# Maple integration test file: "5 Inverse trig functions\5.3 Inverse tangent\5.3.3 (d+e x)^m (a+b arctan(c x^n))^p.txt"

lst:=[

# Integrands of the form (d+e x)^m (a+b ArcTan[c x^n])^p

# Integrands of the form (d+e x)^m (a+b ArcTan[c x^1])^p
[(d+e*x)^4*(a+b*arctan(c*x)),x,6,-b*d*e*(2*c^2*d^2-e^2)*x/c^3-1/10*b*e^2*(10*c^2*d^2-e^2)*x^2/c^3-1/3*b*d*e^3*x^3/c-1/20*b*e^4*x^4/c-1/5*b*d*(c^4*d^4-10*c^2*d^2*e^2+5*e^4)*arctan(c*x)/(c^4*e)+1/5*(d+e*x)^5*(a+b*arctan(c*x))/e-1/10*b*(5*c^4*d^4-10*c^2*d^2*e^2+e^4)*log(1+c^2*x^2)/c^5],
[(d+e*x)^3*(a+b*arctan(c*x)),x,6,-1/4*b*e*(6*c^2*d^2-e^2)*x/c^3-1/2*b*d*e^2*x^2/c-1/12*b*e^3*x^3/c-1/4*b*(c^4*d^4-6*c^2*d^2*e^2+e^4)*arctan(c*x)/(c^4*e)+1/4*(d+e*x)^4*(a+b*arctan(c*x))/e-1/2*b*d*(c*d-e)*(c*d+e)*log(1+c^2*x^2)/c^3],
[(d+e*x)^2*(a+b*arctan(c*x)),x,6,-b*d*e*x/c-1/6*b*e^2*x^2/c-1/3*b*d*(d^2-3*e^2/c^2)*arctan(c*x)/e+1/3*(d+e*x)^3*(a+b*arctan(c*x))/e-1/6*b*(3*c^2*d^2-e^2)*log(1+c^2*x^2)/c^3],
[(d+e*x)*(a+b*arctan(c*x)),x,6,-1/2*b*e*x/c-1/2*b*(d^2-e^2/c^2)*arctan(c*x)/e+1/2*(d+e*x)^2*(a+b*arctan(c*x))/e-1/2*b*d*log(1+c^2*x^2)/c],
[(a+b*arctan(c*x))/(d+e*x),x,4,-(a+b*arctan(c*x))*log(2/(1-I*c*x))/e+(a+b*arctan(c*x))*log(2*c*(d+e*x)/((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*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/e],
[(a+b*arctan(c*x))/(d+e*x)^2,x,6,b*c^2*d*arctan(c*x)/(e*(c^2*d^2+e^2))+(-a-b*arctan(c*x))/(e*(d+e*x))+b*c*log(d+e*x)/(c^2*d^2+e^2)-1/2*b*c*log(1+c^2*x^2)/(c^2*d^2+e^2)],
[(a+b*arctan(c*x))/(d+e*x)^3,x,7,-1/2*b*c/((c^2*d^2+e^2)*(d+e*x))+1/2*b*c^2*(c*d-e)*(c*d+e)*arctan(c*x)/(e*(c^2*d^2+e^2)^2)+1/2*(-a-b*arctan(c*x))/(e*(d+e*x)^2)+b*c^3*d*log(d+e*x)/(c^2*d^2+e^2)^2-1/2*b*c^3*d*log(1+c^2*x^2)/(c^2*d^2+e^2)^2],
[(a+b*arctan(c*x))/(d+e*x)^4,x,7,-1/6*b*c/((c^2*d^2+e^2)*(d+e*x)^2)-2/3*b*c^3*d/((c^2*d^2+e^2)^2*(d+e*x))+1/3*b*c^4*d*(c^2*d^2-3*e^2)*arctan(c*x)/(e*(c^2*d^2+e^2)^3)+1/3*(-a-b*arctan(c*x))/(e*(d+e*x)^3)+1/3*b*c^3*(3*c^2*d^2-e^2)*log(d+e*x)/(c^2*d^2+e^2)^3-1/6*b*c^3*(3*c^2*d^2-e^2)*log(1+c^2*x^2)/(c^2*d^2+e^2)^3],
[(d+e*x)^3*(a+b*arctan(c*x))^2,x,19,b^2*d*e^2*x/c^2-1/2*a*b*e*(6*c^2*d^2-e^2)*x/c^3+1/12*b^2*e^3*x^2/c^2-b^2*d*e^2*arctan(c*x)/c^3-1/2*b^2*e*(6*c^2*d^2-e^2)*x*arctan(c*x)/c^3-b*d*e^2*x^2*(a+b*arctan(c*x))/c-1/6*b*e^3*x^3*(a+b*arctan(c*x))/c+I*d*(c*d-e)*(c*d+e)*(a+b*arctan(c*x))^2/c^3-1/4*(c^4*d^4-6*c^2*d^2*e^2+e^4)*(a+b*arctan(c*x))^2/(c^4*e)+1/4*(d+e*x)^4*(a+b*arctan(c*x))^2/e+2*b*d*(c*d-e)*(c*d+e)*(a+b*arctan(c*x))*log(2/(1+I*c*x))/c^3-1/12*b^2*e^3*log(1+c^2*x^2)/c^4+1/4*b^2*e*(6*c^2*d^2-e^2)*log(1+c^2*x^2)/c^4+I*b^2*d*(c*d-e)*(c*d+e)*polylog(2,1+(-2)/(1+I*c*x))/c^3],
[(d+e*x)^2*(a+b*arctan(c*x))^2,x,15,-2*a*b*d*e*x/c+1/3*b^2*e^2*x/c^2-1/3*b^2*e^2*arctan(c*x)/c^3-2*b^2*d*e*x*arctan(c*x)/c-1/3*b*e^2*x^2*(a+b*arctan(c*x))/c+1/3*I*(3*c^2*d^2-e^2)*(a+b*arctan(c*x))^2/c^3-1/3*d*(d^2-3*e^2/c^2)*(a+b*arctan(c*x))^2/e+1/3*(d+e*x)^3*(a+b*arctan(c*x))^2/e+2/3*b*(3*c^2*d^2-e^2)*(a+b*arctan(c*x))*log(2/(1+I*c*x))/c^3+b^2*d*e*log(1+c^2*x^2)/c^2+1/3*I*b^2*(3*c^2*d^2-e^2)*polylog(2,1+(-2)/(1+I*c*x))/c^3],
