4/3*sqrt(2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c^3-4/3*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/a^2/c^3,1],
[1/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x,14,-2/3/a/c^3/(a^2*x^2+1)^2/arctan(a*x)^(3/2)+16/3*x/c^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))-4/3*sqrt(2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c^3-8/3*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/a/c^3,1],
[1/x/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x,10,-2/3/a/c^3/x/(a^2*x^2+1)^2/arctan(a*x)^(3/2)+20/3/c^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))+4/3/a^2/c^3/x^2/(a^2*x^2+1)^2/sqrt(arctan(a*x))+5/3*sqrt(2*Pi)*FresnelS(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/c^3+20/3*sqrt(Pi)*FresnelS(2*sqrt(arctan(a*x))/sqrt(Pi))/c^3+8/3*Defer(Int)(1/x^3/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x)/a^2+8*Defer(Int)(1/x/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x),0],
[1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x,11,-2/3/a/c^3/x^2/(a^2*x^2+1)^2/arctan(a*x)^(3/2)+8/3/a^2/c^3/x^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))+8/c^3/x/(a^2*x^2+1)^2/sqrt(arctan(a*x))+30*a*sqrt(arctan(a*x))/c^3+5*a*sqrt(1/2*Pi)*FresnelC(2*sqrt(2/Pi)*sqrt(arctan(a*x)))/c^3+20*a*sqrt(Pi)*FresnelC(2*sqrt(arctan(a*x))/sqrt(Pi))/c^3+8*Defer(Int)(1/x^4/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x)/a^2+80/3*Defer(Int)(1/x^2/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x),0],
[1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x,4,-2/3/a/c^3/x^3/(a^2*x^2+1)^2/arctan(a*x)^(3/2)+4/a^2/c^3/x^4/(a^2*x^2+1)^2/sqrt(arctan(a*x))+28/3/c^3/x^2/(a^2*x^2+1)^2/sqrt(arctan(a*x))+16*Defer(Int)(1/x^5/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x)/a^2+152/3*Defer(Int)(1/x^3/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x)+56*a^2*Defer(Int)(1/x/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x),0],
[1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x,4,-2/3/a/c^3/x^4/(a^2*x^2+1)^2/arctan(a*x)^(3/2)+16/3/a^2/c^3/x^5/(a^2*x^2+1)^2/sqrt(arctan(a*x))+32/3/c^3/x^3/(a^2*x^2+1)^2/sqrt(arctan(a*x))+80/3*Defer(Int)(1/x^6/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x)/a^2+80*Defer(Int)(1/x^4/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x)+224/3*a^2*Defer(Int)(1/x^2/(a^2*c*x^2+c)^3/sqrt(arctan(a*x)),x),0],
[x^m*sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,0,Defer(Int)(x^m*sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x),0],
[x*sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,0,Defer(Int)(x*sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x),0],
[sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,0,Defer(Int)(sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x),0],
[sqrt(a^2*c*x^2+c)/x/arctan(a*x)^(5/2),x,0,Defer(Int)(sqrt(a^2*c*x^2+c)/x/arctan(a*x)^(5/2),x),0],
[x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x),0],
[x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x,0,Defer(Int)(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x),0],
[(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x),0],
[(a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(5/2),x,0,Defer(Int)((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(5/2),x),0],
[x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x,0,Defer(Int)(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x),0],
[x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x,0,Defer(Int)(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x),0],
[(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x),0],
[(a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(5/2),x,0,Defer(Int)((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(5/2),x),0],
[x^m/sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,0,Defer(Int)(x^m/sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x),0],
[x/sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,0,Defer(Int)(x/sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x),0],
[1/sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,0,Defer(Int)(1/sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x),0],
[1/x/sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,1,-2/3*sqrt(a^2*c*x^2+c)/a/c/x/arctan(a*x)^(3/2)-2/3*Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2),x)/a,0],
[1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x,0,Defer(Int)(1/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^(5/2),x),0],
[x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x),0],
[x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x,8,-2/3*x^3/a/c/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2)-4*x^2/a^2/c/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))-8/3*x^4/c/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))+8*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^4/c/sqrt(a^2*c*x^2+c)+44/3*Defer(Int)(x^3/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)+8*a^2*Defer(Int)(x^5/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x,7,-2/3*x^2/a/c/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2)-8/3*x/a^2/c/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))-4/3*x^3/c/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))+8/3*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c/sqrt(a^2*c*x^2+c)+4*Defer(Int)(x^2/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)+8/3*a^2*Defer(Int)(x^4/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x,6,-2/3*x/a/c/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2)-4/3/a^2/c/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))-4/3*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c/sqrt(a^2*c*x^2+c),1],
[1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x,6,-2/3/a/c/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2)+4/3*x/c/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))-4/3*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c/sqrt(a^2*c*x^2+c),1],
[1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x,7,-2/3/a/c/x/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2)+8/3/c/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))+4/3/a^2/c/x^2/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))+8/3*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/c/sqrt(a^2*c*x^2+c)+8/3*Defer(Int)(1/x^3/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)/a^2+4*Defer(Int)(1/x/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x,8,-2/3/a/c/x^2/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2)+8/3/a^2/c/x^3/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))+4/c/x/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))+8*a*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/c/sqrt(a^2*c*x^2+c)+8*Defer(Int)(1/x^4/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)/a^2+44/3*Defer(Int)(1/x^2/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x,4,-2/3/a/c/x^3/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2)+4/a^2/c/x^4/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))+16/3/c/x^2/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))+16*Defer(Int)(1/x^5/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)/a^2+92/3*Defer(Int)(1/x^3/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)+16*a^2*Defer(Int)(1/x/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x,4,-2/3/a/c/x^4/sqrt(a^2*c*x^2+c)/arctan(a*x)^(3/2)+16/3/a^2/c/x^5/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))+20/3/c/x^3/sqrt(a^2*c*x^2+c)/sqrt(arctan(a*x))+80/3*Defer(Int)(1/x^6/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)/a^2+52*Defer(Int)(1/x^4/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x)+80/3*a^2*Defer(Int)(1/x^2/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x)),x),0],
[x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x,0,Defer(Int)(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x),0],
[x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x,18,-2/3*x^3/a/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2)-4*x^2/a^2/c/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))-sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^4/c^2/sqrt(a^2*c*x^2+c)+sqrt(6*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^4/c^2/sqrt(a^2*c*x^2+c),1],
[x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x,27,-2/3*x^2/a/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2)-8/3*x/a^2/c/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))+4/3*x^3/c/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))-1/3*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c)+sqrt(6*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^3/c^2/sqrt(a^2*c*x^2+c),1],
[x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x,27,-2/3*x/a/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2)-4/3/a^2/c/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))+8/3*x^2/c/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))-1/3*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c)-sqrt(6*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/a^2/c^2/sqrt(a^2*c*x^2+c),1],
[1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x,18,-2/3/a/c/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2)+4*x/c/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))-sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/a/c^2/sqrt(a^2*c*x^2+c)-sqrt(6*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/a/c^2/sqrt(a^2*c*x^2+c),1],
[1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x,11,-2/3/a/c/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2)+16/3/c/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))+4/3/a^2/c/x^2/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))+4*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(2/Pi)*sqrt(arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)+4*sqrt(2/3*Pi)*sqrt(a^2*x^2+1)*FresnelS(sqrt(6/Pi)*sqrt(arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)+8/3*Defer(Int)(1/x^3/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x)/a^2+20/3*Defer(Int)(1/x/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x),0],
[1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x,12,-2/3/a/c/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2)+8/3/a^2/c/x^3/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))+20/3/c/x/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))+20*a*sqrt(2*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(2/Pi)*sqrt(arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)+20/3*a*sqrt(2/3*Pi)*sqrt(a^2*x^2+1)*FresnelC(sqrt(6/Pi)*sqrt(arctan(a*x)))/c^2/sqrt(a^2*c*x^2+c)+8*Defer(Int)(1/x^4/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x)/a^2+68/3*Defer(Int)(1/x^2/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x),0],
[1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x,4,-2/3/a/c/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2)+4/a^2/c/x^4/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))+8/c/x^2/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))+16*Defer(Int)(1/x^5/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x)/a^2+44*Defer(Int)(1/x^3/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x)+40*a^2*Defer(Int)(1/x/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x),0],
[1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x,4,-2/3/a/c/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2)+16/3/a^2/c/x^5/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))+28/3/c/x^3/(a^2*c*x^2+c)^(3/2)/sqrt(arctan(a*x))+80/3*Defer(Int)(1/x^6/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x)/a^2+212/3*Defer(Int)(1/x^4/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x)+56*a^2*Defer(Int)(1/x^2/(a^2*c*x^2+c)^(5/2)/sqrt(arctan(a*x)),x),0],
