1,1,129,106,1.593000," ","int((a+b*csc(d*x+c)^2)^4,x)","\frac{a^{4} \left(d x +c \right)-4 a^{3} b \cot \left(d x +c \right)+6 a^{2} b^{2} \left(-\frac{2}{3}-\frac{\left(\csc^{2}\left(d x +c \right)\right)}{3}\right) \cot \left(d x +c \right)+4 a \,b^{3} \left(-\frac{8}{15}-\frac{\left(\csc^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\csc^{2}\left(d x +c \right)\right)}{15}\right) \cot \left(d x +c \right)+b^{4} \left(-\frac{16}{35}-\frac{\left(\csc^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\csc^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\csc^{2}\left(d x +c \right)\right)}{35}\right) \cot \left(d x +c \right)}{d}"," ",0,"1/d*(a^4*(d*x+c)-4*a^3*b*cot(d*x+c)+6*a^2*b^2*(-2/3-1/3*csc(d*x+c)^2)*cot(d*x+c)+4*a*b^3*(-8/15-1/5*csc(d*x+c)^4-4/15*csc(d*x+c)^2)*cot(d*x+c)+b^4*(-16/35-1/7*csc(d*x+c)^6-6/35*csc(d*x+c)^4-8/35*csc(d*x+c)^2)*cot(d*x+c))","A"
2,1,83,70,1.355000," ","int((a+b*csc(d*x+c)^2)^3,x)","\frac{a^{3} \left(d x +c \right)-3 a^{2} b \cot \left(d x +c \right)+3 b^{2} a \left(-\frac{2}{3}-\frac{\left(\csc^{2}\left(d x +c \right)\right)}{3}\right) \cot \left(d x +c \right)+b^{3} \left(-\frac{8}{15}-\frac{\left(\csc^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\csc^{2}\left(d x +c \right)\right)}{15}\right) \cot \left(d x +c \right)}{d}"," ",0,"1/d*(a^3*(d*x+c)-3*a^2*b*cot(d*x+c)+3*b^2*a*(-2/3-1/3*csc(d*x+c)^2)*cot(d*x+c)+b^3*(-8/15-1/5*csc(d*x+c)^4-4/15*csc(d*x+c)^2)*cot(d*x+c))","A"
3,1,47,39,1.147000," ","int((a+b*csc(d*x+c)^2)^2,x)","\frac{a^{2} \left(d x +c \right)-2 a b \cot \left(d x +c \right)+b^{2} \left(-\frac{2}{3}-\frac{\left(\csc^{2}\left(d x +c \right)\right)}{3}\right) \cot \left(d x +c \right)}{d}"," ",0,"1/d*(a^2*(d*x+c)-2*a*b*cot(d*x+c)+b^2*(-2/3-1/3*csc(d*x+c)^2)*cot(d*x+c))","A"
4,1,17,16,0.885000," ","int(a+b*csc(d*x+c)^2,x)","a x -\frac{b \cot \left(d x +c \right)}{d}"," ",0,"a*x-b*cot(d*x+c)/d","A"
5,1,50,38,0.614000," ","int(1/(a+b*csc(d*x+c)^2),x)","-\frac{b \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(a +b \right) b}}\right)}{d a \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d a}"," ",0,"-1/d/a*b/((a+b)*b)^(1/2)*arctan((a+b)*tan(d*x+c)/((a+b)*b)^(1/2))+1/d/a*arctan(tan(d*x+c))","A"
6,1,140,80,0.707000," ","int(1/(a+b*csc(d*x+c)^2)^2,x)","\frac{b \tan \left(d x +c \right)}{2 d a \left(a +b \right) \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)}-\frac{3 b \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(a +b \right) b}}\right)}{2 d a \left(a +b \right) \sqrt{\left(a +b \right) b}}-\frac{b^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(a +b \right) b}}\right)}{d \,a^{2} \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \,a^{2}}"," ",0,"1/2/d*b/a/(a+b)*tan(d*x+c)/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)-3/2/d*b/a/(a+b)/((a+b)*b)^(1/2)*arctan((a+b)*tan(d*x+c)/((a+b)*b)^(1/2))-1/d*b^2/a^2/(a+b)/((a+b)*b)^(1/2)*arctan((a+b)*tan(d*x+c)/((a+b)*b)^(1/2))+1/d/a^2*arctan(tan(d*x+c))","A"
7,1,363,130,0.710000," ","int(1/(a+b*csc(d*x+c)^2)^3,x)","\frac{9 b \left(\tan^{3}\left(d x +c \right)\right)}{8 d a \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)^{2} \left(a +b \right)}+\frac{b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{2 d \,a^{2} \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)^{2} \left(a +b \right)}+\frac{7 b^{2} \tan \left(d x +c \right)}{8 d a \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{b^{3} \tan \left(d x +c \right)}{2 d \,a^{2} \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{15 b \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(a +b \right) b}}\right)}{8 d a \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) b}}-\frac{5 b^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(a +b \right) b}}\right)}{2 d \,a^{2} \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) b}}-\frac{b^{3} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(a +b \right) b}}\right)}{d \,a^{3} \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \,a^{3}}"," ",0,"9/8/d/a*b/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)^2/(a+b)*tan(d*x+c)^3+1/2/d/a^2*b^2/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)^2/(a+b)*tan(d*x+c)^3+7/8/d/a*b^2/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)^2/(a^2+2*a*b+b^2)*tan(d*x+c)+1/2/d/a^2*b^3/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)^2/(a^2+2*a*b+b^2)*tan(d*x+c)-15/8/d/a*b/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan((a+b)*tan(d*x+c)/((a+b)*b)^(1/2))-5/2/d/a^2*b^2/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan((a+b)*tan(d*x+c)/((a+b)*b)^(1/2))-1/d/a^3*b^3/(a^2+2*a*b+b^2)/((a+b)*b)^(1/2)*arctan((a+b)*tan(d*x+c)/((a+b)*b)^(1/2))+1/d/a^3*arctan(tan(d*x+c))","B"
8,1,737,188,0.705000," ","int(1/(a+b*csc(d*x+c)^2)^4,x)","\frac{29 b \left(\tan^{5}\left(d x +c \right)\right)}{16 d a \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)^{3} \left(a +b \right)}+\frac{13 b^{2} \left(\tan^{5}\left(d x +c \right)\right)}{8 d \,a^{2} \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)^{3} \left(a +b \right)}+\frac{b^{3} \left(\tan^{5}\left(d x +c \right)\right)}{2 d \,a^{3} \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)^{3} \left(a +b \right)}+\frac{17 b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{6 d a \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)^{3} \left(a^{2}+2 a b +b^{2}\right)}+\frac{3 b^{3} \left(\tan^{3}\left(d x +c \right)\right)}{d \,a^{2} \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)^{3} \left(a^{2}+2 a b +b^{2}\right)}+\frac{b^{4} \left(\tan^{3}\left(d x +c \right)\right)}{d \,a^{3} \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)^{3} \left(a^{2}+2 a b +b^{2}\right)}+\frac{19 b^{3} \tan \left(d x +c \right)}{16 d a \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)^{3} \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{11 b^{4} \tan \left(d x +c \right)}{8 d \,a^{2} \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)^{3} \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{b^{5} \tan \left(d x +c \right)}{2 d \,a^{3} \left(a \left(\tan^{2}\left(d x +c \right)\right)+b \left(\tan^{2}\left(d x +c \right)\right)+b \right)^{3} \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{35 b \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(a +b \right) b}}\right)}{16 d a \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right) \sqrt{\left(a +b \right) b}}-\frac{35 b^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(a +b \right) b}}\right)}{8 d \,a^{2} \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right) \sqrt{\left(a +b \right) b}}-\frac{7 b^{3} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(a +b \right) b}}\right)}{2 d \,a^{3} \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right) \sqrt{\left(a +b \right) b}}-\frac{b^{4} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(a +b \right) b}}\right)}{d \,a^{4} \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right) \sqrt{\left(a +b \right) b}}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \,a^{4}}"," ",0,"29/16/d*b/a/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)^3/(a+b)*tan(d*x+c)^5+13/8/d*b^2/a^2/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)^3/(a+b)*tan(d*x+c)^5+1/2/d*b^3/a^3/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)^3/(a+b)*tan(d*x+c)^5+17/6/d*b^2/a/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)^3/(a^2+2*a*b+b^2)*tan(d*x+c)^3+3/d*b^3/a^2/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)^3/(a^2+2*a*b+b^2)*tan(d*x+c)^3+1/d*b^4/a^3/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)^3/(a^2+2*a*b+b^2)*tan(d*x+c)^3+19/16/d*b^3/a/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)^3/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(d*x+c)+11/8/d*b^4/a^2/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)^3/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(d*x+c)+1/2/d*b^5/a^3/(a*tan(d*x+c)^2+b*tan(d*x+c)^2+b)^3/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(d*x+c)-35/16/d*b/a/(a^3+3*a^2*b+3*a*b^2+b^3)/((a+b)*b)^(1/2)*arctan((a+b)*tan(d*x+c)/((a+b)*b)^(1/2))-35/8/d*b^2/a^2/(a^3+3*a^2*b+3*a*b^2+b^3)/((a+b)*b)^(1/2)*arctan((a+b)*tan(d*x+c)/((a+b)*b)^(1/2))-7/2/d*b^3/a^3/(a^3+3*a^2*b+3*a*b^2+b^3)/((a+b)*b)^(1/2)*arctan((a+b)*tan(d*x+c)/((a+b)*b)^(1/2))-1/d*b^4/a^4/(a^3+3*a^2*b+3*a*b^2+b^3)/((a+b)*b)^(1/2)*arctan((a+b)*tan(d*x+c)/((a+b)*b)^(1/2))+1/d/a^4*arctan(tan(d*x+c))","B"
9,1,3621,145,2.330000," ","int((a+b*csc(d*x+c)^2)^(5/2),x)","\text{output too large to display}"," ",0,"1/16/d*((a*cos(d*x+c)^2-a-b)/(cos(d*x+c)^2-1))^(5/2)*(-1+cos(d*x+c))^4*(3*(-a)^(1/2)*b^(5/2)*cos(d*x+c)*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))+6*(-a)^(1/2)*cos(d*x+c)^3*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^2-10*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^2+10*b^(3/2)*a*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*(-a)^(1/2)-10*b^(3/2)*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*a*(-a)^(1/2)+15*a^2*b^(1/2)*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*(-a)^(1/2)-15*b^(1/2)*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*a^2*(-a)^(1/2)+3*(-a)^(1/2)*b^(5/2)*cos(d*x+c)^3*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))-3*(-a)^(1/2)*b^(5/2)*cos(d*x+c)^3*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))-3*(-a)^(1/2)*b^(5/2)*cos(d*x+c)^2*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))+3*(-a)^(1/2)*b^(5/2)*cos(d*x+c)^2*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))-3*(-a)^(1/2)*b^(5/2)*cos(d*x+c)*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))+3*b^(5/2)*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*(-a)^(1/2)-3*b^(5/2)*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*(-a)^(1/2)-16*cos(d*x+c)^3*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a^3+16*cos(d*x+c)^2*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a^3+16*cos(d*x+c)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a^3-16*a^3*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))-10*(-a)^(1/2)*b^(3/2)*cos(d*x+c)^3*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*a-10*(-a)^(1/2)*b^(3/2)*cos(d*x+c)^2*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*a+10*(-a)^(1/2)*b^(3/2)*cos(d*x+c)^2*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*a+15*(-a)^(1/2)*b^(1/2)*cos(d*x+c)^3*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*a^2-15*(-a)^(1/2)*b^(1/2)*cos(d*x+c)^3*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*a^2-10*(-a)^(1/2)*b^(3/2)*cos(d*x+c)*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*a+10*(-a)^(1/2)*b^(3/2)*cos(d*x+c)*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*a-15*(-a)^(1/2)*b^(1/2)*cos(d*x+c)^2*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*a^2+15*(-a)^(1/2)*b^(1/2)*cos(d*x+c)^2*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*a^2+18*(-a)^(1/2)*cos(d*x+c)^3*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*a*b-15*(-a)^(1/2)*b^(1/2)*cos(d*x+c)*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*a^2+15*(-a)^(1/2)*b^(1/2)*cos(d*x+c)*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*a^2-18*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*a*b+10*(-a)^(1/2)*b^(3/2)*cos(d*x+c)^3*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*a)/sin(d*x+c)^7/(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)/(-a)^(1/2)","B"
10,1,1286,101,2.302000," ","int((a+b*csc(d*x+c)^2)^(3/2),x)","-\frac{\left(\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\cos^{2}\left(d x +c \right)-1}\right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\ln \left(-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(\sqrt{b}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+\sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{b}+a \cos \left(d x +c \right)+a +b \right)}{\sin \left(d x +c \right)^{2} \sqrt{b}}\right) \cos \left(d x +c \right) \sqrt{-a}\, b^{\frac{3}{2}}-\ln \left(-\frac{4 \left(\sqrt{b}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+\sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{b}-a \cos \left(d x +c \right)+a +b \right)}{-1+\cos \left(d x +c \right)}\right) \cos \left(d x +c \right) \sqrt{-a}\, b^{\frac{3}{2}}+3 \ln \left(-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(\sqrt{b}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+\sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{b}+a \cos \left(d x +c \right)+a +b \right)}{\sin \left(d x +c \right)^{2} \sqrt{b}}\right) \cos \left(d x +c \right) \sqrt{-a}\, \sqrt{b}\, a -3 \ln \left(-\frac{4 \left(\sqrt{b}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+\sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{b}-a \cos \left(d x +c \right)+a +b \right)}{-1+\cos \left(d x +c \right)}\right) \cos \left(d x +c \right) \sqrt{-a}\, \sqrt{b}\, a -b^{\frac{3}{2}} \ln \left(-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(\sqrt{b}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+\sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{b}+a \cos \left(d x +c \right)+a +b \right)}{\sin \left(d x +c \right)^{2} \sqrt{b}}\right) \sqrt{-a}+b^{\frac{3}{2}} \ln \left(-\frac{4 \left(\sqrt{b}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+\sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{b}-a \cos \left(d x +c \right)+a +b \right)}{-1+\cos \left(d x +c \right)}\right) \sqrt{-a}+2 \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \cos \left(d x +c \right) \sqrt{-a}\, b -4 \ln \left(4 \sqrt{-a}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 \sqrt{-a}\, \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-4 a \cos \left(d x +c \right)\right) \cos \left(d x +c \right) a^{2}-3 a \sqrt{b}\, \ln \left(-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(\sqrt{b}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+\sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{b}+a \cos \left(d x +c \right)+a +b \right)}{\sin \left(d x +c \right)^{2} \sqrt{b}}\right) \sqrt{-a}+3 \sqrt{b}\, \ln \left(-\frac{4 \left(\sqrt{b}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+\sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{b}-a \cos \left(d x +c \right)+a +b \right)}{-1+\cos \left(d x +c \right)}\right) a \sqrt{-a}+4 a^{2} \ln \left(4 \sqrt{-a}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 \sqrt{-a}\, \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-4 a \cos \left(d x +c \right)\right)\right)}{4 d \sin \left(d x +c \right)^{3} \left(-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}\right)^{\frac{3}{2}} \sqrt{-a}}"," ",0,"-1/4/d*((a*cos(d*x+c)^2-a-b)/(cos(d*x+c)^2-1))^(3/2)*(-1+cos(d*x+c))^2*(ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*cos(d*x+c)*(-a)^(1/2)*b^(3/2)-ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*cos(d*x+c)*(-a)^(1/2)*b^(3/2)+3*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*cos(d*x+c)*(-a)^(1/2)*b^(1/2)*a-3*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*cos(d*x+c)*(-a)^(1/2)*b^(1/2)*a-b^(3/2)*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*(-a)^(1/2)+b^(3/2)*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*(-a)^(1/2)+2*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)*(-a)^(1/2)*b-4*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)*a^2-3*a*b^(1/2)*ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*(-a)^(1/2)+3*b^(1/2)*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*a*(-a)^(1/2)+4*a^2*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c)))/sin(d*x+c)^3/(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(3/2)/(-a)^(1/2)","B"
11,1,419,69,1.908000," ","int((a+b*csc(d*x+c)^2)^(1/2),x)","-\frac{\sqrt{\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\cos^{2}\left(d x +c \right)-1}}\, \left(-1+\cos \left(d x +c \right)\right) \left(\ln \left(-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(\sqrt{b}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+\sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{b}+a \cos \left(d x +c \right)+a +b \right)}{\sin \left(d x +c \right)^{2} \sqrt{b}}\right) \sqrt{b}\, \sqrt{-a}-\sqrt{b}\, \ln \left(-\frac{4 \left(\sqrt{b}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+\sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{b}-a \cos \left(d x +c \right)+a +b \right)}{-1+\cos \left(d x +c \right)}\right) \sqrt{-a}-2 a \ln \left(4 \sqrt{-a}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 \sqrt{-a}\, \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-4 a \cos \left(d x +c \right)\right)\right) \sqrt{4}}{4 d \sin \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{-a}}"," ",0,"-1/4/d*((a*cos(d*x+c)^2-a-b)/(cos(d*x+c)^2-1))^(1/2)*(-1+cos(d*x+c))*(ln(-2*(-1+cos(d*x+c))*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)+a*cos(d*x+c)+a+b)/sin(d*x+c)^2/b^(1/2))*b^(1/2)*(-a)^(1/2)-b^(1/2)*ln(-4*(b^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*b^(1/2)-a*cos(d*x+c)+a+b)/(-1+cos(d*x+c)))*(-a)^(1/2)-2*a*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c)))/sin(d*x+c)/(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*4^(1/2)/(-a)^(1/2)","B"
12,1,182,33,1.456000," ","int(1/(a+b*csc(d*x+c)^2)^(1/2),x)","\frac{\sin \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \ln \left(4 \sqrt{-a}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 \sqrt{-a}\, \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-4 a \cos \left(d x +c \right)\right)}{d \sqrt{\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\cos^{2}\left(d x +c \right)-1}}\, \left(-1+\cos \left(d x +c \right)\right) \sqrt{-a}}"," ",0,"1/d*sin(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))/((a*cos(d*x+c)^2-a-b)/(cos(d*x+c)^2-1))^(1/2)/(-1+cos(d*x+c))/(-a)^(1/2)","B"
13,1,652,69,1.411000," ","int(1/(a+b*csc(d*x+c)^2)^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(a \left(\cos^{2}\left(d x +c \right)\right)-a -b \right) \left(-\cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \ln \left(4 \sqrt{-a}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 \sqrt{-a}\, \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-4 a \cos \left(d x +c \right)\right) a -\cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \ln \left(4 \sqrt{-a}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 \sqrt{-a}\, \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-4 a \cos \left(d x +c \right)\right) b +\sqrt{-a}\, \cos \left(d x +c \right) b -\sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \ln \left(4 \sqrt{-a}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 \sqrt{-a}\, \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-4 a \cos \left(d x +c \right)\right) a -\sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \ln \left(4 \sqrt{-a}\, \cos \left(d x +c \right) \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 \sqrt{-a}\, \sqrt{-\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-4 a \cos \left(d x +c \right)\right) b \right) b}{d \left(\frac{a \left(\cos^{2}\left(d x +c \right)\right)-a -b}{\cos^{2}\left(d x +c \right)-1}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{7} \left(a +b \right) \left(\sqrt{\left(a +b \right) a}+a \right) \left(\sqrt{\left(a +b \right) a}-a \right) \sqrt{-a}}"," ",0,"-1/d*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(a*cos(d*x+c)^2-a-b)*(-cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a-cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*b+(-a)^(1/2)*cos(d*x+c)*b-(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a-(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*b)*b/((a*cos(d*x+c)^2-a-b)/(cos(d*x+c)^2-1))^(3/2)/sin(d*x+c)^7/(a+b)/(((a+b)*a)^(1/2)+a)/(((a+b)*a)^(1/2)-a)/(-a)^(1/2)","B"
14,1,2702,112,1.459000," ","int(1/(a+b*csc(d*x+c)^2)^(5/2),x)","\text{Expression too large to display}"," ",0,"-1/3/d*sin(d*x+c)^5*(-15*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*b^2-12*(-a)^(1/2)*cos(d*x+c)^3*a^3*b-19*(-a)^(1/2)*cos(d*x+c)^3*a^2*b^2-7*(-a)^(1/2)*cos(d*x+c)^3*a*b^3-6*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a*b+6*(-a)^(1/2)*cos(d*x+c)*a^3*b+15*(-a)^(1/2)*cos(d*x+c)*a^2*b^2+12*(-a)^(1/2)*cos(d*x+c)*a*b^3-3*cos(d*x+c)^5*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a^2-3*cos(d*x+c)^5*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*b^2-15*cos(d*x+c)^4*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a^2-15*cos(d*x+c)^4*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*b^2-30*cos(d*x+c)^3*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a^2-30*cos(d*x+c)^3*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*b^2+6*(-a)^(1/2)*cos(d*x+c)^5*a^3*b+4*(-a)^(1/2)*cos(d*x+c)^5*a^2*b^2-30*cos(d*x+c)^2*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a^2-30*cos(d*x+c)^2*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*b^2-15*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a^2-3*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*b^2-3*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a^2+3*(-a)^(1/2)*cos(d*x+c)*b^4-60*cos(d*x+c)^2*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a*b-30*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a*b-6*cos(d*x+c)^5*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a*b-30*cos(d*x+c)^4*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a*b-60*cos(d*x+c)^3*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(5/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a*b)*b^2/(-1+cos(d*x+c))^5/((a*cos(d*x+c)^2-a-b)/(cos(d*x+c)^2-1))^(5/2)/(1+cos(d*x+c))^5/(((a+b)*a)^(1/2)-a)^2/(a+b)^2/(((a+b)*a)^(1/2)+a)^2/(-a)^(1/2)","B"
15,1,4815,162,1.775000," ","int(1/(a+b*csc(d*x+c)^2)^(7/2),x)","\text{output too large to display}"," ",0,"1/15/d*sin(d*x+c)^7*(15*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a^3-15*cos(d*x+c)*(-a)^(1/2)*b^6+15*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*b^3+15*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^7*a^3+15*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^7*b^3+105*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^6*a^3+105*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^6*b^3+315*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^5*a^3+315*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^5*b^3+525*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^4*a^3+525*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^4*b^3+525*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^3*a^3+525*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^3*b^3+45*cos(d*x+c)^7*(-a)^(1/2)*a^5*b+60*cos(d*x+c)^7*(-a)^(1/2)*a^4*b^2+23*cos(d*x+c)^7*(-a)^(1/2)*a^3*b^3+315*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^2*a^3+315*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^2*b^3+105*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)*a^3+105*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)*b^3-135*cos(d*x+c)^5*(-a)^(1/2)*a^5*b-300*cos(d*x+c)^5*(-a)^(1/2)*a^4*b^2-223*cos(d*x+c)^5*(-a)^(1/2)*a^3*b^3-58*cos(d*x+c)^5*(-a)^(1/2)*a^2*b^4+45*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a^2*b+45*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*a*b^2+135*cos(d*x+c)^3*(-a)^(1/2)*a^5*b+420*cos(d*x+c)^3*(-a)^(1/2)*a^4*b^2+485*cos(d*x+c)^3*(-a)^(1/2)*a^3*b^3+250*cos(d*x+c)^3*(-a)^(1/2)*a^2*b^4+50*cos(d*x+c)^3*(-a)^(1/2)*a*b^5-45*cos(d*x+c)*(-a)^(1/2)*a^5*b-180*cos(d*x+c)*(-a)^(1/2)*a^4*b^2-285*cos(d*x+c)*(-a)^(1/2)*a^3*b^3-225*cos(d*x+c)*(-a)^(1/2)*a^2*b^4-90*cos(d*x+c)*(-a)^(1/2)*a*b^5+1575*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^4*a*b^2+1575*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^3*a^2*b+1575*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^3*a*b^2+945*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^2*a^2*b+945*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^2*a*b^2+315*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)*a^2*b+315*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)*a*b^2+45*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^7*a^2*b+45*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^7*a*b^2+315*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^6*a^2*b+315*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^6*a*b^2+945*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^5*a^2*b+945*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^5*a*b^2+1575*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(7/2)*ln(4*(-a)^(1/2)*cos(d*x+c)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)+4*(-a)^(1/2)*(-(a*cos(d*x+c)^2-a-b)/(1+cos(d*x+c))^2)^(1/2)-4*a*cos(d*x+c))*cos(d*x+c)^4*a^2*b)*b^3/(-1+cos(d*x+c))^7/((a*cos(d*x+c)^2-a-b)/(cos(d*x+c)^2-1))^(7/2)/(1+cos(d*x+c))^7/(((a+b)*a)^(1/2)+a)^3/(a+b)^3/(((a+b)*a)^(1/2)-a)^3/(-a)^(1/2)","B"
16,1,312,37,1.225000," ","int((1+csc(x)^2)^(3/2),x)","-\frac{\left(\frac{\cos^{2}\left(x \right)-2}{-1+\cos^{2}\left(x \right)}\right)^{\frac{3}{2}} \left(-1+\cos \left(x \right)\right)^{2} \left(\cos \left(x \right) \sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}+2 \cos \left(x \right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}+\cos^{2}\left(x \right)+\cos \left(x \right)-\sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}-2\right)}{\sin \left(x \right)^{2}}\right)-2 \cos \left(x \right) \arctanh \left(\frac{\cos^{2}\left(x \right)-3 \cos \left(x \right)+2}{\sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}\, \sin \left(x \right)^{2}}\right)+2 \cos \left(x \right) \arctan \left(\frac{\cos \left(x \right) \left(-1+\cos \left(x \right)\right)}{\sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}\, \sin \left(x \right)^{2}}\right)-2 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}+\cos^{2}\left(x \right)+\cos \left(x \right)-\sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}-2\right)}{\sin \left(x \right)^{2}}\right)+2 \arctanh \left(\frac{\cos^{2}\left(x \right)-3 \cos \left(x \right)+2}{\sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}\, \sin \left(x \right)^{2}}\right)-2 \arctan \left(\frac{\cos \left(x \right) \left(-1+\cos \left(x \right)\right)}{\sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}\, \sin \left(x \right)^{2}}\right)\right)}{2 \sin \left(x \right)^{3} \left(-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}\right)^{\frac{3}{2}}}"," ",0,"-1/2*((cos(x)^2-2)/(-1+cos(x)^2))^(3/2)*(-1+cos(x))^2*(cos(x)*(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)+2*cos(x)*ln(-2*(cos(x)^2*(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)+cos(x)^2+cos(x)-(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)-2)/sin(x)^2)-2*cos(x)*arctanh((cos(x)^2-3*cos(x)+2)/(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)/sin(x)^2)+2*cos(x)*arctan(cos(x)*(-1+cos(x))/(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)/sin(x)^2)-2*ln(-2*(cos(x)^2*(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)+cos(x)^2+cos(x)-(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)-2)/sin(x)^2)+2*arctanh((cos(x)^2-3*cos(x)+2)/(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)/sin(x)^2)-2*arctan(cos(x)*(-1+cos(x))/(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)/sin(x)^2))/sin(x)^3/(-(cos(x)^2-2)/(cos(x)+1)^2)^(3/2)","B"
17,1,166,25,1.231000," ","int((1+csc(x)^2)^(1/2),x)","\frac{\sqrt{\frac{\cos^{2}\left(x \right)-2}{-1+\cos^{2}\left(x \right)}}\, \left(-1+\cos \left(x \right)\right) \left(-\ln \left(-\frac{2 \left(\left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}+\cos^{2}\left(x \right)+\cos \left(x \right)-\sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}-2\right)}{\sin \left(x \right)^{2}}\right)+\arctanh \left(\frac{\cos^{2}\left(x \right)-3 \cos \left(x \right)+2}{\sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}\, \sin \left(x \right)^{2}}\right)-2 \arctan \left(\frac{\cos \left(x \right) \left(-1+\cos \left(x \right)\right)}{\sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}\, \sin \left(x \right)^{2}}\right)\right) \sqrt{4}}{4 \sin \left(x \right) \sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}}"," ",0,"1/4*((cos(x)^2-2)/(-1+cos(x)^2))^(1/2)*(-1+cos(x))*(-ln(-2*(cos(x)^2*(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)+cos(x)^2+cos(x)-(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)-2)/sin(x)^2)+arctanh((cos(x)^2-3*cos(x)+2)/(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)/sin(x)^2)-2*arctan(cos(x)*(-1+cos(x))/(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)/sin(x)^2))/sin(x)/(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)*4^(1/2)","B"
18,1,72,14,0.641000," ","int(1/(1+csc(x)^2)^(1/2),x)","-\frac{\sin \left(x \right) \sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}\, \arctan \left(\frac{\cos \left(x \right) \left(-1+\cos \left(x \right)\right)}{\sqrt{-\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}\, \sin \left(x \right)^{2}}\right)}{\sqrt{\frac{\cos^{2}\left(x \right)-2}{-1+\cos^{2}\left(x \right)}}\, \left(-1+\cos \left(x \right)\right)}"," ",0,"-sin(x)*(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)*arctan(cos(x)*(-1+cos(x))/(-(cos(x)^2-2)/(cos(x)+1)^2)^(1/2)/sin(x)^2)/((cos(x)^2-2)/(-1+cos(x)^2))^(1/2)/(-1+cos(x))","B"
19,1,91,27,0.590000," ","int((1-csc(x)^2)^(3/2),x)","\frac{\left(4 \left(\cos^{2}\left(x \right)\right) \ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-4 \left(\cos^{2}\left(x \right)\right) \ln \left(\frac{2}{\cos \left(x \right)+1}\right)-\left(\cos^{2}\left(x \right)\right)-4 \ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)+4 \ln \left(\frac{2}{\cos \left(x \right)+1}\right)-1\right) \sin \left(x \right) \sqrt{4}\, \left(\frac{\cos^{2}\left(x \right)}{-1+\cos^{2}\left(x \right)}\right)^{\frac{3}{2}}}{8 \cos \left(x \right)^{3}}"," ",0,"1/8*(4*cos(x)^2*ln(-(-1+cos(x))/sin(x))-4*cos(x)^2*ln(2/(cos(x)+1))-cos(x)^2-4*ln(-(-1+cos(x))/sin(x))+4*ln(2/(cos(x)+1))-1)*sin(x)*4^(1/2)*(cos(x)^2/(-1+cos(x)^2))^(3/2)/cos(x)^3","B"
20,1,46,14,0.539000," ","int((1-csc(x)^2)^(1/2),x)","\frac{\left(\ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-\ln \left(\frac{2}{\cos \left(x \right)+1}\right)\right) \sin \left(x \right) \sqrt{\frac{\cos^{2}\left(x \right)}{-1+\cos^{2}\left(x \right)}}}{\cos \left(x \right)}"," ",0,"(ln(-(-1+cos(x))/sin(x))-ln(2/(cos(x)+1)))*sin(x)*(cos(x)^2/(-1+cos(x)^2))^(1/2)/cos(x)","B"
21,1,67,15,0.688000," ","int(1/(1-csc(x)^2)^(1/2),x)","-\frac{\left(\ln \left(-\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right)+\ln \left(-\frac{-\sin \left(x \right)-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-\ln \left(\frac{2}{\cos \left(x \right)+1}\right)\right) \cos \left(x \right) \sqrt{4}}{2 \sqrt{\frac{\cos^{2}\left(x \right)}{-1+\cos^{2}\left(x \right)}}\, \sin \left(x \right)}"," ",0,"-1/2*(ln(-(-1+cos(x)+sin(x))/sin(x))+ln(-(-sin(x)-1+cos(x))/sin(x))-ln(2/(cos(x)+1)))*cos(x)*4^(1/2)/(cos(x)^2/(-1+cos(x)^2))^(1/2)/sin(x)","B"
22,1,92,24,0.617000," ","int((-1+csc(x)^2)^(3/2),x)","\frac{\left(4 \left(\cos^{2}\left(x \right)\right) \ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-4 \left(\cos^{2}\left(x \right)\right) \ln \left(\frac{2}{\cos \left(x \right)+1}\right)-\left(\cos^{2}\left(x \right)\right)-4 \ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)+4 \ln \left(\frac{2}{\cos \left(x \right)+1}\right)-1\right) \sin \left(x \right) \left(-\frac{\cos^{2}\left(x \right)}{-1+\cos^{2}\left(x \right)}\right)^{\frac{3}{2}} \sqrt{4}}{8 \cos \left(x \right)^{3}}"," ",0,"1/8*(4*cos(x)^2*ln(-(-1+cos(x))/sin(x))-4*cos(x)^2*ln(2/(cos(x)+1))-cos(x)^2-4*ln(-(-1+cos(x))/sin(x))+4*ln(2/(cos(x)+1))-1)*sin(x)*(-cos(x)^2/(-1+cos(x)^2))^(3/2)/cos(x)^3*4^(1/2)","B"
23,1,51,12,0.684000," ","int((-1+csc(x)^2)^(1/2),x)","\frac{\left(\ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-\ln \left(\frac{2}{\cos \left(x \right)+1}\right)\right) \sin \left(x \right) \sqrt{-\frac{\cos^{2}\left(x \right)}{-1+\cos^{2}\left(x \right)}}\, \sqrt{4}}{2 \cos \left(x \right)}"," ",0,"1/2*(ln(-(-1+cos(x))/sin(x))-ln(2/(cos(x)+1)))*sin(x)*(-cos(x)^2/(-1+cos(x)^2))^(1/2)/cos(x)*4^(1/2)","B"
24,1,68,13,0.612000," ","int(1/(-1+csc(x)^2)^(1/2),x)","-\frac{\left(\ln \left(-\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right)+\ln \left(-\frac{-\sin \left(x \right)-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-\ln \left(\frac{2}{\cos \left(x \right)+1}\right)\right) \cos \left(x \right) \sqrt{4}}{2 \sqrt{-\frac{\cos^{2}\left(x \right)}{-1+\cos^{2}\left(x \right)}}\, \sin \left(x \right)}"," ",0,"-1/2*(ln(-(-1+cos(x)+sin(x))/sin(x))+ln(-(-sin(x)-1+cos(x))/sin(x))-ln(2/(cos(x)+1)))*cos(x)/(-cos(x)^2/(-1+cos(x)^2))^(1/2)/sin(x)*4^(1/2)","B"
25,1,268,47,1.076000," ","int((-1-csc(x)^2)^(3/2),x)","\frac{\sqrt{4}\, \left(-\frac{\cos^{2}\left(x \right)-2}{-1+\cos^{2}\left(x \right)}\right)^{\frac{3}{2}} \left(-1+\cos \left(x \right)\right)^{2} \left(\cos \left(x \right) \sqrt{\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}-2 \cos \left(x \right) \arcsin \left(\frac{\left(2+\cos \left(x \right)\right) \sqrt{2}}{2 \cos \left(x \right)+2}\right)+2 \cos \left(x \right) \arctan \left(\frac{\left(-1+\cos \left(x \right)\right) \left(3 \cos \left(x \right) \sqrt{4}-2 \cos \left(x \right)-3 \sqrt{4}-2\right)}{4 \sin \left(x \right)^{2} \sqrt{\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}}\right)-2 \cos \left(x \right) \arctanh \left(\frac{\cos \left(x \right) \sqrt{4}\, \left(-1+\cos \left(x \right)\right)}{2 \sin \left(x \right)^{2} \sqrt{\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}}\right)+2 \arcsin \left(\frac{\left(2+\cos \left(x \right)\right) \sqrt{2}}{2 \cos \left(x \right)+2}\right)-2 \arctan \left(\frac{\left(-1+\cos \left(x \right)\right) \left(3 \cos \left(x \right) \sqrt{4}-2 \cos \left(x \right)-3 \sqrt{4}-2\right)}{4 \sin \left(x \right)^{2} \sqrt{\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}}\right)+2 \arctanh \left(\frac{\cos \left(x \right) \sqrt{4}\, \left(-1+\cos \left(x \right)\right)}{2 \sin \left(x \right)^{2} \sqrt{\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}}\right)\right)}{4 \sin \left(x \right)^{3} \left(\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/4*4^(1/2)*(-(cos(x)^2-2)/(-1+cos(x)^2))^(3/2)*(-1+cos(x))^2*(cos(x)*((cos(x)^2-2)/(cos(x)+1)^2)^(1/2)-2*cos(x)*arcsin(1/2*(2+cos(x))/(cos(x)+1)*2^(1/2))+2*cos(x)*arctan(1/4*(-1+cos(x))*(3*cos(x)*4^(1/2)-2*cos(x)-3*4^(1/2)-2)/sin(x)^2/((cos(x)^2-2)/(cos(x)+1)^2)^(1/2))-2*cos(x)*arctanh(1/2*cos(x)*4^(1/2)*(-1+cos(x))/sin(x)^2/((cos(x)^2-2)/(cos(x)+1)^2)^(1/2))+2*arcsin(1/2*(2+cos(x))/(cos(x)+1)*2^(1/2))-2*arctan(1/4*(-1+cos(x))*(3*cos(x)*4^(1/2)-2*cos(x)-3*4^(1/2)-2)/sin(x)^2/((cos(x)^2-2)/(cos(x)+1)^2)^(1/2))+2*arctanh(1/2*cos(x)*4^(1/2)*(-1+cos(x))/sin(x)^2/((cos(x)^2-2)/(cos(x)+1)^2)^(1/2)))/sin(x)^3/((cos(x)^2-2)/(cos(x)+1)^2)^(3/2)","B"
26,1,139,29,1.053000," ","int((-1-csc(x)^2)^(1/2),x)","\frac{\sqrt{\frac{\cos^{2}\left(x \right)-2}{\sin \left(x \right)^{2}}}\, \left(-1+\cos \left(x \right)\right) \left(\arcsin \left(\frac{\left(2+\cos \left(x \right)\right) \sqrt{2}}{2 \cos \left(x \right)+2}\right)-\arctan \left(\frac{\cos^{2}\left(x \right)-3 \cos \left(x \right)+2}{\sqrt{\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}\, \sin \left(x \right)^{2}}\right)+2 \arctanh \left(\frac{\cos \left(x \right) \sqrt{4}\, \left(-1+\cos \left(x \right)\right)}{2 \sin \left(x \right)^{2} \sqrt{\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}}\right)\right) \sqrt{\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}\, \left(\cos \left(x \right)+1\right)^{2} \sqrt{4}}{4 \left(\cos^{2}\left(x \right)-2\right) \sin \left(x \right)}"," ",0,"1/4*((cos(x)^2-2)/sin(x)^2)^(1/2)*(-1+cos(x))*(arcsin(1/2*(2+cos(x))/(cos(x)+1)*2^(1/2))-arctan((cos(x)^2-3*cos(x)+2)/((cos(x)^2-2)/(cos(x)+1)^2)^(1/2)/sin(x)^2)+2*arctanh(1/2*cos(x)*4^(1/2)*(-1+cos(x))/sin(x)^2/((cos(x)^2-2)/(cos(x)+1)^2)^(1/2)))*((cos(x)^2-2)/(cos(x)+1)^2)^(1/2)*(cos(x)+1)^2*4^(1/2)/(cos(x)^2-2)/sin(x)","B"
27,1,75,16,0.760000," ","int(1/(-1-csc(x)^2)^(1/2),x)","-\frac{\sin \left(x \right) \sqrt{\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(x \right) \sqrt{4}\, \left(-1+\cos \left(x \right)\right)}{2 \sin \left(x \right)^{2} \sqrt{\frac{\cos^{2}\left(x \right)-2}{\left(\cos \left(x \right)+1\right)^{2}}}}\right)}{\sqrt{-\frac{\cos^{2}\left(x \right)-2}{-1+\cos^{2}\left(x \right)}}\, \left(-1+\cos \left(x \right)\right)}"," ",0,"-sin(x)*((cos(x)^2-2)/(cos(x)+1)^2)^(1/2)*arctanh(1/2*cos(x)*4^(1/2)*(-1+cos(x))/sin(x)^2/((cos(x)^2-2)/(cos(x)+1)^2)^(1/2))/(-(cos(x)^2-2)/(-1+cos(x)^2))^(1/2)/(-1+cos(x))","B"