[(d+e*x)*(a+b*arctan(c*x))^2,x,12,-a*b*e*x/c-b^2*e*x*arctan(c*x)/c+I*d*(a+b*arctan(c*x))^2/c-1/2*(d^2-e^2/c^2)*(a+b*arctan(c*x))^2/e+1/2*(d+e*x)^2*(a+b*arctan(c*x))^2/e+2*b*d*(a+b*arctan(c*x))*log(2/(1+I*c*x))/c+1/2*b^2*e*log(1+c^2*x^2)/c^2+I*b^2*d*polylog(2,1+(-2)/(1+I*c*x))/c],
[(a+b*arctan(c*x))^2/(d+e*x),x,1,-(a+b*arctan(c*x))^2*log(2/(1-I*c*x))/e+(a+b*arctan(c*x))^2*log(2*c*(d+e*x)/((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*(d+e*x)/((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*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/e],
[(a+b*arctan(c*x))^2/(d+e*x)^2,x,13,I*c*(a+b*arctan(c*x))^2/(c^2*d^2+e^2)+c^2*d*(a+b*arctan(c*x))^2/(e*(c^2*d^2+e^2))-(a+b*arctan(c*x))^2/(e*(d+e*x))-2*b*c*(a+b*arctan(c*x))*log(2/(1-I*c*x))/(c^2*d^2+e^2)+2*b*c*(a+b*arctan(c*x))*log(2/(1+I*c*x))/(c^2*d^2+e^2)+2*b*c*(a+b*arctan(c*x))*log(2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/(c^2*d^2+e^2)+I*b^2*c*polylog(2,1+(-2)/(1-I*c*x))/(c^2*d^2+e^2)+I*b^2*c*polylog(2,1+(-2)/(1+I*c*x))/(c^2*d^2+e^2)-I*b^2*c*polylog(2,1-2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/(c^2*d^2+e^2)],
[(a+b*arctan(c*x))^2/(d+e*x)^3,x,19,b^2*c^3*d*arctan(c*x)/(c^2*d^2+e^2)^2-b*c*(a+b*arctan(c*x))/((c^2*d^2+e^2)*(d+e*x))+I*c^3*d*(a+b*arctan(c*x))^2/(c^2*d^2+e^2)^2+1/2*c^2*(c*d-e)*(c*d+e)*(a+b*arctan(c*x))^2/(e*(c^2*d^2+e^2)^2)-1/2*(a+b*arctan(c*x))^2/(e*(d+e*x)^2)-2*b*c^3*d*(a+b*arctan(c*x))*log(2/(1-I*c*x))/(c^2*d^2+e^2)^2+2*b*c^3*d*(a+b*arctan(c*x))*log(2/(1+I*c*x))/(c^2*d^2+e^2)^2+b^2*c^2*e*log(d+e*x)/(c^2*d^2+e^2)^2+2*b*c^3*d*(a+b*arctan(c*x))*log(2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/(c^2*d^2+e^2)^2-1/2*b^2*c^2*e*log(1+c^2*x^2)/(c^2*d^2+e^2)^2+I*b^2*c^3*d*polylog(2,1+(-2)/(1-I*c*x))/(c^2*d^2+e^2)^2+I*b^2*c^3*d*polylog(2,1+(-2)/(1+I*c*x))/(c^2*d^2+e^2)^2-I*b^2*c^3*d*polylog(2,1-2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/(c^2*d^2+e^2)^2],
[(d+e*x)^3*(a+b*arctan(c*x))^3,x,29,3*a*b^2*d*e^2*x/c^2-1/4*b^3*e^3*x/c^3+1/4*b^3*e^3*arctan(c*x)/c^4+3*b^3*d*e^2*x*arctan(c*x)/c^2+1/4*b^2*e^3*x^2*(a+b*arctan(c*x))/c^2-3/2*b*d*e^2*(a+b*arctan(c*x))^2/c^3+1/4*I*b*e^3*(a+b*arctan(c*x))^2/c^4-3/4*I*b*e*(6*c^2*d^2-e^2)*(a+b*arctan(c*x))^2/c^4-3/4*b*e*(6*c^2*d^2-e^2)*x*(a+b*arctan(c*x))^2/c^3-3/2*b*d*e^2*x^2*(a+b*arctan(c*x))^2/c-1/4*b*e^3*x^3*(a+b*arctan(c*x))^2/c+I*d*(c*d-e)*(c*d+e)*(a+b*arctan(c*x))^3/c^3-1/4*(c^4*d^4-6*c^2*d^2*e^2+e^4)*(a+b*arctan(c*x))^3/(c^4*e)+1/4*(d+e*x)^4*(a+b*arctan(c*x))^3/e+1/2*b^2*e^3*(a+b*arctan(c*x))*log(2/(1+I*c*x))/c^4-3/2*b^2*e*(6*c^2*d^2-e^2)*(a+b*arctan(c*x))*log(2/(1+I*c*x))/c^4+3*b*d*(c*d-e)*(c*d+e)*(a+b*arctan(c*x))^2*log(2/(1+I*c*x))/c^3-3/2*b^3*d*e^2*log(1+c^2*x^2)/c^3+1/4*I*b^3*e^3*polylog(2,1+(-2)/(1+I*c*x))/c^4-3/4*I*b^3*e*(6*c^2*d^2-e^2)*polylog(2,1+(-2)/(1+I*c*x))/c^4+3*I*b^2*d*(c*d-e)*(c*d+e)*(a+b*arctan(c*x))*polylog(2,1+(-2)/(1+I*c*x))/c^3+3/2*b^3*d*(c*d-e)*(c*d+e)*polylog(3,1+(-2)/(1+I*c*x))/c^3],