[x*arctan(a*x)^n/(a^2*c*x^2+c),x,1,x*arctan(a*x)^(1+n)/a/c/(1+n)-Defer(Int)(arctan(a*x)^(1+n),x)/a/c/(1+n),0],
[arctan(a*x)^n/(a^2*c*x^2+c),x,1,arctan(a*x)^(1+n)/a/c/(1+n),1],
[(f*x)^m*(c^2*d*x^2+d)^q*(a+b*arctan(c*x))^p,x,0,Defer(Int)((f*x)^m*(c^2*d*x^2+d)^q*(a+b*arctan(c*x))^p,x),0],
[x^3*(e*x^2+d)*(a+b*arctan(c*x)),x,4,1/12*b*(3*c^2*d-2*e)*x/c^5-1/36*b*(3*c^2*d-2*e)*x^3/c^3-1/30*b*e*x^5/c-1/12*b*(3*c^2*d-2*e)*arctan(c*x)/c^6+1/4*d*x^4*(a+b*arctan(c*x))+1/6*e*x^6*(a+b*arctan(c*x)),1],
[x^2*(e*x^2+d)*(a+b*arctan(c*x)),x,4,-1/30*b*(5*c^2*d-3*e)*x^2/c^3-1/20*b*e*x^4/c+1/3*d*x^3*(a+b*arctan(c*x))+1/5*e*x^5*(a+b*arctan(c*x))+1/30*b*(5*c^2*d-3*e)*ln(c^2*x^2+1)/c^5,1],
[x*(e*x^2+d)*(a+b*arctan(c*x)),x,4,-1/4*b*(2*c^2*d-e)*x/c^3-1/12*b*e*x^3/c-1/4*b*(c^2*d-e)^2*arctan(c*x)/c^4/e+1/4*(e*x^2+d)^2*(a+b*arctan(c*x))/e,1],
[(e*x^2+d)*(a+b*arctan(c*x)),x,4,-1/6*b*e*x^2/c+d*x*(a+b*arctan(c*x))+1/3*e*x^3*(a+b*arctan(c*x))-1/6*b*(3*c^2*d-e)*ln(c^2*x^2+1)/c^3,1],
[(e*x^2+d)*(a+b*arctan(c*x))/x,x,8,-1/2*b*e*x/c+1/2*b*e*arctan(c*x)/c^2+1/2*e*x^2*(a+b*arctan(c*x))+a*d*ln(x)+1/2*I*b*d*polylog(2,-I*c*x)-1/2*I*b*d*polylog(2,I*c*x),1],
[(e*x^2+d)*(a+b*arctan(c*x))/x^2,x,4,-d*(a+b*arctan(c*x))/x+e*x*(a+b*arctan(c*x))+b*c*d*ln(x)-1/2*b*(c^2*d+e)*ln(c^2*x^2+1)/c,1],
[(e*x^2+d)*(a+b*arctan(c*x))/x^3,x,8,-1/2*b*c*d/x-1/2*b*c^2*d*arctan(c*x)-1/2*d*(a+b*arctan(c*x))/x^2+a*e*ln(x)+1/2*I*b*e*polylog(2,-I*c*x)-1/2*I*b*e*polylog(2,I*c*x),1],
[(e*x^2+d)*(a+b*arctan(c*x))/x^4,x,5,-1/6*b*c*d/x^2-1/3*d*(a+b*arctan(c*x))/x^3-e*(a+b*arctan(c*x))/x-1/3*b*c*(c^2*d-3*e)*ln(x)+1/6*b*c*(c^2*d-3*e)*ln(c^2*x^2+1),1],
[(e*x^2+d)*(a+b*arctan(c*x))/x^5,x,5,-1/12*b*c*d/x^3+1/4*b*c*(c^2*d-2*e)/x+1/4*b*(c^2*d-e)^2*arctan(c*x)/d-1/4*(e*x^2+d)^2*(a+b*arctan(c*x))/d/x^4,1],
[(e*x^2+d)*(a+b*arctan(c*x))/x^6,x,5,-1/20*b*c*d/x^4+1/30*b*c*(3*c^2*d-5*e)/x^2-1/5*d*(a+b*arctan(c*x))/x^5-1/3*e*(a+b*arctan(c*x))/x^3+1/15*b*c^3*(3*c^2*d-5*e)*ln(x)-1/30*b*c^3*(3*c^2*d-5*e)*ln(c^2*x^2+1),1],
[(e*x^2+d)*(a+b*arctan(c*x))/x^7,x,6,-1/30*b*c*d/x^5+1/36*b*c*(2*c^2*d-3*e)/x^3-1/12*b*c^3*(2*c^2*d-3*e)/x-1/12*b*c^4*(2*c^2*d-3*e)*arctan(c*x)-1/6*d*(a+b*arctan(c*x))/x^6-1/4*e*(a+b*arctan(c*x))/x^4,1],
[x^3*(e*x^2+d)^2*(a+b*arctan(c*x)),x,4,1/24*b*(6*c^4*d^2-8*c^2*d*e+3*e^2)*x/c^7-1/72*b*(6*c^4*d^2-8*c^2*d*e+3*e^2)*x^3/c^5-1/120*b*(8*c^2*d-3*e)*e*x^5/c^3-1/56*b*e^2*x^7/c-1/24*b*(6*c^4*d^2-8*c^2*d*e+3*e^2)*arctan(c*x)/c^8+1/4*d^2*x^4*(a+b*arctan(c*x))+1/3*d*e*x^6*(a+b*arctan(c*x))+1/8*e^2*x^8*(a+b*arctan(c*x)),1],
[x^2*(e*x^2+d)^2*(a+b*arctan(c*x)),x,5,-1/210*b*(35*c^4*d^2-42*c^2*d*e+15*e^2)*x^2/c^5-1/140*b*(14*c^2*d-5*e)*e*x^4/c^3-1/42*b*e^2*x^6/c+1/3*d^2*x^3*(a+b*arctan(c*x))+2/5*d*e*x^5*(a+b*arctan(c*x))+1/7*e^2*x^7*(a+b*arctan(c*x))+1/210*b*(35*c^4*d^2-42*c^2*d*e+15*e^2)*ln(c^2*x^2+1)/c^7,1],
[x*(e*x^2+d)^2*(a+b*arctan(c*x)),x,4,-1/6*b*(3*c^4*d^2-3*c^2*d*e+e^2)*x/c^5-1/18*b*(3*c^2*d-e)*e*x^3/c^3-1/30*b*e^2*x^5/c-1/6*b*(c^2*d-e)^3*arctan(c*x)/c^6/e+1/6*(e*x^2+d)^3*(a+b*arctan(c*x))/e,1],
[(e*x^2+d)^2*(a+b*arctan(c*x)),x,5,-1/30*b*(10*c^2*d-3*e)*e*x^2/c^3-1/20*b*e^2*x^4/c+d^2*x*(a+b*arctan(c*x))+2/3*d*e*x^3*(a+b*arctan(c*x))+1/5*e^2*x^5*(a+b*arctan(c*x))-1/30*b*(15*c^4*d^2-10*c^2*d*e+3*e^2)*ln(c^2*x^2+1)/c^5,1],
[(e*x^2+d)^2*(a+b*arctan(c*x))/x,x,12,-b*d*e*x/c+1/4*b*e^2*x/c^3-1/12*b*e^2*x^3/c+b*d*e*arctan(c*x)/c^2-1/4*b*e^2*arctan(c*x)/c^4+d*e*x^2*(a+b*arctan(c*x))+1/4*e^2*x^4*(a+b*arctan(c*x))+a*d^2*ln(x)+1/2*I*b*d^2*polylog(2,-I*c*x)-1/2*I*b*d^2*polylog(2,I*c*x),1],
[(e*x^2+d)^2*(a+b*arctan(c*x))/x^2,x,4,-1/6*b*e^2*x^2/c-d^2*(a+b*arctan(c*x))/x+2*d*e*x*(a+b*arctan(c*x))+1/3*e^2*x^3*(a+b*arctan(c*x))+b*c*d^2*ln(x)-1/6*b*(3*c^4*d^2+6*c^2*d*e-e^2)*ln(c^2*x^2+1)/c^3,1],
[(e*x^2+d)^2*(a+b*arctan(c*x))/x^3,x,11,-1/2*b*c*d^2/x-1/2*b*e^2*x/c-1/2*b*c^2*d^2*arctan(c*x)+1/2*b*e^2*arctan(c*x)/c^2-1/2*d^2*(a+b*arctan(c*x))/x^2+1/2*e^2*x^2*(a+b*arctan(c*x))+2*a*d*e*ln(x)+I*b*d*e*polylog(2,-I*c*x)-I*b*d*e*polylog(2,I*c*x),1],
[(e*x^2+d)^2*(a+b*arctan(c*x))/x^4,x,5,-1/6*b*c*d^2/x^2-1/3*d^2*(a+b*arctan(c*x))/x^3-2*d*e*(a+b*arctan(c*x))/x+e^2*x*(a+b*arctan(c*x))-1/3*b*c*d*(c^2*d-6*e)*ln(x)+1/6*b*(c^4*d^2-6*c^2*d*e-3*e^2)*ln(c^2*x^2+1)/c,1],
[(e*x^2+d)^2*(a+b*arctan(c*x))/x^5,x,12,-1/12*b*c*d^2/x^3+1/4*b*c^3*d^2/x-b*c*d*e/x+1/4*b*c^4*d^2*arctan(c*x)-b*c^2*d*e*arctan(c*x)-1/4*d^2*(a+b*arctan(c*x))/x^4-d*e*(a+b*arctan(c*x))/x^2+a*e^2*ln(x)+1/2*I*b*e^2*polylog(2,-I*c*x)-1/2*I*b*e^2*polylog(2,I*c*x),1],
[(e*x^2+d)^2*(a+b*arctan(c*x))/x^6,x,5,-1/20*b*c*d^2/x^4+1/30*b*c*d*(3*c^2*d-10*e)/x^2-1/5*d^2*(a+b*arctan(c*x))/x^5-2/3*d*e*(a+b*arctan(c*x))/x^3-e^2*(a+b*arctan(c*x))/x+1/15*b*c*(3*c^4*d^2-10*c^2*d*e+15*e^2)*ln(x)-1/30*b*c*(3*c^4*d^2-10*c^2*d*e+15*e^2)*ln(c^2*x^2+1),1],
[(e*x^2+d)^2*(a+b*arctan(c*x))/x^7,x,5,-1/30*b*c*d^2/x^5+1/18*b*c*d*(c^2*d-3*e)/x^3-1/6*b*c*(c^4*d^2-3*c^2*d*e+3*e^2)/x-1/6*b*(c^2*d-e)^3*arctan(c*x)/d-1/6*(e*x^2+d)^3*(a+b*arctan(c*x))/d/x^6,1],
[(e*x^2+d)^2*(a+b*arctan(c*x))/x^8,x,5,-1/42*b*c*d^2/x^6+1/140*b*c*d*(5*c^2*d-14*e)/x^4-1/210*b*c*(15*c^4*d^2-42*c^2*d*e+35*e^2)/x^2-1/7*d^2*(a+b*arctan(c*x))/x^7-2/5*d*e*(a+b*arctan(c*x))/x^5-1/3*e^2*(a+b*arctan(c*x))/x^3-1/105*b*c^3*(15*c^4*d^2-42*c^2*d*e+35*e^2)*ln(x)+1/210*b*c^3*(15*c^4*d^2-42*c^2*d*e+35*e^2)*ln(c^2*x^2+1),1],
[x^3*(e*x^2+d)^3*(a+b*arctan(c*x)),x,5,1/40*b*(10*c^6*d^3-20*c^4*d^2*e+15*c^2*d*e^2-4*e^3)*x/c^9-1/120*b*(10*c^6*d^3-20*c^4*d^2*e+15*c^2*d*e^2-4*e^3)*x^3/c^7-1/200*b*e*(20*c^4*d^2-15*c^2*d*e+4*e^2)*x^5/c^5-1/280*b*(15*c^2*d-4*e)*e^2*x^7/c^3-1/90*b*e^3*x^9/c+1/40*b*(c^2*d-e)^4*(c^2*d+4*e)*arctan(c*x)/c^10/e^2-1/8*d*(e*x^2+d)^4*(a+b*arctan(c*x))/e^2+1/10*(e*x^2+d)^5*(a+b*arctan(c*x))/e^2,1],
[x^2*(e*x^2+d)^3*(a+b*arctan(c*x)),x,5,-1/630*b*(105*c^6*d^3-189*c^4*d^2*e+135*c^2*d*e^2-35*e^3)*x^2/c^7-1/1260*b*e*(189*c^4*d^2-135*c^2*d*e+35*e^2)*x^4/c^5-1/378*b*(27*c^2*d-7*e)*e^2*x^6/c^3-1/72*b*e^3*x^8/c+1/3*d^3*x^3*(a+b*arctan(c*x))+3/5*d^2*e*x^5*(a+b*arctan(c*x))+3/7*d*e^2*x^7*(a+b*arctan(c*x))+1/9*e^3*x^9*(a+b*arctan(c*x))+1/630*b*(105*c^6*d^3-189*c^4*d^2*e+135*c^2*d*e^2-35*e^3)*ln(c^2*x^2+1)/c^9,1],
[x*(e*x^2+d)^3*(a+b*arctan(c*x)),x,4,-1/8*b*(2*c^2*d-e)*(2*c^4*d^2-2*c^2*d*e+e^2)*x/c^7-1/24*b*e*(6*c^4*d^2-4*c^2*d*e+e^2)*x^3/c^5-1/40*b*(4*c^2*d-e)*e^2*x^5/c^3-1/56*b*e^3*x^7/c-1/8*b*(c^2*d-e)^4*arctan(c*x)/c^8/e+1/8*(e*x^2+d)^4*(a+b*arctan(c*x))/e,1],
[(e*x^2+d)^3*(a+b*arctan(c*x)),x,5,-1/70*b*e*(35*c^4*d^2-21*c^2*d*e+5*e^2)*x^2/c^5-1/140*b*(21*c^2*d-5*e)*e^2*x^4/c^3-1/42*b*e^3*x^6/c+d^3*x*(a+b*arctan(c*x))+d^2*e*x^3*(a+b*arctan(c*x))+3/5*d*e^2*x^5*(a+b*arctan(c*x))+1/7*e^3*x^7*(a+b*arctan(c*x))-1/70*b*(35*c^6*d^3-35*c^4*d^2*e+21*c^2*d*e^2-5*e^3)*ln(c^2*x^2+1)/c^7,1],
[(e*x^2+d)^3*(a+b*arctan(c*x))/x,x,16,-3/2*b*d^2*e*x/c+3/4*b*d*e^2*x/c^3-1/6*b*e^3*x/c^5-1/4*b*d*e^2*x^3/c+1/18*b*e^3*x^3/c^3-1/30*b*e^3*x^5/c+3/2*b*d^2*e*arctan(c*x)/c^2-3/4*b*d*e^2*arctan(c*x)/c^4+1/6*b*e^3*arctan(c*x)/c^6+3/2*d^2*e*x^2*(a+b*arctan(c*x))+3/4*d*e^2*x^4*(a+b*arctan(c*x))+1/6*e^3*x^6*(a+b*arctan(c*x))+a*d^3*ln(x)+1/2*I*b*d^3*polylog(2,-I*c*x)-1/2*I*b*d^3*polylog(2,I*c*x),1],
[(e*x^2+d)^3*(a+b*arctan(c*x))/x^2,x,4,-1/10*b*(5*c^2*d-e)*e^2*x^2/c^3-1/20*b*e^3*x^4/c-d^3*(a+b*arctan(c*x))/x+3*d^2*e*x*(a+b*arctan(c*x))+d*e^2*x^3*(a+b*arctan(c*x))+1/5*e^3*x^5*(a+b*arctan(c*x))+b*c*d^3*ln(x)-1/10*b*(5*c^6*d^3+15*c^4*d^2*e-5*c^2*d*e^2+e^3)*ln(c^2*x^2+1)/c^5,1],
[(e*x^2+d)^3*(a+b*arctan(c*x))/x^3,x,15,-1/2*b*c*d^3/x-3/2*b*d*e^2*x/c+1/4*b*e^3*x/c^3-1/12*b*e^3*x^3/c-1/2*b*c^2*d^3*arctan(c*x)+3/2*b*d*e^2*arctan(c*x)/c^2-1/4*b*e^3*arctan(c*x)/c^4-1/2*d^3*(a+b*arctan(c*x))/x^2+3/2*d*e^2*x^2*(a+b*arctan(c*x))+1/4*e^3*x^4*(a+b*arctan(c*x))+3*a*d^2*e*ln(x)+3/2*I*b*d^2*e*polylog(2,-I*c*x)-3/2*I*b*d^2*e*polylog(2,I*c*x),1],
[(e*x^2+d)^3*(a+b*arctan(c*x))/x^4,x,5,-1/6*b*c*d^3/x^2-1/6*b*e^3*x^2/c-1/3*d^3*(a+b*arctan(c*x))/x^3-3*d^2*e*(a+b*arctan(c*x))/x+3*d*e^2*x*(a+b*arctan(c*x))+1/3*e^3*x^3*(a+b*arctan(c*x))-1/3*b*c*d^2*(c^2*d-9*e)*ln(x)+1/6*b*(c^2*d+e)*(c^4*d^2-10*c^2*d*e+e^2)*ln(c^2*x^2+1)/c^3,1],
[(e*x^2+d)^3*(a+b*arctan(c*x))/x^5,x,15,-1/12*b*c*d^3/x^3+1/4*b*c^3*d^3/x-3/2*b*c*d^2*e/x-1/2*b*e^3*x/c+1/4*b*c^4*d^3*arctan(c*x)-3/2*b*c^2*d^2*e*arctan(c*x)+1/2*b*e^3*arctan(c*x)/c^2-1/4*d^3*(a+b*arctan(c*x))/x^4-3/2*d^2*e*(a+b*arctan(c*x))/x^2+1/2*e^3*x^2*(a+b*arctan(c*x))+3*a*d*e^2*ln(x)+3/2*I*b*d*e^2*polylog(2,-I*c*x)-3/2*I*b*d*e^2*polylog(2,I*c*x),1],
[(e*x^2+d)^3*(a+b*arctan(c*x))/x^6,x,5,-1/20*b*c*d^3/x^4+1/10*b*c*d^2*(c^2*d-5*e)/x^2-1/5*d^3*(a+b*arctan(c*x))/x^5-d^2*e*(a+b*arctan(c*x))/x^3-3*d*e^2*(a+b*arctan(c*x))/x+e^3*x*(a+b*arctan(c*x))+1/5*b*c*d*(c^4*d^2-5*c^2*d*e+15*e^2)*ln(x)-1/10*b*(c^6*d^3-5*c^4*d^2*e+15*c^2*d*e^2+5*e^3)*ln(c^2*x^2+1)/c,1],
[(e*x^2+d)^3*(a+b*arctan(c*x))/x^7,x,17,-1/30*b*c*d^3/x^5+1/18*b*c^3*d^3/x^3-1/4*b*c*d^2*e/x^3-1/6*b*c^5*d^3/x+3/4*b*c^3*d^2*e/x-3/2*b*c*d*e^2/x-1/6*b*c^6*d^3*arctan(c*x)+3/4*b*c^4*d^2*e*arctan(c*x)-3/2*b*c^2*d*e^2*arctan(c*x)-1/6*d^3*(a+b*arctan(c*x))/x^6-3/4*d^2*e*(a+b*arctan(c*x))/x^4-3/2*d*e^2*(a+b*arctan(c*x))/x^2+a*e^3*ln(x)+1/2*I*b*e^3*polylog(2,-I*c*x)-1/2*I*b*e^3*polylog(2,I*c*x),1],
[(e*x^2+d)^3*(a+b*arctan(c*x))/x^8,x,5,-1/42*b*c*d^3/x^6+1/140*b*c*d^2*(5*c^2*d-21*e)/x^4-1/70*b*c*d*(5*c^4*d^2-21*c^2*d*e+35*e^2)/x^2-1/7*d^3*(a+b*arctan(c*x))/x^7-3/5*d^2*e*(a+b*arctan(c*x))/x^5-d*e^2*(a+b*arctan(c*x))/x^3-e^3*(a+b*arctan(c*x))/x-1/35*b*c*(5*c^6*d^3-21*c^4*d^2*e+35*c^2*d*e^2-35*e^3)*ln(x)+1/70*b*c*(5*c^6*d^3-21*c^4*d^2*e+35*c^2*d*e^2-35*e^3)*ln(c^2*x^2+1),1],
[(e*x^2+d)^3*(a+b*arctan(c*x))/x^9,x,5,-1/56*b*c*d^3/x^7+1/40*b*c*d^2*(c^2*d-4*e)/x^5-1/24*b*c*d*(c^4*d^2-4*c^2*d*e+6*e^2)/x^3+1/8*b*c*(c^2*d-2*e)*(c^4*d^2-2*c^2*d*e+2*e^2)/x+1/8*b*(c^2*d-e)^4*arctan(c*x)/d-1/8*(e*x^2+d)^4*(a+b*arctan(c*x))/d/x^8,1],
[(d*x^2+c)^4*arctan(a*x),x,5,-1/630*d*(420*a^6*c^3-378*a^4*c^2*d+180*a^2*c*d^2-35*d^3)*x^2/a^7-1/1260*d^2*(378*a^4*c^2-180*a^2*c*d+35*d^2)*x^4/a^5-1/378*(36*a^2*c-7*d)*d^3*x^6/a^3-1/72*d^4*x^8/a+c^4*x*arctan(a*x)+4/3*c^3*d*x^3*arctan(a*x)+6/5*c^2*d^2*x^5*arctan(a*x)+4/7*c*d^3*x^7*arctan(a*x)+1/9*d^4*x^9*arctan(a*x)-1/630*(315*a^8*c^4-420*a^6*c^3*d+378*a^4*c^2*d^2-180*a^2*c*d^3+35*d^4)*ln(a^2*x^2+1)/a^9,1],
[x^3*(a+b*arctan(c*x))/(e*x^2+d),x,14,-1/2*b*x/c/e+1/2*b*arctan(c*x)/c^2/e+1/2*x^2*(a+b*arctan(c*x))/e+d*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/e^2-1/2*d*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^2-1/2*d*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^2-1/2*I*b*d*polylog(2,1-2/(1-I*c*x))/e^2+1/4*I*b*d*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^2+1/4*I*b*d*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^2,1],
[x*(a+b*arctan(c*x))/(e*x^2+d),x,10,-(a+b*arctan(c*x))*ln(2/(1-I*c*x))/e+1/2*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e+1/2*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e+1/2*I*b*polylog(2,1-2/(1-I*c*x))/e-1/4*I*b*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e-1/4*I*b*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e,1],
[(a+b*arctan(c*x))/x/(e*x^2+d),x,15,a*ln(x)/d+(a+b*arctan(c*x))*ln(2/(1-I*c*x))/d-1/2*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d-1/2*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d+1/2*I*b*polylog(2,-I*c*x)/d-1/2*I*b*polylog(2,I*c*x)/d-1/2*I*b*polylog(2,1-2/(1-I*c*x))/d+1/4*I*b*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d+1/4*I*b*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d,1],
