1,1,133,112,0.7994088,"\int \frac{(a+b \csc (x)) \left(A+B \csc (x)+C \csc ^2(x)\right)}{\sqrt{\csc (x)}} \, dx","Integrate[((a + b*Csc[x])*(A + B*Csc[x] + C*Csc[x]^2))/Sqrt[Csc[x]],x]","-\frac{4 (a+b \csc (x)) \left(A+B \csc (x)+C \csc ^2(x)\right) \left(\sqrt{\sin (x)} F\left(\left.\frac{1}{4} (\pi -2 x)\right|2\right) (3 a B+3 A b+b C)-3 \sqrt{\sin (x)} E\left(\left.\frac{1}{4} (\pi -2 x)\right|2\right) (a (C-A)+b B)+3 a C \cos (x)+3 b B \cos (x)+b C \cot (x)\right)}{3 \csc ^{\frac{5}{2}}(x) (a \sin (x)+b) (A (-\cos (2 x))+A+2 B \sin (x)+2 C)}","-\frac{2}{3} \sqrt{\sin (x)} \sqrt{\csc (x)} F\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right) (3 a B+3 A b+b C)+2 \sqrt{\sin (x)} \sqrt{\csc (x)} E\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right) (b B-a (A-C))-2 \cos (x) \sqrt{\csc (x)} (a C+b B)-\frac{2}{3} b C \cos (x) \csc ^{\frac{3}{2}}(x)",1,"(-4*(a + b*Csc[x])*(A + B*Csc[x] + C*Csc[x]^2)*(3*b*B*Cos[x] + 3*a*C*Cos[x] + b*C*Cot[x] - 3*(b*B + a*(-A + C))*EllipticE[(Pi - 2*x)/4, 2]*Sqrt[Sin[x]] + (3*A*b + 3*a*B + b*C)*EllipticF[(Pi - 2*x)/4, 2]*Sqrt[Sin[x]]))/(3*Csc[x]^(5/2)*(b + a*Sin[x])*(A + 2*C - A*Cos[2*x] + 2*B*Sin[x]))","A",1