[(d+e*x)^2*(a+b*arctan(c*x))^3,x,20,a*b^2*e^2*x/c^2+b^3*e^2*x*arctan(c*x)/c^2-3*I*b*d*e*(a+b*arctan(c*x))^2/c^2-1/2*b*e^2*(a+b*arctan(c*x))^2/c^3-3*b*d*e*x*(a+b*arctan(c*x))^2/c-1/2*b*e^2*x^2*(a+b*arctan(c*x))^2/c+1/3*I*(3*c^2*d^2-e^2)*(a+b*arctan(c*x))^3/c^3-1/3*d*(d^2-3*e^2/c^2)*(a+b*arctan(c*x))^3/e+1/3*(d+e*x)^3*(a+b*arctan(c*x))^3/e-6*b^2*d*e*(a+b*arctan(c*x))*log(2/(1+I*c*x))/c^2+b*(3*c^2*d^2-e^2)*(a+b*arctan(c*x))^2*log(2/(1+I*c*x))/c^3-1/2*b^3*e^2*log(1+c^2*x^2)/c^3-3*I*b^3*d*e*polylog(2,1+(-2)/(1+I*c*x))/c^2+I*b^2*(3*c^2*d^2-e^2)*(a+b*arctan(c*x))*polylog(2,1+(-2)/(1+I*c*x))/c^3+1/2*b^3*(3*c^2*d^2-e^2)*polylog(3,1+(-2)/(1+I*c*x))/c^3],
[(d+e*x)*(a+b*arctan(c*x))^3,x,14,-3/2*I*b*e*(a+b*arctan(c*x))^2/c^2-3/2*b*e*x*(a+b*arctan(c*x))^2/c+I*d*(a+b*arctan(c*x))^3/c-1/2*(d^2-e^2/c^2)*(a+b*arctan(c*x))^3/e+1/2*(d+e*x)^2*(a+b*arctan(c*x))^3/e-3*b^2*e*(a+b*arctan(c*x))*log(2/(1+I*c*x))/c^2+3*b*d*(a+b*arctan(c*x))^2*log(2/(1+I*c*x))/c-3/2*I*b^3*e*polylog(2,1+(-2)/(1+I*c*x))/c^2+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(3,1+(-2)/(1+I*c*x))/c],
[(a+b*arctan(c*x))^3/(d+e*x),x,1,-(a+b*arctan(c*x))^3*log(2/(1-I*c*x))/e+(a+b*arctan(c*x))^3*log(2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/e+3/2*I*b*(a+b*arctan(c*x))^2*polylog(2,1+(-2)/(1-I*c*x))/e-3/2*I*b*(a+b*arctan(c*x))^2*polylog(2,1-2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/e-3/2*b^2*(a+b*arctan(c*x))*polylog(3,1+(-2)/(1-I*c*x))/e+3/2*b^2*(a+b*arctan(c*x))*polylog(3,1-2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/e-3/4*I*b^3*polylog(4,1+(-2)/(1-I*c*x))/e+3/4*I*b^3*polylog(4,1-2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/e],
[(a+b*arctan(c*x))^3/(d+e*x)^2,x,10,I*c*(a+b*arctan(c*x))^3/(c^2*d^2+e^2)+c^2*d*(a+b*arctan(c*x))^3/(e*(c^2*d^2+e^2))-(a+b*arctan(c*x))^3/(e*(d+e*x))-3*b*c*(a+b*arctan(c*x))^2*log(2/(1-I*c*x))/(c^2*d^2+e^2)+3*b*c*(a+b*arctan(c*x))^2*log(2/(1+I*c*x))/(c^2*d^2+e^2)+3*b*c*(a+b*arctan(c*x))^2*log(2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/(c^2*d^2+e^2)+3*I*b^2*c*(a+b*arctan(c*x))*polylog(2,1+(-2)/(1-I*c*x))/(c^2*d^2+e^2)+3*I*b^2*c*(a+b*arctan(c*x))*polylog(2,1+(-2)/(1+I*c*x))/(c^2*d^2+e^2)-3*I*b^2*c*(a+b*arctan(c*x))*polylog(2,1-2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/(c^2*d^2+e^2)-3/2*b^3*c*polylog(3,1+(-2)/(1-I*c*x))/(c^2*d^2+e^2)+3/2*b^3*c*polylog(3,1+(-2)/(1+I*c*x))/(c^2*d^2+e^2)+3/2*b^3*c*polylog(3,1-2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/(c^2*d^2+e^2)],