[(a+b*arctan(c*x))/x^3/(e*x^2+d),x,19,-1/2*b*c/d/x-1/2*b*c^2*arctan(c*x)/d-1/2*(a+b*arctan(c*x))/d/x^2-a*e*ln(x)/d^2-e*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/d^2+1/2*e*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^2+1/2*e*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^2-1/2*I*b*e*polylog(2,-I*c*x)/d^2+1/2*I*b*e*polylog(2,I*c*x)/d^2+1/2*I*b*e*polylog(2,1-2/(1-I*c*x))/d^2-1/4*I*b*e*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^2-1/4*I*b*e*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^2,1],
[x^2*(a+b*arctan(c*x))/(e*x^2+d),x,23,a*x/e+b*x*arctan(c*x)/e-a*sqrt(d)*arctan(sqrt(e)*x/sqrt(d))/e^(3/2)-1/4*I*b*sqrt(-d)*ln(1+I*c*x)*ln(c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e)))/e^(3/2)+1/4*I*b*sqrt(-d)*ln(1-I*c*x)*ln(c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e)))/e^(3/2)-1/4*I*b*sqrt(-d)*ln(1-I*c*x)*ln(c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e)))/e^(3/2)+1/4*I*b*sqrt(-d)*ln(1+I*c*x)*ln(c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e)))/e^(3/2)-1/2*b*ln(c^2*x^2+1)/c/e+1/4*I*b*sqrt(-d)*polylog(2,sqrt(e)*(I-c*x)/(c*sqrt(-d)+I*sqrt(e)))/e^(3/2)-1/4*I*b*sqrt(-d)*polylog(2,sqrt(e)*(1-I*c*x)/(I*c*sqrt(-d)+sqrt(e)))/e^(3/2)-1/4*I*b*sqrt(-d)*polylog(2,sqrt(e)*(1+I*c*x)/(I*c*sqrt(-d)+sqrt(e)))/e^(3/2)+1/4*I*b*sqrt(-d)*polylog(2,sqrt(e)*(I+c*x)/(c*sqrt(-d)+I*sqrt(e)))/e^(3/2),1],
[(a+b*arctan(c*x))/(e*x^2+d),x,19,a*arctan(sqrt(e)*x/sqrt(d))/sqrt(d)/sqrt(e)-1/4*I*b*ln(1+I*c*x)*ln(c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e)))/sqrt(-d)/sqrt(e)+1/4*I*b*ln(1-I*c*x)*ln(c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e)))/sqrt(-d)/sqrt(e)-1/4*I*b*ln(1-I*c*x)*ln(c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e)))/sqrt(-d)/sqrt(e)+1/4*I*b*ln(1+I*c*x)*ln(c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e)))/sqrt(-d)/sqrt(e)+1/4*I*b*polylog(2,sqrt(e)*(I-c*x)/(c*sqrt(-d)+I*sqrt(e)))/sqrt(-d)/sqrt(e)-1/4*I*b*polylog(2,sqrt(e)*(1-I*c*x)/(I*c*sqrt(-d)+sqrt(e)))/sqrt(-d)/sqrt(e)-1/4*I*b*polylog(2,sqrt(e)*(1+I*c*x)/(I*c*sqrt(-d)+sqrt(e)))/sqrt(-d)/sqrt(e)+1/4*I*b*polylog(2,sqrt(e)*(I+c*x)/(c*sqrt(-d)+I*sqrt(e)))/sqrt(-d)/sqrt(e),1],
[(a+b*arctan(c*x))/x^2/(e*x^2+d),x,25,-(a+b*arctan(c*x))/d/x-a*sqrt(e)*arctan(sqrt(e)*x/sqrt(d))/d^(3/2)+b*c*ln(x)/d-1/4*I*b*sqrt(e)*ln(1+I*c*x)*ln(c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e)))/(-d)^(3/2)+1/4*I*b*sqrt(e)*ln(1-I*c*x)*ln(c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e)))/(-d)^(3/2)-1/4*I*b*sqrt(e)*ln(1-I*c*x)*ln(c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e)))/(-d)^(3/2)+1/4*I*b*sqrt(e)*ln(1+I*c*x)*ln(c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e)))/(-d)^(3/2)-1/2*b*c*ln(c^2*x^2+1)/d+1/4*I*b*sqrt(e)*polylog(2,sqrt(e)*(I-c*x)/(c*sqrt(-d)+I*sqrt(e)))/(-d)^(3/2)-1/4*I*b*sqrt(e)*polylog(2,sqrt(e)*(1-I*c*x)/(I*c*sqrt(-d)+sqrt(e)))/(-d)^(3/2)-1/4*I*b*sqrt(e)*polylog(2,sqrt(e)*(1+I*c*x)/(I*c*sqrt(-d)+sqrt(e)))/(-d)^(3/2)+1/4*I*b*sqrt(e)*polylog(2,sqrt(e)*(I+c*x)/(c*sqrt(-d)+I*sqrt(e)))/(-d)^(3/2),1],
[x^3*(a+b*arctan(c*x))/(e*x^2+d)^2,x,16,-1/2*b*c^2*d*arctan(c*x)/(c^2*d-e)/e^2+1/2*d*(a+b*arctan(c*x))/e^2/(e*x^2+d)+1/2*b*c*sqrt(d)*arctan(sqrt(e)*x/sqrt(d))/(c^2*d-e)/e^(3/2)-(a+b*arctan(c*x))*ln(2/(1-I*c*x))/e^2+1/2*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^2+1/2*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^2+1/2*I*b*polylog(2,1-2/(1-I*c*x))/e^2-1/4*I*b*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^2-1/4*I*b*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^2,1],
[x*(a+b*arctan(c*x))/(e*x^2+d)^2,x,4,1/2*b*c^2*arctan(c*x)/(c^2*d-e)/e-1/2*(a+b*arctan(c*x))/e/(e*x^2+d)-1/2*b*c*arctan(sqrt(e)*x/sqrt(d))/sqrt(d)/(c^2*d-e)/sqrt(e),1],
[(a+b*arctan(c*x))/x/(e*x^2+d)^2,x,19,-1/2*b*c^2*arctan(c*x)/d/(c^2*d-e)+1/2*(a+b*arctan(c*x))/d/(e*x^2+d)+1/2*b*c*sqrt(e)*arctan(sqrt(e)*x/sqrt(d))/d^(3/2)/(c^2*d-e)+a*ln(x)/d^2+(a+b*arctan(c*x))*ln(2/(1-I*c*x))/d^2-1/2*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^2-1/2*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^2+1/2*I*b*polylog(2,-I*c*x)/d^2-1/2*I*b*polylog(2,I*c*x)/d^2-1/2*I*b*polylog(2,1-2/(1-I*c*x))/d^2+1/4*I*b*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^2+1/4*I*b*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^2,1],
[(a+b*arctan(c*x))/x^3/(e*x^2+d)^2,x,22,-1/2*b*c/d^2/x-1/2*b*c^2*arctan(c*x)/d^2+1/2*b*c^2*e*arctan(c*x)/d^2/(c^2*d-e)-1/2*(a+b*arctan(c*x))/d^2/x^2-1/2*e*(a+b*arctan(c*x))/d^2/(e*x^2+d)-1/2*b*c*e^(3/2)*arctan(sqrt(e)*x/sqrt(d))/d^(5/2)/(c^2*d-e)-2*a*e*ln(x)/d^3-2*e*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/d^3+e*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^3+e*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^3-I*b*e*polylog(2,-I*c*x)/d^3+I*b*e*polylog(2,I*c*x)/d^3+I*b*e*polylog(2,1-2/(1-I*c*x))/d^3-1/2*I*b*e*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^3-1/2*I*b*e*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^3,1],
[x^2*(a+b*arctan(c*x))/(e*x^2+d)^2,x,45,-1/2*x*(a+b*arctan(c*x))/e/(e*x^2+d)+a*arctan(sqrt(e)*x/sqrt(d))/sqrt(d)/e^(3/2)-1/2*(a+b*arctan(c*x))*arctan(sqrt(e)*x/sqrt(d))/sqrt(d)/e^(3/2)-1/8*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)-I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)-I*sqrt(e)))/sqrt(-c^2)/sqrt(d)/e^(3/2)-1/8*I*b*c*ln(sqrt(e)*(1-sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)+sqrt(e)))*ln(1-I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/sqrt(d)/e^(3/2)-1/8*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)+I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)-I*sqrt(e)))/sqrt(-c^2)/sqrt(d)/e^(3/2)-1/4*I*b*ln(1-I*c*x)*ln(c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e)))/sqrt(-d)/e^(3/2)+1/4*I*b*polylog(2,sqrt(e)*(I+c*x)/(c*sqrt(-d)+I*sqrt(e)))/sqrt(-d)/e^(3/2)+1/4*I*b*polylog(2,sqrt(e)*(I-c*x)/(c*sqrt(-d)+I*sqrt(e)))/sqrt(-d)/e^(3/2)-1/8*I*b*c*ln(sqrt(e)*(1+sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)+sqrt(e)))*ln(1+I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/sqrt(d)/e^(3/2)+1/4*I*b*ln(1-I*c*x)*ln(c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e)))/sqrt(-d)/e^(3/2)+1/4*b*c*ln(c^2*x^2+1)/(c^2*d-e)/e-1/4*b*c*ln(e*x^2+d)/(c^2*d-e)/e+1/8*I*b*c*ln(-sqrt(e)*(1+sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)-sqrt(e)))*ln(1-I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/sqrt(d)/e^(3/2)+1/8*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)+I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)+I*sqrt(e)))/sqrt(-c^2)/sqrt(d)/e^(3/2)-1/4*I*b*polylog(2,sqrt(e)*(1-I*c*x)/(I*c*sqrt(-d)+sqrt(e)))/sqrt(-d)/e^(3/2)+1/8*I*b*c*ln(-sqrt(e)*(1-sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)-sqrt(e)))*ln(1+I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/sqrt(d)/e^(3/2)-1/4*I*b*polylog(2,sqrt(e)*(1+I*c*x)/(I*c*sqrt(-d)+sqrt(e)))/sqrt(-d)/e^(3/2)-1/4*I*b*ln(1+I*c*x)*ln(c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e)))/sqrt(-d)/e^(3/2)+1/4*I*b*ln(1+I*c*x)*ln(c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e)))/sqrt(-d)/e^(3/2)+1/8*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)-I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)+I*sqrt(e)))/sqrt(-c^2)/sqrt(d)/e^(3/2),1],
[(a+b*arctan(c*x))/(e*x^2+d)^2,x,24,1/2*x*(a+b*arctan(c*x))/d/(e*x^2+d)+1/2*(a+b*arctan(c*x))*arctan(sqrt(e)*x/sqrt(d))/d^(3/2)/sqrt(e)+1/8*I*b*c*ln(sqrt(e)*(1-sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)+sqrt(e)))*ln(1-I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(3/2)/sqrt(e)-1/8*I*b*c*ln(-sqrt(e)*(1+sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)-sqrt(e)))*ln(1-I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(3/2)/sqrt(e)-1/8*I*b*c*ln(-sqrt(e)*(1-sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)-sqrt(e)))*ln(1+I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(3/2)/sqrt(e)+1/8*I*b*c*ln(sqrt(e)*(1+sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)+sqrt(e)))*ln(1+I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(3/2)/sqrt(e)-1/4*b*c*ln(c^2*x^2+1)/d/(c^2*d-e)+1/4*b*c*ln(e*x^2+d)/d/(c^2*d-e)+1/8*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)-I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)-I*sqrt(e)))/sqrt(-c^2)/d^(3/2)/sqrt(e)-1/8*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)-I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)+I*sqrt(e)))/sqrt(-c^2)/d^(3/2)/sqrt(e)+1/8*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)+I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)-I*sqrt(e)))/sqrt(-c^2)/d^(3/2)/sqrt(e)-1/8*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)+I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)+I*sqrt(e)))/sqrt(-c^2)/d^(3/2)/sqrt(e),1],
[(a+b*arctan(c*x))/x^2/(e*x^2+d)^2,x,50,-(a+b*arctan(c*x))/d^2/x-1/2*e*x*(a+b*arctan(c*x))/d^2/(e*x^2+d)-a*sqrt(e)*arctan(sqrt(e)*x/sqrt(d))/d^(5/2)-1/2*sqrt(e)*(a+b*arctan(c*x))*arctan(sqrt(e)*x/sqrt(d))/d^(5/2)+b*c*ln(x)/d^2+1/4*I*b*sqrt(e)*ln(1+I*c*x)*ln(c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e)))/(-d)^(5/2)+1/4*I*b*sqrt(e)*polylog(2,sqrt(e)*(1+I*c*x)/(I*c*sqrt(-d)+sqrt(e)))/(-d)^(5/2)+1/8*I*b*c*sqrt(e)*polylog(2,sqrt(-c^2)*(sqrt(d)-I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)+I*sqrt(e)))/sqrt(-c^2)/d^(5/2)-1/4*I*b*sqrt(e)*ln(1-I*c*x)*ln(c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e)))/(-d)^(5/2)-1/4*I*b*sqrt(e)*polylog(2,sqrt(e)*(I+c*x)/(c*sqrt(-d)+I*sqrt(e)))/(-d)^(5/2)-1/4*I*b*sqrt(e)*polylog(2,sqrt(e)*(I-c*x)/(c*sqrt(-d)+I*sqrt(e)))/(-d)^(5/2)-1/8*I*b*c*sqrt(e)*ln(sqrt(e)*(1-sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)+sqrt(e)))*ln(1-I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(5/2)+1/8*I*b*c*sqrt(e)*polylog(2,sqrt(-c^2)*(sqrt(d)+I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)+I*sqrt(e)))/sqrt(-c^2)/d^(5/2)-1/2*b*c*ln(c^2*x^2+1)/d^2+1/4*b*c*e*ln(c^2*x^2+1)/d^2/(c^2*d-e)-1/4*b*c*e*ln(e*x^2+d)/d^2/(c^2*d-e)-1/8*I*b*c*sqrt(e)*ln(sqrt(e)*(1+sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)+sqrt(e)))*ln(1+I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(5/2)-1/8*I*b*c*sqrt(e)*polylog(2,sqrt(-c^2)*(sqrt(d)-I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)-I*sqrt(e)))/sqrt(-c^2)/d^(5/2)-1/4*I*b*sqrt(e)*ln(1+I*c*x)*ln(c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e)))/(-d)^(5/2)+1/4*I*b*sqrt(e)*polylog(2,sqrt(e)*(1-I*c*x)/(I*c*sqrt(-d)+sqrt(e)))/(-d)^(5/2)-1/8*I*b*c*sqrt(e)*polylog(2,sqrt(-c^2)*(sqrt(d)+I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)-I*sqrt(e)))/sqrt(-c^2)/d^(5/2)+1/8*I*b*c*sqrt(e)*ln(-sqrt(e)*(1+sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)-sqrt(e)))*ln(1-I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(5/2)+1/8*I*b*c*sqrt(e)*ln(-sqrt(e)*(1-sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)-sqrt(e)))*ln(1+I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(5/2)+1/4*I*b*sqrt(e)*ln(1-I*c*x)*ln(c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e)))/(-d)^(5/2),1],
[x^5*(a+b*arctan(c*x))/(e*x^2+d)^3,x,21,-1/8*b*c*d*x/(c^2*d-e)/e^2/(e*x^2+d)+1/4*b*c^4*d^2*arctan(c*x)/(c^2*d-e)^2/e^3-b*c^2*d*arctan(c*x)/(c^2*d-e)/e^3-1/4*d^2*(a+b*arctan(c*x))/e^3/(e*x^2+d)^2+d*(a+b*arctan(c*x))/e^3/(e*x^2+d)+b*c*sqrt(d)*arctan(sqrt(e)*x/sqrt(d))/(c^2*d-e)/e^(5/2)-1/8*b*c*sqrt(d)*(3*c^2*d-e)*arctan(sqrt(e)*x/sqrt(d))/(c^2*d-e)^2/e^(5/2)-(a+b*arctan(c*x))*ln(2/(1-I*c*x))/e^3+1/2*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^3+1/2*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^3+1/2*I*b*polylog(2,1-2/(1-I*c*x))/e^3-1/4*I*b*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^3-1/4*I*b*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^3,1],
[x^3*(a+b*arctan(c*x))/(e*x^2+d)^3,x,6,1/8*b*c*x/(c^2*d-e)/e/(e*x^2+d)-1/4*b*arctan(c*x)/d/(c^2*d-e)^2+1/4*x^4*(a+b*arctan(c*x))/d/(e*x^2+d)^2-1/8*b*c*(c^2*d-3*e)*arctan(sqrt(e)*x/sqrt(d))/sqrt(d)/(c^2*d-e)^2/e^(3/2),1],
[x*(a+b*arctan(c*x))/(e*x^2+d)^3,x,5,-1/8*b*c*x/d/(c^2*d-e)/(e*x^2+d)+1/4*b*c^4*arctan(c*x)/(c^2*d-e)^2/e-1/4*(a+b*arctan(c*x))/e/(e*x^2+d)^2-1/8*b*c*(3*c^2*d-e)*arctan(sqrt(e)*x/sqrt(d))/d^(3/2)/(c^2*d-e)^2/sqrt(e),1],
[(a+b*arctan(c*x))/x/(e*x^2+d)^3,x,24,1/8*b*c*e*x/d^2/(c^2*d-e)/(e*x^2+d)-1/4*b*c^4*arctan(c*x)/d/(c^2*d-e)^2-1/2*b*c^2*arctan(c*x)/d^2/(c^2*d-e)+1/4*(a+b*arctan(c*x))/d/(e*x^2+d)^2+1/2*(a+b*arctan(c*x))/d^2/(e*x^2+d)+1/2*b*c*sqrt(e)*arctan(sqrt(e)*x/sqrt(d))/d^(5/2)/(c^2*d-e)+1/8*b*c*(3*c^2*d-e)*sqrt(e)*arctan(sqrt(e)*x/sqrt(d))/d^(5/2)/(c^2*d-e)^2+a*ln(x)/d^3+(a+b*arctan(c*x))*ln(2/(1-I*c*x))/d^3-1/2*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^3-1/2*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^3+1/4*I*b*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^3-1/2*I*b*polylog(2,1-2/(1-I*c*x))/d^3+1/2*I*b*polylog(2,-I*c*x)/d^3-1/2*I*b*polylog(2,I*c*x)/d^3+1/4*I*b*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^3,1],
[(a+b*arctan(c*x))/x^3/(e*x^2+d)^3,x,27,-1/2*b*c/d^3/x-1/8*b*c*e^2*x/d^3/(c^2*d-e)/(e*x^2+d)-1/2*b*c^2*arctan(c*x)/d^3+1/4*b*c^4*e*arctan(c*x)/d^2/(c^2*d-e)^2+b*c^2*e*arctan(c*x)/d^3/(c^2*d-e)-1/2*(a+b*arctan(c*x))/d^3/x^2-1/4*e*(a+b*arctan(c*x))/d^2/(e*x^2+d)^2-e*(a+b*arctan(c*x))/d^3/(e*x^2+d)-b*c*e^(3/2)*arctan(sqrt(e)*x/sqrt(d))/d^(7/2)/(c^2*d-e)-1/8*b*c*(3*c^2*d-e)*e^(3/2)*arctan(sqrt(e)*x/sqrt(d))/d^(7/2)/(c^2*d-e)^2-3*a*e*ln(x)/d^4-3*e*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/d^4+3/2*e*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^4+3/2*e*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^4+3/2*I*b*e*polylog(2,1-2/(1-I*c*x))/d^4-3/4*I*b*e*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^4+3/2*I*b*e*polylog(2,I*c*x)/d^4-3/4*I*b*e*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^4-3/2*I*b*e*polylog(2,-I*c*x)/d^4,1],
[x^2*(a+b*arctan(c*x))/(e*x^2+d)^3,x,49,1/8*b*c/(c^2*d-e)/e/(e*x^2+d)-1/4*x*(a+b*arctan(c*x))/e/(e*x^2+d)^2+1/8*x*(a+b*arctan(c*x))/d/e/(e*x^2+d)+1/8*(a+b*arctan(c*x))*arctan(sqrt(e)*x/sqrt(d))/d^(3/2)/e^(3/2)-1/32*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)-I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)+I*sqrt(e)))/sqrt(-c^2)/d^(3/2)/e^(3/2)+1/32*I*b*c*ln(sqrt(e)*(1+sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)+sqrt(e)))*ln(1+I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(3/2)/e^(3/2)+1/32*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)+I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)-I*sqrt(e)))/sqrt(-c^2)/d^(3/2)/e^(3/2)-1/32*I*b*c*ln(-sqrt(e)*(1+sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)-sqrt(e)))*ln(1-I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(3/2)/e^(3/2)+1/16*b*c*(5*c^2*d-3*e)*ln(c^2*x^2+1)/d/(c^2*d-e)^2/e-1/4*b*c*ln(c^2*x^2+1)/d/(c^2*d-e)/e-1/16*b*c*(5*c^2*d-3*e)*ln(e*x^2+d)/d/(c^2*d-e)^2/e+1/4*b*c*ln(e*x^2+d)/d/(c^2*d-e)/e-1/32*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)+I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)+I*sqrt(e)))/sqrt(-c^2)/d^(3/2)/e^(3/2)+1/32*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)-I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)-I*sqrt(e)))/sqrt(-c^2)/d^(3/2)/e^(3/2)+1/32*I*b*c*ln(sqrt(e)*(1-sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)+sqrt(e)))*ln(1-I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(3/2)/e^(3/2)-1/32*I*b*c*ln(-sqrt(e)*(1-sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)-sqrt(e)))*ln(1+I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(3/2)/e^(3/2),1],
[(a+b*arctan(c*x))/(e*x^2+d)^3,x,23,-1/8*b*c/d/(c^2*d-e)/(e*x^2+d)+1/4*x*(a+b*arctan(c*x))/d/(e*x^2+d)^2+3/8*x*(a+b*arctan(c*x))/d^2/(e*x^2+d)+3/8*(a+b*arctan(c*x))*arctan(sqrt(e)*x/sqrt(d))/d^(5/2)/sqrt(e)+3/32*I*b*c*ln(sqrt(e)*(1-sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)+sqrt(e)))*ln(1-I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(5/2)/sqrt(e)-3/32*I*b*c*ln(-sqrt(e)*(1+sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)-sqrt(e)))*ln(1-I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(5/2)/sqrt(e)-3/32*I*b*c*ln(-sqrt(e)*(1-sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)-sqrt(e)))*ln(1+I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(5/2)/sqrt(e)+3/32*I*b*c*ln(sqrt(e)*(1+sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)+sqrt(e)))*ln(1+I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(5/2)/sqrt(e)-1/16*b*c*(5*c^2*d-3*e)*ln(c^2*x^2+1)/d^2/(c^2*d-e)^2+1/16*b*c*(5*c^2*d-3*e)*ln(e*x^2+d)/d^2/(c^2*d-e)^2+3/32*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)-I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)-I*sqrt(e)))/sqrt(-c^2)/d^(5/2)/sqrt(e)-3/32*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)-I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)+I*sqrt(e)))/sqrt(-c^2)/d^(5/2)/sqrt(e)+3/32*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)+I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)-I*sqrt(e)))/sqrt(-c^2)/d^(5/2)/sqrt(e)-3/32*I*b*c*polylog(2,sqrt(-c^2)*(sqrt(d)+I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)+I*sqrt(e)))/sqrt(-c^2)/d^(5/2)/sqrt(e),1],
[(a+b*arctan(c*x))/x^2/(e*x^2+d)^3,x,73,7/32*I*b*c*sqrt(e)*polylog(2,sqrt(-c^2)*(sqrt(d)+I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)+I*sqrt(e)))/sqrt(-c^2)/d^(7/2)-7/32*I*b*c*sqrt(e)*polylog(2,sqrt(-c^2)*(sqrt(d)+I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)-I*sqrt(e)))/sqrt(-c^2)/d^(7/2)+7/32*I*b*c*sqrt(e)*polylog(2,sqrt(-c^2)*(sqrt(d)-I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)+I*sqrt(e)))/sqrt(-c^2)/d^(7/2)-7/32*I*b*c*sqrt(e)*polylog(2,sqrt(-c^2)*(sqrt(d)-I*sqrt(e)*x)/(sqrt(-c^2)*sqrt(d)-I*sqrt(e)))/sqrt(-c^2)/d^(7/2)-1/16*b*c*(5*c^2*d-3*e)*e*ln(e*x^2+d)/d^3/(c^2*d-e)^2+1/16*b*c*(5*c^2*d-3*e)*e*ln(c^2*x^2+1)/d^3/(c^2*d-e)^2-1/2*b*c*ln(c^2*x^2+1)/d^3-a*sqrt(e)*arctan(sqrt(e)*x/sqrt(d))/d^(7/2)-7/8*sqrt(e)*(a+b*arctan(c*x))*arctan(sqrt(e)*x/sqrt(d))/d^(7/2)+b*c*ln(x)/d^3+1/8*b*c*e/d^2/(c^2*d-e)/(e*x^2+d)-(a+b*arctan(c*x))/d^3/x+7/32*I*b*c*sqrt(e)*ln(-sqrt(e)*(1-sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)-sqrt(e)))*ln(1+I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(7/2)-7/32*I*b*c*sqrt(e)*ln(sqrt(e)*(1+sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)+sqrt(e)))*ln(1+I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(7/2)-7/32*I*b*c*sqrt(e)*ln(sqrt(e)*(1-sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)+sqrt(e)))*ln(1-I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(7/2)+7/32*I*b*c*sqrt(e)*ln(-sqrt(e)*(1+sqrt(-c^2)*x)/(I*sqrt(-c^2)*sqrt(d)-sqrt(e)))*ln(1-I*sqrt(e)*x/sqrt(d))/sqrt(-c^2)/d^(7/2)-1/4*b*c*e*ln(e*x^2+d)/d^3/(c^2*d-e)+1/4*b*c*e*ln(c^2*x^2+1)/d^3/(c^2*d-e)-1/4*I*b*sqrt(e)*ln(1-I*c*x)*ln(c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e)))/(-d)^(7/2)+1/4*I*b*sqrt(e)*ln(1-I*c*x)*ln(c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e)))/(-d)^(7/2)+1/4*I*b*sqrt(e)*ln(1+I*c*x)*ln(c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e)))/(-d)^(7/2)-1/4*I*b*sqrt(e)*ln(1+I*c*x)*ln(c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e)))/(-d)^(7/2)-1/4*e*x*(a+b*arctan(c*x))/d^2/(e*x^2+d)^2-7/8*e*x*(a+b*arctan(c*x))/d^3/(e*x^2+d)+1/4*I*b*sqrt(e)*polylog(2,sqrt(e)*(I+c*x)/(c*sqrt(-d)+I*sqrt(e)))/(-d)^(7/2)+1/4*I*b*sqrt(e)*polylog(2,sqrt(e)*(I-c*x)/(c*sqrt(-d)+I*sqrt(e)))/(-d)^(7/2)-1/4*I*b*sqrt(e)*polylog(2,sqrt(e)*(1+I*c*x)/(I*c*sqrt(-d)+sqrt(e)))/(-d)^(7/2)-1/4*I*b*sqrt(e)*polylog(2,sqrt(e)*(1-I*c*x)/(I*c*sqrt(-d)+sqrt(e)))/(-d)^(7/2),1],
[x^3*sqrt(e*x^2+d)*(a+b*arctan(c*x)),x,9,-1/120*b*(c^2*d-12*e)*x*sqrt(e*x^2+d)/c^3/e-1/20*b*x*(e*x^2+d)^(3/2)/c/e-1/3*d*(e*x^2+d)^(3/2)*(a+b*arctan(c*x))/e^2+1/5*(e*x^2+d)^(5/2)*(a+b*arctan(c*x))/e^2+1/15*b*(c^2*d-e)^(3/2)*(2*c^2*d+3*e)*arctan(sqrt(c^2*d-e)*x/sqrt(e*x^2+d))/c^5/e^2+1/120*b*(15*c^4*d^2+20*c^2*d*e-24*e^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^5/e^(3/2),1],
[x^2*sqrt(e*x^2+d)*(a+b*arctan(c*x)),x,5,1/8*a*d*x*sqrt(e*x^2+d)/e+1/4*a*x^3*sqrt(e*x^2+d)-1/8*a*d^2*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(3/2)+b*Defer(Int)(x^2*sqrt(e*x^2+d)*arctan(c*x),x),0],
[x*sqrt(e*x^2+d)*(a+b*arctan(c*x)),x,7,-1/6*b*x*sqrt(e*x^2+d)/c+1/3*(e*x^2+d)^(3/2)*(a+b*arctan(c*x))/e-1/3*b*(c^2*d-e)^(3/2)*arctan(sqrt(c^2*d-e)*x/sqrt(e*x^2+d))/c^3/e-1/6*b*(3*c^2*d-2*e)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^3/sqrt(e),1],
[sqrt(e*x^2+d)*(a+b*arctan(c*x)),x,0,Defer(Int)(sqrt(e*x^2+d)*(a+b*arctan(c*x)),x),0],
[sqrt(e*x^2+d)*(a+b*arctan(c*x))/x,x,5,a*sqrt(e*x^2+d)-a*sqrt(d)*arctanh(sqrt(e*x^2+d)/sqrt(d))+b*Defer(Int)(sqrt(e*x^2+d)*arctan(c*x)/x,x),0],
[sqrt(e*x^2+d)*(a+b*arctan(c*x))/x^2,x,4,-a*sqrt(e*x^2+d)/x+a*sqrt(e)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))+b*Defer(Int)(sqrt(e*x^2+d)*arctan(c*x)/x^2,x),0],
[sqrt(e*x^2+d)*(a+b*arctan(c*x))/x^3,x,5,-1/2*a*sqrt(e*x^2+d)/x^2-1/2*a*e*arctanh(sqrt(e*x^2+d)/sqrt(d))/sqrt(d)+b*Defer(Int)(sqrt(e*x^2+d)*arctan(c*x)/x^3,x),0],
[sqrt(e*x^2+d)*(a+b*arctan(c*x))/x^4,x,9,-1/6*b*c*sqrt(e*x^2+d)/x^2-1/3*(e*x^2+d)^(3/2)*(a+b*arctan(c*x))/d/x^3+1/6*b*c*(2*c^2*d-3*e)*arctanh(sqrt(e*x^2+d)/sqrt(d))/sqrt(d)-1/3*b*(c^2*d-e)^(3/2)*arctanh(c*sqrt(e*x^2+d)/sqrt(c^2*d-e))/d,1],
[sqrt(e*x^2+d)*(a+b*arctan(c*x))/x^5,x,6,-1/4*a*sqrt(e*x^2+d)/x^4-1/8*a*e*sqrt(e*x^2+d)/d/x^2+1/8*a*e^2*arctanh(sqrt(e*x^2+d)/sqrt(d))/d^(3/2)+b*Defer(Int)(sqrt(e*x^2+d)*arctan(c*x)/x^5,x),0],
[sqrt(e*x^2+d)*(a+b*arctan(c*x))/x^6,x,10,1/120*b*c*(12*c^2*d-e)*sqrt(e*x^2+d)/d/x^2-1/20*b*c*(e*x^2+d)^(3/2)/d/x^4-1/5*(e*x^2+d)^(3/2)*(a+b*arctan(c*x))/d/x^5+2/15*e*(e*x^2+d)^(3/2)*(a+b*arctan(c*x))/d^2/x^3-1/120*b*c*(24*c^4*d^2-20*c^2*d*e-15*e^2)*arctanh(sqrt(e*x^2+d)/sqrt(d))/d^(3/2)+1/15*b*(c^2*d-e)^(3/2)*(3*c^2*d+2*e)*arctanh(c*sqrt(e*x^2+d)/sqrt(c^2*d-e))/d^2,1],
[x^3*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x,10,1/560*b*(3*c^4*d^2+54*c^2*d*e-40*e^2)*x*sqrt(e*x^2+d)/c^5/e-1/840*b*(13*c^2*d-30*e)*x*(e*x^2+d)^(3/2)/c^3/e-1/42*b*x*(e*x^2+d)^(5/2)/c/e-1/5*d*(e*x^2+d)^(5/2)*(a+b*arctan(c*x))/e^2+1/7*(e*x^2+d)^(7/2)*(a+b*arctan(c*x))/e^2+1/35*b*(c^2*d-e)^(5/2)*(2*c^2*d+5*e)*arctan(sqrt(c^2*d-e)*x/sqrt(e*x^2+d))/c^7/e^2+1/560*b*(35*c^6*d^3+70*c^4*d^2*e-168*c^2*d*e^2+80*e^3)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^7/e^(3/2),1],
[x^2*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x,6,1/16*a*d^2*x*sqrt(e*x^2+d)/e+1/8*a*d*x^3*sqrt(e*x^2+d)+1/6*a*x^3*(e*x^2+d)^(3/2)-1/16*a*d^3*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(3/2)+b*Defer(Int)(x^2*(e*x^2+d)^(3/2)*arctan(c*x),x),0],
[x*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x,8,-1/40*b*(7*c^2*d-4*e)*x*sqrt(e*x^2+d)/c^3-1/20*b*x*(e*x^2+d)^(3/2)/c+1/5*(e*x^2+d)^(5/2)*(a+b*arctan(c*x))/e-1/5*b*(c^2*d-e)^(5/2)*arctan(sqrt(c^2*d-e)*x/sqrt(e*x^2+d))/c^5/e-1/40*b*(15*c^4*d^2-20*c^2*d*e+8*e^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^5/sqrt(e),1],
[(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x,0,Defer(Int)((e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x),0],
[(e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x,x,6,a*d*sqrt(e*x^2+d)+1/3*a*(e*x^2+d)^(3/2)-a*d^(3/2)*arctanh(sqrt(e*x^2+d)/sqrt(d))+b*Defer(Int)((e*x^2+d)^(3/2)*arctan(c*x)/x,x),0],
[(e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^2,x,5,3/2*a*e*x*sqrt(e*x^2+d)-a*(e*x^2+d)^(3/2)/x+3/2*a*d*sqrt(e)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))+b*Defer(Int)((e*x^2+d)^(3/2)*arctan(c*x)/x^2,x),0],
