1,1,141,0,0.332038," ","integrate((a+b*csc(d*x+c)^2)^4,x, algorithm=""maxima"")","a^{4} x - \frac{4 \, a^{3} b}{d \tan\left(d x + c\right)} - \frac{2 \, {\left(3 \, \tan\left(d x + c\right)^{2} + 1\right)} a^{2} b^{2}}{d \tan\left(d x + c\right)^{3}} - \frac{4 \, {\left(15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} + 3\right)} a b^{3}}{15 \, d \tan\left(d x + c\right)^{5}} - \frac{{\left(35 \, \tan\left(d x + c\right)^{6} + 35 \, \tan\left(d x + c\right)^{4} + 21 \, \tan\left(d x + c\right)^{2} + 5\right)} b^{4}}{35 \, d \tan\left(d x + c\right)^{7}}"," ",0,"a^4*x - 4*a^3*b/(d*tan(d*x + c)) - 2*(3*tan(d*x + c)^2 + 1)*a^2*b^2/(d*tan(d*x + c)^3) - 4/15*(15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 + 3)*a*b^3/(d*tan(d*x + c)^5) - 1/35*(35*tan(d*x + c)^6 + 35*tan(d*x + c)^4 + 21*tan(d*x + c)^2 + 5)*b^4/(d*tan(d*x + c)^7)","A",0
2,1,90,0,0.322877," ","integrate((a+b*csc(d*x+c)^2)^3,x, algorithm=""maxima"")","a^{3} x - \frac{3 \, a^{2} b}{d \tan\left(d x + c\right)} - \frac{{\left(3 \, \tan\left(d x + c\right)^{2} + 1\right)} a b^{2}}{d \tan\left(d x + c\right)^{3}} - \frac{{\left(15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} + 3\right)} b^{3}}{15 \, d \tan\left(d x + c\right)^{5}}"," ",0,"a^3*x - 3*a^2*b/(d*tan(d*x + c)) - (3*tan(d*x + c)^2 + 1)*a*b^2/(d*tan(d*x + c)^3) - 1/15*(15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 + 3)*b^3/(d*tan(d*x + c)^5)","A",0
3,1,49,0,0.332695," ","integrate((a+b*csc(d*x+c)^2)^2,x, algorithm=""maxima"")","a^{2} x - \frac{2 \, a b}{d \tan\left(d x + c\right)} - \frac{{\left(3 \, \tan\left(d x + c\right)^{2} + 1\right)} b^{2}}{3 \, d \tan\left(d x + c\right)^{3}}"," ",0,"a^2*x - 2*a*b/(d*tan(d*x + c)) - 1/3*(3*tan(d*x + c)^2 + 1)*b^2/(d*tan(d*x + c)^3)","A",0
4,1,18,0,0.321689," ","integrate(a+b*csc(d*x+c)^2,x, algorithm=""maxima"")","a x - \frac{b}{d \tan\left(d x + c\right)}"," ",0,"a*x - b/(d*tan(d*x + c))","A",0
5,1,46,0,0.458748," ","integrate(1/(a+b*csc(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{b \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a} - \frac{d x + c}{a}}{d}"," ",0,"-(b*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a) - (d*x + c)/a)/d","A",0
6,1,109,0,0.434281," ","integrate(1/(a+b*csc(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{b \tan\left(d x + c\right)}{a^{2} b + a b^{2} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \tan\left(d x + c\right)^{2}} - \frac{{\left(3 \, a b + 2 \, b^{2}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{3} + a^{2} b\right)} \sqrt{{\left(a + b\right)} b}} + \frac{2 \, {\left(d x + c\right)}}{a^{2}}}{2 \, d}"," ",0,"1/2*(b*tan(d*x + c)/(a^2*b + a*b^2 + (a^3 + 2*a^2*b + a*b^2)*tan(d*x + c)^2) - (3*a*b + 2*b^2)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*b))/((a^3 + a^2*b)*sqrt((a + b)*b)) + 2*(d*x + c)/a^2)/d","A",0
7,1,234,0,0.428950," ","integrate(1/(a+b*csc(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{{\left(a + b\right)} b}} - \frac{{\left(9 \, a^{2} b + 13 \, a b^{2} + 4 \, b^{3}\right)} \tan\left(d x + c\right)^{3} + {\left(7 \, a b^{2} + 4 \, b^{3}\right)} \tan\left(d x + c\right)}{a^{4} b^{2} + 2 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} \tan\left(d x + c\right)^{2}} - \frac{8 \, {\left(d x + c\right)}}{a^{3}}}{8 \, d}"," ",0,"-1/8*((15*a^2*b + 20*a*b^2 + 8*b^3)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*b))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt((a + b)*b)) - ((9*a^2*b + 13*a*b^2 + 4*b^3)*tan(d*x + c)^3 + (7*a*b^2 + 4*b^3)*tan(d*x + c))/(a^4*b^2 + 2*a^3*b^3 + a^2*b^4 + (a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*tan(d*x + c)^4 + 2*(a^5*b + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*tan(d*x + c)^2) - 8*(d*x + c)/a^3)/d","A",0
8,1,404,0,0.466879," ","integrate(1/(a+b*csc(d*x+c)^2)^4,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(35 \, a^{3} b + 70 \, a^{2} b^{2} + 56 \, a b^{3} + 16 \, b^{4}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} \sqrt{{\left(a + b\right)} b}} - \frac{3 \, {\left(29 \, a^{4} b + 84 \, a^{3} b^{2} + 89 \, a^{2} b^{3} + 42 \, a b^{4} + 8 \, b^{5}\right)} \tan\left(d x + c\right)^{5} + 8 \, {\left(17 \, a^{3} b^{2} + 35 \, a^{2} b^{3} + 24 \, a b^{4} + 6 \, b^{5}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(19 \, a^{2} b^{3} + 22 \, a b^{4} + 8 \, b^{5}\right)} \tan\left(d x + c\right)}{a^{6} b^{3} + 3 \, a^{5} b^{4} + 3 \, a^{4} b^{5} + a^{3} b^{6} + {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} \tan\left(d x + c\right)^{6} + 3 \, {\left(a^{8} b + 5 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 10 \, a^{5} b^{4} + 5 \, a^{4} b^{5} + a^{3} b^{6}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(a^{7} b^{2} + 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} + 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} \tan\left(d x + c\right)^{2}} - \frac{48 \, {\left(d x + c\right)}}{a^{4}}}{48 \, d}"," ",0,"-1/48*(3*(35*a^3*b + 70*a^2*b^2 + 56*a*b^3 + 16*b^4)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*b))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*sqrt((a + b)*b)) - (3*(29*a^4*b + 84*a^3*b^2 + 89*a^2*b^3 + 42*a*b^4 + 8*b^5)*tan(d*x + c)^5 + 8*(17*a^3*b^2 + 35*a^2*b^3 + 24*a*b^4 + 6*b^5)*tan(d*x + c)^3 + 3*(19*a^2*b^3 + 22*a*b^4 + 8*b^5)*tan(d*x + c))/(a^6*b^3 + 3*a^5*b^4 + 3*a^4*b^5 + a^3*b^6 + (a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*tan(d*x + c)^6 + 3*(a^8*b + 5*a^7*b^2 + 10*a^6*b^3 + 10*a^5*b^4 + 5*a^4*b^5 + a^3*b^6)*tan(d*x + c)^4 + 3*(a^7*b^2 + 4*a^6*b^3 + 6*a^5*b^4 + 4*a^4*b^5 + a^3*b^6)*tan(d*x + c)^2) - 48*(d*x + c)/a^4)/d","B",0
9,0,0,0,0.000000," ","integrate((a+b*csc(d*x+c)^2)^(5/2),x, algorithm=""maxima"")","\int {\left(b \csc\left(d x + c\right)^{2} + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*csc(d*x + c)^2 + a)^(5/2), x)","F",0
10,0,0,0,0.000000," ","integrate((a+b*csc(d*x+c)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \csc\left(d x + c\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*csc(d*x + c)^2 + a)^(3/2), x)","F",0
11,-2,0,0,0.000000," ","integrate((a+b*csc(d*x+c)^2)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found %i","F(-2)",0
12,1,987,0,0.658255," ","integrate(1/(a+b*csc(d*x+c)^2)^(1/2),x, algorithm=""maxima"")","\frac{\arctan\left(2 \, a \sin\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + 2 \, {\left(a^{2} - 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right), 2 \, a \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + 2 \, {\left(a^{2} - 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right) - 2 \, a - 4 \, b\right) + \arctan\left(2 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + 2 \, {\left(a^{2} - 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right), 2 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + 2 \, {\left(a^{2} - 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right) - 4 \, b\right)}{2 \, \sqrt{a} d}"," ",0,"1/2*(arctan2(2*a*sin(2*d*x + 2*c) + 2*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*d*x + 2*c)^2 - 4*(a^2 + 2*a*b)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*d*x + 2*c)^2 + a^2 + 2*(a^2 - 2*(a^2 + 2*a*b)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(a^2 + 2*a*b)*cos(2*d*x + 2*c))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a)), 2*a*cos(2*d*x + 2*c) + 2*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*d*x + 2*c)^2 - 4*(a^2 + 2*a*b)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*d*x + 2*c)^2 + a^2 + 2*(a^2 - 2*(a^2 + 2*a*b)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(a^2 + 2*a*b)*cos(2*d*x + 2*c))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a)) - 2*a - 4*b) + arctan2(2*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*d*x + 2*c)^2 - 4*(a^2 + 2*a*b)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*d*x + 2*c)^2 + a^2 + 2*(a^2 - 2*(a^2 + 2*a*b)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(a^2 + 2*a*b)*cos(2*d*x + 2*c))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a)), 2*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*d*x + 2*c)^2 - 4*(a^2 + 2*a*b)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*d*x + 2*c)^2 + a^2 + 2*(a^2 - 2*(a^2 + 2*a*b)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(a^2 + 2*a*b)*cos(2*d*x + 2*c))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a)) - 4*b))/(sqrt(a)*d)","B",0
13,1,2050,0,0.890152," ","integrate(1/(a+b*csc(d*x+c)^2)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, a b \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} + a b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right)^{3} - 2 \, {\left(a b \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} + a b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right)^{2} + a^{2} + 2 \, a b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right) - {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + 2 \, {\left(a^{2} - 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} {\left({\left({\left(a + b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right)^{2} + {\left(a + b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right)^{2}\right)} \arctan\left(2 \, a \sin\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + 2 \, {\left(a^{2} - 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right), 2 \, a \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + 2 \, {\left(a^{2} - 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right) - 2 \, a - 4 \, b\right) + {\left({\left(a + b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right)^{2} + {\left(a + b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right)^{2}\right)} \arctan\left(2 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + 2 \, {\left(a^{2} - 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right), 2 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + 2 \, {\left(a^{2} - 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right) - 4 \, b\right)\right)} \sqrt{a}}{2 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + 2 \, {\left(a^{2} - 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} {\left({\left(a^{3} + a^{2} b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right)^{2} + {\left(a^{3} + a^{2} b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, d x + 2 \, c\right), a \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a\right)\right)^{2}\right)} d}"," ",0,"-1/2*(2*a*b*cos(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a))*sin(2*d*x + 2*c) + 2*(a^2 + a*b)*sin(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a))^3 - 2*(a*b*cos(2*d*x + 2*c) - (a^2 + a*b)*cos(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a))^2 + a^2 + 2*a*b)*sin(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a)) - (a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*d*x + 2*c)^2 - 4*(a^2 + 2*a*b)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*d*x + 2*c)^2 + a^2 + 2*(a^2 - 2*(a^2 + 2*a*b)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(a^2 + 2*a*b)*cos(2*d*x + 2*c))^(1/4)*(((a + b)*cos(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a))^2 + (a + b)*sin(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a))^2)*arctan2(2*a*sin(2*d*x + 2*c) + 2*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*d*x + 2*c)^2 - 4*(a^2 + 2*a*b)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*d*x + 2*c)^2 + a^2 + 2*(a^2 - 2*(a^2 + 2*a*b)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(a^2 + 2*a*b)*cos(2*d*x + 2*c))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a)), 2*a*cos(2*d*x + 2*c) + 2*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*d*x + 2*c)^2 - 4*(a^2 + 2*a*b)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*d*x + 2*c)^2 + a^2 + 2*(a^2 - 2*(a^2 + 2*a*b)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(a^2 + 2*a*b)*cos(2*d*x + 2*c))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a)) - 2*a - 4*b) + ((a + b)*cos(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a))^2 + (a + b)*sin(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a))^2)*arctan2(2*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*d*x + 2*c)^2 - 4*(a^2 + 2*a*b)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*d*x + 2*c)^2 + a^2 + 2*(a^2 - 2*(a^2 + 2*a*b)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(a^2 + 2*a*b)*cos(2*d*x + 2*c))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a)), 2*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*d*x + 2*c)^2 - 4*(a^2 + 2*a*b)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*d*x + 2*c)^2 + a^2 + 2*(a^2 - 2*(a^2 + 2*a*b)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(a^2 + 2*a*b)*cos(2*d*x + 2*c))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a)) - 4*b))*sqrt(a))/((a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*d*x + 2*c)^2 - 4*(a^2 + 2*a*b)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*d*x + 2*c)^2 + a^2 + 2*(a^2 - 2*(a^2 + 2*a*b)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(a^2 + 2*a*b)*cos(2*d*x + 2*c))^(1/4)*((a^3 + a^2*b)*cos(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a))^2 + (a^3 + a^2*b)*sin(1/2*arctan2(a*sin(4*d*x + 4*c) - 2*(a + 2*b)*sin(2*d*x + 2*c), a*cos(4*d*x + 4*c) - 2*(a + 2*b)*cos(2*d*x + 2*c) + a))^2)*d)","B",0
14,-1,0,0,0.000000," ","integrate(1/(a+b*csc(d*x+c)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,-1,0,0,0.000000," ","integrate(1/(a+b*csc(d*x+c)^2)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,0,0,0,0.000000," ","integrate((1+csc(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(\csc\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((csc(x)^2 + 1)^(3/2), x)","F",0
17,0,0,0,0.000000," ","integrate((1+csc(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\csc\left(x\right)^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(csc(x)^2 + 1), x)","F",0
18,1,388,0,0.558272," ","integrate(1/(1+csc(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \arctan\left(2 \, {\left(-2 \, {\left(6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 36 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} - 12 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 36 \, \sin\left(2 \, x\right)^{2} - 12 \, \cos\left(2 \, x\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right) - 6 \, \sin\left(2 \, x\right), \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)\right), 2 \, {\left(-2 \, {\left(6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 36 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} - 12 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 36 \, \sin\left(2 \, x\right)^{2} - 12 \, \cos\left(2 \, x\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right) - 6 \, \sin\left(2 \, x\right), \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)\right) - 4\right) + \frac{1}{2} \, \arctan\left(2 \, {\left(-2 \, {\left(6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 36 