[(a+b*arctan(c*x))^3/(d+e*x)^3,x,23,3/2*b*c^3*d*(a+b*arctan(c*x))^2/(c^2*d^2+e^2)^2+3/2*I*b*c^2*e*(a+b*arctan(c*x))^2/(c^2*d^2+e^2)^2-3/2*b*c*(a+b*arctan(c*x))^2/((c^2*d^2+e^2)*(d+e*x))+I*c^3*d*(a+b*arctan(c*x))^3/(c^2*d^2+e^2)^2+1/2*c^2*(c*d-e)*(c*d+e)*(a+b*arctan(c*x))^3/(e*(c^2*d^2+e^2)^2)-1/2*(a+b*arctan(c*x))^3/(e*(d+e*x)^2)-3*b^2*c^2*e*(a+b*arctan(c*x))*log(2/(1-I*c*x))/(c^2*d^2+e^2)^2-3*b*c^3*d*(a+b*arctan(c*x))^2*log(2/(1-I*c*x))/(c^2*d^2+e^2)^2+3*b^2*c^2*e*(a+b*arctan(c*x))*log(2/(1+I*c*x))/(c^2*d^2+e^2)^2+3*b*c^3*d*(a+b*arctan(c*x))^2*log(2/(1+I*c*x))/(c^2*d^2+e^2)^2+3*b^2*c^2*e*(a+b*arctan(c*x))*log(2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/(c^2*d^2+e^2)^2+3*b*c^3*d*(a+b*arctan(c*x))^2*log(2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/(c^2*d^2+e^2)^2+3/2*I*b^3*c^2*e*polylog(2,1+(-2)/(1-I*c*x))/(c^2*d^2+e^2)^2+3*I*b^2*c^3*d*(a+b*arctan(c*x))*polylog(2,1+(-2)/(1-I*c*x))/(c^2*d^2+e^2)^2+3/2*I*b^3*c^2*e*polylog(2,1+(-2)/(1+I*c*x))/(c^2*d^2+e^2)^2+3*I*b^2*c^3*d*(a+b*arctan(c*x))*polylog(2,1+(-2)/(1+I*c*x))/(c^2*d^2+e^2)^2-3/2*I*b^3*c^2*e*polylog(2,1-2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/(c^2*d^2+e^2)^2-3*I*b^2*c^3*d*(a+b*arctan(c*x))*polylog(2,1-2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/(c^2*d^2+e^2)^2-3/2*b^3*c^3*d*polylog(3,1+(-2)/(1-I*c*x))/(c^2*d^2+e^2)^2+3/2*b^3*c^3*d*polylog(3,1+(-2)/(1+I*c*x))/(c^2*d^2+e^2)^2+3/2*b^3*c^3*d*polylog(3,1-2*c*(d+e*x)/((c*d+I*e)*(1-I*c*x)))/(c^2*d^2+e^2)^2],

# Integrands of the form (d+e x)^m (a+b ArcTan[c x^2])^p

# Integrands of the form (d+e x)^m (a+b ArcTan[c x^2])^p
[(d+e*x)^2*(a+b*arctan(c*x^2)),x,17,-2/3*b*e^2*x/c-1/3*b*d^3*arctan(c*x^2)/e+1/3*(d+e*x)^3*(a+b*arctan(c*x^2))/e-1/2*b*d*e*log(1+c^2*x^4)/c+1/3*b*(3*c*d^2-e^2)*arctan(1-x*sqrt(2)*sqrt(c))/(c^(3/2)*sqrt(2))-1/3*b*(3*c*d^2-e^2)*arctan(1+x*sqrt(2)*sqrt(c))/(c^(3/2)*sqrt(2))-1/6*b*(3*c*d^2+e^2)*log(1+c*x^2-x*sqrt(2)*sqrt(c))/(c^(3/2)*sqrt(2))+1/6*b*(3*c*d^2+e^2)*log(1+c*x^2+x*sqrt(2)*sqrt(c))/(c^(3/2)*sqrt(2))],
[(d+e*x)*(a+b*arctan(c*x^2)),x,16,-1/2*b*d^2*arctan(c*x^2)/e+1/2*(d+e*x)^2*(a+b*arctan(c*x^2))/e-1/4*b*e*log(1+c^2*x^4)/c+b*d*arctan(1-x*sqrt(2)*sqrt(c))/(sqrt(2)*sqrt(c))-b*d*arctan(1+x*sqrt(2)*sqrt(c))/(sqrt(2)*sqrt(c))-1/2*b*d*log(1+c*x^2-x*sqrt(2)*sqrt(c))/(sqrt(2)*sqrt(c))+1/2*b*d*log(1+c*x^2+x*sqrt(2)*sqrt(c))/(sqrt(2)*sqrt(c))],
[(a+b*arctan(c*x^2))/(d+e*x),x,19,(a+b*arctan(c*x^2))*log(d+e*x)/e+1/2*b*c*log(e*(1-(-c^2)^(1/4)*x)/((-c^2)^(1/4)*d+e))*log(d+e*x)/(e*sqrt(-c^2))+1/2*b*c*log(-e*(1+(-c^2)^(1/4)*x)/((-c^2)^(1/4)*d-e))*log(d+e*x)/(e*sqrt(-c^2))-1/2*b*c*log(d+e*x)*log(e*(1-x*sqrt(-sqrt(-c^2)))/(e+d*sqrt(-sqrt(-c^2))))/(e*sqrt(-c^2))-1/2*b*c*log(d+e*x)*log(-e*(1+x*sqrt(-sqrt(-c^2)))/(-e+d*sqrt(-sqrt(-c^2))))/(e*sqrt(-c^2))+1/2*b*c*polylog(2,(-c^2)^(1/4)*(d+e*x)/((-c^2)^(1/4)*d-e))/(e*sqrt(-c^2))+1/2*b*c*polylog(2,(-c^2)^(1/4)*(d+e*x)/((-c^2)^(1/4)*d+e))/(e*sqrt(-c^2))-1/2*b*c*polylog(2,(d+e*x)*sqrt(-sqrt(-c^2))/(-e+d*sqrt(-sqrt(-c^2))))/(e*sqrt(-c^2))-1/2*b*c*polylog(2,(d+e*x)*sqrt(-sqrt(-c^2))/(e+d*sqrt(-sqrt(-c^2))))/(e*sqrt(-c^2))],
[(a+b*arctan(c*x^2))/(d+e*x)^2,x,18,b*c^2*d^3*arctan(c*x^2)/(e*(c^2*d^4+e^4))+(-a-b*arctan(c*x^2))/(e*(d+e*x))-2*b*c*d*e*log(d+e*x)/(c^2*d^4+e^4)+1/2*b*c*d*e*log(1+c^2*x^4)/(c^2*d^4+e^4)+b*(c*d^2-e^2)*arctan(1-x*sqrt(2)*sqrt(c))*sqrt(c)/((c^2*d^4+e^4)*sqrt(2))-b*(c*d^2-e^2)*arctan(1+x*sqrt(2)*sqrt(c))*sqrt(c)/((c^2*d^4+e^4)*sqrt(2))-1/2*b*(c*d^2+e^2)*log(1+c*x^2-x*sqrt(2)*sqrt(c))*sqrt(c)/((c^2*d^4+e^4)*sqrt(2))+1/2*b*(c*d^2+e^2)*log(1+c*x^2+x*sqrt(2)*sqrt(c))*sqrt(c)/((c^2*d^4+e^4)*sqrt(2))],