[(e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^3,x,6,3/2*a*e*sqrt(e*x^2+d)-1/2*a*(e*x^2+d)^(3/2)/x^2-3/2*a*sqrt(d)*e*arctanh(sqrt(e*x^2+d)/sqrt(d))+b*Defer(Int)((e*x^2+d)^(3/2)*arctan(c*x)/x^3,x),0],
[(e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^4,x,5,-a*e*sqrt(e*x^2+d)/x-1/3*a*(e*x^2+d)^(3/2)/x^3+a*e^(3/2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))+b*Defer(Int)((e*x^2+d)^(3/2)*arctan(c*x)/x^4,x),0],
[(e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^5,x,6,-3/8*a*e*sqrt(e*x^2+d)/x^2-1/4*a*(e*x^2+d)^(3/2)/x^4-3/8*a*e^2*arctanh(sqrt(e*x^2+d)/sqrt(d))/sqrt(d)+b*Defer(Int)((e*x^2+d)^(3/2)*arctan(c*x)/x^5,x),0],
[(e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^6,x,10,1/40*b*c*(4*c^2*d-7*e)*sqrt(e*x^2+d)/x^2-1/20*b*c*(e*x^2+d)^(3/2)/x^4-1/5*(e*x^2+d)^(5/2)*(a+b*arctan(c*x))/d/x^5-1/40*b*c*(8*c^4*d^2-20*c^2*d*e+15*e^2)*arctanh(sqrt(e*x^2+d)/sqrt(d))/sqrt(d)+1/5*b*(c^2*d-e)^(5/2)*arctanh(c*sqrt(e*x^2+d)/sqrt(c^2*d-e))/d,1],
[x^3*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x,11,1/8064*b*(59*c^6*d^3+712*c^4*d^2*e-1104*c^2*d*e^2+448*e^3)*x*sqrt(e*x^2+d)/c^7/e-1/12096*b*(69*c^4*d^2-520*c^2*d*e+336*e^2)*x*(e*x^2+d)^(3/2)/c^5/e-1/3024*b*(33*c^2*d-56*e)*x*(e*x^2+d)^(5/2)/c^3/e-1/72*b*x*(e*x^2+d)^(7/2)/c/e-1/7*d*(e*x^2+d)^(7/2)*(a+b*arctan(c*x))/e^2+1/9*(e*x^2+d)^(9/2)*(a+b*arctan(c*x))/e^2+1/63*b*(c^2*d-e)^(7/2)*(2*c^2*d+7*e)*arctan(sqrt(c^2*d-e)*x/sqrt(e*x^2+d))/c^9/e^2+1/8064*b*(315*c^8*d^4+840*c^6*d^3*e-3024*c^4*d^2*e^2+2880*c^2*d*e^3-896*e^4)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^9/e^(3/2),1],
[x^2*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x,7,5/128*a*d^3*x*sqrt(e*x^2+d)/e+5/64*a*d^2*x^3*sqrt(e*x^2+d)+5/48*a*d*x^3*(e*x^2+d)^(3/2)+1/8*a*x^3*(e*x^2+d)^(5/2)-5/128*a*d^4*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(3/2)+b*Defer(Int)(x^2*(e*x^2+d)^(5/2)*arctan(c*x),x),0],
[x*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x,9,-1/112*b*(19*c^4*d^2-22*c^2*d*e+8*e^2)*x*sqrt(e*x^2+d)/c^5-1/168*b*(11*c^2*d-6*e)*x*(e*x^2+d)^(3/2)/c^3-1/42*b*x*(e*x^2+d)^(5/2)/c+1/7*(e*x^2+d)^(7/2)*(a+b*arctan(c*x))/e-1/7*b*(c^2*d-e)^(7/2)*arctan(sqrt(c^2*d-e)*x/sqrt(e*x^2+d))/c^7/e-1/112*b*(35*c^6*d^3-70*c^4*d^2*e+56*c^2*d*e^2-16*e^3)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^7/sqrt(e),1],
[(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x,0,Defer(Int)((e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x),0],
[(e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x,x,7,a*d^2*sqrt(e*x^2+d)+1/3*a*d*(e*x^2+d)^(3/2)+1/5*a*(e*x^2+d)^(5/2)-a*d^(5/2)*arctanh(sqrt(e*x^2+d)/sqrt(d))+b*Defer(Int)((e*x^2+d)^(5/2)*arctan(c*x)/x,x),0],
[(e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^2,x,6,15/8*a*d*e*x*sqrt(e*x^2+d)+5/4*a*e*x*(e*x^2+d)^(3/2)-a*(e*x^2+d)^(5/2)/x+15/8*a*d^2*sqrt(e)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))+b*Defer(Int)((e*x^2+d)^(5/2)*arctan(c*x)/x^2,x),0],
[(e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^3,x,7,5/2*a*d*e*sqrt(e*x^2+d)+5/6*a*e*(e*x^2+d)^(3/2)-1/2*a*(e*x^2+d)^(5/2)/x^2-5/2*a*d^(3/2)*e*arctanh(sqrt(e*x^2+d)/sqrt(d))+b*Defer(Int)((e*x^2+d)^(5/2)*arctan(c*x)/x^3,x),0],
[(e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^4,x,6,5/2*a*e^2*x*sqrt(e*x^2+d)-5/3*a*e*(e*x^2+d)^(3/2)/x-1/3*a*(e*x^2+d)^(5/2)/x^3+5/2*a*d*e^(3/2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))+b*Defer(Int)((e*x^2+d)^(5/2)*arctan(c*x)/x^4,x),0],
[x^3*(a+b*arctan(c*x))/sqrt(e*x^2+d),x,8,-1/6*b*x*sqrt(e*x^2+d)/c/e-d*sqrt(e*x^2+d)*(a+b*arctan(c*x))/e^2+1/3*(e*x^2+d)^(3/2)*(a+b*arctan(c*x))/e^2+1/3*b*sqrt(c^2*d-e)*(2*c^2*d+e)*arctan(sqrt(c^2*d-e)*x/sqrt(e*x^2+d))/c^3/e^2+1/6*b*(3*c^2*d+2*e)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^3/e^(3/2),1],
[x^2*(a+b*arctan(c*x))/sqrt(e*x^2+d),x,4,1/2*a*x*sqrt(e*x^2+d)/e-1/2*a*d*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(3/2)+b*Defer(Int)(x^2*arctan(c*x)/sqrt(e*x^2+d),x),0],
[x*(a+b*arctan(c*x))/sqrt(e*x^2+d),x,6,sqrt(e*x^2+d)*(a+b*arctan(c*x))/e-b*sqrt(c^2*d-e)*arctan(sqrt(c^2*d-e)*x/sqrt(e*x^2+d))/c/e-b*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c/sqrt(e),1],
[(a+b*arctan(c*x))/sqrt(e*x^2+d),x,0,Defer(Int)((a+b*arctan(c*x))/sqrt(e*x^2+d),x),0],
[(a+b*arctan(c*x))/x/sqrt(e*x^2+d),x,4,-a*arctanh(sqrt(e*x^2+d)/sqrt(d))/sqrt(d)+b*Defer(Int)(arctan(c*x)/x/sqrt(e*x^2+d),x),0],
[(a+b*arctan(c*x))/x^2/sqrt(e*x^2+d),x,7,-sqrt(e*x^2+d)*(a+b*arctan(c*x))/d/x-b*c*arctanh(sqrt(e*x^2+d)/sqrt(d))/sqrt(d)+b*sqrt(c^2*d-e)*arctanh(c*sqrt(e*x^2+d)/sqrt(c^2*d-e))/d,1],
[(a+b*arctan(c*x))/x^3/sqrt(e*x^2+d),x,5,-1/2*a*sqrt(e*x^2+d)/d/x^2+1/2*a*e*arctanh(sqrt(e*x^2+d)/sqrt(d))/d^(3/2)+b*Defer(Int)(arctan(c*x)/x^3/sqrt(e*x^2+d),x),0],
[(a+b*arctan(c*x))/x^4/sqrt(e*x^2+d),x,9,-1/6*b*c*sqrt(e*x^2+d)/d/x^2-1/3*sqrt(e*x^2+d)*(a+b*arctan(c*x))/d/x^3+2/3*e*sqrt(e*x^2+d)*(a+b*arctan(c*x))/d^2/x+1/6*b*c*(2*c^2*d+3*e)*arctanh(sqrt(e*x^2+d)/sqrt(d))/d^(3/2)-1/3*b*sqrt(c^2*d-e)*(c^2*d+2*e)*arctanh(c*sqrt(e*x^2+d)/sqrt(c^2*d-e))/d^2,1],
[x^3*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x,7,d*(a+b*arctan(c*x))/e^2/sqrt(e*x^2+d)+sqrt(e*x^2+d)*(a+b*arctan(c*x))/e^2-b*(2*c^2*d-e)*arctan(sqrt(c^2*d-e)*x/sqrt(e*x^2+d))/c/sqrt(c^2*d-e)/e^2-b*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c/e^(3/2),1],
[x^2*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x,4,-a*x/e/sqrt(e*x^2+d)+a*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(3/2)+b*Defer(Int)(x^2*arctan(c*x)/(e*x^2+d)^(3/2),x),0],
[x*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x,3,-(a+b*arctan(c*x))/e/sqrt(e*x^2+d)+b*c*arctan(sqrt(c^2*d-e)*x/sqrt(e*x^2+d))/sqrt(c^2*d-e)/e,1],
[(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x,4,x*(a+b*arctan(c*x))/d/sqrt(e*x^2+d)+b*arctanh(c*sqrt(e*x^2+d)/sqrt(c^2*d-e))/d/sqrt(c^2*d-e),1],
[(a+b*arctan(c*x))/x/(e*x^2+d)^(3/2),x,5,a/d/sqrt(e*x^2+d)-a*arctanh(sqrt(e*x^2+d)/sqrt(d))/d^(3/2)+b*Defer(Int)(arctan(c*x)/x/(e*x^2+d)^(3/2),x),0],
[(a+b*arctan(c*x))/x^2/(e*x^2+d)^(3/2),x,8,(a+b*arctan(c*x))/d/x/sqrt(e*x^2+d)-2*sqrt(e*x^2+d)*(a+b*arctan(c*x))/d^2/x-b*c*arctanh(sqrt(e*x^2+d)/sqrt(d))/d^(3/2)+b*(c^2*d-2*e)*arctanh(c*sqrt(e*x^2+d)/sqrt(c^2*d-e))/d^2/sqrt(c^2*d-e),1],
[(a+b*arctan(c*x))/x^3/(e*x^2+d)^(3/2),x,6,-3/2*a*e/d^2/sqrt(e*x^2+d)-1/2*a/d/x^2/sqrt(e*x^2+d)+3/2*a*e*arctanh(sqrt(e*x^2+d)/sqrt(d))/d^(5/2)+b*Defer(Int)(arctan(c*x)/x^3/(e*x^2+d)^(3/2),x),0],
[(a+b*arctan(c*x))/x^4/(e*x^2+d)^(3/2),x,9,-1/6*b*c*sqrt(e*x^2+d)/d^2/x^2+(a+b*arctan(c*x))/d/x^3/sqrt(e*x^2+d)-4/3*sqrt(e*x^2+d)*(a+b*arctan(c*x))/d^2/x^3+8/3*e*sqrt(e*x^2+d)*(a+b*arctan(c*x))/d^3/x+1/6*b*c*(2*c^2*d+9*e)*arctanh(sqrt(e*x^2+d)/sqrt(d))/d^(5/2)-1/3*b*(c^4*d^2+4*c^2*d*e-8*e^2)*arctanh(c*sqrt(e*x^2+d)/sqrt(c^2*d-e))/d^3/sqrt(c^2*d-e),1],
[x^4*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x,5,-1/3*a*x^3/e/(e*x^2+d)^(3/2)-a*x/e^2/sqrt(e*x^2+d)+a*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(5/2)+b*Defer(Int)(x^4*arctan(c*x)/(e*x^2+d)^(5/2),x),0],
[x^3*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x,5,1/3*b*c*x/(c^2*d-e)/e/sqrt(e*x^2+d)+1/3*d*(a+b*arctan(c*x))/e^2/(e*x^2+d)^(3/2)-(a+b*arctan(c*x))/e^2/sqrt(e*x^2+d)+1/3*b*c*(2*c^2*d-3*e)*arctan(sqrt(c^2*d-e)*x/sqrt(e*x^2+d))/(c^2*d-e)^(3/2)/e^2,1],
[x^2*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x,5,1/3*b*c/(c^2*d-e)/e/sqrt(e*x^2+d)+1/3*x^3*(a+b*arctan(c*x))/d/(e*x^2+d)^(3/2)-1/3*b*arctanh(c*sqrt(e*x^2+d)/sqrt(c^2*d-e))/d/(c^2*d-e)^(3/2),1],
[x*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x,4,-1/3*b*c*x/d/(c^2*d-e)/sqrt(e*x^2+d)-1/3*(a+b*arctan(c*x))/e/(e*x^2+d)^(3/2)+1/3*b*c^3*arctan(sqrt(c^2*d-e)*x/sqrt(e*x^2+d))/(c^2*d-e)^(3/2)/e,1],
[(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x,6,-1/3*b*c/d/(c^2*d-e)/sqrt(e*x^2+d)+1/3*x*(a+b*arctan(c*x))/d/(e*x^2+d)^(3/2)+2/3*x*(a+b*arctan(c*x))/d^2/sqrt(e*x^2+d)+1/3*b*(3*c^2*d-2*e)*arctanh(c*sqrt(e*x^2+d)/sqrt(c^2*d-e))/d^2/(c^2*d-e)^(3/2),1],
[(a+b*arctan(c*x))/x/(e*x^2+d)^(5/2),x,6,1/3*a/d/(e*x^2+d)^(3/2)+a/d^2/sqrt(e*x^2+d)-a*arctanh(sqrt(e*x^2+d)/sqrt(d))/d^(5/2)+b*Defer(Int)(arctan(c*x)/x/(e*x^2+d)^(5/2),x),0],
[(a+b*arctan(c*x))/x^2/(e*x^2+d)^(5/2),x,9,1/3*b*c*e/d^2/(c^2*d-e)/sqrt(e*x^2+d)+1/3*(a+b*arctan(c*x))/d/x/(e*x^2+d)^(3/2)+4/3*(a+b*arctan(c*x))/d^2/x/sqrt(e*x^2+d)-8/3*sqrt(e*x^2+d)*(a+b*arctan(c*x))/d^3/x-b*c*arctanh(sqrt(e*x^2+d)/sqrt(d))/d^(5/2)+1/3*b*(3*c^4*d^2-12*c^2*d*e+8*e^2)*arctanh(c*sqrt(e*x^2+d)/sqrt(c^2*d-e))/d^3/(c^2*d-e)^(3/2),1],
[(a+b*arctan(c*x))/x^3/(e*x^2+d)^(5/2),x,7,-5/6*a*e/d^2/(e*x^2+d)^(3/2)-1/2*a/d/x^2/(e*x^2+d)^(3/2)-5/2*a*e/d^3/sqrt(e*x^2+d)+5/2*a*e*arctanh(sqrt(e*x^2+d)/sqrt(d))/d^(7/2)+b*Defer(Int)(arctan(c*x)/x^3/(e*x^2+d)^(5/2),x),0],
[(a+b*arctan(c*x))/x^4/(e*x^2+d)^(5/2),x,10,-1/6*b*c*e*(c^2*d+e)/d^3/(c^2*d-e)/sqrt(e*x^2+d)-1/6*b*c/d^2/x^2/sqrt(e*x^2+d)+1/3*(a+b*arctan(c*x))/d/x^3/(e*x^2+d)^(3/2)+2*(a+b*arctan(c*x))/d^2/x^3/sqrt(e*x^2+d)-8/3*sqrt(e*x^2+d)*(a+b*arctan(c*x))/d^3/x^3+16/3*e*sqrt(e*x^2+d)*(a+b*arctan(c*x))/d^4/x+1/6*b*c*(2*c^2*d+15*e)*arctanh(sqrt(e*x^2+d)/sqrt(d))/d^(7/2)-1/3*b*(c^2*d-2*e)*(c^4*d^2+8*c^2*d*e-8*e^2)*arctanh(c*sqrt(e*x^2+d)/sqrt(c^2*d-e))/d^4/(c^2*d-e)^(3/2),1],
[arctan(a*x)/(d*x^2+c)^(7/2),x,7,-1/15*a/c/(a^2*c-d)/(d*x^2+c)^(3/2)-1/15*a*(7*a^2*c-4*d)/c^2/(a^2*c-d)^2/sqrt(d*x^2+c)+1/5*x*arctan(a*x)/c/(d*x^2+c)^(5/2)+4/15*x*arctan(a*x)/c^2/(d*x^2+c)^(3/2)+8/15*x*arctan(a*x)/c^3/sqrt(d*x^2+c)+1/15*(15*a^4*c^2-20*a^2*c*d+8*d^2)*arctanh(a*sqrt(d*x^2+c)/sqrt(a^2*c-d))/c^3/(a^2*c-d)^(5/2),1],
[arctan(a*x)/(d*x^2+c)^(9/2),x,7,-1/35*a/c/(a^2*c-d)/(d*x^2+c)^(5/2)-1/105*a*(11*a^2*c-6*d)/c^2/(a^2*c-d)^2/(d*x^2+c)^(3/2)-1/35*a*(19*a^4*c^2-22*a^2*c*d+8*d^2)/c^3/(a^2*c-d)^3/sqrt(d*x^2+c)+1/7*x*arctan(a*x)/c/(d*x^2+c)^(7/2)+6/35*x*arctan(a*x)/c^2/(d*x^2+c)^(5/2)+8/35*x*arctan(a*x)/c^3/(d*x^2+c)^(3/2)+16/35*x*arctan(a*x)/c^4/sqrt(d*x^2+c)+1/35*(35*a^6*c^3-70*a^4*c^2*d+56*a^2*c*d^2-16*d^3)*arctanh(a*sqrt(d*x^2+c)/sqrt(a^2*c-d))/c^4/(a^2*c-d)^(7/2),1],
[x^m*(e*x^2+d)^3*(a+b*arctan(c*x)),x,5,-b*e*(e^2*(m^2+8*m+15)-3*c^2*d*e*(m^2+10*m+21)+3*c^4*d^2*(m^2+12*m+35))*x^(2+m)/c^5/(m^2+5*m+6)/(m^2+12*m+35)+b*e^2*(e*(5+m)-3*c^2*d*(7+m))*x^(4+m)/c^3/(4+m)/(m^2+12*m+35)-b*e^3*x^(6+m)/c/(6+m)/(7+m)+d^3*x^(1+m)*(a+b*arctan(c*x))/(1+m)+3*d^2*e*x^(3+m)*(a+b*arctan(c*x))/(3+m)+3*d*e^2*x^(5+m)*(a+b*arctan(c*x))/(5+m)+e^3*x^(7+m)*(a+b*arctan(c*x))/(7+m)-b*(c^6*d^3/(1+m)-e*(e^2*(m^2+8*m+15)-3*c^2*d*e*(m^2+10*m+21)+3*c^4*d^2*(m^2+12*m+35))/(3+m)/(m^2+12*m+35))*x^(2+m)*hypergeom([1, 1+1/2*m],[2+1/2*m],-c^2*x^2)/c^5/(2+m),1],
[x^m*(e*x^2+d)^2*(a+b*arctan(c*x)),x,4,-b*e*(2*c^2*d/(3+m)-e/(5+m))*x^(2+m)/c^3/(2+m)-b*e^2*x^(4+m)/c/(4+m)/(5+m)+d^2*x^(1+m)*(a+b*arctan(c*x))/(1+m)+2*d*e*x^(3+m)*(a+b*arctan(c*x))/(3+m)+e^2*x^(5+m)*(a+b*arctan(c*x))/(5+m)-b*(c^4*d^2/(1+m)-2*c^2*d*e/(3+m)+e^2/(5+m))*x^(2+m)*hypergeom([1, 1+1/2*m],[2+1/2*m],-c^2*x^2)/c^3/(2+m),1],
[x^m*(e*x^2+d)*(a+b*arctan(c*x)),x,3,-b*e*x^(2+m)/c/(m^2+5*m+6)+d*x^(1+m)*(a+b*arctan(c*x))/(1+m)+e*x^(3+m)*(a+b*arctan(c*x))/(3+m)-b*(c^2*d/(1+m)-e/(3+m))*x^(2+m)*hypergeom([1, 1+1/2*m],[2+1/2*m],-c^2*x^2)/c/(2+m),1],
[x^m*(a+b*arctan(c*x))/(e*x^2+d),x,2,a*x^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-e*x^2/d)/d/(1+m)+b*Defer(Int)(x^m*arctan(c*x)/(e*x^2+d),x),0],
[x^m*(a+b*arctan(c*x))/(e*x^2+d)^2,x,2,a*x^(1+m)*hypergeom([2, 1/2+1/2*m],[3/2+1/2*m],-e*x^2/d)/d^2/(1+m)+b*Defer(Int)(x^m*arctan(c*x)/(e*x^2+d)^2,x),0],
[x^m*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x,3,a*d*x^(1+m)*sqrt(e*x^2+d)*hypergeom([-3/2, 1/2+1/2*m],[3/2+1/2*m],-e*x^2/d)/(1+m)/sqrt(1+e*x^2/d)+b*Defer(Int)(x^m*(e*x^2+d)^(3/2)*arctan(c*x),x),0],
[x^m*sqrt(e*x^2+d)*(a+b*arctan(c*x)),x,3,a*x^(1+m)*sqrt(e*x^2+d)*hypergeom([-1/2, 1/2+1/2*m],[3/2+1/2*m],-e*x^2/d)/(1+m)/sqrt(1+e*x^2/d)+b*Defer(Int)(x^m*sqrt(e*x^2+d)*arctan(c*x),x),0],
[x^m*(a+b*arctan(c*x))/sqrt(e*x^2+d),x,3,a*x^(1+m)*sqrt(1+e*x^2/d)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],-e*x^2/d)/(1+m)/sqrt(e*x^2+d)+b*Defer(Int)(x^m*arctan(c*x)/sqrt(e*x^2+d),x),0],
[x^m*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x,3,a*x^(1+m)*sqrt(1+e*x^2/d)*hypergeom([3/2, 1/2+1/2*m],[3/2+1/2*m],-e*x^2/d)/d/(1+m)/sqrt(e*x^2+d)+b*Defer(Int)(x^m*arctan(c*x)/(e*x^2+d)^(3/2),x),0],
[x^m*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x,3,a*x^(1+m)*sqrt(1+e*x^2/d)*hypergeom([5/2, 1/2+1/2*m],[3/2+1/2*m],-e*x^2/d)/d^2/(1+m)/sqrt(e*x^2+d)+b*Defer(Int)(x^m*arctan(c*x)/(e*x^2+d)^(5/2),x),0],
[x^m*(e*x^2+d)^p*(a+b*arctan(c*x)),x,3,a*x^(1+m)*(e*x^2+d)^p*hypergeom([1/2+1/2*m, -p],[3/2+1/2*m],-e*x^2/d)/(1+m)/((1+e*x^2/d)^p)+b*Defer(Int)(x^m*(e*x^2+d)^p*arctan(c*x),x),0],
[x^(-2-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x,3,-a*x^(-1-2*p)*(e*x^2+d)^p*hypergeom([-1/2-p, -p],[1/2-p],-e*x^2/d)/(1+2*p)/((1+e*x^2/d)^p)+b*Defer(Int)(x^(-2-2*p)*(e*x^2+d)^p*arctan(c*x),x),0],
[x^(-3-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x,5,-1/2*b*c*x^(-1-2*p)*(e*x^2+d)^p*AppellF1(-1/2-p,1,-1-p,1/2-p,-c^2*x^2,-e*x^2/d)/(2*p^2+3*p+1)/((1+e*x^2/d)^p)-1/2*(e*x^2+d)^(p+1)*(a+b*arctan(c*x))/d/(p+1)/(x^(2*p+2)),1],
[x^(-4-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x,3,-a*x^(-3-2*p)*(e*x^2+d)^p*hypergeom([-3/2-p, -p],[-1/2-p],-e*x^2/d)/(3+2*p)/((1+e*x^2/d)^p)+b*Defer(Int)(x^(-4-2*p)*(e*x^2+d)^p*arctan(c*x),x),0],
[x^(-5-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x,9,-1/2*b*(e+c^2*d*(p+1))*x^(-3-2*p)*(e*x^2+d)^p*AppellF1(-3/2-p,1,-1-p,-1/2-p,-c^2*x^2,-e*x^2/d)/c/d/(p+1)/(2+p)/(3+2*p)/((1+e*x^2/d)^p)+1/2*e*(e*x^2+d)^(p+1)*(a+b*arctan(c*x))/d^2/(p+1)/(2+p)/(x^(2*p+2))-1/2*(e*x^2+d)^(p+1)*(a+b*arctan(c*x))/d/(2+p)/(x^(4+2*p))+1/2*b*e*x^(-3-2*p)*(e*x^2+d)^p*hypergeom([-3/2-p, -1-p],[-1/2-p],-e*x^2/d)/c/d/(2*p^3+9*p^2+13*p+6)/((1+e*x^2/d)^p),1],
[x^(-6-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x,3,-a*x^(-5-2*p)*(e*x^2+d)^p*hypergeom([-5/2-p, -p],[-3/2-p],-e*x^2/d)/(5+2*p)/((1+e*x^2/d)^p)+b*Defer(Int)(x^(-6-2*p)*(e*x^2+d)^p*arctan(c*x),x),0],
[x^(-7-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x,11,-1/2*b*(2*e^2+2*c^2*d*e*(p+1)+c^4*d^2*(p^2+3*p+2))*x^(-5-2*p)*(e*x^2+d)^p*AppellF1(-5/2-p,1,-1-p,-3/2-p,-c^2*x^2,-e*x^2/d)/c^3/d^2/(p+1)/(2+p)/(3+p)/(5+2*p)/((1+e*x^2/d)^p)-e^2*(e*x^2+d)^(p+1)*(a+b*arctan(c*x))/d^3/(p+1)/(2+p)/(3+p)/(x^(2*p+2))+e*(e*x^2+d)^(p+1)*(a+b*arctan(c*x))/d^2/(2+p)/(3+p)/(x^(4+2*p))-1/2*(e*x^2+d)^(p+1)*(a+b*arctan(c*x))/d/(3+p)/(x^(6+2*p))+b*e*(e+c^2*d*(p+1))*x^(-5-2*p)*(e*x^2+d)^p*hypergeom([-5/2-p, -1-p],[-3/2-p],-e*x^2/d)/c^3/d^2/(p+1)/(2+p)/(3+p)/(5+2*p)/((1+e*x^2/d)^p)-b*e^2*x^(-3-2*p)*(e*x^2+d)^p*hypergeom([-3/2-p, -1-p],[-1/2-p],-e*x^2/d)/c/d^2/(p+1)/(2+p)/(3+p)/(3+2*p)/((1+e*x^2/d)^p),1],
[x^(-8-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x,3,-a*x^(-7-2*p)*(e*x^2+d)^p*hypergeom([-7/2-p, -p],[-5/2-p],-e*x^2/d)/(7+2*p)/((1+e*x^2/d)^p)+b*Defer(Int)(x^(-8-2*p)*(e*x^2+d)^p*arctan(c*x),x),0],
[x^3*(e*x^2+d)*(a+b*arctan(c*x))^2,x,29,1/2*a*b*d*x/c^3-1/3*a*b*e*x/c^5+1/12*b^2*d*x^2/c^2-4/45*b^2*e*x^2/c^4+1/60*b^2*e*x^4/c^2+1/2*b^2*d*x*arctan(c*x)/c^3-1/3*b^2*e*x*arctan(c*x)/c^5-1/6*b*d*x^3*(a+b*arctan(c*x))/c+1/9*b*e*x^3*(a+b*arctan(c*x))/c^3-1/15*b*e*x^5*(a+b*arctan(c*x))/c-1/4*d*(a+b*arctan(c*x))^2/c^4+1/6*e*(a+b*arctan(c*x))^2/c^6+1/4*d*x^4*(a+b*arctan(c*x))^2+1/6*e*x^6*(a+b*arctan(c*x))^2-1/3*b^2*d*ln(c^2*x^2+1)/c^4+23/90*b^2*e*ln(c^2*x^2+1)/c^6,1],
[x^2*(e*x^2+d)*(a+b*arctan(c*x))^2,x,25,1/3*b^2*d*x/c^2-3/10*b^2*e*x/c^4+1/30*b^2*e*x^3/c^2-1/3*b^2*d*arctan(c*x)/c^3+3/10*b^2*e*arctan(c*x)/c^5-1/3*b*d*x^2*(a+b*arctan(c*x))/c+1/5*b*e*x^2*(a+b*arctan(c*x))/c^3-1/10*b*e*x^4*(a+b*arctan(c*x))/c+1/5*I*e*(a+b*arctan(c*x))^2/c^5-1/3*I*d*(a+b*arctan(c*x))^2/c^3+1/3*d*x^3*(a+b*arctan(c*x))^2+1/5*e*x^5*(a+b*arctan(c*x))^2-2/3*b*d*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3+2/5*b*e*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^5-1/3*I*b^2*d*polylog(2,1-2/(1+I*c*x))/c^3+1/5*I*b^2*e*polylog(2,1-2/(1+I*c*x))/c^5,1],
[x*(e*x^2+d)*(a+b*arctan(c*x))^2,x,19,-a*b*d*x/c+1/2*a*b*e*x/c^3+1/12*b^2*e*x^2/c^2-b^2*d*x*arctan(c*x)/c+1/2*b^2*e*x*arctan(c*x)/c^3-1/6*b*e*x^3*(a+b*arctan(c*x))/c+1/2*d*(a+b*arctan(c*x))^2/c^2-1/4*e*(a+b*arctan(c*x))^2/c^4+1/2*d*x^2*(a+b*arctan(c*x))^2+1/4*e*x^4*(a+b*arctan(c*x))^2+1/2*b^2*d*ln(c^2*x^2+1)/c^2-1/3*b^2*e*ln(c^2*x^2+1)/c^4,1],
[(e*x^2+d)*(a+b*arctan(c*x))^2,x,16,1/3*b^2*e*x/c^2-1/3*b^2*e*arctan(c*x)/c^3-1/3*b*e*x^2*(a+b*arctan(c*x))/c+I*d*(a+b*arctan(c*x))^2/c-1/3*I*e*(a+b*arctan(c*x))^2/c^3+d*x*(a+b*arctan(c*x))^2+1/3*e*x^3*(a+b*arctan(c*x))^2+2*b*d*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c-2/3*b*e*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3+I*b^2*d*polylog(2,1-2/(1+I*c*x))/c-1/3*I*b^2*e*polylog(2,1-2/(1+I*c*x))/c^3,1],
[(e*x^2+d)*(a+b*arctan(c*x))^2/x,x,14,-a*b*e*x/c-b^2*e*x*arctan(c*x)/c+1/2*e*(a+b*arctan(c*x))^2/c^2+1/2*e*x^2*(a+b*arctan(c*x))^2+2*d*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))+1/2*b^2*e*ln(c^2*x^2+1)/c^2-I*b*d*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))+I*b*d*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))-1/2*b^2*d*polylog(3,1-2/(1+I*c*x))+1/2*b^2*d*polylog(3,-1+2/(1+I*c*x)),1],
[(e*x^2+d)*(a+b*arctan(c*x))^2/x^2,x,11,-I*c*d*(a+b*arctan(c*x))^2+I*e*(a+b*arctan(c*x))^2/c-d*(a+b*arctan(c*x))^2/x+e*x*(a+b*arctan(c*x))^2+2*b*e*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c+2*b*c*d*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))-I*b^2*c*d*polylog(2,-1+2/(1-I*c*x))+I*b^2*e*polylog(2,1-2/(1+I*c*x))/c,1],
[(e*x^2+d)*(a+b*arctan(c*x))^2/x^3,x,16,-b*c*d*(a+b*arctan(c*x))/x-1/2*c^2*d*(a+b*arctan(c*x))^2-1/2*d*(a+b*arctan(c*x))^2/x^2+2*e*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))+b^2*c^2*d*ln(x)-1/2*b^2*c^2*d*ln(c^2*x^2+1)-I*b*e*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))+I*b*e*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))-1/2*b^2*e*polylog(3,1-2/(1+I*c*x))+1/2*b^2*e*polylog(3,-1+2/(1+I*c*x)),1],
[x^3*(e*x^2+d)^2*(a+b*arctan(c*x))^2,x,50,-22/105*b^2*e^2*ln(c^2*x^2+1)/c^8-1/3*b^2*d^2*ln(c^2*x^2+1)/c^4+1/3*d*e*(a+b*arctan(c*x))^2/c^6+1/3*d*e*x^6*(a+b*arctan(c*x))^2+1/12*b^2*d^2*x^2/c^2+71/840*b^2*e^2*x^2/c^6-3/140*b^2*e^2*x^4/c^4+1/168*b^2*e^2*x^6/c^2-2/15*b*d*e*x^5*(a+b*arctan(c*x))/c+1/4*d^2*x^4*(a+b*arctan(c*x))^2-1/4*d^2*(a+b*arctan(c*x))^2/c^4+1/8*e^2*x^8*(a+b*arctan(c*x))^2-2/3*a*b*d*e*x/c^5-2/3*b^2*d*e*x*arctan(c*x)/c^5+2/9*b*d*e*x^3*(a+b*arctan(c*x))/c^3+1/2*a*b*d^2*x/c^3+1/4*a*b*e^2*x/c^7-8/45*b^2*d*e*x^2/c^4+1/30*b^2*d*e*x^4/c^2+23/45*b^2*d*e*ln(c^2*x^2+1)/c^6+1/2*b^2*d^2*x*arctan(c*x)/c^3+1/4*b^2*e^2*x*arctan(c*x)/c^7-1/6*b*d^2*x^3*(a+b*arctan(c*x))/c-1/12*b*e^2*x^3*(a+b*arctan(c*x))/c^5+1/20*b*e^2*x^5*(a+b*arctan(c*x))/c^3-1/28*b*e^2*x^7*(a+b*arctan(c*x))/c-1/8*e^2*(a+b*arctan(c*x))^2/c^8,1],
[x^2*(e*x^2+d)^2*(a+b*arctan(c*x))^2,x,44,2/5*d*e*x^5*(a+b*arctan(c*x))^2-1/3*I*d^2*(a+b*arctan(c*x))^2/c^3-1/7*I*e^2*(a+b*arctan(c*x))^2/c^7-1/3*b^2*d^2*arctan(c*x)/c^3-11/42*b^2*e^2*arctan(c*x)/c^7+1/3*b^2*d^2*x/c^2+11/42*b^2*e^2*x/c^6-5/126*b^2*e^2*x^3/c^4+1/105*b^2*e^2*x^5/c^2+2/5*I*b^2*d*e*polylog(2,1-2/(1+I*c*x))/c^5+1/7*e^2*x^7*(a+b*arctan(c*x))^2+1/3*d^2*x^3*(a+b*arctan(c*x))^2-3/5*b^2*d*e*x/c^4+1/15*b^2*d*e*x^3/c^2+2/5*b*d*e*x^2*(a+b*arctan(c*x))/c^3-1/5*b*d*e*x^4*(a+b*arctan(c*x))/c+4/5*b*d*e*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^5-1/3*I*b^2*d^2*polylog(2,1-2/(1+I*c*x))/c^3-1/7*I*b^2*e^2*polylog(2,1-2/(1+I*c*x))/c^7+2/5*I*d*e*(a+b*arctan(c*x))^2/c^5+3/5*b^2*d*e*arctan(c*x)/c^5-1/3*b*d^2*x^2*(a+b*arctan(c*x))/c-1/7*b*e^2*x^2*(a+b*arctan(c*x))/c^5+1/14*b*e^2*x^4*(a+b*arctan(c*x))/c^3-1/21*b*e^2*x^6*(a+b*arctan(c*x))/c-2/3*b*d^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3-2/7*b*e^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^7,1],
[x*(e*x^2+d)^2*(a+b*arctan(c*x))^2,x,35,-a*b*d^2*x/c+a*b*d*e*x/c^3-1/3*a*b*e^2*x/c^5+1/6*b^2*d*e*x^2/c^2-4/45*b^2*e^2*x^2/c^4+1/60*b^2*e^2*x^4/c^2-b^2*d^2*x*arctan(c*x)/c+b^2*d*e*x*arctan(c*x)/c^3-1/3*b^2*e^2*x*arctan(c*x)/c^5-1/3*b*d*e*x^3*(a+b*arctan(c*x))/c+1/9*b*e^2*x^3*(a+b*arctan(c*x))/c^3-1/15*b*e^2*x^5*(a+b*arctan(c*x))/c+1/2*d^2*(a+b*arctan(c*x))^2/c^2-1/2*d*e*(a+b*arctan(c*x))^2/c^4+1/6*e^2*(a+b*arctan(c*x))^2/c^6+1/2*d^2*x^2*(a+b*arctan(c*x))^2+1/2*d*e*x^4*(a+b*arctan(c*x))^2+1/6*e^2*x^6*(a+b*arctan(c*x))^2+1/2*b^2*d^2*ln(c^2*x^2+1)/c^2-2/3*b^2*d*e*ln(c^2*x^2+1)/c^4+23/90*b^2*e^2*ln(c^2*x^2+1)/c^6,1],
[(e*x^2+d)^2*(a+b*arctan(c*x))^2,x,30,2/3*b^2*d*e*x/c^2-3/10*b^2*e^2*x/c^4+1/30*b^2*e^2*x^3/c^2-2/3*b^2*d*e*arctan(c*x)/c^3+3/10*b^2*e^2*arctan(c*x)/c^5-2/3*b*d*e*x^2*(a+b*arctan(c*x))/c+1/5*b*e^2*x^2*(a+b*arctan(c*x))/c^3-1/10*b*e^2*x^4*(a+b*arctan(c*x))/c+I*d^2*(a+b*arctan(c*x))^2/c+I*b^2*d^2*polylog(2,1-2/(1+I*c*x))/c+1/5*I*b^2*e^2*polylog(2,1-2/(1+I*c*x))/c^5+d^2*x*(a+b*arctan(c*x))^2+2/3*d*e*x^3*(a+b*arctan(c*x))^2+1/5*e^2*x^5*(a+b*arctan(c*x))^2+2*b*d^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c-4/3*b*d*e*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3+2/5*b*e^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^5+1/5*I*e^2*(a+b*arctan(c*x))^2/c^5-2/3*I*d*e*(a+b*arctan(c*x))^2/c^3-2/3*I*b^2*d*e*polylog(2,1-2/(1+I*c*x))/c^3,1],
[(e*x^2+d)^2*(a+b*arctan(c*x))^2/x,x,25,-2*a*b*d*e*x/c+1/2*a*b*e^2*x/c^3+1/12*b^2*e^2*x^2/c^2-2*b^2*d*e*x*arctan(c*x)/c+1/2*b^2*e^2*x*arctan(c*x)/c^3-1/6*b*e^2*x^3*(a+b*arctan(c*x))/c+d*e*(a+b*arctan(c*x))^2/c^2-1/4*e^2*(a+b*arctan(c*x))^2/c^4+d*e*x^2*(a+b*arctan(c*x))^2+1/4*e^2*x^4*(a+b*arctan(c*x))^2+2*d^2*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))+b^2*d*e*ln(c^2*x^2+1)/c^2-1/3*b^2*e^2*ln(c^2*x^2+1)/c^4-I*b*d^2*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))+I*b*d^2*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))-1/2*b^2*d^2*polylog(3,1-2/(1+I*c*x))+1/2*b^2*d^2*polylog(3,-1+2/(1+I*c*x)),1],
[(e*x^2+d)^2*(a+b*arctan(c*x))^2/x^2,x,20,1/3*b^2*e^2*x/c^2-1/3*b^2*e^2*arctan(c*x)/c^3-1/3*b*e^2*x^2*(a+b*arctan(c*x))/c-I*c*d^2*(a+b*arctan(c*x))^2+2*I*d*e*(a+b*arctan(c*x))^2/c-1/3*I*e^2*(a+b*arctan(c*x))^2/c^3-d^2*(a+b*arctan(c*x))^2/x+2*d*e*x*(a+b*arctan(c*x))^2+1/3*e^2*x^3*(a+b*arctan(c*x))^2+4*b*d*e*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c-2/3*b*e^2*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c^3+2*b*c*d^2*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))-I*b^2*c*d^2*polylog(2,-1+2/(1-I*c*x))+2*I*b^2*d*e*polylog(2,1-2/(1+I*c*x))/c-1/3*I*b^2*e^2*polylog(2,1-2/(1+I*c*x))/c^3,1],
[(e*x^2+d)^2*(a+b*arctan(c*x))^2/x^3,x,22,-a*b*e^2*x/c-b^2*e^2*x*arctan(c*x)/c-b*c*d^2*(a+b*arctan(c*x))/x-1/2*c^2*d^2*(a+b*arctan(c*x))^2+1/2*e^2*(a+b*arctan(c*x))^2/c^2-1/2*d^2*(a+b*arctan(c*x))^2/x^2+1/2*e^2*x^2*(a+b*arctan(c*x))^2+4*d*e*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))+b^2*c^2*d^2*ln(x)-1/2*b^2*c^2*d^2*ln(c^2*x^2+1)+1/2*b^2*e^2*ln(c^2*x^2+1)/c^2-2*I*b*d*e*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))+2*I*b*d*e*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))-b^2*d*e*polylog(3,1-2/(1+I*c*x))+b^2*d*e*polylog(3,-1+2/(1+I*c*x)),1],
[x^3*(a+b*arctan(c*x))^2/(e*x^2+d),x,11,-a*b*x/c/e-b^2*x*arctan(c*x)/c/e+1/2*(a+b*arctan(c*x))^2/c^2/e+1/2*x^2*(a+b*arctan(c*x))^2/e+d*(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/e^2-1/2*d*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^2-1/2*d*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^2+1/2*b^2*ln(c^2*x^2+1)/c^2/e-I*b*d*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/e^2+1/2*I*b*d*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^2+1/2*I*b*d*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^2+1/2*b^2*d*polylog(3,1-2/(1-I*c*x))/e^2-1/4*b^2*d*polylog(3,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^2-1/4*b^2*d*polylog(3,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^2,1],
[x^2*(a+b*arctan(c*x))^2/(e*x^2+d),x,10,I*(a+b*arctan(c*x))^2/c/e+x*(a+b*arctan(c*x))^2/e+2*b*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/c/e+1/2*sqrt(-d)*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^(3/2)-1/2*sqrt(-d)*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^(3/2)+I*b^2*polylog(2,1-2/(1+I*c*x))/c/e-1/2*I*b*sqrt(-d)*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^(3/2)+1/2*I*b*sqrt(-d)*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^(3/2)+1/4*b^2*sqrt(-d)*polylog(3,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^(3/2)-1/4*b^2*sqrt(-d)*polylog(3,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^(3/2),1],
[x*(a+b*arctan(c*x))^2/(e*x^2+d),x,4,-(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/e+1/2*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e+1/2*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e+I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/e-1/2*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e-1/2*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e-1/2*b^2*polylog(3,1-2/(1-I*c*x))/e+1/4*b^2*polylog(3,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e+1/4*b^2*polylog(3,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e,1],
[(a+b*arctan(c*x))^2/(e*x^2+d),x,4,1/2*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/sqrt(-d)/sqrt(e)-1/2*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/sqrt(-d)/sqrt(e)-1/2*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/sqrt(-d)/sqrt(e)+1/2*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/sqrt(-d)/sqrt(e)+1/4*b^2*polylog(3,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/sqrt(-d)/sqrt(e)-1/4*b^2*polylog(3,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/sqrt(-d)/sqrt(e),1],
[(a+b*arctan(c*x))^2/x/(e*x^2+d),x,12,2*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))/d+(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/d-1/2*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d-1/2*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d-I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/d-I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/d+I*b*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d+1/2*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d+1/2*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d+1/2*b^2*polylog(3,1-2/(1-I*c*x))/d-1/2*b^2*polylog(3,1-2/(1+I*c*x))/d+1/2*b^2*polylog(3,-1+2/(1+I*c*x))/d-1/4*b^2*polylog(3,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d-1/4*b^2*polylog(3,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d,1],
[(a+b*arctan(c*x))^2/x^2/(e*x^2+d),x,9,-I*c*(a+b*arctan(c*x))^2/d-(a+b*arctan(c*x))^2/d/x+1/2*sqrt(e)*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)-1/2*sqrt(e)*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)+2*b*c*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))/d-I*b^2*c*polylog(2,-1+2/(1-I*c*x))/d-1/2*I*b*sqrt(e)*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)+1/2*I*b*sqrt(e)*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)+1/4*b^2*sqrt(e)*polylog(3,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)-1/4*b^2*sqrt(e)*polylog(3,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(-d)^(3/2),1],
[(a+b*arctan(c*x))^2/x^3/(e*x^2+d),x,21,-b*c*(a+b*arctan(c*x))/d/x-1/2*c^2*(a+b*arctan(c*x))^2/d-1/2*(a+b*arctan(c*x))^2/d/x^2-2*e*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))/d^2+b^2*c^2*ln(x)/d-e*(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/d^2+1/2*e*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^2+1/2*e*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^2-1/2*b^2*c^2*ln(c^2*x^2+1)/d-1/2*I*b*e*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^2-1/2*I*b*e*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^2-I*b*e*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d^2+I*b*e*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/d^2+I*b*e*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/d^2-1/2*b^2*e*polylog(3,1-2/(1-I*c*x))/d^2+1/2*b^2*e*polylog(3,1-2/(1+I*c*x))/d^2-1/2*b^2*e*polylog(3,-1+2/(1+I*c*x))/d^2+1/4*b^2*e*polylog(3,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^2+1/4*b^2*e*polylog(3,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^2,1],
[x^3*(a+b*arctan(c*x))^2/(e*x^2+d)^2,x,33,-1/2*c^2*d*(a+b*arctan(c*x))^2/(c^2*d-e)/e^2+1/4*(a+b*arctan(c*x))^2/e^2/(1-sqrt(e)*x/sqrt(-d))+1/4*(a+b*arctan(c*x))^2/e^2/(1+sqrt(e)*x/sqrt(-d))-(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/e^2-1/2*b*c*sqrt(-d)*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(c^2*d-e)/e^(3/2)+1/2*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^2+1/2*b*c*sqrt(-d)*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(c^2*d-e)/e^(3/2)+1/2*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^2+1/4*I*b^2*c*sqrt(-d)*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(c^2*d-e)/e^(3/2)+I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/e^2-1/2*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^2-1/2*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^2-1/4*I*b^2*c*sqrt(-d)*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(c^2*d-e)/e^(3/2)-1/2*b^2*polylog(3,1-2/(1-I*c*x))/e^2+1/4*b^2*polylog(3,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/e^2+1/4*b^2*polylog(3,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/e^2,1],
[x^2*(a+b*arctan(c*x))^2/(e*x^2+d)^2,x,38,-1/2*I*b^2*c*polylog(2,1-2/(1-I*c*x))/(c^2*d-e)/e+1/4*(a+b*arctan(c*x))^2/e^(3/2)/(sqrt(-d)-sqrt(e)*x)-1/4*(a+b*arctan(c*x))^2/e^(3/2)/(sqrt(-d)+sqrt(e)*x)+b*c*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/(c^2*d-e)/e-b*c*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/(c^2*d-e)/e-1/2*b*c*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(c^2*d-e)/e+1/4*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/sqrt(-d)/e^(3/2)-1/2*b*c*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(c^2*d-e)/e-1/4*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/sqrt(-d)/e^(3/2)+1/4*I*b^2*c*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(c^2*d-e)/e+1/4*I*b^2*c*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(c^2*d-e)/e-1/2*I*c*(a+b*arctan(c*x))^2/(c^2*d-e)/e-1/2*I*b^2*c*polylog(2,1-2/(1+I*c*x))/(c^2*d-e)/e-1/4*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/sqrt(-d)/e^(3/2)+1/4*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/sqrt(-d)/e^(3/2)+1/8*b^2*polylog(3,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/sqrt(-d)/e^(3/2)-1/8*b^2*polylog(3,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/sqrt(-d)/e^(3/2),1],
[x*(a+b*arctan(c*x))^2/(e*x^2+d)^2,x,27,1/2*c^2*(a+b*arctan(c*x))^2/(c^2*d-e)/e-1/4*(a+b*arctan(c*x))^2/d/e/(1-sqrt(e)*x/sqrt(-d))-1/4*(a+b*arctan(c*x))^2/d/e/(1+sqrt(e)*x/sqrt(-d))-1/2*b*c*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/sqrt(-d)/(c^2*d-e)/sqrt(e)+1/2*b*c*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/sqrt(-d)/(c^2*d-e)/sqrt(e)+1/4*I*b^2*c*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/sqrt(-d)/(c^2*d-e)/sqrt(e)-1/4*I*b^2*c*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/sqrt(-d)/(c^2*d-e)/sqrt(e),1],
[(a+b*arctan(c*x))^2/(e*x^2+d)^2,x,32,-1/4*I*b^2*c*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d/(c^2*d-e)-1/4*(a+b*arctan(c*x))^2/d/sqrt(e)/(sqrt(-d)-sqrt(e)*x)+1/4*(a+b*arctan(c*x))^2/d/sqrt(e)/(sqrt(-d)+sqrt(e)*x)-b*c*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/d/(c^2*d-e)+b*c*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/d/(c^2*d-e)+1/2*b*c*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d/(c^2*d-e)-1/4*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)/sqrt(e)+1/2*b*c*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d/(c^2*d-e)+1/4*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)/sqrt(e)+1/2*I*b^2*c*polylog(2,1-2/(1-I*c*x))/d/(c^2*d-e)-1/4*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)/sqrt(e)+1/2*I*b^2*c*polylog(2,1-2/(1+I*c*x))/d/(c^2*d-e)+1/2*I*c*(a+b*arctan(c*x))^2/d/(c^2*d-e)+1/4*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)/sqrt(e)-1/4*I*b^2*c*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d/(c^2*d-e)-1/8*b^2*polylog(3,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)/sqrt(e)+1/8*b^2*polylog(3,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)/sqrt(e),1],
[(a+b*arctan(c*x))^2/x/(e*x^2+d)^2,x,39,-1/2*c^2*(a+b*arctan(c*x))^2/d/(c^2*d-e)+1/4*(a+b*arctan(c*x))^2/d^2/(1-sqrt(e)*x/sqrt(-d))+1/4*(a+b*arctan(c*x))^2/d^2/(1+sqrt(e)*x/sqrt(-d))+2*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))/d^2+(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/d^2-1/2*b*c*sqrt(e)*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)/(c^2*d-e)-1/2*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^2+1/2*b*c*sqrt(e)*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)/(c^2*d-e)-1/2*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^2-I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/d^2+1/2*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^2-I*b*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/d^2+I*b*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d^2+1/2*I*b*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^2-1/4*I*b^2*c*sqrt(e)*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)/(c^2*d-e)+1/4*I*b^2*c*sqrt(e)*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(-d)^(3/2)/(c^2*d-e)+1/2*b^2*polylog(3,1-2/(1-I*c*x))/d^2-1/2*b^2*polylog(3,1-2/(1+I*c*x))/d^2+1/2*b^2*polylog(3,-1+2/(1+I*c*x))/d^2-1/4*b^2*polylog(3,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^2-1/4*b^2*polylog(3,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^2,1],
[(a+b*arctan(c*x))^2/x^2/(e*x^2+d)^2,x,42,-I*c*(a+b*arctan(c*x))^2/d^2+3/4*I*b*sqrt(e)*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(-d)^(5/2)-(a+b*arctan(c*x))^2/d^2/x+1/4*sqrt(e)*(a+b*arctan(c*x))^2/d^2/(sqrt(-d)-sqrt(e)*x)-1/4*sqrt(e)*(a+b*arctan(c*x))^2/d^2/(sqrt(-d)+sqrt(e)*x)+b*c*e*(a+b*arctan(c*x))*ln(2/(1-I*c*x))/d^2/(c^2*d-e)-b*c*e*(a+b*arctan(c*x))*ln(2/(1+I*c*x))/d^2/(c^2*d-e)-1/2*b*c*e*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^2/(c^2*d-e)-3/4*sqrt(e)*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(-d)^(5/2)-1/2*b*c*e*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^2/(c^2*d-e)+3/4*sqrt(e)*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(-d)^(5/2)+2*b*c*(a+b*arctan(c*x))*ln(2-2/(1-I*c*x))/d^2-1/2*I*b^2*c*e*polylog(2,1-2/(1+I*c*x))/d^2/(c^2*d-e)-3/4*I*b*sqrt(e)*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(-d)^(5/2)-1/2*I*b^2*c*e*polylog(2,1-2/(1-I*c*x))/d^2/(c^2*d-e)+1/4*I*b^2*c*e*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^2/(c^2*d-e)-I*b^2*c*polylog(2,-1+2/(1-I*c*x))/d^2+1/4*I*b^2*c*e*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^2/(c^2*d-e)-1/2*I*c*e*(a+b*arctan(c*x))^2/d^2/(c^2*d-e)-3/8*b^2*sqrt(e)*polylog(3,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(-d)^(5/2)+3/8*b^2*sqrt(e)*polylog(3,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(-d)^(5/2),1],