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} - 12 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 36 \, \sin\left(2 \, x\right)^{2} - 12 \, \cos\left(2 \, x\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right) - 6 \, \sin\left(2 \, x\right), \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)\right) + 2 \, \sin\left(2 \, x\right), 2 \, {\left(-2 \, {\left(6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 36 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} - 12 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 36 \, \sin\left(2 \, x\right)^{2} - 12 \, \cos\left(2 \, x\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right) - 6 \, \sin\left(2 \, x\right), \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)\right) + 2 \, \cos\left(2 \, x\right) - 6\right)"," ",0,"1/2*arctan2(2*(-2*(6*cos(2*x) - 1)*cos(4*x) + cos(4*x)^2 + 36*cos(2*x)^2 + sin(4*x)^2 - 12*sin(4*x)*sin(2*x) + 36*sin(2*x)^2 - 12*cos(2*x) + 1)^(1/4)*sin(1/2*arctan2(sin(4*x) - 6*sin(2*x), cos(4*x) - 6*cos(2*x) + 1)), 2*(-2*(6*cos(2*x) - 1)*cos(4*x) + cos(4*x)^2 + 36*cos(2*x)^2 + sin(4*x)^2 - 12*sin(4*x)*sin(2*x) + 36*sin(2*x)^2 - 12*cos(2*x) + 1)^(1/4)*cos(1/2*arctan2(sin(4*x) - 6*sin(2*x), cos(4*x) - 6*cos(2*x) + 1)) - 4) + 1/2*arctan2(2*(-2*(6*cos(2*x) - 1)*cos(4*x) + cos(4*x)^2 + 36*cos(2*x)^2 + sin(4*x)^2 - 12*sin(4*x)*sin(2*x) + 36*sin(2*x)^2 - 12*cos(2*x) + 1)^(1/4)*sin(1/2*arctan2(sin(4*x) - 6*sin(2*x), cos(4*x) - 6*cos(2*x) + 1)) + 2*sin(2*x), 2*(-2*(6*cos(2*x) - 1)*cos(4*x) + cos(4*x)^2 + 36*cos(2*x)^2 + sin(4*x)^2 - 12*sin(4*x)*sin(2*x) + 36*sin(2*x)^2 - 12*cos(2*x) + 1)^(1/4)*cos(1/2*arctan2(sin(4*x) - 6*sin(2*x), cos(4*x) - 6*cos(2*x) + 1)) + 2*cos(2*x) - 6)","B",0
19,1,21,0,0.420456," ","integrate((1-csc(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{i}{2 \, \tan\left(x\right)^{2}} - \frac{1}{2} i \, \log\left(\tan\left(x\right)^{2} + 1\right) + i \, \log\left(\tan\left(x\right)\right)"," ",0,"1/2*I/tan(x)^2 - 1/2*I*log(tan(x)^2 + 1) + I*log(tan(x))","C",0
20,1,15,0,0.414435," ","integrate((1-csc(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} i \, \log\left(\tan\left(x\right)^{2} + 1\right) + i \, \log\left(\tan\left(x\right)\right)"," ",0,"-1/2*I*log(tan(x)^2 + 1) + I*log(tan(x))","C",0
21,1,9,0,0.414108," ","integrate(1/(1-csc(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} i \, \log\left(\tan\left(x\right)^{2} + 1\right)"," ",0,"-1/2*I*log(tan(x)^2 + 1)","C",0
22,1,21,0,0.412081," ","integrate((-1+csc(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2 \, \tan\left(x\right)^{2}} + \frac{1}{2} \, \log\left(\tan\left(x\right)^{2} + 1\right) - \log\left(\tan\left(x\right)\right)"," ",0,"-1/2/tan(x)^2 + 1/2*log(tan(x)^2 + 1) - log(tan(x))","A",0
23,1,13,0,0.414112," ","integrate((-1+csc(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \log\left(\tan\left(x\right)^{2} + 1\right) + \log\left(\tan\left(x\right)\right)"," ",0,"-1/2*log(tan(x)^2 + 1) + log(tan(x))","A",0
24,1,9,0,0.425579," ","integrate(1/(-1+csc(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(\tan\left(x\right)^{2} + 1\right)"," ",0,"1/2*log(tan(x)^2 + 1)","A",0
25,0,0,0,0.000000," ","integrate((-1-csc(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(-\csc\left(x\right)^{2} - 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-csc(x)^2 - 1)^(3/2), x)","F",0
26,0,0,0,0.000000," ","integrate((-1-csc(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-\csc\left(x\right)^{2} - 1}\,{d x}"," ",0,"integrate(sqrt(-csc(x)^2 - 1), x)","F",0
27,0,0,0,0.000000," ","integrate(1/(-1-csc(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\csc\left(x\right)^{2} - 1}}\,{d x}"," ",0,"integrate(1/sqrt(-csc(x)^2 - 1), x)","F",0