#  {(d + e*x)^2*(a + b*ArcTan[c*x^2])^2, x, 163, a^2*d^2*x - (4*a*b*e^2*x)/(3*c) + (2/9)*I*a*b*e^2*x^3 - (2*(-1)^(3/4)*a*b*d^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x])/Sqrt[c] + (4*(-1)^(3/4)*b^2*e^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x])/(3*c^(3/2)) + ((-1)^(3/4)*b^2*d^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]^2)/Sqrt[c] + ((-1)^(1/4)*b^2*e^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]^2)/(3*c^(3/2)) + (I*d*e*(a + b*ArcTan[c*x^2])^2)/c + d*e*x^2*(a + b*ArcTan[c*x^2])^2 + (2*(-1)^(3/4)*a*b*d^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x])/Sqrt[c] - (2*(-1)^(1/4)*a*b*e^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x])/(3*c^(3/2)) - (4*(-1)^(3/4)*b^2*e^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x])/(3*c^(3/2)) - ((-1)^(1/4)*b^2*d^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]^2)/Sqrt[c] - ((-1)^(3/4)*b^2*e^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]^2)/(3*c^(3/2)) + (2*(-1)^(1/4)*b^2*d^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] - (2*(-1)^(3/4)*b^2*e^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/(3*c^(3/2)) - (2*(-1)^(1/4)*b^2*d^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] + (2*(-1)^(3/4)*b^2*e^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(3*c^(3/2)) + ((-1)^(1/4)*b^2*d^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[(Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] - ((-1)^(3/4)*b^2*e^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[(Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(3*c^(3/2)) + (2*(-1)^(1/4)*b^2*d^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] + (2*(-1)^(3/4)*b^2*e^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/(3*c^(3/2)) - (2*(-1)^(1/4)*b^2*d^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] - (2*(-1)^(3/4)*b^2*e^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(3*c^(3/2)) + ((-1)^(1/4)*b^2*d^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[-((Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x))])/Sqrt[c] + ((-1)^(3/4)*b^2*e^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[-((Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x))])/(3*c^(3/2)) + ((-1)^(1/4)*b^2*d^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(3/4)*b^2*e^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(3*c^(3/2)) + ((-1)^(1/4)*b^2*d^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] - ((-1)^(3/4)*b^2*e^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(3*c^(3/2)) + I*a*b*d^2*x*Log[1 - I*c*x^2] - (2*I*b^2*e^2*x*Log[1 - I*c*x^2])/(3*c) - (1/9)*b^2*e^2*x^3*Log[1 - I*c*x^2] + ((-1)^(1/4)*b^2*d^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[1 - I*c*x^2])/Sqrt[c] - ((-1)^(1/4)*b^2*d^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 - I*c*x^2])/Sqrt[c] - ((-1)^(3/4)*b^2*e^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 - I*c*x^2])/(3*c^(3/2)) - (1/4)*b^2*d^2*x*Log[1 - I*c*x^2]^2 - (1/9)*I*b*e^2*x^3*(2*a + I*b*Log[1 - I*c*x^2]) - ((-1)^(1/4)*b*e^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*(2*a + I*b*Log[1 - I*c*x^2]))/(3*c^(3/2)) + (1/12)*e^2*x^3*(2*a + I*b*Log[1 - I*c*x^2])^2 + (2*b*d*e*(a + b*ArcTan[c*x^2])*Log[2/(1 + I*c*x^2)])/c - I*a*b*d^2*x*Log[1 + I*c*x^2] + (2*I*b^2*e^2*x*Log[1 + I*c*x^2])/(3*c) - (1/3)*I*a*b*e^2*x^3*Log[1 + I*c*x^2] - ((-1)^(1/4)*b^2*d^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/Sqrt[c] + ((-1)^(3/4)*b^2*e^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/(3*c^(3/2)) + ((-1)^(1/4)*b^2*d^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/Sqrt[c] + ((-1)^(3/4)*b^2*e^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/(3*c^(3/2)) + (1/2)*b^2*d^2*x*Log[1 - I*c*x^2]*Log[1 + I*c*x^2] + (1/6)*b^2*e^2*x^3*Log[1 - I*c*x^2]*Log[1 + I*c*x^2] - (1/4)*b^2*d^2*x*Log[1 + I*c*x^2]^2 - (1/12)*b^2*e^2*x^3*Log[1 + I*c*x^2]^2 + ((-1)^(3/4)*b^2*d^2*PolyLog[2, 1 - 2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(1/4)*b^2*e^2*PolyLog[2, 1 - 2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/(3*c^(3/2)) + ((-1)^(3/4)*b^2*d^2*PolyLog[2, 1 - 2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(1/4)*b^2*e^2*PolyLog[2, 1 - 2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(3*c^(3/2)) - ((-1)^(3/4)*b^2*d^2*PolyLog[2, 1 - (Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(2*Sqrt[c]) - ((-1)^(1/4)*b^2*e^2*PolyLog[2, 1 - (Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(6*c^(3/2)) + ((-1)^(1/4)*b^2*d^2*PolyLog[2, 1 - 2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(3/4)*b^2*e^2*PolyLog[2, 1 - 2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/(3*c^(3/2)) + ((-1)^(1/4)*b^2*d^2*PolyLog[2, 1 - 2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(3/4)*b^2*e^2*PolyLog[2, 1 - 2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(3*c^(3/2)) - ((-1)^(1/4)*b^2*d^2*PolyLog[2, 1 + (Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(2*Sqrt[c]) - ((-1)^(3/4)*b^2*e^2*PolyLog[2, 1 + (Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(6*c^(3/2)) - ((-1)^(1/4)*b^2*d^2*PolyLog[2, 1 - ((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(2*Sqrt[c]) - ((-1)^(3/4)*b^2*e^2*PolyLog[2, 1 - ((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(6*c^(3/2)) - ((-1)^(3/4)*b^2*d^2*PolyLog[2, 1 - ((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(2*Sqrt[c]) - ((-1)^(1/4)*b^2*e^2*PolyLog[2, 1 - ((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(6*c^(3/2)) + (I*b^2*d*e*PolyLog[2, 1 - 2/(1 + I*c*x^2)])/c} 