[(a+b*arctan(c*x))^2/x^3/(e*x^2+d)^2,x,47,-1/2*c^2*(a+b*arctan(c*x))^2/d^2-1/2*(a+b*arctan(c*x))^2/d^2/x^2-1/4*I*b^2*c*e^(3/2)*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(-d)^(5/2)/(c^2*d-e)+1/4*I*b^2*c*e^(3/2)*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(-d)^(5/2)/(c^2*d-e)-b*c*(a+b*arctan(c*x))/d^2/x+1/2*c^2*e*(a+b*arctan(c*x))^2/d^2/(c^2*d-e)-I*b*e*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^3-I*b*e*(a+b*arctan(c*x))*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^3+2*I*b*e*(a+b*arctan(c*x))*polylog(2,1-2/(1+I*c*x))/d^3+2*I*b*e*(a+b*arctan(c*x))*polylog(2,1-2/(1-I*c*x))/d^3-2*I*b*e*(a+b*arctan(c*x))*polylog(2,-1+2/(1+I*c*x))/d^3+1/2*b^2*e*polylog(3,1-2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^3+1/2*b^2*e*polylog(3,1-2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^3+b^2*e*polylog(3,1-2/(1+I*c*x))/d^3-b^2*e*polylog(3,1-2/(1-I*c*x))/d^3-b^2*e*polylog(3,-1+2/(1+I*c*x))/d^3-1/2*b^2*c^2*ln(c^2*x^2+1)/d^2+e*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/d^3+e*(a+b*arctan(c*x))^2*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/d^3-4*e*(a+b*arctan(c*x))^2*arctanh(1-2/(1+I*c*x))/d^3-2*e*(a+b*arctan(c*x))^2*ln(2/(1-I*c*x))/d^3-1/4*e*(a+b*arctan(c*x))^2/d^3/(1-sqrt(e)*x/sqrt(-d))-1/4*e*(a+b*arctan(c*x))^2/d^3/(1+sqrt(e)*x/sqrt(-d))+b^2*c^2*ln(x)/d^2+1/2*b*c*e^(3/2)*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)+sqrt(e)*x)/(c*sqrt(-d)+I*sqrt(e))/(1-I*c*x))/(-d)^(5/2)/(c^2*d-e)-1/2*b*c*e^(3/2)*(a+b*arctan(c*x))*ln(2*c*(sqrt(-d)-sqrt(e)*x)/(c*sqrt(-d)-I*sqrt(e))/(1-I*c*x))/(-d)^(5/2)/(c^2*d-e),1],
[x^4*arctan(x)*ln(x^2+1),x,24,-77/300*x^2+9/200*x^4-2/5*x*arctan(x)+2/15*x^3*arctan(x)-2/25*x^5*arctan(x)+1/5*arctan(x)^2+137/300*ln(x^2+1)+1/10*x^2*ln(x^2+1)-1/20*x^4*ln(x^2+1)+1/5*x^5*arctan(x)*ln(x^2+1)-1/20*ln(x^2+1)^2,1],
[x^3*arctan(x)*ln(x^2+1),x,17,-25/24*x+7/72*x^3+25/24*arctan(x)+1/4*x^2*arctan(x)-1/8*x^4*arctan(x)+1/4*x*ln(x^2+1)-1/12*x^3*ln(x^2+1)-1/4*arctan(x)*ln(x^2+1)+1/4*x^4*arctan(x)*ln(x^2+1),1],
[x^2*arctan(x)*ln(x^2+1),x,22,5/18*x^2+2/3*x*arctan(x)-2/9*x^3*arctan(x)-1/3*arctan(x)^2-11/18*ln(x^2+1)-1/6*x^2*ln(x^2+1)+1/3*x^3*arctan(x)*ln(x^2+1)+1/12*ln(x^2+1)^2,1],
[x*arctan(x)*ln(x^2+1),x,8,3/2*x-3/2*arctan(x)-1/2*x^2*arctan(x)-1/2*x*ln(x^2+1)+1/2*(x^2+1)*arctan(x)*ln(x^2+1),1],
[arctan(x)*ln(x^2+1),x,8,-2*x*arctan(x)+arctan(x)^2+ln(x^2+1)+x*arctan(x)*ln(x^2+1)-1/4*ln(x^2+1)^2,1],
[arctan(x)*ln(x^2+1)/x,x,12,-1/2*I*ln(1+I*x)^2*ln(-I*x)+1/2*I*ln(1-I*x)^2*ln(I*x)+I*ln(1-I*x)*polylog(2,1-I*x)-I*ln(1+I*x)*polylog(2,1+I*x)-1/2*I*(ln(1-I*x)+ln(1+I*x)-ln(x^2+1))*polylog(2,-I*x)+1/2*I*(ln(1-I*x)+ln(1+I*x)-ln(x^2+1))*polylog(2,I*x)-I*polylog(3,1-I*x)+I*polylog(3,1+I*x),1],
[arctan(x)*ln(x^2+1)/x^2,x,8,arctan(x)^2-arctan(x)*ln(x^2+1)/x-1/4*ln(x^2+1)^2-1/2*polylog(2,-x^2),1],
[arctan(x)*ln(x^2+1)/x^3,x,8,arctan(x)-1/2*ln(x^2+1)/x-1/2*arctan(x)*ln(x^2+1)-1/2*arctan(x)*ln(x^2+1)/x^2+1/2*I*polylog(2,-I*x)-1/2*I*polylog(2,I*x),1],
[arctan(x)*ln(x^2+1)/x^4,x,18,-2/3*arctan(x)/x-1/3*arctan(x)^2+ln(x)-1/2*ln(x^2+1)-1/6*ln(x^2+1)/x^2-1/3*arctan(x)*ln(x^2+1)/x^3+1/12*ln(x^2+1)^2+1/6*polylog(2,-x^2),1],
[arctan(x)*ln(x^2+1)/x^5,x,15,-5/12/x-11/12*arctan(x)-1/4*arctan(x)/x^2-1/12*ln(x^2+1)/x^3+1/4*ln(x^2+1)/x+1/4*arctan(x)*ln(x^2+1)-1/4*arctan(x)*ln(x^2+1)/x^4-1/4*I*polylog(2,-I*x)+1/4*I*polylog(2,I*x),1],
[arctan(x)*ln(x^2+1)/x^6,x,26,-7/60/x^2-2/15*arctan(x)/x^3+2/5*arctan(x)/x+1/5*arctan(x)^2-5/6*ln(x)+5/12*ln(x^2+1)-1/20*ln(x^2+1)/x^4+1/10*ln(x^2+1)/x^2-1/5*arctan(x)*ln(x^2+1)/x^5-1/20*ln(x^2+1)^2-1/10*polylog(2,-x^2),1],
[x^4*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1)),x,28,-2/5*a*e*x/c^4-77/300*b*e*x^2/c^3+2/15*a*e*x^3/c^2+9/200*b*e*x^4/c-2/25*a*e*x^5+2/5*a*e*arctan(c*x)/c^5-2/5*b*e*x*arctan(c*x)/c^4+2/15*b*e*x^3*arctan(c*x)/c^2-2/25*b*e*x^5*arctan(c*x)+1/5*b*e*arctan(c*x)^2/c^5+137/300*b*e*ln(c^2*x^2+1)/c^5+1/20*b*e*ln(c^2*x^2+1)^2/c^5+1/10*b*x^2*(d+e*ln(c^2*x^2+1))/c^3-1/20*b*x^4*(d+e*ln(c^2*x^2+1))/c+1/5*x^5*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))-1/10*b*ln(c^2*x^2+1)*(d+e*ln(c^2*x^2+1))/c^5,1],
[x^3*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1)),x,17,1/8*b*(2*d-3*e)*x/c^3-2/3*b*e*x/c^3-1/24*b*(2*d-e)*x^3/c+1/18*b*e*x^3/c-1/8*b*(2*d-3*e)*arctan(c*x)/c^4+2/3*b*e*arctan(c*x)/c^4+1/4*e*x^2*(a+b*arctan(c*x))/c^2-1/8*e*x^4*(a+b*arctan(c*x))+1/4*b*e*x*ln(c^2*x^2+1)/c^3-1/12*b*e*x^3*ln(c^2*x^2+1)/c-1/4*e*(a+b*arctan(c*x))*ln(c^2*x^2+1)/c^4+1/4*x^4*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1)),1],
[x^2*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1)),x,28,2/3*a*e*x/c^2+5/18*b*e*x^2/c-2/9*a*e*x^3-2/3*a*e*arctan(c*x)/c^3+2/3*b*e*x*arctan(c*x)/c^2-2/9*b*e*x^3*arctan(c*x)-1/3*b*e*arctan(c*x)^2/c^3-11/18*b*e*ln(c^2*x^2+1)/c^3-1/12*b*e*ln(c^2*x^2+1)^2/c^3-1/6*b*x^2*(d+e*ln(c^2*x^2+1))/c+1/3*x^3*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))+1/6*b*ln(c^2*x^2+1)*(d+e*ln(c^2*x^2+1))/c^3,1],
[x*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1)),x,9,-1/2*b*(d-e)*x/c+b*e*x/c+1/2*b*(d-e)*arctan(c*x)/c^2-b*e*arctan(c*x)/c^2+1/2*d*x^2*(a+b*arctan(c*x))-1/2*e*x^2*(a+b*arctan(c*x))-1/2*b*e*x*ln(c^2*x^2+1)/c+1/2*e*(c^2*x^2+1)*(a+b*arctan(c*x))*ln(c^2*x^2+1)/c^2,1],
[(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1)),x,9,-2*a*e*x-2*b*e*x*arctan(c*x)+e*(a+b*arctan(c*x))^2/b/c+b*e*ln(c^2*x^2+1)/c+x*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))-1/4*b*(d+e*ln(c^2*x^2+1))^2/c/e,1],
[(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x,x,18,a*d*ln(x)+1/2*I*b*e*ln(I*c*x)*ln(1-I*c*x)^2-1/2*I*b*e*ln(-I*c*x)*ln(1+I*c*x)^2+1/2*I*b*d*polylog(2,-I*c*x)-1/2*I*b*e*(ln(1-I*c*x)+ln(1+I*c*x)-ln(c^2*x^2+1))*polylog(2,-I*c*x)-1/2*I*b*d*polylog(2,I*c*x)+1/2*I*b*e*(ln(1-I*c*x)+ln(1+I*c*x)-ln(c^2*x^2+1))*polylog(2,I*c*x)-1/2*a*e*polylog(2,-c^2*x^2)+I*b*e*ln(1-I*c*x)*polylog(2,1-I*c*x)-I*b*e*ln(1+I*c*x)*polylog(2,1+I*c*x)-I*b*e*polylog(3,1-I*c*x)+I*b*e*polylog(3,1+I*c*x),1],
[(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^2,x,6,c*e*(a+b*arctan(c*x))^2/b-(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x+1/2*b*c*(d+e*ln(c^2*x^2+1))*ln(1-1/(c^2*x^2+1))-1/2*b*c*e*polylog(2,1/(c^2*x^2+1)),1],
[(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^3,x,12,b*c^2*e*arctan(c*x)+a*c^2*e*ln(x)-1/2*a*c^2*e*ln(c^2*x^2+1)-1/2*b*c*(d+e*ln(c^2*x^2+1))/x-1/2*b*c^2*arctan(c*x)*(d+e*ln(c^2*x^2+1))-1/2*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^2+1/2*I*b*c^2*e*polylog(2,-I*c*x)-1/2*I*b*c^2*e*polylog(2,I*c*x),1],
[(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^4,x,15,-2/3*c^2*e*(a+b*arctan(c*x))/x-1/3*c^3*e*(a+b*arctan(c*x))^2/b+b*c^3*e*ln(x)-1/3*b*c^3*e*ln(c^2*x^2+1)-1/6*b*c*(c^2*x^2+1)*(d+e*ln(c^2*x^2+1))/x^2-1/3*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^3-1/6*b*c^3*(d+e*ln(c^2*x^2+1))*ln(1-1/(c^2*x^2+1))+1/6*b*c^3*e*polylog(2,1/(c^2*x^2+1)),1],
[(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^5,x,18,-1/4*a*c^2*e/x^2-5/12*b*c^3*e/x-11/12*b*c^4*e*arctan(c*x)-1/4*b*c^2*e*arctan(c*x)/x^2-1/2*a*c^4*e*ln(x)+1/4*a*c^4*e*ln(c^2*x^2+1)-1/12*b*c*(d+e*ln(c^2*x^2+1))/x^3+1/4*b*c^3*(d+e*ln(c^2*x^2+1))/x+1/4*b*c^4*arctan(c*x)*(d+e*ln(c^2*x^2+1))-1/4*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^4-1/4*I*b*c^4*e*polylog(2,-I*c*x)+1/4*I*b*c^4*e*polylog(2,I*c*x),1],
[(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^6,x,24,-7/60*b*c^3*e/x^2-2/15*c^2*e*(a+b*arctan(c*x))/x^3+2/5*c^4*e*(a+b*arctan(c*x))/x+1/5*c^5*e*(a+b*arctan(c*x))^2/b-5/6*b*c^5*e*ln(x)+19/60*b*c^5*e*ln(c^2*x^2+1)-1/20*b*c*(d+e*ln(c^2*x^2+1))/x^4+1/10*b*c^3*(c^2*x^2+1)*(d+e*ln(c^2*x^2+1))/x^2-1/5*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^5+1/10*b*c^5*(d+e*ln(c^2*x^2+1))*ln(1-1/(c^2*x^2+1))-1/10*b*c^5*e*polylog(2,1/(c^2*x^2+1)),1],
[x*(a+b*arctan(c*x))*(d+e*ln(g*x^2+f)),x,23,-1/2*b*(d-e)*x/c+b*e*x/c+1/2*b*(d-e)*arctan(c*x)/c^2+1/2*d*x^2*(a+b*arctan(c*x))-1/2*e*x^2*(a+b*arctan(c*x))-b*e*sqrt(f)*arctan(sqrt(g)*x/sqrt(f))/c/sqrt(g)-b*e*(c^2*f-g)*arctan(c*x)*ln(2/(1-I*c*x))/c^2/g+1/2*b*e*(c^2*f-g)*arctan(c*x)*ln(2*c*(sqrt(-f)-sqrt(g)*x)/(c*sqrt(-f)-I*sqrt(g))/(1-I*c*x))/c^2/g+1/2*b*e*(c^2*f-g)*arctan(c*x)*ln(2*c*(sqrt(-f)+sqrt(g)*x)/(c*sqrt(-f)+I*sqrt(g))/(1-I*c*x))/c^2/g-1/2*b*e*x*ln(g*x^2+f)/c-1/2*b*e*(c^2*f-g)*arctan(c*x)*ln(g*x^2+f)/c^2/g+1/2*e*(g*x^2+f)*(a+b*arctan(c*x))*ln(g*x^2+f)/g+1/2*I*b*e*(c^2*f-g)*polylog(2,1-2/(1-I*c*x))/c^2/g-1/4*I*b*e*(c^2*f-g)*polylog(2,1-2*c*(sqrt(-f)-sqrt(g)*x)/(c*sqrt(-f)-I*sqrt(g))/(1-I*c*x))/c^2/g-1/4*I*b*e*(c^2*f-g)*polylog(2,1-2*c*(sqrt(-f)+sqrt(g)*x)/(c*sqrt(-f)+I*sqrt(g))/(1-I*c*x))/c^2/g,1],
[(a+b*arctan(c*x))*(d+e*ln(g*x^2+f)),x,28,-2*a*e*x-2*b*e*x*arctan(c*x)+2*a*e*sqrt(f)*arctan(sqrt(g)*x/sqrt(f))/sqrt(g)+1/2*I*b*e*sqrt(-f)*ln(1+I*c*x)*ln(c*(sqrt(-f)-sqrt(g)*x)/(c*sqrt(-f)-I*sqrt(g)))/sqrt(g)-1/2*I*b*e*sqrt(-f)*ln(1-I*c*x)*ln(c*(sqrt(-f)-sqrt(g)*x)/(c*sqrt(-f)+I*sqrt(g)))/sqrt(g)+1/2*I*b*e*sqrt(-f)*ln(1-I*c*x)*ln(c*(sqrt(-f)+sqrt(g)*x)/(c*sqrt(-f)-I*sqrt(g)))/sqrt(g)-1/2*I*b*e*sqrt(-f)*ln(1+I*c*x)*ln(c*(sqrt(-f)+sqrt(g)*x)/(c*sqrt(-f)+I*sqrt(g)))/sqrt(g)+b*e*ln(c^2*x^2+1)/c+x*(a+b*arctan(c*x))*(d+e*ln(g*x^2+f))-1/2*b*ln(-g*(c^2*x^2+1)/(c^2*f-g))*(d+e*ln(g*x^2+f))/c-1/2*I*b*e*sqrt(-f)*polylog(2,sqrt(g)*(I-c*x)/(c*sqrt(-f)+I*sqrt(g)))/sqrt(g)+1/2*I*b*e*sqrt(-f)*polylog(2,sqrt(g)*(1-I*c*x)/(I*c*sqrt(-f)+sqrt(g)))/sqrt(g)+1/2*I*b*e*sqrt(-f)*polylog(2,sqrt(g)*(1+I*c*x)/(I*c*sqrt(-f)+sqrt(g)))/sqrt(g)-1/2*I*b*e*sqrt(-f)*polylog(2,sqrt(g)*(I+c*x)/(c*sqrt(-f)+I*sqrt(g)))/sqrt(g)-1/2*b*e*polylog(2,c^2*(g*x^2+f)/(c^2*f-g))/c,1],
[(a+b*arctan(c*x))*(d+e*ln(g*x^2+f))/x,x,8,a*d*ln(x)+1/2*a*e*ln(-g*x^2/f)*ln(g*x^2+f)+1/2*I*b*d*polylog(2,-I*c*x)-1/2*I*b*d*polylog(2,I*c*x)+1/2*a*e*polylog(2,1+g*x^2/f)+b*e*Defer(Int)(arctan(c*x)*ln(g*x^2+f)/x,x),0],
[(a+b*arctan(c*x))*(d+e*ln(g*x^2+f))/x^2,x,28,2*a*e*sqrt(g)*arctan(sqrt(g)*x/sqrt(f))/sqrt(f)-1/2*I*b*e*sqrt(g)*ln(1+I*c*x)*ln(c*(sqrt(-f)-sqrt(g)*x)/(c*sqrt(-f)-I*sqrt(g)))/sqrt(-f)+1/2*I*b*e*sqrt(g)*ln(1-I*c*x)*ln(c*(sqrt(-f)-sqrt(g)*x)/(c*sqrt(-f)+I*sqrt(g)))/sqrt(-f)-1/2*I*b*e*sqrt(g)*ln(1-I*c*x)*ln(c*(sqrt(-f)+sqrt(g)*x)/(c*sqrt(-f)-I*sqrt(g)))/sqrt(-f)+1/2*I*b*e*sqrt(g)*ln(1+I*c*x)*ln(c*(sqrt(-f)+sqrt(g)*x)/(c*sqrt(-f)+I*sqrt(g)))/sqrt(-f)-(a+b*arctan(c*x))*(d+e*ln(g*x^2+f))/x+1/2*b*c*ln(-g*x^2/f)*(d+e*ln(g*x^2+f))-1/2*b*c*ln(-g*(c^2*x^2+1)/(c^2*f-g))*(d+e*ln(g*x^2+f))+1/2*I*b*e*sqrt(g)*polylog(2,sqrt(g)*(I-c*x)/(c*sqrt(-f)+I*sqrt(g)))/sqrt(-f)-1/2*I*b*e*sqrt(g)*polylog(2,sqrt(g)*(1-I*c*x)/(I*c*sqrt(-f)+sqrt(g)))/sqrt(-f)-1/2*I*b*e*sqrt(g)*polylog(2,sqrt(g)*(1+I*c*x)/(I*c*sqrt(-f)+sqrt(g)))/sqrt(-f)+1/2*I*b*e*sqrt(g)*polylog(2,sqrt(g)*(I+c*x)/(c*sqrt(-f)+I*sqrt(g)))/sqrt(-f)-1/2*b*c*e*polylog(2,c^2*(g*x^2+f)/(c^2*f-g))+1/2*b*c*e*polylog(2,1+g*x^2/f),1],
[(a+b*arctan(c*x))*(d+e*ln(g*x^2+f))/x^3,x,24,b*c*e*sqrt(g)*arctan(sqrt(g)*x/sqrt(f))/sqrt(f)+a*e*g*ln(x)/f-b*e*(c^2*f-g)*arctan(c*x)*ln(2/(1-I*c*x))/f+1/2*b*e*(c^2*f-g)*arctan(c*x)*ln(2*c*(sqrt(-f)-sqrt(g)*x)/(c*sqrt(-f)-I*sqrt(g))/(1-I*c*x))/f+1/2*b*e*(c^2*f-g)*arctan(c*x)*ln(2*c*(sqrt(-f)+sqrt(g)*x)/(c*sqrt(-f)+I*sqrt(g))/(1-I*c*x))/f-1/2*a*e*g*ln(g*x^2+f)/f-1/2*b*c*(d+e*ln(g*x^2+f))/x-1/2*b*c^2*arctan(c*x)*(d+e*ln(g*x^2+f))-1/2*(a+b*arctan(c*x))*(d+e*ln(g*x^2+f))/x^2+1/2*I*b*e*g*polylog(2,-I*c*x)/f-1/2*I*b*e*g*polylog(2,I*c*x)/f+1/2*I*b*e*(c^2*f-g)*polylog(2,1-2/(1-I*c*x))/f-1/4*I*b*e*(c^2*f-g)*polylog(2,1-2*c*(sqrt(-f)-sqrt(g)*x)/(c*sqrt(-f)-I*sqrt(g))/(1-I*c*x))/f-1/4*I*b*e*(c^2*f-g)*polylog(2,1-2*c*(sqrt(-f)+sqrt(g)*x)/(c*sqrt(-f)+I*sqrt(g))/(1-I*c*x))/f,1]]: