1,1,112,0,0.0667195,"\int \left(a+b \csc ^2(c+d x)\right)^4 \, dx","Int[(a + b*Csc[c + d*x]^2)^4,x]","-\frac{b^2 \left(6 a^2+8 a b+3 b^2\right) \cot ^3(c+d x)}{3 d}-\frac{b (2 a+b) \left(2 a^2+2 a b+b^2\right) \cot (c+d x)}{d}+a^4 x-\frac{b^3 (4 a+3 b) \cot ^5(c+d x)}{5 d}-\frac{b^4 \cot ^7(c+d x)}{7 d}","-\frac{b^2 \left(6 a^2+8 a b+3 b^2\right) \cot ^3(c+d x)}{3 d}-\frac{b (2 a+b) \left(2 a^2+2 a b+b^2\right) \cot (c+d x)}{d}+a^4 x-\frac{b^3 (4 a+3 b) \cot ^5(c+d x)}{5 d}-\frac{b^4 \cot ^7(c+d x)}{7 d}",1,"a^4*x - (b*(2*a + b)*(2*a^2 + 2*a*b + b^2)*Cot[c + d*x])/d - (b^2*(6*a^2 + 8*a*b + 3*b^2)*Cot[c + d*x]^3)/(3*d) - (b^3*(4*a + 3*b)*Cot[c + d*x]^5)/(5*d) - (b^4*Cot[c + d*x]^7)/(7*d)","A",4,3,14,0.2143,1,"{4128, 390, 203}"
2,1,74,0,0.0462957,"\int \left(a+b \csc ^2(c+d x)\right)^3 \, dx","Int[(a + b*Csc[c + d*x]^2)^3,x]","-\frac{b \left(3 a^2+3 a b+b^2\right) \cot (c+d x)}{d}+a^3 x-\frac{b^2 (3 a+2 b) \cot ^3(c+d x)}{3 d}-\frac{b^3 \cot ^5(c+d x)}{5 d}","-\frac{b \left(3 a^2+3 a b+b^2\right) \cot (c+d x)}{d}+a^3 x-\frac{b^2 (3 a+2 b) \cot ^3(c+d x)}{3 d}-\frac{b^3 \cot ^5(c+d x)}{5 d}",1,"a^3*x - (b*(3*a^2 + 3*a*b + b^2)*Cot[c + d*x])/d - (b^2*(3*a + 2*b)*Cot[c + d*x]^3)/(3*d) - (b^3*Cot[c + d*x]^5)/(5*d)","A",4,3,14,0.2143,1,"{4128, 390, 203}"
3,1,41,0,0.0301582,"\int \left(a+b \csc ^2(c+d x)\right)^2 \, dx","Int[(a + b*Csc[c + d*x]^2)^2,x]","a^2 x-\frac{b (2 a+b) \cot (c+d x)}{d}-\frac{b^2 \cot ^3(c+d x)}{3 d}","a^2 x-\frac{b (2 a+b) \cot (c+d x)}{d}-\frac{b^2 \cot ^3(c+d x)}{3 d}",1,"a^2*x - (b*(2*a + b)*Cot[c + d*x])/d - (b^2*Cot[c + d*x]^3)/(3*d)","A",4,3,14,0.2143,1,"{4128, 390, 203}"
4,1,16,0,0.0124905,"\int \left(a+b \csc ^2(c+d x)\right) \, dx","Int[a + b*Csc[c + d*x]^2,x]","a x-\frac{b \cot (c+d x)}{d}","a x-\frac{b \cot (c+d x)}{d}",1,"a*x - (b*Cot[c + d*x])/d","A",3,2,12,0.1667,1,"{3767, 8}"
5,1,46,0,0.0470416,"\int \frac{1}{a+b \csc ^2(c+d x)} \, dx","Int[(a + b*Csc[c + d*x]^2)^(-1),x]","\frac{x}{a}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a+b} \tan (c+d x)}{\sqrt{b}}\right)}{a d \sqrt{a+b}}","\frac{x}{a}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a+b} \tan (c+d x)}{\sqrt{b}}\right)}{a d \sqrt{a+b}}",1,"x/a - (Sqrt[b]*ArcTan[(Sqrt[a + b]*Tan[c + d*x])/Sqrt[b]])/(a*Sqrt[a + b]*d)","A",3,3,14,0.2143,1,"{4127, 3181, 205}"
6,1,92,0,0.1073483,"\int \frac{1}{\left(a+b \csc ^2(c+d x)\right)^2} \, dx","Int[(a + b*Csc[c + d*x]^2)^(-2),x]","\frac{\sqrt{b} (3 a+2 b) \tan ^{-1}\left(\frac{\sqrt{b} \cot (c+d x)}{\sqrt{a+b}}\right)}{2 a^2 d (a+b)^{3/2}}+\frac{x}{a^2}+\frac{b \cot (c+d x)}{2 a d (a+b) \left(a+b \cot ^2(c+d x)+b\right)}","\frac{\sqrt{b} (3 a+2 b) \tan ^{-1}\left(\frac{\sqrt{b} \cot (c+d x)}{\sqrt{a+b}}\right)}{2 a^2 d (a+b)^{3/2}}+\frac{x}{a^2}+\frac{b \cot (c+d x)}{2 a d (a+b) \left(a+b \cot ^2(c+d x)+b\right)}",1,"x/a^2 + (Sqrt[b]*(3*a + 2*b)*ArcTan[(Sqrt[b]*Cot[c + d*x])/Sqrt[a + b]])/(2*a^2*(a + b)^(3/2)*d) + (b*Cot[c + d*x])/(2*a*(a + b)*d*(a + b + b*Cot[c + d*x]^2))","A",5,5,14,0.3571,1,"{4128, 414, 522, 203, 205}"
7,1,144,0,0.1838718,"\int \frac{1}{\left(a+b \csc ^2(c+d x)\right)^3} \, dx","Int[(a + b*Csc[c + d*x]^2)^(-3),x]","\frac{\sqrt{b} \left(15 a^2+20 a b+8 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \cot (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 d (a+b)^{5/2}}+\frac{b (7 a+4 b) \cot (c+d x)}{8 a^2 d (a+b)^2 \left(a+b \cot ^2(c+d x)+b\right)}+\frac{x}{a^3}+\frac{b \cot (c+d x)}{4 a d (a+b) \left(a+b \cot ^2(c+d x)+b\right)^2}","\frac{\sqrt{b} \left(15 a^2+20 a b+8 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \cot (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 d (a+b)^{5/2}}+\frac{b (7 a+4 b) \cot (c+d x)}{8 a^2 d (a+b)^2 \left(a+b \cot ^2(c+d x)+b\right)}+\frac{x}{a^3}+\frac{b \cot (c+d x)}{4 a d (a+b) \left(a+b \cot ^2(c+d x)+b\right)^2}",1,"x/a^3 + (Sqrt[b]*(15*a^2 + 20*a*b + 8*b^2)*ArcTan[(Sqrt[b]*Cot[c + d*x])/Sqrt[a + b]])/(8*a^3*(a + b)^(5/2)*d) + (b*Cot[c + d*x])/(4*a*(a + b)*d*(a + b + b*Cot[c + d*x]^2)^2) + (b*(7*a + 4*b)*Cot[c + d*x])/(8*a^2*(a + b)^2*d*(a + b + b*Cot[c + d*x]^2))","A",6,6,14,0.4286,1,"{4128, 414, 527, 522, 203, 205}"
8,1,204,0,0.32453,"\int \frac{1}{\left(a+b \csc ^2(c+d x)\right)^4} \, dx","Int[(a + b*Csc[c + d*x]^2)^(-4),x]","\frac{b \left(19 a^2+22 a b+8 b^2\right) \cot (c+d x)}{16 a^3 d (a+b)^3 \left(a+b \cot ^2(c+d x)+b\right)}+\frac{\sqrt{b} \left(70 a^2 b+35 a^3+56 a b^2+16 b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \cot (c+d x)}{\sqrt{a+b}}\right)}{16 a^4 d (a+b)^{7/2}}+\frac{b (11 a+6 b) \cot (c+d x)}{24 a^2 d (a+b)^2 \left(a+b \cot ^2(c+d x)+b\right)^2}+\frac{x}{a^4}+\frac{b \cot (c+d x)}{6 a d (a+b) \left(a+b \cot ^2(c+d x)+b\right)^3}","\frac{b \left(19 a^2+22 a b+8 b^2\right) \cot (c+d x)}{16 a^3 d (a+b)^3 \left(a+b \cot ^2(c+d x)+b\right)}+\frac{\sqrt{b} \left(70 a^2 b+35 a^3+56 a b^2+16 b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \cot (c+d x)}{\sqrt{a+b}}\right)}{16 a^4 d (a+b)^{7/2}}+\frac{b (11 a+6 b) \cot (c+d x)}{24 a^2 d (a+b)^2 \left(a+b \cot ^2(c+d x)+b\right)^2}+\frac{x}{a^4}+\frac{b \cot (c+d x)}{6 a d (a+b) \left(a+b \cot ^2(c+d x)+b\right)^3}",1,"x/a^4 + (Sqrt[b]*(35*a^3 + 70*a^2*b + 56*a*b^2 + 16*b^3)*ArcTan[(Sqrt[b]*Cot[c + d*x])/Sqrt[a + b]])/(16*a^4*(a + b)^(7/2)*d) + (b*Cot[c + d*x])/(6*a*(a + b)*d*(a + b + b*Cot[c + d*x]^2)^3) + (b*(11*a + 6*b)*Cot[c + d*x])/(24*a^2*(a + b)^2*d*(a + b + b*Cot[c + d*x]^2)^2) + (b*(19*a^2 + 22*a*b + 8*b^2)*Cot[c + d*x])/(16*a^3*(a + b)^3*d*(a + b + b*Cot[c + d*x]^2))","A",7,6,14,0.4286,1,"{4128, 414, 527, 522, 203, 205}"
9,1,167,0,0.1819479,"\int \left(a+b \csc ^2(c+d x)\right)^{5/2} \, dx","Int[(a + b*Csc[c + d*x]^2)^(5/2),x]","-\frac{\sqrt{b} \left(15 a^2+10 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{8 d}-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{d}-\frac{b \cot (c+d x) \left(a+b \cot ^2(c+d x)+b\right)^{3/2}}{4 d}-\frac{b (7 a+3 b) \cot (c+d x) \sqrt{a+b \cot ^2(c+d x)+b}}{8 d}","-\frac{\sqrt{b} \left(15 a^2+10 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{8 d}-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{d}-\frac{b \cot (c+d x) \left(a+b \cot ^2(c+d x)+b\right)^{3/2}}{4 d}-\frac{b (7 a+3 b) \cot (c+d x) \sqrt{a+b \cot ^2(c+d x)+b}}{8 d}",1,"-((a^(5/2)*ArcTan[(Sqrt[a]*Cot[c + d*x])/Sqrt[a + b + b*Cot[c + d*x]^2]])/d) - (Sqrt[b]*(15*a^2 + 10*a*b + 3*b^2)*ArcTanh[(Sqrt[b]*Cot[c + d*x])/Sqrt[a + b + b*Cot[c + d*x]^2]])/(8*d) - (b*(7*a + 3*b)*Cot[c + d*x]*Sqrt[a + b + b*Cot[c + d*x]^2])/(8*d) - (b*Cot[c + d*x]*(a + b + b*Cot[c + d*x]^2)^(3/2))/(4*d)","A",8,8,16,0.5000,1,"{4128, 416, 528, 523, 217, 206, 377, 203}"
10,1,119,0,0.0963157,"\int \left(a+b \csc ^2(c+d x)\right)^{3/2} \, dx","Int[(a + b*Csc[c + d*x]^2)^(3/2),x]","-\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{d}-\frac{b \cot (c+d x) \sqrt{a+b \cot ^2(c+d x)+b}}{2 d}-\frac{\sqrt{b} (3 a+b) \tanh ^{-1}\left(\frac{\sqrt{b} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{2 d}","-\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{d}-\frac{b \cot (c+d x) \sqrt{a+b \cot ^2(c+d x)+b}}{2 d}-\frac{\sqrt{b} (3 a+b) \tanh ^{-1}\left(\frac{\sqrt{b} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{2 d}",1,"-((a^(3/2)*ArcTan[(Sqrt[a]*Cot[c + d*x])/Sqrt[a + b + b*Cot[c + d*x]^2]])/d) - (Sqrt[b]*(3*a + b)*ArcTanh[(Sqrt[b]*Cot[c + d*x])/Sqrt[a + b + b*Cot[c + d*x]^2]])/(2*d) - (b*Cot[c + d*x]*Sqrt[a + b + b*Cot[c + d*x]^2])/(2*d)","A",7,7,16,0.4375,1,"{4128, 416, 523, 217, 206, 377, 203}"
11,1,81,0,0.0496097,"\int \sqrt{a+b \csc ^2(c+d x)} \, dx","Int[Sqrt[a + b*Csc[c + d*x]^2],x]","-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{d}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{d}","-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{d}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{d}",1,"-((Sqrt[a]*ArcTan[(Sqrt[a]*Cot[c + d*x])/Sqrt[a + b + b*Cot[c + d*x]^2]])/d) - (Sqrt[b]*ArcTanh[(Sqrt[b]*Cot[c + d*x])/Sqrt[a + b + b*Cot[c + d*x]^2]])/d","A",6,6,16,0.3750,1,"{4128, 402, 217, 206, 377, 203}"
12,1,40,0,0.0360174,"\int \frac{1}{\sqrt{a+b \csc ^2(c+d x)}} \, dx","Int[1/Sqrt[a + b*Csc[c + d*x]^2],x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{\sqrt{a} d}","-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \csc ^2(c+d x)}}\right)}{\sqrt{a} d}",1,"-(ArcTan[(Sqrt[a]*Cot[c + d*x])/Sqrt[a + b + b*Cot[c + d*x]^2]]/(Sqrt[a]*d))","A",3,3,16,0.1875,1,"{4128, 377, 203}"
13,1,77,0,0.0494553,"\int \frac{1}{\left(a+b \csc ^2(c+d x)\right)^{3/2}} \, dx","Int[(a + b*Csc[c + d*x]^2)^(-3/2),x]","\frac{b \cot (c+d x)}{a d (a+b) \sqrt{a+b \cot ^2(c+d x)+b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{a^{3/2} d}","\frac{b \cot (c+d x)}{a d (a+b) \sqrt{a+b \cot ^2(c+d x)+b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{a^{3/2} d}",1,"-(ArcTan[(Sqrt[a]*Cot[c + d*x])/Sqrt[a + b + b*Cot[c + d*x]^2]]/(a^(3/2)*d)) + (b*Cot[c + d*x])/(a*(a + b)*d*Sqrt[a + b + b*Cot[c + d*x]^2])","A",4,4,16,0.2500,1,"{4128, 382, 377, 203}"
14,1,126,0,0.1002156,"\int \frac{1}{\left(a+b \csc ^2(c+d x)\right)^{5/2}} \, dx","Int[(a + b*Csc[c + d*x]^2)^(-5/2),x]","\frac{b (5 a+3 b) \cot (c+d x)}{3 a^2 d (a+b)^2 \sqrt{a+b \cot ^2(c+d x)+b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{a^{5/2} d}+\frac{b \cot (c+d x)}{3 a d (a+b) \left(a+b \cot ^2(c+d x)+b\right)^{3/2}}","\frac{b (5 a+3 b) \cot (c+d x)}{3 a^2 d (a+b)^2 \sqrt{a+b \cot ^2(c+d x)+b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{a^{5/2} d}+\frac{b \cot (c+d x)}{3 a d (a+b) \left(a+b \cot ^2(c+d x)+b\right)^{3/2}}",1,"-(ArcTan[(Sqrt[a]*Cot[c + d*x])/Sqrt[a + b + b*Cot[c + d*x]^2]]/(a^(5/2)*d)) + (b*Cot[c + d*x])/(3*a*(a + b)*d*(a + b + b*Cot[c + d*x]^2)^(3/2)) + (b*(5*a + 3*b)*Cot[c + d*x])/(3*a^2*(a + b)^2*d*Sqrt[a + b + b*Cot[c + d*x]^2])","A",6,6,16,0.3750,1,"{4128, 414, 527, 12, 377, 203}"
15,1,180,0,0.1756577,"\int \frac{1}{\left(a+b \csc ^2(c+d x)\right)^{7/2}} \, dx","Int[(a + b*Csc[c + d*x]^2)^(-7/2),x]","\frac{b \left(33 a^2+40 a b+15 b^2\right) \cot (c+d x)}{15 a^3 d (a+b)^3 \sqrt{a+b \cot ^2(c+d x)+b}}+\frac{b (9 a+5 b) \cot (c+d x)}{15 a^2 d (a+b)^2 \left(a+b \cot ^2(c+d x)+b\right)^{3/2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{a^{7/2} d}+\frac{b \cot (c+d x)}{5 a d (a+b) \left(a+b \cot ^2(c+d x)+b\right)^{5/2}}","\frac{b \left(33 a^2+40 a b+15 b^2\right) \cot (c+d x)}{15 a^3 d (a+b)^3 \sqrt{a+b \cot ^2(c+d x)+b}}+\frac{b (9 a+5 b) \cot (c+d x)}{15 a^2 d (a+b)^2 \left(a+b \cot ^2(c+d x)+b\right)^{3/2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \cot (c+d x)}{\sqrt{a+b \cot ^2(c+d x)+b}}\right)}{a^{7/2} d}+\frac{b \cot (c+d x)}{5 a d (a+b) \left(a+b \cot ^2(c+d x)+b\right)^{5/2}}",1,"-(ArcTan[(Sqrt[a]*Cot[c + d*x])/Sqrt[a + b + b*Cot[c + d*x]^2]]/(a^(7/2)*d)) + (b*Cot[c + d*x])/(5*a*(a + b)*d*(a + b + b*Cot[c + d*x]^2)^(5/2)) + (b*(9*a + 5*b)*Cot[c + d*x])/(15*a^2*(a + b)^2*d*(a + b + b*Cot[c + d*x]^2)^(3/2)) + (b*(33*a^2 + 40*a*b + 15*b^2)*Cot[c + d*x])/(15*a^3*(a + b)^3*d*Sqrt[a + b + b*Cot[c + d*x]^2])","A",7,6,16,0.3750,1,"{4128, 414, 527, 12, 377, 203}"
16,1,44,0,0.0394003,"\int \left(1+\csc ^2(x)\right)^{3/2} \, dx","Int[(1 + Csc[x]^2)^(3/2),x]","-\frac{1}{2} \cot (x) \sqrt{\cot ^2(x)+2}-\tan ^{-1}\left(\frac{\cot (x)}{\sqrt{\cot ^2(x)+2}}\right)-2 \sinh ^{-1}\left(\frac{\cot (x)}{\sqrt{2}}\right)","-\frac{1}{2} \cot (x) \sqrt{\cot ^2(x)+2}-\tan ^{-1}\left(\frac{\cot (x)}{\sqrt{\cot ^2(x)+2}}\right)-2 \sinh ^{-1}\left(\frac{\cot (x)}{\sqrt{2}}\right)",1,"-2*ArcSinh[Cot[x]/Sqrt[2]] - ArcTan[Cot[x]/Sqrt[2 + Cot[x]^2]] - (Cot[x]*Sqrt[2 + Cot[x]^2])/2","A",6,6,10,0.6000,1,"{4128, 416, 523, 215, 377, 203}"
17,1,28,0,0.0211046,"\int \sqrt{1+\csc ^2(x)} \, dx","Int[Sqrt[1 + Csc[x]^2],x]","-\tan ^{-1}\left(\frac{\cot (x)}{\sqrt{\cot ^2(x)+2}}\right)-\sinh ^{-1}\left(\frac{\cot (x)}{\sqrt{2}}\right)","-\tan ^{-1}\left(\frac{\cot (x)}{\sqrt{\cot ^2(x)+2}}\right)-\sinh ^{-1}\left(\frac{\cot (x)}{\sqrt{2}}\right)",1,"-ArcSinh[Cot[x]/Sqrt[2]] - ArcTan[Cot[x]/Sqrt[2 + Cot[x]^2]]","A",5,5,10,0.5000,1,"{4128, 402, 215, 377, 203}"
18,1,16,0,0.0169859,"\int \frac{1}{\sqrt{1+\csc ^2(x)}} \, dx","Int[1/Sqrt[1 + Csc[x]^2],x]","-\tan ^{-1}\left(\frac{\cot (x)}{\sqrt{\cot ^2(x)+2}}\right)","-\tan ^{-1}\left(\frac{\cot (x)}{\sqrt{\cot ^2(x)+2}}\right)",1,"-ArcTan[Cot[x]/Sqrt[2 + Cot[x]^2]]","A",3,3,10,0.3000,1,"{4128, 377, 203}"
19,1,33,0,0.0272457,"\int \left(1-\csc ^2(x)\right)^{3/2} \, dx","Int[(1 - Csc[x]^2)^(3/2),x]","\frac{1}{2} \sqrt{-\cot ^2(x)} \cot (x)+\tan (x) \sqrt{-\cot ^2(x)} \log (\sin (x))","\frac{1}{2} \sqrt{-\cot ^2(x)} \cot (x)+\tan (x) \sqrt{-\cot ^2(x)} \log (\sin (x))",1,"(Cot[x]*Sqrt[-Cot[x]^2])/2 + Sqrt[-Cot[x]^2]*Log[Sin[x]]*Tan[x]","A",4,4,12,0.3333,1,"{4121, 3658, 3473, 3475}"
20,1,16,0,0.0276965,"\int \sqrt{1-\csc ^2(x)} \, dx","Int[Sqrt[1 - Csc[x]^2],x]","\tan (x) \sqrt{-\cot ^2(x)} \log (\sin (x))","\tan (x) \sqrt{-\cot ^2(x)} \log (\sin (x))",1,"Sqrt[-Cot[x]^2]*Log[Sin[x]]*Tan[x]","A",3,3,12,0.2500,1,"{4121, 3658, 3475}"
21,1,17,0,0.0243337,"\int \frac{1}{\sqrt{1-\csc ^2(x)}} \, dx","Int[1/Sqrt[1 - Csc[x]^2],x]","-\frac{\cot (x) \log (\cos (x))}{\sqrt{-\cot ^2(x)}}","-\frac{\cot (x) \log (\cos (x))}{\sqrt{-\cot ^2(x)}}",1,"-((Cot[x]*Log[Cos[x]])/Sqrt[-Cot[x]^2])","A",3,3,12,0.2500,1,"{4121, 3658, 3475}"
22,1,30,0,0.0218156,"\int \left(-1+\csc ^2(x)\right)^{3/2} \, dx","Int[(-1 + Csc[x]^2)^(3/2),x]","-\frac{1}{2} \tan (x) \cot ^2(x)^{3/2}-\tan (x) \sqrt{\cot ^2(x)} \log (\sin (x))","-\frac{1}{2} \tan (x) \cot ^2(x)^{3/2}-\tan (x) \sqrt{\cot ^2(x)} \log (\sin (x))",1,"-((Cot[x]^2)^(3/2)*Tan[x])/2 - Sqrt[Cot[x]^2]*Log[Sin[x]]*Tan[x]","A",4,4,10,0.4000,1,"{4121, 3658, 3473, 3475}"
23,1,14,0,0.0236293,"\int \sqrt{-1+\csc ^2(x)} \, dx","Int[Sqrt[-1 + Csc[x]^2],x]","\tan (x) \sqrt{\cot ^2(x)} \log (\sin (x))","\tan (x) \sqrt{\cot ^2(x)} \log (\sin (x))",1,"Sqrt[Cot[x]^2]*Log[Sin[x]]*Tan[x]","A",3,3,10,0.3000,1,"{4121, 3658, 3475}"
24,1,15,0,0.0185607,"\int \frac{1}{\sqrt{-1+\csc ^2(x)}} \, dx","Int[1/Sqrt[-1 + Csc[x]^2],x]","-\frac{\cot (x) \log (\cos (x))}{\sqrt{\cot ^2(x)}}","-\frac{\cot (x) \log (\cos (x))}{\sqrt{\cot ^2(x)}}",1,"-((Cot[x]*Log[Cos[x]])/Sqrt[Cot[x]^2])","A",3,3,10,0.3000,1,"{4121, 3658, 3475}"
25,1,55,0,0.045857,"\int \left(-1-\csc ^2(x)\right)^{3/2} \, dx","Int[(-1 - Csc[x]^2)^(3/2),x]","\frac{1}{2} \cot (x) \sqrt{-\cot ^2(x)-2}-2 \tan ^{-1}\left(\frac{\cot (x)}{\sqrt{-\cot ^2(x)-2}}\right)-\tanh ^{-1}\left(\frac{\cot (x)}{\sqrt{-\cot ^2(x)-2}}\right)","\frac{1}{2} \cot (x) \sqrt{-\cot ^2(x)-2}-2 \tan ^{-1}\left(\frac{\cot (x)}{\sqrt{-\cot ^2(x)-2}}\right)-\tanh ^{-1}\left(\frac{\cot (x)}{\sqrt{-\cot ^2(x)-2}}\right)",1,"-2*ArcTan[Cot[x]/Sqrt[-2 - Cot[x]^2]] - ArcTanh[Cot[x]/Sqrt[-2 - Cot[x]^2]] + (Cot[x]*Sqrt[-2 - Cot[x]^2])/2","A",7,7,12,0.5833,1,"{4128, 416, 523, 217, 203, 377, 206}"
26,1,33,0,0.0248605,"\int \sqrt{-1-\csc ^2(x)} \, dx","Int[Sqrt[-1 - Csc[x]^2],x]","\tan ^{-1}\left(\frac{\cot (x)}{\sqrt{-\cot ^2(x)-2}}\right)+\tanh ^{-1}\left(\frac{\cot (x)}{\sqrt{-\cot ^2(x)-2}}\right)","\tan ^{-1}\left(\frac{\cot (x)}{\sqrt{-\cot ^2(x)-2}}\right)+\tanh ^{-1}\left(\frac{\cot (x)}{\sqrt{-\cot ^2(x)-2}}\right)",1,"ArcTan[Cot[x]/Sqrt[-2 - Cot[x]^2]] + ArcTanh[Cot[x]/Sqrt[-2 - Cot[x]^2]]","A",6,6,12,0.5000,1,"{4128, 402, 217, 203, 377, 206}"
27,1,18,0,0.0197279,"\int \frac{1}{\sqrt{-1-\csc ^2(x)}} \, dx","Int[1/Sqrt[-1 - Csc[x]^2],x]","-\tanh ^{-1}\left(\frac{\cot (x)}{\sqrt{-\cot ^2(x)-2}}\right)","-\tanh ^{-1}\left(\frac{\cot (x)}{\sqrt{-\cot ^2(x)-2}}\right)",1,"-ArcTanh[Cot[x]/Sqrt[-2 - Cot[x]^2]]","A",3,3,12,0.2500,1,"{4128, 377, 206}"