[(d+e*x)*(a+b*arctan(c*x^2))^2,x,77,a^2*d*x+1/2*I*e*(a+b*arctan(c*x^2))^2/c+1/2*e*x^2*(a+b*arctan(c*x^2))^2+I*a*b*d*x*log(1-I*c*x^2)-1/4*b^2*d*x*log(1-I*c*x^2)^2+b*e*(a+b*arctan(c*x^2))*log(2/(1+I*c*x^2))/c-I*a*b*d*x*log(1+I*c*x^2)+1/2*b^2*d*x*log(1-I*c*x^2)*log(1+I*c*x^2)-1/4*b^2*d*x*log(1+I*c*x^2)^2+1/2*I*b^2*e*polylog(2,1+(-2)/(1+I*c*x^2))/c-2*(-1)^(3/4)*a*b*d*arctan((-1)^(3/4)*x*sqrt(c))/sqrt(c)+(-1)^(3/4)*b^2*d*arctan((-1)^(3/4)*x*sqrt(c))^2/sqrt(c)+2*(-1)^(3/4)*a*b*d*arctanh((-1)^(3/4)*x*sqrt(c))/sqrt(c)-(-1)^(1/4)*b^2*d*arctanh((-1)^(3/4)*x*sqrt(c))^2/sqrt(c)+(-1)^(1/4)*b^2*d*arctan((-1)^(3/4)*x*sqrt(c))*log(1-I*c*x^2)/sqrt(c)-(-1)^(1/4)*b^2*d*arctanh((-1)^(3/4)*x*sqrt(c))*log(1-I*c*x^2)/sqrt(c)-(-1)^(1/4)*b^2*d*arctan((-1)^(3/4)*x*sqrt(c))*log(1+I*c*x^2)/sqrt(c)+(-1)^(1/4)*b^2*d*arctanh((-1)^(3/4)*x*sqrt(c))*log(1+I*c*x^2)/sqrt(c)+2*(-1)^(1/4)*b^2*d*arctan((-1)^(3/4)*x*sqrt(c))*log(2/(1-(-1)^(1/4)*x*sqrt(c)))/sqrt(c)-2*(-1)^(1/4)*b^2*d*arctan((-1)^(3/4)*x*sqrt(c))*log(2/(1+(-1)^(1/4)*x*sqrt(c)))/sqrt(c)+(-1)^(1/4)*b^2*d*arctan((-1)^(3/4)*x*sqrt(c))*log(sqrt(2)*((-1)^(1/4)+x*sqrt(c))/(1+(-1)^(1/4)*x*sqrt(c)))/sqrt(c)+2*(-1)^(1/4)*b^2*d*arctanh((-1)^(3/4)*x*sqrt(c))*log(2/(1-(-1)^(3/4)*x*sqrt(c)))/sqrt(c)-2*(-1)^(1/4)*b^2*d*arctanh((-1)^(3/4)*x*sqrt(c))*log(2/(1+(-1)^(3/4)*x*sqrt(c)))/sqrt(c)+(-1)^(1/4)*b^2*d*arctanh((-1)^(3/4)*x*sqrt(c))*log(-sqrt(2)*((-1)^(3/4)+x*sqrt(c))/(1+(-1)^(3/4)*x*sqrt(c)))/sqrt(c)+(-1)^(1/4)*b^2*d*arctanh((-1)^(3/4)*x*sqrt(c))*log((1+I)*(1+(-1)^(1/4)*x*sqrt(c))/(1+(-1)^(3/4)*x*sqrt(c)))/sqrt(c)+(-1)^(1/4)*b^2*d*arctan((-1)^(3/4)*x*sqrt(c))*log((1-I)*(1+(-1)^(3/4)*x*sqrt(c))/(1+(-1)^(1/4)*x*sqrt(c)))/sqrt(c)+(-1)^(3/4)*b^2*d*polylog(2,1+(-2)/(1-(-1)^(1/4)*x*sqrt(c)))/sqrt(c)+(-1)^(3/4)*b^2*d*polylog(2,1+(-2)/(1+(-1)^(1/4)*x*sqrt(c)))/sqrt(c)-1/2*(-1)^(3/4)*b^2*d*polylog(2,1-sqrt(2)*((-1)^(1/4)+x*sqrt(c))/(1+(-1)^(1/4)*x*sqrt(c)))/sqrt(c)+(-1)^(1/4)*b^2*d*polylog(2,1+(-2)/(1-(-1)^(3/4)*x*sqrt(c)))/sqrt(c)+(-1)^(1/4)*b^2*d*polylog(2,1+(-2)/(1+(-1)^(3/4)*x*sqrt(c)))/sqrt(c)-1/2*(-1)^(1/4)*b^2*d*polylog(2,1+sqrt(2)*((-1)^(3/4)+x*sqrt(c))/(1+(-1)^(3/4)*x*sqrt(c)))/sqrt(c)-1/2*(-1)^(1/4)*b^2*d*polylog(2,1+(-1-I)*(1+(-1)^(1/4)*x*sqrt(c))/(1+(-1)^(3/4)*x*sqrt(c)))/sqrt(c)-1/2*(-1)^(3/4)*b^2*d*polylog(2,1+(-1+I)*(1+(-1)^(3/4)*x*sqrt(c))/(1+(-1)^(1/4)*x*sqrt(c)))/sqrt(c)],
[(a+b*arctan(c*x^2))^2/(d+e*x),x,0,Unintegrable((a+b*arctan(c*x^2))^2/(d+e*x),x)],
[(a+b*arctan(c*x^2))^2/(d+e*x)^2,x,0,Unintegrable((a+b*arctan(c*x^2))^2/(d+e*x)^2,x)],

# Integrands of the form (d+e x)^m (a+b ArcTan[c x^3])^p

# Integrands of the form (d+e x)^m (a+b ArcTan[c x^3])^p
[(d+e*x)^2*(a+b*arctan(c*x^3)),x,24,-b*d*e*arctan(c^(1/3)*x)/c^(2/3)-1/3*b*d^3*arctan(c*x^3)/e+1/3*(d+e*x)^3*(a+b*arctan(c*x^3))/e+1/2*b*d*e*arctan(-2*c^(1/3)*x+sqrt(3))/c^(2/3)-1/2*b*d*e*arctan(2*c^(1/3)*x+sqrt(3))/c^(2/3)+1/2*b*d^2*log(1+c^(2/3)*x^2)/c^(1/3)-1/4*b*d^2*log(1-c^(2/3)*x^2+c^(4/3)*x^4)/c^(1/3)-1/6*b*e^2*log(1+c^2*x^6)/c+1/2*b*d^2*arctan((1-2*c^(2/3)*x^2)/sqrt(3))*sqrt(3)/c^(1/3)-1/4*b*d*e*log(1+c^(2/3)*x^2-c^(1/3)*x*sqrt(3))*sqrt(3)/c^(2/3)+1/4*b*d*e*log(1+c^(2/3)*x^2+c^(1/3)*x*sqrt(3))*sqrt(3)/c^(2/3)],
[(d+e*x)*(a+b*arctan(c*x^3)),x,22,-1/2*b*e*arctan(c^(1/3)*x)/c^(2/3)-1/2*b*d^2*arctan(c*x^3)/e+1/2*(d+e*x)^2*(a+b*arctan(c*x^3))/e+1/4*b*e*arctan(-2*c^(1/3)*x+sqrt(3))/c^(2/3)-1/4*b*e*arctan(2*c^(1/3)*x+sqrt(3))/c^(2/3)+1/2*b*d*log(1+c^(2/3)*x^2)/c^(1/3)-1/4*b*d*log(1-c^(2/3)*x^2+c^(4/3)*x^4)/c^(1/3)+1/2*b*d*arctan((1-2*c^(2/3)*x^2)/sqrt(3))*sqrt(3)/c^(1/3)-1/8*b*e*log(1+c^(2/3)*x^2-c^(1/3)*x*sqrt(3))*sqrt(3)/c^(2/3)+1/8*b*e*log(1+c^(2/3)*x^2+c^(1/3)*x*sqrt(3))*sqrt(3)/c^(2/3)],
[(a+b*arctan(c*x^3))/(d+e*x),x,25,(a+b*arctan(c*x^3))*log(d+e*x)/e+1/2*b*c*log(e*(1-(-c^2)^(1/6)*x)/((-c^2)^(1/6)*d+e))*log(d+e*x)/(e*sqrt(-c^2))-1/2*b*c*log(-e*(1+(-c^2)^(1/6)*x)/((-c^2)^(1/6)*d-e))*log(d+e*x)/(e*sqrt(-c^2))+1/2*b*c*log(-e*((-1)^(1/3)+(-c^2)^(1/6)*x)/((-c^2)^(1/6)*d-(-1)^(1/3)*e))*log(d+e*x)/(e*sqrt(-c^2))-1/2*b*c*log(-e*((-1)^(2/3)+(-c^2)^(1/6)*x)/((-c^2)^(1/6)*d-(-1)^(2/3)*e))*log(d+e*x)/(e*sqrt(-c^2))+1/2*b*c*log((-1)^(2/3)*e*(1+(-1)^(1/3)*(-c^2)^(1/6)*x)/((-c^2)^(1/6)*d+(-1)^(2/3)*e))*log(d+e*x)/(e*sqrt(-c^2))-1/2*b*c*log((-1)^(1/3)*e*(1+(-1)^(2/3)*(-c^2)^(1/6)*x)/((-c^2)^(1/6)*d+(-1)^(1/3)*e))*log(d+e*x)/(e*sqrt(-c^2))-1/2*b*c*polylog(2,(-c^2)^(1/6)*(d+e*x)/((-c^2)^(1/6)*d-e))/(e*sqrt(-c^2))+1/2*b*c*polylog(2,(-c^2)^(1/6)*(d+e*x)/((-c^2)^(1/6)*d+e))/(e*sqrt(-c^2))+1/2*b*c*polylog(2,(-c^2)^(1/6)*(d+e*x)/((-c^2)^(1/6)*d-(-1)^(1/3)*e))/(e*sqrt(-c^2))-1/2*b*c*polylog(2,(-c^2)^(1/6)*(d+e*x)/((-c^2)^(1/6)*d+(-1)^(1/3)*e))/(e*sqrt(-c^2))-1/2*b*c*polylog(2,(-c^2)^(1/6)*(d+e*x)/((-c^2)^(1/6)*d-(-1)^(2/3)*e))/(e*sqrt(-c^2))+1/2*b*c*polylog(2,(-c^2)^(1/6)*(d+e*x)/((-c^2)^(1/6)*d+(-1)^(2/3)*e))/(e*sqrt(-c^2))],
[(a+b*arctan(c*x^3))/(d+e*x)^2,x,34,-b*c^(2/3)*d*e^3*arctan(c^(1/3)*x)/(c^2*d^6+e^6)+b*c^2*d^5*arctan(c*x^3)/(e*(c^2*d^6+e^6))+(-a-b*arctan(c*x^3))/(e*(d+e*x))+3*b*c*d^2*e^2*log(d+e*x)/(c^2*d^6+e^6)+1/2*b*c^(5/3)*d^4*log(1+c^(2/3)*x^2)/(c^2*d^6+e^6)-1/2*b*c*d^2*e^2*log(1+c^2*x^6)/(c^2*d^6+e^6)+1/2*b*c^(2/3)*d*arctan(2*c^(1/3)*x+sqrt(3))*(-e^3+c*d^3*sqrt(3))/(c^2*d^6+e^6)+1/2*b*c^(2/3)*d*arctan(-2*c^(1/3)*x+sqrt(3))*(e^3+c*d^3*sqrt(3))/(c^2*d^6+e^6)-1/4*b*c^(2/3)*d*log(1+c^(2/3)*x^2-c^(1/3)*x*sqrt(3))*(c*d^3-e^3*sqrt(3))/(c^2*d^6+e^6)-1/4*b*c^(2/3)*d*log(1+c^(2/3)*x^2+c^(1/3)*x*sqrt(3))*(c*d^3+e^3*sqrt(3))/(c^2*d^6+e^6)-1/2*b*c^(5/3)*e*log((-c^2)^(1/6)+c^(2/3)*x)*(-e^3+d^3*sqrt(-c^2))/((-c^2)^(2/3)*(c^2*d^6+e^6))+1/4*b*c^(5/3)*e*log((-c^2)^(1/3)-c^(2/3)*(-c^2)^(1/6)*x+c^(4/3)*x^2)*(-e^3+d^3*sqrt(-c^2))/((-c^2)^(2/3)*(c^2*d^6+e^6))-1/2*b*c^(5/3)*e*arctan((c^(4/3)+2*(-c^2)^(5/6)*x)/(c^(4/3)*sqrt(3)))*sqrt(3)*(-e^3+d^3*sqrt(-c^2))/((-c^2)^(2/3)*(c^2*d^6+e^6))+1/2*b*c^(5/3)*e*log((-c^2)^(1/6)-c^(2/3)*x)*(e^3+d^3*sqrt(-c^2))/((-c^2)^(2/3)*(c^2*d^6+e^6))-1/4*b*c^(5/3)*e*log((-c^2)^(1/3)+c^(2/3)*(-c^2)^(1/6)*x+c^(4/3)*x^2)*(e^3+d^3*sqrt(-c^2))/((-c^2)^(2/3)*(c^2*d^6+e^6))+1/2*b*c^(5/3)*e*arctan((1+2*c^(2/3)*x/(-c^2)^(1/6))/sqrt(3))*sqrt(3)*(e^3+d^3*sqrt(-c^2))/((-c^2)^(2/3)*(c^2*d^6+e^6))]]:
