1,1,12,0,0.004157,"\int \tan (c+d x) \, dx","Int[Tan[c + d*x],x]","-\frac{\log (\cos (c+d x))}{d}","-\frac{\log (\cos (c+d x))}{d}",1,"-(Log[Cos[c + d*x]]/d)","A",1,1,6,0.1667,1,"{3475}"
2,1,14,0,0.0076875,"\int \tan ^2(c+d x) \, dx","Int[Tan[c + d*x]^2,x]","\frac{\tan (c+d x)}{d}-x","\frac{\tan (c+d x)}{d}-x",1,"-x + Tan[c + d*x]/d","A",2,2,8,0.2500,1,"{3473, 8}"
3,1,27,0,0.0114313,"\int \tan ^3(c+d x) \, dx","Int[Tan[c + d*x]^3,x]","\frac{\tan ^2(c+d x)}{2 d}+\frac{\log (\cos (c+d x))}{d}","\frac{\tan ^2(c+d x)}{2 d}+\frac{\log (\cos (c+d x))}{d}",1,"Log[Cos[c + d*x]]/d + Tan[c + d*x]^2/(2*d)","A",2,2,8,0.2500,1,"{3473, 3475}"
4,1,28,0,0.015247,"\int \tan ^4(c+d x) \, dx","Int[Tan[c + d*x]^4,x]","\frac{\tan ^3(c+d x)}{3 d}-\frac{\tan (c+d x)}{d}+x","\frac{\tan ^3(c+d x)}{3 d}-\frac{\tan (c+d x)}{d}+x",1,"x - Tan[c + d*x]/d + Tan[c + d*x]^3/(3*d)","A",3,2,8,0.2500,1,"{3473, 8}"
5,1,43,0,0.0197208,"\int \tan ^5(c+d x) \, dx","Int[Tan[c + d*x]^5,x]","\frac{\tan ^4(c+d x)}{4 d}-\frac{\tan ^2(c+d x)}{2 d}-\frac{\log (\cos (c+d x))}{d}","\frac{\tan ^4(c+d x)}{4 d}-\frac{\tan ^2(c+d x)}{2 d}-\frac{\log (\cos (c+d x))}{d}",1,"-(Log[Cos[c + d*x]]/d) - Tan[c + d*x]^2/(2*d) + Tan[c + d*x]^4/(4*d)","A",3,2,8,0.2500,1,"{3473, 3475}"
6,1,44,0,0.0246057,"\int \tan ^6(c+d x) \, dx","Int[Tan[c + d*x]^6,x]","\frac{\tan ^5(c+d x)}{5 d}-\frac{\tan ^3(c+d x)}{3 d}+\frac{\tan (c+d x)}{d}-x","\frac{\tan ^5(c+d x)}{5 d}-\frac{\tan ^3(c+d x)}{3 d}+\frac{\tan (c+d x)}{d}-x",1,"-x + Tan[c + d*x]/d - Tan[c + d*x]^3/(3*d) + Tan[c + d*x]^5/(5*d)","A",4,2,8,0.2500,1,"{3473, 8}"
7,1,57,0,0.0267256,"\int \tan ^7(c+d x) \, dx","Int[Tan[c + d*x]^7,x]","\frac{\tan ^6(c+d x)}{6 d}-\frac{\tan ^4(c+d x)}{4 d}+\frac{\tan ^2(c+d x)}{2 d}+\frac{\log (\cos (c+d x))}{d}","\frac{\tan ^6(c+d x)}{6 d}-\frac{\tan ^4(c+d x)}{4 d}+\frac{\tan ^2(c+d x)}{2 d}+\frac{\log (\cos (c+d x))}{d}",1,"Log[Cos[c + d*x]]/d + Tan[c + d*x]^2/(2*d) - Tan[c + d*x]^4/(4*d) + Tan[c + d*x]^6/(6*d)","A",4,2,8,0.2500,1,"{3473, 3475}"
8,1,58,0,0.0299271,"\int \tan ^8(c+d x) \, dx","Int[Tan[c + d*x]^8,x]","\frac{\tan ^7(c+d x)}{7 d}-\frac{\tan ^5(c+d x)}{5 d}+\frac{\tan ^3(c+d x)}{3 d}-\frac{\tan (c+d x)}{d}+x","\frac{\tan ^7(c+d x)}{7 d}-\frac{\tan ^5(c+d x)}{5 d}+\frac{\tan ^3(c+d x)}{3 d}-\frac{\tan (c+d x)}{d}+x",1,"x - Tan[c + d*x]/d + Tan[c + d*x]^3/(3*d) - Tan[c + d*x]^5/(5*d) + Tan[c + d*x]^7/(7*d)","A",5,2,8,0.2500,1,"{3473, 8}"
9,1,232,0,0.1960077,"\int (b \tan (c+d x))^{7/2} \, dx","Int[(b*Tan[c + d*x])^(7/2),x]","-\frac{b^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} d}+\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} d}-\frac{2 b^3 \sqrt{b \tan (c+d x)}}{d}-\frac{b^{7/2} \log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}+\frac{b^{7/2} \log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}+\frac{2 b (b \tan (c+d x))^{5/2}}{5 d}","-\frac{b^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} d}+\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} d}-\frac{2 b^3 \sqrt{b \tan (c+d x)}}{d}-\frac{b^{7/2} \log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}+\frac{b^{7/2} \log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}+\frac{2 b (b \tan (c+d x))^{5/2}}{5 d}",1,"-((b^(7/2)*ArcTan[1 - (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]])/(Sqrt[2]*d)) + (b^(7/2)*ArcTan[1 + (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]])/(Sqrt[2]*d) - (b^(7/2)*Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] - Sqrt[2]*Sqrt[b*Tan[c + d*x]]])/(2*Sqrt[2]*d) + (b^(7/2)*Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] + Sqrt[2]*Sqrt[b*Tan[c + d*x]]])/(2*Sqrt[2]*d) - (2*b^3*Sqrt[b*Tan[c + d*x]])/d + (2*b*(b*Tan[c + d*x])^(5/2))/(5*d)","A",13,9,12,0.7500,1,"{3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
10,1,212,0,0.1446973,"\int (b \tan (c+d x))^{5/2} \, dx","Int[(b*Tan[c + d*x])^(5/2),x]","\frac{b^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} d}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} d}-\frac{b^{5/2} \log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}+\frac{b^{5/2} \log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}+\frac{2 b (b \tan (c+d x))^{3/2}}{3 d}","\frac{b^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} d}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} d}-\frac{b^{5/2} \log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}+\frac{b^{5/2} \log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}+\frac{2 b (b \tan (c+d x))^{3/2}}{3 d}",1,"(b^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]])/(Sqrt[2]*d) - (b^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]])/(Sqrt[2]*d) - (b^(5/2)*Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] - Sqrt[2]*Sqrt[b*Tan[c + d*x]]])/(2*Sqrt[2]*d) + (b^(5/2)*Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] + Sqrt[2]*Sqrt[b*Tan[c + d*x]]])/(2*Sqrt[2]*d) + (2*b*(b*Tan[c + d*x])^(3/2))/(3*d)","A",12,9,12,0.7500,1,"{3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
11,1,210,0,0.1511636,"\int (b \tan (c+d x))^{3/2} \, dx","Int[(b*Tan[c + d*x])^(3/2),x]","\frac{b^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} d}-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} d}+\frac{b^{3/2} \log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}-\frac{b^{3/2} \log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}+\frac{2 b \sqrt{b \tan (c+d x)}}{d}","\frac{b^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} d}-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} d}+\frac{b^{3/2} \log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}-\frac{b^{3/2} \log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}+\frac{2 b \sqrt{b \tan (c+d x)}}{d}",1,"(b^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]])/(Sqrt[2]*d) - (b^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]])/(Sqrt[2]*d) + (b^(3/2)*Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] - Sqrt[2]*Sqrt[b*Tan[c + d*x]]])/(2*Sqrt[2]*d) - (b^(3/2)*Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] + Sqrt[2]*Sqrt[b*Tan[c + d*x]]])/(2*Sqrt[2]*d) + (2*b*Sqrt[b*Tan[c + d*x]])/d","A",12,9,12,0.7500,1,"{3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
12,1,192,0,0.1206005,"\int \sqrt{b \tan (c+d x)} \, dx","Int[Sqrt[b*Tan[c + d*x]],x]","-\frac{\sqrt{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} d}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} d}+\frac{\sqrt{b} \log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}-\frac{\sqrt{b} \log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}","-\frac{\sqrt{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} d}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} d}+\frac{\sqrt{b} \log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}-\frac{\sqrt{b} \log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} d}",1,"-((Sqrt[b]*ArcTan[1 - (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]])/(Sqrt[2]*d)) + (Sqrt[b]*ArcTan[1 + (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]])/(Sqrt[2]*d) + (Sqrt[b]*Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] - Sqrt[2]*Sqrt[b*Tan[c + d*x]]])/(2*Sqrt[2]*d) - (Sqrt[b]*Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] + Sqrt[2]*Sqrt[b*Tan[c + d*x]]])/(2*Sqrt[2]*d)","A",11,8,12,0.6667,1,"{3476, 329, 297, 1162, 617, 204, 1165, 628}"
13,1,192,0,0.121426,"\int \frac{1}{\sqrt{b \tan (c+d x)}} \, dx","Int[1/Sqrt[b*Tan[c + d*x]],x]","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} \sqrt{b} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} \sqrt{b} d}-\frac{\log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} \sqrt{b} d}+\frac{\log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} \sqrt{b} d}","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} \sqrt{b} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} \sqrt{b} d}-\frac{\log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} \sqrt{b} d}+\frac{\log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} \sqrt{b} d}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]]/(Sqrt[2]*Sqrt[b]*d)) + ArcTan[1 + (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]]/(Sqrt[2]*Sqrt[b]*d) - Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] - Sqrt[2]*Sqrt[b*Tan[c + d*x]]]/(2*Sqrt[2]*Sqrt[b]*d) + Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] + Sqrt[2]*Sqrt[b*Tan[c + d*x]]]/(2*Sqrt[2]*Sqrt[b]*d)","A",11,8,12,0.6667,1,"{3476, 329, 211, 1165, 628, 1162, 617, 204}"
14,1,212,0,0.1462467,"\int \frac{1}{(b \tan (c+d x))^{3/2}} \, dx","Int[(b*Tan[c + d*x])^(-3/2),x]","\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} b^{3/2} d}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} b^{3/2} d}-\frac{\log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} b^{3/2} d}+\frac{\log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} b^{3/2} d}-\frac{2}{b d \sqrt{b \tan (c+d x)}}","\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} b^{3/2} d}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} b^{3/2} d}-\frac{\log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} b^{3/2} d}+\frac{\log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} b^{3/2} d}-\frac{2}{b d \sqrt{b \tan (c+d x)}}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]]/(Sqrt[2]*b^(3/2)*d) - ArcTan[1 + (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]]/(Sqrt[2]*b^(3/2)*d) - Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] - Sqrt[2]*Sqrt[b*Tan[c + d*x]]]/(2*Sqrt[2]*b^(3/2)*d) + Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] + Sqrt[2]*Sqrt[b*Tan[c + d*x]]]/(2*Sqrt[2]*b^(3/2)*d) - 2/(b*d*Sqrt[b*Tan[c + d*x]])","A",12,9,12,0.7500,1,"{3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
15,1,214,0,0.1504889,"\int \frac{1}{(b \tan (c+d x))^{5/2}} \, dx","Int[(b*Tan[c + d*x])^(-5/2),x]","\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} b^{5/2} d}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} b^{5/2} d}+\frac{\log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} b^{5/2} d}-\frac{\log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} b^{5/2} d}-\frac{2}{3 b d (b \tan (c+d x))^{3/2}}","\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} b^{5/2} d}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} b^{5/2} d}+\frac{\log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} b^{5/2} d}-\frac{\log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} b^{5/2} d}-\frac{2}{3 b d (b \tan (c+d x))^{3/2}}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]]/(Sqrt[2]*b^(5/2)*d) - ArcTan[1 + (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]]/(Sqrt[2]*b^(5/2)*d) + Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] - Sqrt[2]*Sqrt[b*Tan[c + d*x]]]/(2*Sqrt[2]*b^(5/2)*d) - Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] + Sqrt[2]*Sqrt[b*Tan[c + d*x]]]/(2*Sqrt[2]*b^(5/2)*d) - 2/(3*b*d*(b*Tan[c + d*x])^(3/2))","A",12,9,12,0.7500,1,"{3474, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
16,1,234,0,0.1809528,"\int \frac{1}{(b \tan (c+d x))^{7/2}} \, dx","Int[(b*Tan[c + d*x])^(-7/2),x]","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} b^{7/2} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} b^{7/2} d}+\frac{2}{b^3 d \sqrt{b \tan (c+d x)}}+\frac{\log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} b^{7/2} d}-\frac{\log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} b^{7/2} d}-\frac{2}{5 b d (b \tan (c+d x))^{5/2}}","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}\right)}{\sqrt{2} b^{7/2} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \tan (c+d x)}}{\sqrt{b}}+1\right)}{\sqrt{2} b^{7/2} d}+\frac{2}{b^3 d \sqrt{b \tan (c+d x)}}+\frac{\log \left(\sqrt{b} \tan (c+d x)-\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} b^{7/2} d}-\frac{\log \left(\sqrt{b} \tan (c+d x)+\sqrt{2} \sqrt{b \tan (c+d x)}+\sqrt{b}\right)}{2 \sqrt{2} b^{7/2} d}-\frac{2}{5 b d (b \tan (c+d x))^{5/2}}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]]/(Sqrt[2]*b^(7/2)*d)) + ArcTan[1 + (Sqrt[2]*Sqrt[b*Tan[c + d*x]])/Sqrt[b]]/(Sqrt[2]*b^(7/2)*d) + Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] - Sqrt[2]*Sqrt[b*Tan[c + d*x]]]/(2*Sqrt[2]*b^(7/2)*d) - Log[Sqrt[b] + Sqrt[b]*Tan[c + d*x] + Sqrt[2]*Sqrt[b*Tan[c + d*x]]]/(2*Sqrt[2]*b^(7/2)*d) - 2/(5*b*d*(b*Tan[c + d*x])^(5/2)) + 2/(b^3*d*Sqrt[b*Tan[c + d*x]])","A",13,9,12,0.7500,1,"{3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
17,1,243,0,0.4176823,"\int (b \tan (c+d x))^{4/3} \, dx","Int[(b*Tan[c + d*x])^(4/3),x]","-\frac{b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{d}+\frac{b^{4/3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{2 d}-\frac{b^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}+\sqrt{3}\right)}{2 d}+\frac{\sqrt{3} b^{4/3} \log \left(b^{2/3}-\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 d}-\frac{\sqrt{3} b^{4/3} \log \left(b^{2/3}+\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 d}+\frac{3 b \sqrt[3]{b \tan (c+d x)}}{d}","-\frac{b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{d}+\frac{b^{4/3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{2 d}-\frac{b^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}+\sqrt{3}\right)}{2 d}+\frac{\sqrt{3} b^{4/3} \log \left(b^{2/3}-\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 d}-\frac{\sqrt{3} b^{4/3} \log \left(b^{2/3}+\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 d}+\frac{3 b \sqrt[3]{b \tan (c+d x)}}{d}",1,"-((b^(4/3)*ArcTan[(b*Tan[c + d*x])^(1/3)/b^(1/3)])/d) + (b^(4/3)*ArcTan[Sqrt[3] - (2*(b*Tan[c + d*x])^(1/3))/b^(1/3)])/(2*d) - (b^(4/3)*ArcTan[Sqrt[3] + (2*(b*Tan[c + d*x])^(1/3))/b^(1/3)])/(2*d) + (Sqrt[3]*b^(4/3)*Log[b^(2/3) - Sqrt[3]*b^(1/3)*(b*Tan[c + d*x])^(1/3) + (b*Tan[c + d*x])^(2/3)])/(4*d) - (Sqrt[3]*b^(4/3)*Log[b^(2/3) + Sqrt[3]*b^(1/3)*(b*Tan[c + d*x])^(1/3) + (b*Tan[c + d*x])^(2/3)])/(4*d) + (3*b*(b*Tan[c + d*x])^(1/3))/d","A",13,9,12,0.7500,1,"{3473, 3476, 329, 209, 634, 618, 204, 628, 203}"
18,1,224,0,0.3938513,"\int (b \tan (c+d x))^{2/3} \, dx","Int[(b*Tan[c + d*x])^(2/3),x]","\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{d}-\frac{b^{2/3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{2 d}+\frac{b^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}+\sqrt{3}\right)}{2 d}+\frac{\sqrt{3} b^{2/3} \log \left(b^{2/3}-\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 d}-\frac{\sqrt{3} b^{2/3} \log \left(b^{2/3}+\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 d}","\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{d}-\frac{b^{2/3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{2 d}+\frac{b^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}+\sqrt{3}\right)}{2 d}+\frac{\sqrt{3} b^{2/3} \log \left(b^{2/3}-\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 d}-\frac{\sqrt{3} b^{2/3} \log \left(b^{2/3}+\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 d}",1,"(b^(2/3)*ArcTan[(b*Tan[c + d*x])^(1/3)/b^(1/3)])/d - (b^(2/3)*ArcTan[Sqrt[3] - (2*(b*Tan[c + d*x])^(1/3))/b^(1/3)])/(2*d) + (b^(2/3)*ArcTan[Sqrt[3] + (2*(b*Tan[c + d*x])^(1/3))/b^(1/3)])/(2*d) + (Sqrt[3]*b^(2/3)*Log[b^(2/3) - Sqrt[3]*b^(1/3)*(b*Tan[c + d*x])^(1/3) + (b*Tan[c + d*x])^(2/3)])/(4*d) - (Sqrt[3]*b^(2/3)*Log[b^(2/3) + Sqrt[3]*b^(1/3)*(b*Tan[c + d*x])^(1/3) + (b*Tan[c + d*x])^(2/3)])/(4*d)","A",12,8,12,0.6667,1,"{3476, 329, 295, 634, 618, 204, 628, 203}"
19,1,131,0,0.103936,"\int \sqrt[3]{b \tan (c+d x)} \, dx","Int[(b*Tan[c + d*x])^(1/3),x]","-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{b^{2/3}-2 (b \tan (c+d x))^{2/3}}{\sqrt{3} b^{2/3}}\right)}{2 d}-\frac{\sqrt[3]{b} \log \left(b^{2/3}+(b \tan (c+d x))^{2/3}\right)}{2 d}+\frac{\sqrt[3]{b} \log \left(-b^{2/3} (b \tan (c+d x))^{2/3}+b^{4/3}+(b \tan (c+d x))^{4/3}\right)}{4 d}","-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{b^{2/3}-2 (b \tan (c+d x))^{2/3}}{\sqrt{3} b^{2/3}}\right)}{2 d}-\frac{\sqrt[3]{b} \log \left(b^{2/3}+(b \tan (c+d x))^{2/3}\right)}{2 d}+\frac{\sqrt[3]{b} \log \left(-b^{2/3} (b \tan (c+d x))^{2/3}+b^{4/3}+(b \tan (c+d x))^{4/3}\right)}{4 d}",1,"-(Sqrt[3]*b^(1/3)*ArcTan[(b^(2/3) - 2*(b*Tan[c + d*x])^(2/3))/(Sqrt[3]*b^(2/3))])/(2*d) - (b^(1/3)*Log[b^(2/3) + (b*Tan[c + d*x])^(2/3)])/(2*d) + (b^(1/3)*Log[b^(4/3) - b^(2/3)*(b*Tan[c + d*x])^(2/3) + (b*Tan[c + d*x])^(4/3)])/(4*d)","A",9,9,12,0.7500,1,"{3476, 329, 275, 292, 31, 634, 617, 204, 628}"
20,1,131,0,0.0996872,"\int \frac{1}{\sqrt[3]{b \tan (c+d x)}} \, dx","Int[(b*Tan[c + d*x])^(-1/3),x]","-\frac{\sqrt{3} \tan ^{-1}\left(\frac{b^{2/3}-2 (b \tan (c+d x))^{2/3}}{\sqrt{3} b^{2/3}}\right)}{2 \sqrt[3]{b} d}+\frac{\log \left(b^{2/3}+(b \tan (c+d x))^{2/3}\right)}{2 \sqrt[3]{b} d}-\frac{\log \left(-b^{2/3} (b \tan (c+d x))^{2/3}+b^{4/3}+(b \tan (c+d x))^{4/3}\right)}{4 \sqrt[3]{b} d}","-\frac{\sqrt{3} \tan ^{-1}\left(\frac{b^{2/3}-2 (b \tan (c+d x))^{2/3}}{\sqrt{3} b^{2/3}}\right)}{2 \sqrt[3]{b} d}+\frac{\log \left(b^{2/3}+(b \tan (c+d x))^{2/3}\right)}{2 \sqrt[3]{b} d}-\frac{\log \left(-b^{2/3} (b \tan (c+d x))^{2/3}+b^{4/3}+(b \tan (c+d x))^{4/3}\right)}{4 \sqrt[3]{b} d}",1,"-(Sqrt[3]*ArcTan[(b^(2/3) - 2*(b*Tan[c + d*x])^(2/3))/(Sqrt[3]*b^(2/3))])/(2*b^(1/3)*d) + Log[b^(2/3) + (b*Tan[c + d*x])^(2/3)]/(2*b^(1/3)*d) - Log[b^(4/3) - b^(2/3)*(b*Tan[c + d*x])^(2/3) + (b*Tan[c + d*x])^(4/3)]/(4*b^(1/3)*d)","A",9,9,12,0.7500,1,"{3476, 329, 275, 200, 31, 634, 617, 204, 628}"
21,1,224,0,0.3264314,"\int \frac{1}{(b \tan (c+d x))^{2/3}} \, dx","Int[(b*Tan[c + d*x])^(-2/3),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{b^{2/3} d}-\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{2 b^{2/3} d}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}+\sqrt{3}\right)}{2 b^{2/3} d}-\frac{\sqrt{3} \log \left(b^{2/3}-\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 b^{2/3} d}+\frac{\sqrt{3} \log \left(b^{2/3}+\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 b^{2/3} d}","\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{b^{2/3} d}-\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{2 b^{2/3} d}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}+\sqrt{3}\right)}{2 b^{2/3} d}-\frac{\sqrt{3} \log \left(b^{2/3}-\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 b^{2/3} d}+\frac{\sqrt{3} \log \left(b^{2/3}+\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 b^{2/3} d}",1,"ArcTan[(b*Tan[c + d*x])^(1/3)/b^(1/3)]/(b^(2/3)*d) - ArcTan[Sqrt[3] - (2*(b*Tan[c + d*x])^(1/3))/b^(1/3)]/(2*b^(2/3)*d) + ArcTan[Sqrt[3] + (2*(b*Tan[c + d*x])^(1/3))/b^(1/3)]/(2*b^(2/3)*d) - (Sqrt[3]*Log[b^(2/3) - Sqrt[3]*b^(1/3)*(b*Tan[c + d*x])^(1/3) + (b*Tan[c + d*x])^(2/3)])/(4*b^(2/3)*d) + (Sqrt[3]*Log[b^(2/3) + Sqrt[3]*b^(1/3)*(b*Tan[c + d*x])^(1/3) + (b*Tan[c + d*x])^(2/3)])/(4*b^(2/3)*d)","A",12,8,12,0.6667,1,"{3476, 329, 209, 634, 618, 204, 628, 203}"
22,1,245,0,0.4357196,"\int \frac{1}{(b \tan (c+d x))^{4/3}} \, dx","Int[(b*Tan[c + d*x])^(-4/3),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{b^{4/3} d}+\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{2 b^{4/3} d}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}+\sqrt{3}\right)}{2 b^{4/3} d}-\frac{\sqrt{3} \log \left(b^{2/3}-\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 b^{4/3} d}+\frac{\sqrt{3} \log \left(b^{2/3}+\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 b^{4/3} d}-\frac{3}{b d \sqrt[3]{b \tan (c+d x)}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{b^{4/3} d}+\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}\right)}{2 b^{4/3} d}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{b \tan (c+d x)}}{\sqrt[3]{b}}+\sqrt{3}\right)}{2 b^{4/3} d}-\frac{\sqrt{3} \log \left(b^{2/3}-\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 b^{4/3} d}+\frac{\sqrt{3} \log \left(b^{2/3}+\sqrt{3} \sqrt[3]{b} \sqrt[3]{b \tan (c+d x)}+(b \tan (c+d x))^{2/3}\right)}{4 b^{4/3} d}-\frac{3}{b d \sqrt[3]{b \tan (c+d x)}}",1,"-(ArcTan[(b*Tan[c + d*x])^(1/3)/b^(1/3)]/(b^(4/3)*d)) + ArcTan[Sqrt[3] - (2*(b*Tan[c + d*x])^(1/3))/b^(1/3)]/(2*b^(4/3)*d) - ArcTan[Sqrt[3] + (2*(b*Tan[c + d*x])^(1/3))/b^(1/3)]/(2*b^(4/3)*d) - (Sqrt[3]*Log[b^(2/3) - Sqrt[3]*b^(1/3)*(b*Tan[c + d*x])^(1/3) + (b*Tan[c + d*x])^(2/3)])/(4*b^(4/3)*d) + (Sqrt[3]*Log[b^(2/3) + Sqrt[3]*b^(1/3)*(b*Tan[c + d*x])^(1/3) + (b*Tan[c + d*x])^(2/3)])/(4*b^(4/3)*d) - 3/(b*d*(b*Tan[c + d*x])^(1/3))","A",13,9,12,0.7500,1,"{3474, 3476, 329, 295, 634, 618, 204, 628, 203}"
23,1,50,0,0.028416,"\int (b \tan (c+d x))^n \, dx","Int[(b*Tan[c + d*x])^n,x]","\frac{(b \tan (c+d x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(c+d x)\right)}{b d (n+1)}","\frac{(b \tan (c+d x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(c+d x)\right)}{b d (n+1)}",1,"(Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Tan[c + d*x]^2]*(b*Tan[c + d*x])^(1 + n))/(b*d*(1 + n))","A",2,2,10,0.2000,1,"{3476, 364}"
24,1,98,0,0.0416749,"\int \left(b \tan ^2(c+d x)\right)^{5/2} \, dx","Int[(b*Tan[c + d*x]^2)^(5/2),x]","\frac{b^2 \tan ^3(c+d x) \sqrt{b \tan ^2(c+d x)}}{4 d}-\frac{b^2 \tan (c+d x) \sqrt{b \tan ^2(c+d x)}}{2 d}-\frac{b^2 \cot (c+d x) \sqrt{b \tan ^2(c+d x)} \log (\cos (c+d x))}{d}","\frac{b^2 \tan ^3(c+d x) \sqrt{b \tan ^2(c+d x)}}{4 d}-\frac{b^2 \tan (c+d x) \sqrt{b \tan ^2(c+d x)}}{2 d}-\frac{b^2 \cot (c+d x) \sqrt{b \tan ^2(c+d x)} \log (\cos (c+d x))}{d}",1,"-((b^2*Cot[c + d*x]*Log[Cos[c + d*x]]*Sqrt[b*Tan[c + d*x]^2])/d) - (b^2*Tan[c + d*x]*Sqrt[b*Tan[c + d*x]^2])/(2*d) + (b^2*Tan[c + d*x]^3*Sqrt[b*Tan[c + d*x]^2])/(4*d)","A",4,3,14,0.2143,1,"{3658, 3473, 3475}"
25,1,61,0,0.027738,"\int \left(b \tan ^2(c+d x)\right)^{3/2} \, dx","Int[(b*Tan[c + d*x]^2)^(3/2),x]","\frac{b \tan (c+d x) \sqrt{b \tan ^2(c+d x)}}{2 d}+\frac{b \cot (c+d x) \sqrt{b \tan ^2(c+d x)} \log (\cos (c+d x))}{d}","\frac{b \tan (c+d x) \sqrt{b \tan ^2(c+d x)}}{2 d}+\frac{b \cot (c+d x) \sqrt{b \tan ^2(c+d x)} \log (\cos (c+d x))}{d}",1,"(b*Cot[c + d*x]*Log[Cos[c + d*x]]*Sqrt[b*Tan[c + d*x]^2])/d + (b*Tan[c + d*x]*Sqrt[b*Tan[c + d*x]^2])/(2*d)","A",3,3,14,0.2143,1,"{3658, 3473, 3475}"
26,1,32,0,0.0166386,"\int \sqrt{b \tan ^2(c+d x)} \, dx","Int[Sqrt[b*Tan[c + d*x]^2],x]","-\frac{\cot (c+d x) \sqrt{b \tan ^2(c+d x)} \log (\cos (c+d x))}{d}","-\frac{\cot (c+d x) \sqrt{b \tan ^2(c+d x)} \log (\cos (c+d x))}{d}",1,"-((Cot[c + d*x]*Log[Cos[c + d*x]]*Sqrt[b*Tan[c + d*x]^2])/d)","A",2,2,14,0.1429,1,"{3658, 3475}"
27,1,31,0,0.0160449,"\int \frac{1}{\sqrt{b \tan ^2(c+d x)}} \, dx","Int[1/Sqrt[b*Tan[c + d*x]^2],x]","\frac{\tan (c+d x) \log (\sin (c+d x))}{d \sqrt{b \tan ^2(c+d x)}}","\frac{\tan (c+d x) \log (\sin (c+d x))}{d \sqrt{b \tan ^2(c+d x)}}",1,"(Log[Sin[c + d*x]]*Tan[c + d*x])/(d*Sqrt[b*Tan[c + d*x]^2])","A",2,2,14,0.1429,1,"{3658, 3475}"
28,1,66,0,0.0291696,"\int \frac{1}{\left(b \tan ^2(c+d x)\right)^{3/2}} \, dx","Int[(b*Tan[c + d*x]^2)^(-3/2),x]","-\frac{\cot (c+d x)}{2 b d \sqrt{b \tan ^2(c+d x)}}-\frac{\tan (c+d x) \log (\sin (c+d x))}{b d \sqrt{b \tan ^2(c+d x)}}","-\frac{\cot (c+d x)}{2 b d \sqrt{b \tan ^2(c+d x)}}-\frac{\tan (c+d x) \log (\sin (c+d x))}{b d \sqrt{b \tan ^2(c+d x)}}",1,"-Cot[c + d*x]/(2*b*d*Sqrt[b*Tan[c + d*x]^2]) - (Log[Sin[c + d*x]]*Tan[c + d*x])/(b*d*Sqrt[b*Tan[c + d*x]^2])","A",3,3,14,0.2143,1,"{3658, 3473, 3475}"
29,1,97,0,0.0398231,"\int \frac{1}{\left(b \tan ^2(c+d x)\right)^{5/2}} \, dx","Int[(b*Tan[c + d*x]^2)^(-5/2),x]","-\frac{\cot ^3(c+d x)}{4 b^2 d \sqrt{b \tan ^2(c+d x)}}+\frac{\cot (c+d x)}{2 b^2 d \sqrt{b \tan ^2(c+d x)}}+\frac{\tan (c+d x) \log (\sin (c+d x))}{b^2 d \sqrt{b \tan ^2(c+d x)}}","-\frac{\cot ^3(c+d x)}{4 b^2 d \sqrt{b \tan ^2(c+d x)}}+\frac{\cot (c+d x)}{2 b^2 d \sqrt{b \tan ^2(c+d x)}}+\frac{\tan (c+d x) \log (\sin (c+d x))}{b^2 d \sqrt{b \tan ^2(c+d x)}}",1,"Cot[c + d*x]/(2*b^2*d*Sqrt[b*Tan[c + d*x]^2]) - Cot[c + d*x]^3/(4*b^2*d*Sqrt[b*Tan[c + d*x]^2]) + (Log[Sin[c + d*x]]*Tan[c + d*x])/(b^2*d*Sqrt[b*Tan[c + d*x]^2])","A",4,3,14,0.2143,1,"{3658, 3473, 3475}"
30,1,364,0,0.1503365,"\int \left(b \tan ^3(c+d x)\right)^{5/2} \, dx","Int[(b*Tan[c + d*x]^3)^(5/2),x]","\frac{2 b^2 \tan ^5(c+d x) \sqrt{b \tan ^3(c+d x)}}{13 d}-\frac{2 b^2 \tan ^3(c+d x) \sqrt{b \tan ^3(c+d x)}}{9 d}+\frac{2 b^2 \tan (c+d x) \sqrt{b \tan ^3(c+d x)}}{5 d}-\frac{b^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right) \sqrt{b \tan ^3(c+d x)}}{\sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}+\frac{b^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right) \sqrt{b \tan ^3(c+d x)}}{\sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}-\frac{b^2 \sqrt{b \tan ^3(c+d x)} \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}+\frac{b^2 \sqrt{b \tan ^3(c+d x)} \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 b^2 \cot (c+d x) \sqrt{b \tan ^3(c+d x)}}{d}","\frac{2 b^2 \tan ^5(c+d x) \sqrt{b \tan ^3(c+d x)}}{13 d}-\frac{2 b^2 \tan ^3(c+d x) \sqrt{b \tan ^3(c+d x)}}{9 d}+\frac{2 b^2 \tan (c+d x) \sqrt{b \tan ^3(c+d x)}}{5 d}-\frac{b^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right) \sqrt{b \tan ^3(c+d x)}}{\sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}+\frac{b^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right) \sqrt{b \tan ^3(c+d x)}}{\sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}-\frac{b^2 \sqrt{b \tan ^3(c+d x)} \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}+\frac{b^2 \sqrt{b \tan ^3(c+d x)} \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 b^2 \cot (c+d x) \sqrt{b \tan ^3(c+d x)}}{d}",1,"(-2*b^2*Cot[c + d*x]*Sqrt[b*Tan[c + d*x]^3])/d - (b^2*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]]*Sqrt[b*Tan[c + d*x]^3])/(Sqrt[2]*d*Tan[c + d*x]^(3/2)) + (b^2*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]]*Sqrt[b*Tan[c + d*x]^3])/(Sqrt[2]*d*Tan[c + d*x]^(3/2)) - (b^2*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]]*Sqrt[b*Tan[c + d*x]^3])/(2*Sqrt[2]*d*Tan[c + d*x]^(3/2)) + (b^2*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]]*Sqrt[b*Tan[c + d*x]^3])/(2*Sqrt[2]*d*Tan[c + d*x]^(3/2)) + (2*b^2*Tan[c + d*x]*Sqrt[b*Tan[c + d*x]^3])/(5*d) - (2*b^2*Tan[c + d*x]^3*Sqrt[b*Tan[c + d*x]^3])/(9*d) + (2*b^2*Tan[c + d*x]^5*Sqrt[b*Tan[c + d*x]^3])/(13*d)","A",16,10,14,0.7143,1,"{3658, 3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
31,1,286,0,0.1260658,"\int \left(b \tan ^3(c+d x)\right)^{3/2} \, dx","Int[(b*Tan[c + d*x]^3)^(3/2),x]","\frac{2 b \tan ^2(c+d x) \sqrt{b \tan ^3(c+d x)}}{7 d}-\frac{2 b \sqrt{b \tan ^3(c+d x)}}{3 d}-\frac{b \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right) \sqrt{b \tan ^3(c+d x)}}{\sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}+\frac{b \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right) \sqrt{b \tan ^3(c+d x)}}{\sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}+\frac{b \sqrt{b \tan ^3(c+d x)} \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}-\frac{b \sqrt{b \tan ^3(c+d x)} \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}","\frac{2 b \tan ^2(c+d x) \sqrt{b \tan ^3(c+d x)}}{7 d}-\frac{2 b \sqrt{b \tan ^3(c+d x)}}{3 d}-\frac{b \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right) \sqrt{b \tan ^3(c+d x)}}{\sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}+\frac{b \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right) \sqrt{b \tan ^3(c+d x)}}{\sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}+\frac{b \sqrt{b \tan ^3(c+d x)} \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}-\frac{b \sqrt{b \tan ^3(c+d x)} \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}",1,"(-2*b*Sqrt[b*Tan[c + d*x]^3])/(3*d) - (b*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]]*Sqrt[b*Tan[c + d*x]^3])/(Sqrt[2]*d*Tan[c + d*x]^(3/2)) + (b*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]]*Sqrt[b*Tan[c + d*x]^3])/(Sqrt[2]*d*Tan[c + d*x]^(3/2)) + (b*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]]*Sqrt[b*Tan[c + d*x]^3])/(2*Sqrt[2]*d*Tan[c + d*x]^(3/2)) - (b*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]]*Sqrt[b*Tan[c + d*x]^3])/(2*Sqrt[2]*d*Tan[c + d*x]^(3/2)) + (2*b*Tan[c + d*x]^2*Sqrt[b*Tan[c + d*x]^3])/(7*d)","A",14,10,14,0.7143,1,"{3658, 3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
32,1,255,0,0.1134149,"\int \sqrt{b \tan ^3(c+d x)} \, dx","Int[Sqrt[b*Tan[c + d*x]^3],x]","\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right) \sqrt{b \tan ^3(c+d x)}}{\sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right) \sqrt{b \tan ^3(c+d x)}}{\sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}+\frac{\sqrt{b \tan ^3(c+d x)} \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}-\frac{\sqrt{b \tan ^3(c+d x)} \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \cot (c+d x) \sqrt{b \tan ^3(c+d x)}}{d}","\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right) \sqrt{b \tan ^3(c+d x)}}{\sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right) \sqrt{b \tan ^3(c+d x)}}{\sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}+\frac{\sqrt{b \tan ^3(c+d x)} \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}-\frac{\sqrt{b \tan ^3(c+d x)} \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \cot (c+d x) \sqrt{b \tan ^3(c+d x)}}{d}",1,"(2*Cot[c + d*x]*Sqrt[b*Tan[c + d*x]^3])/d + (ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]]*Sqrt[b*Tan[c + d*x]^3])/(Sqrt[2]*d*Tan[c + d*x]^(3/2)) - (ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]]*Sqrt[b*Tan[c + d*x]^3])/(Sqrt[2]*d*Tan[c + d*x]^(3/2)) + (Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]]*Sqrt[b*Tan[c + d*x]^3])/(2*Sqrt[2]*d*Tan[c + d*x]^(3/2)) - (Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]]*Sqrt[b*Tan[c + d*x]^3])/(2*Sqrt[2]*d*Tan[c + d*x]^(3/2))","A",13,10,14,0.7143,1,"{3658, 3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
33,1,255,0,0.1178487,"\int \frac{1}{\sqrt{b \tan ^3(c+d x)}} \, dx","Int[1/Sqrt[b*Tan[c + d*x]^3],x]","\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right) \tan ^{\frac{3}{2}}(c+d x)}{\sqrt{2} d \sqrt{b \tan ^3(c+d x)}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right) \tan ^{\frac{3}{2}}(c+d x)}{\sqrt{2} d \sqrt{b \tan ^3(c+d x)}}-\frac{2 \tan (c+d x)}{d \sqrt{b \tan ^3(c+d x)}}-\frac{\tan ^{\frac{3}{2}}(c+d x) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \sqrt{b \tan ^3(c+d x)}}+\frac{\tan ^{\frac{3}{2}}(c+d x) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \sqrt{b \tan ^3(c+d x)}}","\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right) \tan ^{\frac{3}{2}}(c+d x)}{\sqrt{2} d \sqrt{b \tan ^3(c+d x)}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right) \tan ^{\frac{3}{2}}(c+d x)}{\sqrt{2} d \sqrt{b \tan ^3(c+d x)}}-\frac{2 \tan (c+d x)}{d \sqrt{b \tan ^3(c+d x)}}-\frac{\tan ^{\frac{3}{2}}(c+d x) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \sqrt{b \tan ^3(c+d x)}}+\frac{\tan ^{\frac{3}{2}}(c+d x) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \sqrt{b \tan ^3(c+d x)}}",1,"(-2*Tan[c + d*x])/(d*Sqrt[b*Tan[c + d*x]^3]) + (ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]]*Tan[c + d*x]^(3/2))/(Sqrt[2]*d*Sqrt[b*Tan[c + d*x]^3]) - (ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]]*Tan[c + d*x]^(3/2))/(Sqrt[2]*d*Sqrt[b*Tan[c + d*x]^3]) - (Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]]*Tan[c + d*x]^(3/2))/(2*Sqrt[2]*d*Sqrt[b*Tan[c + d*x]^3]) + (Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]]*Tan[c + d*x]^(3/2))/(2*Sqrt[2]*d*Sqrt[b*Tan[c + d*x]^3])","A",13,10,14,0.7143,1,"{3658, 3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
34,1,298,0,0.1300038,"\int \frac{1}{\left(b \tan ^3(c+d x)\right)^{3/2}} \, dx","Int[(b*Tan[c + d*x]^3)^(-3/2),x]","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right) \tan ^{\frac{3}{2}}(c+d x)}{\sqrt{2} b d \sqrt{b \tan ^3(c+d x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right) \tan ^{\frac{3}{2}}(c+d x)}{\sqrt{2} b d \sqrt{b \tan ^3(c+d x)}}+\frac{2}{3 b d \sqrt{b \tan ^3(c+d x)}}-\frac{\tan ^{\frac{3}{2}}(c+d x) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} b d \sqrt{b \tan ^3(c+d x)}}+\frac{\tan ^{\frac{3}{2}}(c+d x) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} b d \sqrt{b \tan ^3(c+d x)}}-\frac{2 \cot ^2(c+d x)}{7 b d \sqrt{b \tan ^3(c+d x)}}","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right) \tan ^{\frac{3}{2}}(c+d x)}{\sqrt{2} b d \sqrt{b \tan ^3(c+d x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right) \tan ^{\frac{3}{2}}(c+d x)}{\sqrt{2} b d \sqrt{b \tan ^3(c+d x)}}+\frac{2}{3 b d \sqrt{b \tan ^3(c+d x)}}-\frac{\tan ^{\frac{3}{2}}(c+d x) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} b d \sqrt{b \tan ^3(c+d x)}}+\frac{\tan ^{\frac{3}{2}}(c+d x) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} b d \sqrt{b \tan ^3(c+d x)}}-\frac{2 \cot ^2(c+d x)}{7 b d \sqrt{b \tan ^3(c+d x)}}",1,"2/(3*b*d*Sqrt[b*Tan[c + d*x]^3]) - (2*Cot[c + d*x]^2)/(7*b*d*Sqrt[b*Tan[c + d*x]^3]) - (ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]]*Tan[c + d*x]^(3/2))/(Sqrt[2]*b*d*Sqrt[b*Tan[c + d*x]^3]) + (ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]]*Tan[c + d*x]^(3/2))/(Sqrt[2]*b*d*Sqrt[b*Tan[c + d*x]^3]) - (Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]]*Tan[c + d*x]^(3/2))/(2*Sqrt[2]*b*d*Sqrt[b*Tan[c + d*x]^3]) + (Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]]*Tan[c + d*x]^(3/2))/(2*Sqrt[2]*b*d*Sqrt[b*Tan[c + d*x]^3])","A",14,10,14,0.7143,1,"{3658, 3474, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
35,1,364,0,0.1514341,"\int \frac{1}{\left(b \tan ^3(c+d x)\right)^{5/2}} \, dx","Int[(b*Tan[c + d*x]^3)^(-5/2),x]","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right) \tan ^{\frac{3}{2}}(c+d x)}{\sqrt{2} b^2 d \sqrt{b \tan ^3(c+d x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right) \tan ^{\frac{3}{2}}(c+d x)}{\sqrt{2} b^2 d \sqrt{b \tan ^3(c+d x)}}+\frac{2 \tan (c+d x)}{b^2 d \sqrt{b \tan ^3(c+d x)}}+\frac{\tan ^{\frac{3}{2}}(c+d x) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} b^2 d \sqrt{b \tan ^3(c+d x)}}-\frac{\tan ^{\frac{3}{2}}(c+d x) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} b^2 d \sqrt{b \tan ^3(c+d x)}}-\frac{2 \cot ^5(c+d x)}{13 b^2 d \sqrt{b \tan ^3(c+d x)}}+\frac{2 \cot ^3(c+d x)}{9 b^2 d \sqrt{b \tan ^3(c+d x)}}-\frac{2 \cot (c+d x)}{5 b^2 d \sqrt{b \tan ^3(c+d x)}}","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right) \tan ^{\frac{3}{2}}(c+d x)}{\sqrt{2} b^2 d \sqrt{b \tan ^3(c+d x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right) \tan ^{\frac{3}{2}}(c+d x)}{\sqrt{2} b^2 d \sqrt{b \tan ^3(c+d x)}}+\frac{2 \tan (c+d x)}{b^2 d \sqrt{b \tan ^3(c+d x)}}+\frac{\tan ^{\frac{3}{2}}(c+d x) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} b^2 d \sqrt{b \tan ^3(c+d x)}}-\frac{\tan ^{\frac{3}{2}}(c+d x) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} b^2 d \sqrt{b \tan ^3(c+d x)}}-\frac{2 \cot ^5(c+d x)}{13 b^2 d \sqrt{b \tan ^3(c+d x)}}+\frac{2 \cot ^3(c+d x)}{9 b^2 d \sqrt{b \tan ^3(c+d x)}}-\frac{2 \cot (c+d x)}{5 b^2 d \sqrt{b \tan ^3(c+d x)}}",1,"(-2*Cot[c + d*x])/(5*b^2*d*Sqrt[b*Tan[c + d*x]^3]) + (2*Cot[c + d*x]^3)/(9*b^2*d*Sqrt[b*Tan[c + d*x]^3]) - (2*Cot[c + d*x]^5)/(13*b^2*d*Sqrt[b*Tan[c + d*x]^3]) + (2*Tan[c + d*x])/(b^2*d*Sqrt[b*Tan[c + d*x]^3]) - (ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]]*Tan[c + d*x]^(3/2))/(Sqrt[2]*b^2*d*Sqrt[b*Tan[c + d*x]^3]) + (ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]]*Tan[c + d*x]^(3/2))/(Sqrt[2]*b^2*d*Sqrt[b*Tan[c + d*x]^3]) + (Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]]*Tan[c + d*x]^(3/2))/(2*Sqrt[2]*b^2*d*Sqrt[b*Tan[c + d*x]^3]) - (Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]]*Tan[c + d*x]^(3/2))/(2*Sqrt[2]*b^2*d*Sqrt[b*Tan[c + d*x]^3])","A",16,10,14,0.7143,1,"{3658, 3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
36,1,182,0,0.0628983,"\int \left(b \tan ^4(c+d x)\right)^{5/2} \, dx","Int[(b*Tan[c + d*x]^4)^(5/2),x]","\frac{b^2 \tan ^7(c+d x) \sqrt{b \tan ^4(c+d x)}}{9 d}-\frac{b^2 \tan ^5(c+d x) \sqrt{b \tan ^4(c+d x)}}{7 d}+\frac{b^2 \tan ^3(c+d x) \sqrt{b \tan ^4(c+d x)}}{5 d}-\frac{b^2 \tan (c+d x) \sqrt{b \tan ^4(c+d x)}}{3 d}-b^2 x \cot ^2(c+d x) \sqrt{b \tan ^4(c+d x)}+\frac{b^2 \cot (c+d x) \sqrt{b \tan ^4(c+d x)}}{d}","\frac{b^2 \tan ^7(c+d x) \sqrt{b \tan ^4(c+d x)}}{9 d}-\frac{b^2 \tan ^5(c+d x) \sqrt{b \tan ^4(c+d x)}}{7 d}+\frac{b^2 \tan ^3(c+d x) \sqrt{b \tan ^4(c+d x)}}{5 d}-\frac{b^2 \tan (c+d x) \sqrt{b \tan ^4(c+d x)}}{3 d}-b^2 x \cot ^2(c+d x) \sqrt{b \tan ^4(c+d x)}+\frac{b^2 \cot (c+d x) \sqrt{b \tan ^4(c+d x)}}{d}",1,"(b^2*Cot[c + d*x]*Sqrt[b*Tan[c + d*x]^4])/d - b^2*x*Cot[c + d*x]^2*Sqrt[b*Tan[c + d*x]^4] - (b^2*Tan[c + d*x]*Sqrt[b*Tan[c + d*x]^4])/(3*d) + (b^2*Tan[c + d*x]^3*Sqrt[b*Tan[c + d*x]^4])/(5*d) - (b^2*Tan[c + d*x]^5*Sqrt[b*Tan[c + d*x]^4])/(7*d) + (b^2*Tan[c + d*x]^7*Sqrt[b*Tan[c + d*x]^4])/(9*d)","A",7,3,14,0.2143,1,"{3658, 3473, 8}"
37,1,110,0,0.0427885,"\int \left(b \tan ^4(c+d x)\right)^{3/2} \, dx","Int[(b*Tan[c + d*x]^4)^(3/2),x]","\frac{b \tan ^3(c+d x) \sqrt{b \tan ^4(c+d x)}}{5 d}-\frac{b \tan (c+d x) \sqrt{b \tan ^4(c+d x)}}{3 d}-b x \cot ^2(c+d x) \sqrt{b \tan ^4(c+d x)}+\frac{b \cot (c+d x) \sqrt{b \tan ^4(c+d x)}}{d}","\frac{b \tan ^3(c+d x) \sqrt{b \tan ^4(c+d x)}}{5 d}-\frac{b \tan (c+d x) \sqrt{b \tan ^4(c+d x)}}{3 d}-b x \cot ^2(c+d x) \sqrt{b \tan ^4(c+d x)}+\frac{b \cot (c+d x) \sqrt{b \tan ^4(c+d x)}}{d}",1,"(b*Cot[c + d*x]*Sqrt[b*Tan[c + d*x]^4])/d - b*x*Cot[c + d*x]^2*Sqrt[b*Tan[c + d*x]^4] - (b*Tan[c + d*x]*Sqrt[b*Tan[c + d*x]^4])/(3*d) + (b*Tan[c + d*x]^3*Sqrt[b*Tan[c + d*x]^4])/(5*d)","A",5,3,14,0.2143,1,"{3658, 3473, 8}"
38,1,50,0,0.020658,"\int \sqrt{b \tan ^4(c+d x)} \, dx","Int[Sqrt[b*Tan[c + d*x]^4],x]","\frac{\cot (c+d x) \sqrt{b \tan ^4(c+d x)}}{d}-x \cot ^2(c+d x) \sqrt{b \tan ^4(c+d x)}","\frac{\cot (c+d x) \sqrt{b \tan ^4(c+d x)}}{d}-x \cot ^2(c+d x) \sqrt{b \tan ^4(c+d x)}",1,"(Cot[c + d*x]*Sqrt[b*Tan[c + d*x]^4])/d - x*Cot[c + d*x]^2*Sqrt[b*Tan[c + d*x]^4]","A",3,3,14,0.2143,1,"{3658, 3473, 8}"
39,1,51,0,0.0217256,"\int \frac{1}{\sqrt{b \tan ^4(c+d x)}} \, dx","Int[1/Sqrt[b*Tan[c + d*x]^4],x]","-\frac{x \tan ^2(c+d x)}{\sqrt{b \tan ^4(c+d x)}}-\frac{\tan (c+d x)}{d \sqrt{b \tan ^4(c+d x)}}","-\frac{x \tan ^2(c+d x)}{\sqrt{b \tan ^4(c+d x)}}-\frac{\tan (c+d x)}{d \sqrt{b \tan ^4(c+d x)}}",1,"-(Tan[c + d*x]/(d*Sqrt[b*Tan[c + d*x]^4])) - (x*Tan[c + d*x]^2)/Sqrt[b*Tan[c + d*x]^4]","A",3,3,14,0.2143,1,"{3658, 3473, 8}"
40,1,119,0,0.0430769,"\int \frac{1}{\left(b \tan ^4(c+d x)\right)^{3/2}} \, dx","Int[(b*Tan[c + d*x]^4)^(-3/2),x]","-\frac{x \tan ^2(c+d x)}{b \sqrt{b \tan ^4(c+d x)}}-\frac{\tan (c+d x)}{b d \sqrt{b \tan ^4(c+d x)}}-\frac{\cot ^3(c+d x)}{5 b d \sqrt{b \tan ^4(c+d x)}}+\frac{\cot (c+d x)}{3 b d \sqrt{b \tan ^4(c+d x)}}","-\frac{x \tan ^2(c+d x)}{b \sqrt{b \tan ^4(c+d x)}}-\frac{\tan (c+d x)}{b d \sqrt{b \tan ^4(c+d x)}}-\frac{\cot ^3(c+d x)}{5 b d \sqrt{b \tan ^4(c+d x)}}+\frac{\cot (c+d x)}{3 b d \sqrt{b \tan ^4(c+d x)}}",1,"Cot[c + d*x]/(3*b*d*Sqrt[b*Tan[c + d*x]^4]) - Cot[c + d*x]^3/(5*b*d*Sqrt[b*Tan[c + d*x]^4]) - Tan[c + d*x]/(b*d*Sqrt[b*Tan[c + d*x]^4]) - (x*Tan[c + d*x]^2)/(b*Sqrt[b*Tan[c + d*x]^4])","A",5,3,14,0.2143,1,"{3658, 3473, 8}"
41,1,183,0,0.0640348,"\int \frac{1}{\left(b \tan ^4(c+d x)\right)^{5/2}} \, dx","Int[(b*Tan[c + d*x]^4)^(-5/2),x]","-\frac{x \tan ^2(c+d x)}{b^2 \sqrt{b \tan ^4(c+d x)}}-\frac{\tan (c+d x)}{b^2 d \sqrt{b \tan ^4(c+d x)}}-\frac{\cot ^7(c+d x)}{9 b^2 d \sqrt{b \tan ^4(c+d x)}}+\frac{\cot ^5(c+d x)}{7 b^2 d \sqrt{b \tan ^4(c+d x)}}-\frac{\cot ^3(c+d x)}{5 b^2 d \sqrt{b \tan ^4(c+d x)}}+\frac{\cot (c+d x)}{3 b^2 d \sqrt{b \tan ^4(c+d x)}}","-\frac{x \tan ^2(c+d x)}{b^2 \sqrt{b \tan ^4(c+d x)}}-\frac{\tan (c+d x)}{b^2 d \sqrt{b \tan ^4(c+d x)}}-\frac{\cot ^7(c+d x)}{9 b^2 d \sqrt{b \tan ^4(c+d x)}}+\frac{\cot ^5(c+d x)}{7 b^2 d \sqrt{b \tan ^4(c+d x)}}-\frac{\cot ^3(c+d x)}{5 b^2 d \sqrt{b \tan ^4(c+d x)}}+\frac{\cot (c+d x)}{3 b^2 d \sqrt{b \tan ^4(c+d x)}}",1,"Cot[c + d*x]/(3*b^2*d*Sqrt[b*Tan[c + d*x]^4]) - Cot[c + d*x]^3/(5*b^2*d*Sqrt[b*Tan[c + d*x]^4]) + Cot[c + d*x]^5/(7*b^2*d*Sqrt[b*Tan[c + d*x]^4]) - Cot[c + d*x]^7/(9*b^2*d*Sqrt[b*Tan[c + d*x]^4]) - Tan[c + d*x]/(b^2*d*Sqrt[b*Tan[c + d*x]^4]) - (x*Tan[c + d*x]^2)/(b^2*Sqrt[b*Tan[c + d*x]^4])","A",7,3,14,0.2143,1,"{3658, 3473, 8}"
42,1,59,0,0.0392326,"\int \left(b \tan ^p(c+d x)\right)^n \, dx","Int[(b*Tan[c + d*x]^p)^n,x]","\frac{\tan (c+d x) \left(b \tan ^p(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(c+d x)\right)}{d (n p+1)}","\frac{\tan (c+d x) \left(b \tan ^p(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(c+d x)\right)}{d (n p+1)}",1,"(Hypergeometric2F1[1, (1 + n*p)/2, (3 + n*p)/2, -Tan[c + d*x]^2]*Tan[c + d*x]*(b*Tan[c + d*x]^p)^n)/(d*(1 + n*p))","A",3,3,12,0.2500,1,"{3659, 3476, 364}"
43,1,59,0,0.0379199,"\int \left(b \tan ^2(c+d x)\right)^n \, dx","Int[(b*Tan[c + d*x]^2)^n,x]","\frac{\tan (c+d x) \left(b \tan ^2(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (2 n+1);\frac{1}{2} (2 n+3);-\tan ^2(c+d x)\right)}{d (2 n+1)}","\frac{\tan (c+d x) \left(b \tan ^2(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (2 n+1);\frac{1}{2} (2 n+3);-\tan ^2(c+d x)\right)}{d (2 n+1)}",1,"(Hypergeometric2F1[1, (1 + 2*n)/2, (3 + 2*n)/2, -Tan[c + d*x]^2]*Tan[c + d*x]*(b*Tan[c + d*x]^2)^n)/(d*(1 + 2*n))","A",3,3,12,0.2500,1,"{3658, 3476, 364}"
44,1,57,0,0.0380648,"\int \left(b \tan ^3(c+d x)\right)^n \, dx","Int[(b*Tan[c + d*x]^3)^n,x]","\frac{\tan (c+d x) \left(b \tan ^3(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (3 n+1);\frac{3 (n+1)}{2};-\tan ^2(c+d x)\right)}{d (3 n+1)}","\frac{\tan (c+d x) \left(b \tan ^3(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (3 n+1);\frac{3 (n+1)}{2};-\tan ^2(c+d x)\right)}{d (3 n+1)}",1,"(Hypergeometric2F1[1, (1 + 3*n)/2, (3*(1 + n))/2, -Tan[c + d*x]^2]*Tan[c + d*x]*(b*Tan[c + d*x]^3)^n)/(d*(1 + 3*n))","A",3,3,12,0.2500,1,"{3658, 3476, 364}"
45,1,59,0,0.0396004,"\int \left(b \tan ^4(c+d x)\right)^n \, dx","Int[(b*Tan[c + d*x]^4)^n,x]","\frac{\tan (c+d x) \left(b \tan ^4(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (4 n+1);\frac{1}{2} (4 n+3);-\tan ^2(c+d x)\right)}{d (4 n+1)}","\frac{\tan (c+d x) \left(b \tan ^4(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (4 n+1);\frac{1}{2} (4 n+3);-\tan ^2(c+d x)\right)}{d (4 n+1)}",1,"(Hypergeometric2F1[1, (1 + 4*n)/2, (3 + 4*n)/2, -Tan[c + d*x]^2]*Tan[c + d*x]*(b*Tan[c + d*x]^4)^n)/(d*(1 + 4*n))","A",3,3,12,0.2500,1,"{3658, 3476, 364}"
46,1,71,0,0.0484212,"\int \left(b \tan ^p(c+d x)\right)^{5/2} \, dx","Int[(b*Tan[c + d*x]^p)^(5/2),x]","\frac{2 b^2 \tan ^{2 p+1}(c+d x) \sqrt{b \tan ^p(c+d x)} \, _2F_1\left(1,\frac{1}{4} (5 p+2);\frac{1}{4} (5 p+6);-\tan ^2(c+d x)\right)}{d (5 p+2)}","\frac{2 b^2 \tan ^{2 p+1}(c+d x) \sqrt{b \tan ^p(c+d x)} \, _2F_1\left(1,\frac{1}{4} (5 p+2);\frac{1}{4} (5 p+6);-\tan ^2(c+d x)\right)}{d (5 p+2)}",1,"(2*b^2*Hypergeometric2F1[1, (2 + 5*p)/4, (6 + 5*p)/4, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + 2*p)*Sqrt[b*Tan[c + d*x]^p])/(d*(2 + 5*p))","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
47,1,65,0,0.0449443,"\int \left(b \tan ^p(c+d x)\right)^{3/2} \, dx","Int[(b*Tan[c + d*x]^p)^(3/2),x]","\frac{2 b \tan ^{p+1}(c+d x) \sqrt{b \tan ^p(c+d x)} \, _2F_1\left(1,\frac{1}{4} (3 p+2);\frac{3 (p+2)}{4};-\tan ^2(c+d x)\right)}{d (3 p+2)}","\frac{2 b \tan ^{p+1}(c+d x) \sqrt{b \tan ^p(c+d x)} \, _2F_1\left(1,\frac{1}{4} (3 p+2);\frac{3 (p+2)}{4};-\tan ^2(c+d x)\right)}{d (3 p+2)}",1,"(2*b*Hypergeometric2F1[1, (2 + 3*p)/4, (3*(2 + p))/4, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + p)*Sqrt[b*Tan[c + d*x]^p])/(d*(2 + 3*p))","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
48,1,56,0,0.0415078,"\int \sqrt{b \tan ^p(c+d x)} \, dx","Int[Sqrt[b*Tan[c + d*x]^p],x]","\frac{2 \tan (c+d x) \sqrt{b \tan ^p(c+d x)} \, _2F_1\left(1,\frac{p+2}{4};\frac{p+6}{4};-\tan ^2(c+d x)\right)}{d (p+2)}","\frac{2 \tan (c+d x) \sqrt{b \tan ^p(c+d x)} \, _2F_1\left(1,\frac{p+2}{4};\frac{p+6}{4};-\tan ^2(c+d x)\right)}{d (p+2)}",1,"(2*Hypergeometric2F1[1, (2 + p)/4, (6 + p)/4, -Tan[c + d*x]^2]*Tan[c + d*x]*Sqrt[b*Tan[c + d*x]^p])/(d*(2 + p))","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
49,1,62,0,0.0485733,"\int \frac{1}{\sqrt{b \tan ^p(c+d x)}} \, dx","Int[1/Sqrt[b*Tan[c + d*x]^p],x]","\frac{2 \tan (c+d x) \, _2F_1\left(1,\frac{2-p}{4};\frac{6-p}{4};-\tan ^2(c+d x)\right)}{d (2-p) \sqrt{b \tan ^p(c+d x)}}","\frac{2 \tan (c+d x) \, _2F_1\left(1,\frac{2-p}{4};\frac{6-p}{4};-\tan ^2(c+d x)\right)}{d (2-p) \sqrt{b \tan ^p(c+d x)}}",1,"(2*Hypergeometric2F1[1, (2 - p)/4, (6 - p)/4, -Tan[c + d*x]^2]*Tan[c + d*x])/(d*(2 - p)*Sqrt[b*Tan[c + d*x]^p])","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
50,1,71,0,0.0481324,"\int \frac{1}{\left(b \tan ^p(c+d x)\right)^{3/2}} \, dx","Int[(b*Tan[c + d*x]^p)^(-3/2),x]","\frac{2 \tan ^{1-p}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2-3 p);\frac{3 (2-p)}{4};-\tan ^2(c+d x)\right)}{b d (2-3 p) \sqrt{b \tan ^p(c+d x)}}","\frac{2 \tan ^{1-p}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2-3 p);\frac{3 (2-p)}{4};-\tan ^2(c+d x)\right)}{b d (2-3 p) \sqrt{b \tan ^p(c+d x)}}",1,"(2*Hypergeometric2F1[1, (2 - 3*p)/4, (3*(2 - p))/4, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 - p))/(b*d*(2 - 3*p)*Sqrt[b*Tan[c + d*x]^p])","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
51,1,71,0,0.0466852,"\int \frac{1}{\left(b \tan ^p(c+d x)\right)^{5/2}} \, dx","Int[(b*Tan[c + d*x]^p)^(-5/2),x]","\frac{2 \tan ^{1-2 p}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2-5 p);\frac{1}{4} (6-5 p);-\tan ^2(c+d x)\right)}{b^2 d (2-5 p) \sqrt{b \tan ^p(c+d x)}}","\frac{2 \tan ^{1-2 p}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2-5 p);\frac{1}{4} (6-5 p);-\tan ^2(c+d x)\right)}{b^2 d (2-5 p) \sqrt{b \tan ^p(c+d x)}}",1,"(2*Hypergeometric2F1[1, (2 - 5*p)/4, (6 - 5*p)/4, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 - 2*p))/(b^2*d*(2 - 5*p)*Sqrt[b*Tan[c + d*x]^p])","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
52,1,32,0,0.0191736,"\int \left(b \tan ^p(c+d x)\right)^{\frac{1}{p}} \, dx","Int[(b*Tan[c + d*x]^p)^p^(-1),x]","-\frac{\cot (c+d x) \log (\cos (c+d x)) \left(b \tan ^p(c+d x)\right)^{\frac{1}{p}}}{d}","-\frac{\cot (c+d x) \log (\cos (c+d x)) \left(b \tan ^p(c+d x)\right)^{\frac{1}{p}}}{d}",1,"-((Cot[c + d*x]*Log[Cos[c + d*x]]*(b*Tan[c + d*x]^p)^p^(-1))/d)","A",2,2,14,0.1429,1,"{3659, 3475}"
53,1,61,0,0.0453724,"\int \left(a (b \tan (c+d x))^p\right)^n \, dx","Int[(a*(b*Tan[c + d*x])^p)^n,x]","\frac{\tan (c+d x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(c+d x)\right) \left(a (b \tan (c+d x))^p\right)^n}{d (n p+1)}","\frac{\tan (c+d x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(c+d x)\right) \left(a (b \tan (c+d x))^p\right)^n}{d (n p+1)}",1,"(Hypergeometric2F1[1, (1 + n*p)/2, (3 + n*p)/2, -Tan[c + d*x]^2]*Tan[c + d*x]*(a*(b*Tan[c + d*x])^p)^n)/(d*(1 + n*p))","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
54,1,257,0,0.1956791,"\int \sin ^4(a+b x) \sqrt{d \tan (a+b x)} \, dx","Int[Sin[a + b*x]^4*Sqrt[d*Tan[a + b*x]],x]","-\frac{\cos ^4(a+b x) (d \tan (a+b x))^{7/2}}{4 b d^3}-\frac{21 \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{32 \sqrt{2} b}+\frac{21 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} b}+\frac{21 \sqrt{d} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b}-\frac{21 \sqrt{d} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b}-\frac{7 \cos ^2(a+b x) (d \tan (a+b x))^{3/2}}{16 b d}","-\frac{\cos ^4(a+b x) (d \tan (a+b x))^{7/2}}{4 b d^3}-\frac{21 \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{32 \sqrt{2} b}+\frac{21 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} b}+\frac{21 \sqrt{d} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b}-\frac{21 \sqrt{d} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b}-\frac{7 \cos ^2(a+b x) (d \tan (a+b x))^{3/2}}{16 b d}",1,"(-21*Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(32*Sqrt[2]*b) + (21*Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(32*Sqrt[2]*b) + (21*Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(64*Sqrt[2]*b) - (21*Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(64*Sqrt[2]*b) - (7*Cos[a + b*x]^2*(d*Tan[a + b*x])^(3/2))/(16*b*d) - (Cos[a + b*x]^4*(d*Tan[a + b*x])^(7/2))/(4*b*d^3)","A",13,9,21,0.4286,1,"{2591, 288, 329, 297, 1162, 617, 204, 1165, 628}"
55,1,227,0,0.1606709,"\int \sin ^2(a+b x) \sqrt{d \tan (a+b x)} \, dx","Int[Sin[a + b*x]^2*Sqrt[d*Tan[a + b*x]],x]","-\frac{3 \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b}+\frac{3 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b}+\frac{3 \sqrt{d} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}-\frac{3 \sqrt{d} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}-\frac{\cos ^2(a+b x) (d \tan (a+b x))^{3/2}}{2 b d}","-\frac{3 \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b}+\frac{3 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b}+\frac{3 \sqrt{d} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}-\frac{3 \sqrt{d} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}-\frac{\cos ^2(a+b x) (d \tan (a+b x))^{3/2}}{2 b d}",1,"(-3*Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(4*Sqrt[2]*b) + (3*Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(4*Sqrt[2]*b) + (3*Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(8*Sqrt[2]*b) - (3*Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(8*Sqrt[2]*b) - (Cos[a + b*x]^2*(d*Tan[a + b*x])^(3/2))/(2*b*d)","A",12,9,21,0.4286,1,"{2591, 288, 329, 297, 1162, 617, 204, 1165, 628}"
56,1,18,0,0.0414481,"\int \csc ^2(a+b x) \sqrt{d \tan (a+b x)} \, dx","Int[Csc[a + b*x]^2*Sqrt[d*Tan[a + b*x]],x]","-\frac{2 d}{b \sqrt{d \tan (a+b x)}}","-\frac{2 d}{b \sqrt{d \tan (a+b x)}}",1,"(-2*d)/(b*Sqrt[d*Tan[a + b*x]])","A",2,2,21,0.09524,1,"{2591, 30}"
57,1,41,0,0.0447967,"\int \csc ^4(a+b x) \sqrt{d \tan (a+b x)} \, dx","Int[Csc[a + b*x]^4*Sqrt[d*Tan[a + b*x]],x]","-\frac{2 d^3}{5 b (d \tan (a+b x))^{5/2}}-\frac{2 d}{b \sqrt{d \tan (a+b x)}}","-\frac{2 d^3}{5 b (d \tan (a+b x))^{5/2}}-\frac{2 d}{b \sqrt{d \tan (a+b x)}}",1,"(-2*d^3)/(5*b*(d*Tan[a + b*x])^(5/2)) - (2*d)/(b*Sqrt[d*Tan[a + b*x]])","A",3,2,21,0.09524,1,"{2591, 14}"
58,1,63,0,0.0515714,"\int \csc ^6(a+b x) \sqrt{d \tan (a+b x)} \, dx","Int[Csc[a + b*x]^6*Sqrt[d*Tan[a + b*x]],x]","-\frac{2 d^5}{9 b (d \tan (a+b x))^{9/2}}-\frac{4 d^3}{5 b (d \tan (a+b x))^{5/2}}-\frac{2 d}{b \sqrt{d \tan (a+b x)}}","-\frac{2 d^5}{9 b (d \tan (a+b x))^{9/2}}-\frac{4 d^3}{5 b (d \tan (a+b x))^{5/2}}-\frac{2 d}{b \sqrt{d \tan (a+b x)}}",1,"(-2*d^5)/(9*b*(d*Tan[a + b*x])^(9/2)) - (4*d^3)/(5*b*(d*Tan[a + b*x])^(5/2)) - (2*d)/(b*Sqrt[d*Tan[a + b*x]])","A",3,2,21,0.09524,1,"{2591, 270}"
59,1,105,0,0.1332079,"\int \sin ^3(a+b x) \sqrt{d \tan (a+b x)} \, dx","Int[Sin[a + b*x]^3*Sqrt[d*Tan[a + b*x]],x]","-\frac{d \sin ^3(a+b x)}{3 b \sqrt{d \tan (a+b x)}}-\frac{5 d \sin (a+b x)}{6 b \sqrt{d \tan (a+b x)}}+\frac{5 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{12 b}","-\frac{d \sin ^3(a+b x)}{3 b \sqrt{d \tan (a+b x)}}-\frac{5 d \sin (a+b x)}{6 b \sqrt{d \tan (a+b x)}}+\frac{5 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{12 b}",1,"(-5*d*Sin[a + b*x])/(6*b*Sqrt[d*Tan[a + b*x]]) - (d*Sin[a + b*x]^3)/(3*b*Sqrt[d*Tan[a + b*x]]) + (5*Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/(12*b)","A",5,4,21,0.1905,1,"{2598, 2601, 2573, 2641}"
60,1,75,0,0.0901895,"\int \sin (a+b x) \sqrt{d \tan (a+b x)} \, dx","Int[Sin[a + b*x]*Sqrt[d*Tan[a + b*x]],x]","\frac{\sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{2 b}-\frac{d \sin (a+b x)}{b \sqrt{d \tan (a+b x)}}","\frac{\sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{2 b}-\frac{d \sin (a+b x)}{b \sqrt{d \tan (a+b x)}}",1,"-((d*Sin[a + b*x])/(b*Sqrt[d*Tan[a + b*x]])) + (Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/(2*b)","A",4,4,19,0.2105,1,"{2598, 2601, 2573, 2641}"
61,1,47,0,0.0681022,"\int \csc (a+b x) \sqrt{d \tan (a+b x)} \, dx","Int[Csc[a + b*x]*Sqrt[d*Tan[a + b*x]],x]","\frac{\sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{b}","\frac{\sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{b}",1,"(Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/b","A",3,3,19,0.1579,1,"{2601, 2573, 2641}"
62,1,77,0,0.1057395,"\int \csc ^3(a+b x) \sqrt{d \tan (a+b x)} \, dx","Int[Csc[a + b*x]^3*Sqrt[d*Tan[a + b*x]],x]","\frac{2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{3 b}-\frac{2 d \csc (a+b x)}{3 b \sqrt{d \tan (a+b x)}}","\frac{2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{3 b}-\frac{2 d \csc (a+b x)}{3 b \sqrt{d \tan (a+b x)}}",1,"(-2*d*Csc[a + b*x])/(3*b*Sqrt[d*Tan[a + b*x]]) + (2*Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/(3*b)","A",4,4,21,0.1905,1,"{2599, 2601, 2573, 2641}"
63,1,105,0,0.1429629,"\int \csc ^5(a+b x) \sqrt{d \tan (a+b x)} \, dx","Int[Csc[a + b*x]^5*Sqrt[d*Tan[a + b*x]],x]","-\frac{2 d \csc ^3(a+b x)}{7 b \sqrt{d \tan (a+b x)}}-\frac{4 d \csc (a+b x)}{7 b \sqrt{d \tan (a+b x)}}+\frac{4 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{7 b}","-\frac{2 d \csc ^3(a+b x)}{7 b \sqrt{d \tan (a+b x)}}-\frac{4 d \csc (a+b x)}{7 b \sqrt{d \tan (a+b x)}}+\frac{4 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{7 b}",1,"(-4*d*Csc[a + b*x])/(7*b*Sqrt[d*Tan[a + b*x]]) - (2*d*Csc[a + b*x]^3)/(7*b*Sqrt[d*Tan[a + b*x]]) + (4*Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/(7*b)","A",5,4,21,0.1905,1,"{2599, 2601, 2573, 2641}"
64,1,277,0,0.19601,"\int \sin ^4(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Sin[a + b*x]^4*(d*Tan[a + b*x])^(3/2),x]","\frac{45 d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{32 \sqrt{2} b}-\frac{45 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} b}+\frac{45 d^{3/2} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b}-\frac{45 d^{3/2} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b}-\frac{\cos ^4(a+b x) (d \tan (a+b x))^{9/2}}{4 b d^3}+\frac{45 d \sqrt{d \tan (a+b x)}}{16 b}-\frac{9 \cos ^2(a+b x) (d \tan (a+b x))^{5/2}}{16 b d}","\frac{45 d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{32 \sqrt{2} b}-\frac{45 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} b}+\frac{45 d^{3/2} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b}-\frac{45 d^{3/2} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b}-\frac{\cos ^4(a+b x) (d \tan (a+b x))^{9/2}}{4 b d^3}+\frac{45 d \sqrt{d \tan (a+b x)}}{16 b}-\frac{9 \cos ^2(a+b x) (d \tan (a+b x))^{5/2}}{16 b d}",1,"(45*d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(32*Sqrt[2]*b) - (45*d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(32*Sqrt[2]*b) + (45*d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(64*Sqrt[2]*b) - (45*d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(64*Sqrt[2]*b) + (45*d*Sqrt[d*Tan[a + b*x]])/(16*b) - (9*Cos[a + b*x]^2*(d*Tan[a + b*x])^(5/2))/(16*b*d) - (Cos[a + b*x]^4*(d*Tan[a + b*x])^(9/2))/(4*b*d^3)","A",14,10,21,0.4762,1,"{2591, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
65,1,247,0,0.1759746,"\int \sin ^2(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Sin[a + b*x]^2*(d*Tan[a + b*x])^(3/2),x]","\frac{5 d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b}-\frac{5 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b}+\frac{5 d^{3/2} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}-\frac{5 d^{3/2} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}+\frac{5 d \sqrt{d \tan (a+b x)}}{2 b}-\frac{\cos ^2(a+b x) (d \tan (a+b x))^{5/2}}{2 b d}","\frac{5 d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b}-\frac{5 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b}+\frac{5 d^{3/2} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}-\frac{5 d^{3/2} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}+\frac{5 d \sqrt{d \tan (a+b x)}}{2 b}-\frac{\cos ^2(a+b x) (d \tan (a+b x))^{5/2}}{2 b d}",1,"(5*d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(4*Sqrt[2]*b) - (5*d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(4*Sqrt[2]*b) + (5*d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(8*Sqrt[2]*b) - (5*d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(8*Sqrt[2]*b) + (5*d*Sqrt[d*Tan[a + b*x]])/(2*b) - (Cos[a + b*x]^2*(d*Tan[a + b*x])^(5/2))/(2*b*d)","A",13,10,21,0.4762,1,"{2591, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
66,1,18,0,0.0429873,"\int \csc ^2(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Csc[a + b*x]^2*(d*Tan[a + b*x])^(3/2),x]","\frac{2 d \sqrt{d \tan (a+b x)}}{b}","\frac{2 d \sqrt{d \tan (a+b x)}}{b}",1,"(2*d*Sqrt[d*Tan[a + b*x]])/b","A",2,2,21,0.09524,1,"{2591, 30}"
67,1,41,0,0.0478271,"\int \csc ^4(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Csc[a + b*x]^4*(d*Tan[a + b*x])^(3/2),x]","\frac{2 d \sqrt{d \tan (a+b x)}}{b}-\frac{2 d^3}{3 b (d \tan (a+b x))^{3/2}}","\frac{2 d \sqrt{d \tan (a+b x)}}{b}-\frac{2 d^3}{3 b (d \tan (a+b x))^{3/2}}",1,"(-2*d^3)/(3*b*(d*Tan[a + b*x])^(3/2)) + (2*d*Sqrt[d*Tan[a + b*x]])/b","A",3,2,21,0.09524,1,"{2591, 14}"
68,1,63,0,0.0547959,"\int \csc ^6(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Csc[a + b*x]^6*(d*Tan[a + b*x])^(3/2),x]","-\frac{2 d^5}{7 b (d \tan (a+b x))^{7/2}}-\frac{4 d^3}{3 b (d \tan (a+b x))^{3/2}}+\frac{2 d \sqrt{d \tan (a+b x)}}{b}","-\frac{2 d^5}{7 b (d \tan (a+b x))^{7/2}}-\frac{4 d^3}{3 b (d \tan (a+b x))^{3/2}}+\frac{2 d \sqrt{d \tan (a+b x)}}{b}",1,"(-2*d^5)/(7*b*(d*Tan[a + b*x])^(7/2)) - (4*d^3)/(3*b*(d*Tan[a + b*x])^(3/2)) + (2*d*Sqrt[d*Tan[a + b*x]])/b","A",3,2,21,0.09524,1,"{2591, 270}"
69,1,110,0,0.1410574,"\int \sin ^3(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Sin[a + b*x]^3*(d*Tan[a + b*x])^(3/2),x]","\frac{7 d^3 \sin ^3(a+b x)}{3 b (d \tan (a+b x))^{3/2}}-\frac{7 d^2 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}+\frac{2 d \sin ^3(a+b x) \sqrt{d \tan (a+b x)}}{b}","\frac{7 d^3 \sin ^3(a+b x)}{3 b (d \tan (a+b x))^{3/2}}-\frac{7 d^2 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}+\frac{2 d \sin ^3(a+b x) \sqrt{d \tan (a+b x)}}{b}",1,"(7*d^3*Sin[a + b*x]^3)/(3*b*(d*Tan[a + b*x])^(3/2)) - (7*d^2*EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(2*b*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]]) + (2*d*Sin[a + b*x]^3*Sqrt[d*Tan[a + b*x]])/b","A",5,5,21,0.2381,1,"{2594, 2598, 2601, 2572, 2639}"
70,1,76,0,0.0868062,"\int \sin (a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Sin[a + b*x]*(d*Tan[a + b*x])^(3/2),x]","\frac{2 d \sin (a+b x) \sqrt{d \tan (a+b x)}}{b}-\frac{3 d^2 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}","\frac{2 d \sin (a+b x) \sqrt{d \tan (a+b x)}}{b}-\frac{3 d^2 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}",1,"(-3*d^2*EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(b*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]]) + (2*d*Sin[a + b*x]*Sqrt[d*Tan[a + b*x]])/b","A",4,4,19,0.2105,1,"{2594, 2601, 2572, 2639}"
71,1,76,0,0.0940729,"\int \csc (a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Csc[a + b*x]*(d*Tan[a + b*x])^(3/2),x]","\frac{2 d \sin (a+b x) \sqrt{d \tan (a+b x)}}{b}-\frac{2 d^2 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}","\frac{2 d \sin (a+b x) \sqrt{d \tan (a+b x)}}{b}-\frac{2 d^2 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}",1,"(-2*d^2*EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(b*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]]) + (2*d*Sin[a + b*x]*Sqrt[d*Tan[a + b*x]])/b","A",4,4,19,0.2105,1,"{2593, 2601, 2572, 2639}"
72,1,102,0,0.1428775,"\int \csc ^3(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Csc[a + b*x]^3*(d*Tan[a + b*x])^(3/2),x]","-\frac{4 d^2 \cos (a+b x)}{b \sqrt{d \tan (a+b x)}}-\frac{4 d^2 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}+\frac{2 d \csc (a+b x) \sqrt{d \tan (a+b x)}}{b}","-\frac{4 d^2 \cos (a+b x)}{b \sqrt{d \tan (a+b x)}}-\frac{4 d^2 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}+\frac{2 d \csc (a+b x) \sqrt{d \tan (a+b x)}}{b}",1,"(-4*d^2*Cos[a + b*x])/(b*Sqrt[d*Tan[a + b*x]]) - (4*d^2*EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(b*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]]) + (2*d*Csc[a + b*x]*Sqrt[d*Tan[a + b*x]])/b","A",5,5,21,0.2381,1,"{2593, 2601, 2570, 2572, 2639}"
73,1,277,0,0.194189,"\int \sin ^4(a+b x) (d \tan (a+b x))^{5/2} \, dx","Int[Sin[a + b*x]^4*(d*Tan[a + b*x])^(5/2),x]","\frac{77 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{32 \sqrt{2} b}-\frac{77 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} b}-\frac{77 d^{5/2} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b}+\frac{77 d^{5/2} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b}-\frac{\cos ^4(a+b x) (d \tan (a+b x))^{11/2}}{4 b d^3}+\frac{77 d (d \tan (a+b x))^{3/2}}{48 b}-\frac{11 \cos ^2(a+b x) (d \tan (a+b x))^{7/2}}{16 b d}","\frac{77 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{32 \sqrt{2} b}-\frac{77 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} b}-\frac{77 d^{5/2} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b}+\frac{77 d^{5/2} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b}-\frac{\cos ^4(a+b x) (d \tan (a+b x))^{11/2}}{4 b d^3}+\frac{77 d (d \tan (a+b x))^{3/2}}{48 b}-\frac{11 \cos ^2(a+b x) (d \tan (a+b x))^{7/2}}{16 b d}",1,"(77*d^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(32*Sqrt[2]*b) - (77*d^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(32*Sqrt[2]*b) - (77*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(64*Sqrt[2]*b) + (77*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(64*Sqrt[2]*b) + (77*d*(d*Tan[a + b*x])^(3/2))/(48*b) - (11*Cos[a + b*x]^2*(d*Tan[a + b*x])^(7/2))/(16*b*d) - (Cos[a + b*x]^4*(d*Tan[a + b*x])^(11/2))/(4*b*d^3)","A",14,10,21,0.4762,1,"{2591, 288, 321, 329, 297, 1162, 617, 204, 1165, 628}"
74,1,247,0,0.1751314,"\int \sin ^2(a+b x) (d \tan (a+b x))^{5/2} \, dx","Int[Sin[a + b*x]^2*(d*Tan[a + b*x])^(5/2),x]","\frac{7 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b}-\frac{7 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b}-\frac{7 d^{5/2} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}+\frac{7 d^{5/2} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}+\frac{7 d (d \tan (a+b x))^{3/2}}{6 b}-\frac{\cos ^2(a+b x) (d \tan (a+b x))^{7/2}}{2 b d}","\frac{7 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b}-\frac{7 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b}-\frac{7 d^{5/2} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}+\frac{7 d^{5/2} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}+\frac{7 d (d \tan (a+b x))^{3/2}}{6 b}-\frac{\cos ^2(a+b x) (d \tan (a+b x))^{7/2}}{2 b d}",1,"(7*d^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(4*Sqrt[2]*b) - (7*d^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(4*Sqrt[2]*b) - (7*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(8*Sqrt[2]*b) + (7*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(8*Sqrt[2]*b) + (7*d*(d*Tan[a + b*x])^(3/2))/(6*b) - (Cos[a + b*x]^2*(d*Tan[a + b*x])^(7/2))/(2*b*d)","A",13,10,21,0.4762,1,"{2591, 288, 321, 329, 297, 1162, 617, 204, 1165, 628}"
75,1,20,0,0.0420846,"\int \csc ^2(a+b x) (d \tan (a+b x))^{5/2} \, dx","Int[Csc[a + b*x]^2*(d*Tan[a + b*x])^(5/2),x]","\frac{2 d (d \tan (a+b x))^{3/2}}{3 b}","\frac{2 d (d \tan (a+b x))^{3/2}}{3 b}",1,"(2*d*(d*Tan[a + b*x])^(3/2))/(3*b)","A",2,2,21,0.09524,1,"{2591, 30}"
76,1,41,0,0.0482106,"\int \csc ^4(a+b x) (d \tan (a+b x))^{5/2} \, dx","Int[Csc[a + b*x]^4*(d*Tan[a + b*x])^(5/2),x]","\frac{2 d (d \tan (a+b x))^{3/2}}{3 b}-\frac{2 d^3}{b \sqrt{d \tan (a+b x)}}","\frac{2 d (d \tan (a+b x))^{3/2}}{3 b}-\frac{2 d^3}{b \sqrt{d \tan (a+b x)}}",1,"(-2*d^3)/(b*Sqrt[d*Tan[a + b*x]]) + (2*d*(d*Tan[a + b*x])^(3/2))/(3*b)","A",3,2,21,0.09524,1,"{2591, 14}"
77,1,63,0,0.0539081,"\int \csc ^6(a+b x) (d \tan (a+b x))^{5/2} \, dx","Int[Csc[a + b*x]^6*(d*Tan[a + b*x])^(5/2),x]","-\frac{2 d^5}{5 b (d \tan (a+b x))^{5/2}}-\frac{4 d^3}{b \sqrt{d \tan (a+b x)}}+\frac{2 d (d \tan (a+b x))^{3/2}}{3 b}","-\frac{2 d^5}{5 b (d \tan (a+b x))^{5/2}}-\frac{4 d^3}{b \sqrt{d \tan (a+b x)}}+\frac{2 d (d \tan (a+b x))^{3/2}}{3 b}",1,"(-2*d^5)/(5*b*(d*Tan[a + b*x])^(5/2)) - (4*d^3)/(b*Sqrt[d*Tan[a + b*x]]) + (2*d*(d*Tan[a + b*x])^(3/2))/(3*b)","A",3,2,21,0.09524,1,"{2591, 270}"
78,1,137,0,0.1745264,"\int \sin ^3(a+b x) (d \tan (a+b x))^{5/2} \, dx","Int[Sin[a + b*x]^3*(d*Tan[a + b*x])^(5/2),x]","\frac{d^3 \sin ^3(a+b x)}{b \sqrt{d \tan (a+b x)}}+\frac{5 d^3 \sin (a+b x)}{2 b \sqrt{d \tan (a+b x)}}-\frac{5 d^2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{4 b}+\frac{2 d \sin ^3(a+b x) (d \tan (a+b x))^{3/2}}{3 b}","\frac{d^3 \sin ^3(a+b x)}{b \sqrt{d \tan (a+b x)}}+\frac{5 d^3 \sin (a+b x)}{2 b \sqrt{d \tan (a+b x)}}-\frac{5 d^2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{4 b}+\frac{2 d \sin ^3(a+b x) (d \tan (a+b x))^{3/2}}{3 b}",1,"(5*d^3*Sin[a + b*x])/(2*b*Sqrt[d*Tan[a + b*x]]) + (d^3*Sin[a + b*x]^3)/(b*Sqrt[d*Tan[a + b*x]]) - (5*d^2*Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/(4*b) + (2*d*Sin[a + b*x]^3*(d*Tan[a + b*x])^(3/2))/(3*b)","A",6,5,21,0.2381,1,"{2594, 2598, 2601, 2573, 2641}"
79,1,108,0,0.1163946,"\int \sin (a+b x) (d \tan (a+b x))^{5/2} \, dx","Int[Sin[a + b*x]*(d*Tan[a + b*x])^(5/2),x]","\frac{5 d^3 \sin (a+b x)}{3 b \sqrt{d \tan (a+b x)}}-\frac{5 d^2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{6 b}+\frac{2 d \sin (a+b x) (d \tan (a+b x))^{3/2}}{3 b}","\frac{5 d^3 \sin (a+b x)}{3 b \sqrt{d \tan (a+b x)}}-\frac{5 d^2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{6 b}+\frac{2 d \sin (a+b x) (d \tan (a+b x))^{3/2}}{3 b}",1,"(5*d^3*Sin[a + b*x])/(3*b*Sqrt[d*Tan[a + b*x]]) - (5*d^2*Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/(6*b) + (2*d*Sin[a + b*x]*(d*Tan[a + b*x])^(3/2))/(3*b)","A",5,5,19,0.2632,1,"{2594, 2598, 2601, 2573, 2641}"
80,1,80,0,0.1012854,"\int \csc (a+b x) (d \tan (a+b x))^{5/2} \, dx","Int[Csc[a + b*x]*(d*Tan[a + b*x])^(5/2),x]","\frac{2 d \csc (a+b x) (d \tan (a+b x))^{3/2}}{3 b}-\frac{d^2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{3 b}","\frac{2 d \csc (a+b x) (d \tan (a+b x))^{3/2}}{3 b}-\frac{d^2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{3 b}",1,"-(d^2*Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/(3*b) + (2*d*Csc[a + b*x]*(d*Tan[a + b*x])^(3/2))/(3*b)","A",4,4,19,0.2105,1,"{2594, 2601, 2573, 2641}"
81,1,80,0,0.107196,"\int \csc ^3(a+b x) (d \tan (a+b x))^{5/2} \, dx","Int[Csc[a + b*x]^3*(d*Tan[a + b*x])^(5/2),x]","\frac{2 d^2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{3 b}+\frac{2 d \csc (a+b x) (d \tan (a+b x))^{3/2}}{3 b}","\frac{2 d^2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{3 b}+\frac{2 d \csc (a+b x) (d \tan (a+b x))^{3/2}}{3 b}",1,"(2*d^2*Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/(3*b) + (2*d*Csc[a + b*x]*(d*Tan[a + b*x])^(3/2))/(3*b)","A",4,4,21,0.1905,1,"{2593, 2601, 2573, 2641}"
82,1,110,0,0.1468656,"\int \csc ^5(a+b x) (d \tan (a+b x))^{5/2} \, dx","Int[Csc[a + b*x]^5*(d*Tan[a + b*x])^(5/2),x]","-\frac{4 d^3 \csc (a+b x)}{3 b \sqrt{d \tan (a+b x)}}+\frac{4 d^2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{3 b}+\frac{2 d \csc ^3(a+b x) (d \tan (a+b x))^{3/2}}{3 b}","-\frac{4 d^3 \csc (a+b x)}{3 b \sqrt{d \tan (a+b x)}}+\frac{4 d^2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{3 b}+\frac{2 d \csc ^3(a+b x) (d \tan (a+b x))^{3/2}}{3 b}",1,"(-4*d^3*Csc[a + b*x])/(3*b*Sqrt[d*Tan[a + b*x]]) + (4*d^2*Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/(3*b) + (2*d*Csc[a + b*x]^3*(d*Tan[a + b*x])^(3/2))/(3*b)","A",5,5,21,0.2381,1,"{2593, 2599, 2601, 2573, 2641}"
83,1,140,0,0.1848407,"\int \csc ^7(a+b x) (d \tan (a+b x))^{5/2} \, dx","Int[Csc[a + b*x]^7*(d*Tan[a + b*x])^(5/2),x]","-\frac{20 d^3 \csc ^3(a+b x)}{21 b \sqrt{d \tan (a+b x)}}-\frac{40 d^3 \csc (a+b x)}{21 b \sqrt{d \tan (a+b x)}}+\frac{40 d^2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{21 b}+\frac{2 d \csc ^5(a+b x) (d \tan (a+b x))^{3/2}}{3 b}","-\frac{20 d^3 \csc ^3(a+b x)}{21 b \sqrt{d \tan (a+b x)}}-\frac{40 d^3 \csc (a+b x)}{21 b \sqrt{d \tan (a+b x)}}+\frac{40 d^2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{21 b}+\frac{2 d \csc ^5(a+b x) (d \tan (a+b x))^{3/2}}{3 b}",1,"(-40*d^3*Csc[a + b*x])/(21*b*Sqrt[d*Tan[a + b*x]]) - (20*d^3*Csc[a + b*x]^3)/(21*b*Sqrt[d*Tan[a + b*x]]) + (40*d^2*Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/(21*b) + (2*d*Csc[a + b*x]^5*(d*Tan[a + b*x])^(3/2))/(3*b)","A",6,5,21,0.2381,1,"{2593, 2599, 2601, 2573, 2641}"
84,1,257,0,0.1739852,"\int \frac{\sin ^4(a+b x)}{\sqrt{d \tan (a+b x)}} \, dx","Int[Sin[a + b*x]^4/Sqrt[d*Tan[a + b*x]],x]","-\frac{\cos ^4(a+b x) (d \tan (a+b x))^{5/2}}{4 b d^3}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{32 \sqrt{2} b \sqrt{d}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} b \sqrt{d}}-\frac{5 \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b \sqrt{d}}+\frac{5 \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b \sqrt{d}}-\frac{5 \cos ^2(a+b x) \sqrt{d \tan (a+b x)}}{16 b d}","-\frac{\cos ^4(a+b x) (d \tan (a+b x))^{5/2}}{4 b d^3}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{32 \sqrt{2} b \sqrt{d}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} b \sqrt{d}}-\frac{5 \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b \sqrt{d}}+\frac{5 \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b \sqrt{d}}-\frac{5 \cos ^2(a+b x) \sqrt{d \tan (a+b x)}}{16 b d}",1,"(-5*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(32*Sqrt[2]*b*Sqrt[d]) + (5*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(32*Sqrt[2]*b*Sqrt[d]) - (5*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(64*Sqrt[2]*b*Sqrt[d]) + (5*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(64*Sqrt[2]*b*Sqrt[d]) - (5*Cos[a + b*x]^2*Sqrt[d*Tan[a + b*x]])/(16*b*d) - (Cos[a + b*x]^4*(d*Tan[a + b*x])^(5/2))/(4*b*d^3)","A",13,9,21,0.4286,1,"{2591, 288, 329, 211, 1165, 628, 1162, 617, 204}"
85,1,227,0,0.1502868,"\int \frac{\sin ^2(a+b x)}{\sqrt{d \tan (a+b x)}} \, dx","Int[Sin[a + b*x]^2/Sqrt[d*Tan[a + b*x]],x]","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b \sqrt{d}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b \sqrt{d}}-\frac{\log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b \sqrt{d}}+\frac{\log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b \sqrt{d}}-\frac{\cos ^2(a+b x) \sqrt{d \tan (a+b x)}}{2 b d}","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b \sqrt{d}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b \sqrt{d}}-\frac{\log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b \sqrt{d}}+\frac{\log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b \sqrt{d}}-\frac{\cos ^2(a+b x) \sqrt{d \tan (a+b x)}}{2 b d}",1,"-ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]]/(4*Sqrt[2]*b*Sqrt[d]) + ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]]/(4*Sqrt[2]*b*Sqrt[d]) - Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]]/(8*Sqrt[2]*b*Sqrt[d]) + Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]]/(8*Sqrt[2]*b*Sqrt[d]) - (Cos[a + b*x]^2*Sqrt[d*Tan[a + b*x]])/(2*b*d)","A",12,9,21,0.4286,1,"{2591, 288, 329, 211, 1165, 628, 1162, 617, 204}"
86,1,20,0,0.0363285,"\int \frac{\csc ^2(a+b x)}{\sqrt{d \tan (a+b x)}} \, dx","Int[Csc[a + b*x]^2/Sqrt[d*Tan[a + b*x]],x]","-\frac{2 d}{3 b (d \tan (a+b x))^{3/2}}","-\frac{2 d}{3 b (d \tan (a+b x))^{3/2}}",1,"(-2*d)/(3*b*(d*Tan[a + b*x])^(3/2))","A",2,2,21,0.09524,1,"{2591, 30}"
87,1,43,0,0.0427622,"\int \frac{\csc ^4(a+b x)}{\sqrt{d \tan (a+b x)}} \, dx","Int[Csc[a + b*x]^4/Sqrt[d*Tan[a + b*x]],x]","-\frac{2 d^3}{7 b (d \tan (a+b x))^{7/2}}-\frac{2 d}{3 b (d \tan (a+b x))^{3/2}}","-\frac{2 d^3}{7 b (d \tan (a+b x))^{7/2}}-\frac{2 d}{3 b (d \tan (a+b x))^{3/2}}",1,"(-2*d^3)/(7*b*(d*Tan[a + b*x])^(7/2)) - (2*d)/(3*b*(d*Tan[a + b*x])^(3/2))","A",3,2,21,0.09524,1,"{2591, 14}"
88,1,65,0,0.0489785,"\int \frac{\csc ^6(a+b x)}{\sqrt{d \tan (a+b x)}} \, dx","Int[Csc[a + b*x]^6/Sqrt[d*Tan[a + b*x]],x]","-\frac{2 d^5}{11 b (d \tan (a+b x))^{11/2}}-\frac{4 d^3}{7 b (d \tan (a+b x))^{7/2}}-\frac{2 d}{3 b (d \tan (a+b x))^{3/2}}","-\frac{2 d^5}{11 b (d \tan (a+b x))^{11/2}}-\frac{4 d^3}{7 b (d \tan (a+b x))^{7/2}}-\frac{2 d}{3 b (d \tan (a+b x))^{3/2}}",1,"(-2*d^5)/(11*b*(d*Tan[a + b*x])^(11/2)) - (4*d^3)/(7*b*(d*Tan[a + b*x])^(7/2)) - (2*d)/(3*b*(d*Tan[a + b*x])^(3/2))","A",3,2,21,0.09524,1,"{2591, 270}"
89,1,107,0,0.132531,"\int \frac{\sin ^5(a+b x)}{\sqrt{d \tan (a+b x)}} \, dx","Int[Sin[a + b*x]^5/Sqrt[d*Tan[a + b*x]],x]","-\frac{d \sin ^5(a+b x)}{5 b (d \tan (a+b x))^{3/2}}-\frac{7 d \sin ^3(a+b x)}{30 b (d \tan (a+b x))^{3/2}}+\frac{7 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{20 b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}","-\frac{d \sin ^5(a+b x)}{5 b (d \tan (a+b x))^{3/2}}-\frac{7 d \sin ^3(a+b x)}{30 b (d \tan (a+b x))^{3/2}}+\frac{7 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{20 b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}",1,"(-7*d*Sin[a + b*x]^3)/(30*b*(d*Tan[a + b*x])^(3/2)) - (d*Sin[a + b*x]^5)/(5*b*(d*Tan[a + b*x])^(3/2)) + (7*EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(20*b*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])","A",5,4,21,0.1905,1,"{2598, 2601, 2572, 2639}"
90,1,79,0,0.0943914,"\int \frac{\sin ^3(a+b x)}{\sqrt{d \tan (a+b x)}} \, dx","Int[Sin[a + b*x]^3/Sqrt[d*Tan[a + b*x]],x]","\frac{\sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}-\frac{d \sin ^3(a+b x)}{3 b (d \tan (a+b x))^{3/2}}","\frac{\sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}-\frac{d \sin ^3(a+b x)}{3 b (d \tan (a+b x))^{3/2}}",1,"-(d*Sin[a + b*x]^3)/(3*b*(d*Tan[a + b*x])^(3/2)) + (EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(2*b*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])","A",4,4,21,0.1905,1,"{2598, 2601, 2572, 2639}"
91,1,47,0,0.0572691,"\int \frac{\sin (a+b x)}{\sqrt{d \tan (a+b x)}} \, dx","Int[Sin[a + b*x]/Sqrt[d*Tan[a + b*x]],x]","\frac{\sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}","\frac{\sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}",1,"(EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(b*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])","A",3,3,19,0.1579,1,"{2601, 2572, 2639}"
92,1,72,0,0.0971656,"\int \frac{\csc (a+b x)}{\sqrt{d \tan (a+b x)}} \, dx","Int[Csc[a + b*x]/Sqrt[d*Tan[a + b*x]],x]","-\frac{2 \cos (a+b x)}{b \sqrt{d \tan (a+b x)}}-\frac{2 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}","-\frac{2 \cos (a+b x)}{b \sqrt{d \tan (a+b x)}}-\frac{2 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}",1,"(-2*Cos[a + b*x])/(b*Sqrt[d*Tan[a + b*x]]) - (2*EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(b*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])","A",4,4,19,0.2105,1,"{2601, 2570, 2572, 2639}"
93,1,102,0,0.1338958,"\int \frac{\csc ^3(a+b x)}{\sqrt{d \tan (a+b x)}} \, dx","Int[Csc[a + b*x]^3/Sqrt[d*Tan[a + b*x]],x]","-\frac{4 \cos (a+b x)}{5 b \sqrt{d \tan (a+b x)}}-\frac{2 d \csc (a+b x)}{5 b (d \tan (a+b x))^{3/2}}-\frac{4 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}","-\frac{4 \cos (a+b x)}{5 b \sqrt{d \tan (a+b x)}}-\frac{2 d \csc (a+b x)}{5 b (d \tan (a+b x))^{3/2}}-\frac{4 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}",1,"(-2*d*Csc[a + b*x])/(5*b*(d*Tan[a + b*x])^(3/2)) - (4*Cos[a + b*x])/(5*b*Sqrt[d*Tan[a + b*x]]) - (4*EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(5*b*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])","A",5,5,21,0.2381,1,"{2599, 2601, 2570, 2572, 2639}"
94,1,257,0,0.1819126,"\int \frac{\sin ^4(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Sin[a + b*x]^4/(d*Tan[a + b*x])^(3/2),x]","-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{32 \sqrt{2} b d^{3/2}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} b d^{3/2}}+\frac{3 \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b d^{3/2}}-\frac{3 \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b d^{3/2}}-\frac{\cos ^4(a+b x) (d \tan (a+b x))^{3/2}}{4 b d^3}+\frac{3 \cos ^2(a+b x) (d \tan (a+b x))^{3/2}}{16 b d^3}","-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{32 \sqrt{2} b d^{3/2}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} b d^{3/2}}+\frac{3 \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b d^{3/2}}-\frac{3 \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b d^{3/2}}-\frac{\cos ^4(a+b x) (d \tan (a+b x))^{3/2}}{4 b d^3}+\frac{3 \cos ^2(a+b x) (d \tan (a+b x))^{3/2}}{16 b d^3}",1,"(-3*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(32*Sqrt[2]*b*d^(3/2)) + (3*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(32*Sqrt[2]*b*d^(3/2)) + (3*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(64*Sqrt[2]*b*d^(3/2)) - (3*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(64*Sqrt[2]*b*d^(3/2)) + (3*Cos[a + b*x]^2*(d*Tan[a + b*x])^(3/2))/(16*b*d^3) - (Cos[a + b*x]^4*(d*Tan[a + b*x])^(3/2))/(4*b*d^3)","A",13,10,21,0.4762,1,"{2591, 288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
95,1,227,0,0.1577291,"\int \frac{\sin ^2(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Sin[a + b*x]^2/(d*Tan[a + b*x])^(3/2),x]","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b d^{3/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b d^{3/2}}+\frac{\log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b d^{3/2}}-\frac{\log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b d^{3/2}}+\frac{\cos ^2(a+b x) (d \tan (a+b x))^{3/2}}{2 b d^3}","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b d^{3/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b d^{3/2}}+\frac{\log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b d^{3/2}}-\frac{\log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b d^{3/2}}+\frac{\cos ^2(a+b x) (d \tan (a+b x))^{3/2}}{2 b d^3}",1,"-ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]]/(4*Sqrt[2]*b*d^(3/2)) + ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]]/(4*Sqrt[2]*b*d^(3/2)) + Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]]/(8*Sqrt[2]*b*d^(3/2)) - Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]]/(8*Sqrt[2]*b*d^(3/2)) + (Cos[a + b*x]^2*(d*Tan[a + b*x])^(3/2))/(2*b*d^3)","A",12,9,21,0.4286,1,"{2591, 290, 329, 297, 1162, 617, 204, 1165, 628}"
96,1,20,0,0.0429692,"\int \frac{\csc ^2(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Csc[a + b*x]^2/(d*Tan[a + b*x])^(3/2),x]","-\frac{2 d}{5 b (d \tan (a+b x))^{5/2}}","-\frac{2 d}{5 b (d \tan (a+b x))^{5/2}}",1,"(-2*d)/(5*b*(d*Tan[a + b*x])^(5/2))","A",2,2,21,0.09524,1,"{2591, 30}"
97,1,43,0,0.0496197,"\int \frac{\csc ^4(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Csc[a + b*x]^4/(d*Tan[a + b*x])^(3/2),x]","-\frac{2 d^3}{9 b (d \tan (a+b x))^{9/2}}-\frac{2 d}{5 b (d \tan (a+b x))^{5/2}}","-\frac{2 d^3}{9 b (d \tan (a+b x))^{9/2}}-\frac{2 d}{5 b (d \tan (a+b x))^{5/2}}",1,"(-2*d^3)/(9*b*(d*Tan[a + b*x])^(9/2)) - (2*d)/(5*b*(d*Tan[a + b*x])^(5/2))","A",3,2,21,0.09524,1,"{2591, 14}"
98,1,65,0,0.0541373,"\int \frac{\csc ^6(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Csc[a + b*x]^6/(d*Tan[a + b*x])^(3/2),x]","-\frac{2 d^5}{13 b (d \tan (a+b x))^{13/2}}-\frac{4 d^3}{9 b (d \tan (a+b x))^{9/2}}-\frac{2 d}{5 b (d \tan (a+b x))^{5/2}}","-\frac{2 d^5}{13 b (d \tan (a+b x))^{13/2}}-\frac{4 d^3}{9 b (d \tan (a+b x))^{9/2}}-\frac{2 d}{5 b (d \tan (a+b x))^{5/2}}",1,"(-2*d^5)/(13*b*(d*Tan[a + b*x])^(13/2)) - (4*d^3)/(9*b*(d*Tan[a + b*x])^(9/2)) - (2*d)/(5*b*(d*Tan[a + b*x])^(5/2))","A",3,2,21,0.09524,1,"{2591, 270}"
99,1,112,0,0.1326233,"\int \frac{\sin ^3(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Sin[a + b*x]^3/(d*Tan[a + b*x])^(3/2),x]","\frac{\sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{12 b d^2}+\frac{\sin ^3(a+b x)}{3 b d \sqrt{d \tan (a+b x)}}-\frac{\sin (a+b x)}{6 b d \sqrt{d \tan (a+b x)}}","\frac{\sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{12 b d^2}+\frac{\sin ^3(a+b x)}{3 b d \sqrt{d \tan (a+b x)}}-\frac{\sin (a+b x)}{6 b d \sqrt{d \tan (a+b x)}}",1,"-Sin[a + b*x]/(6*b*d*Sqrt[d*Tan[a + b*x]]) + Sin[a + b*x]^3/(3*b*d*Sqrt[d*Tan[a + b*x]]) + (Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/(12*b*d^2)","A",5,5,21,0.2381,1,"{2596, 2598, 2601, 2573, 2641}"
100,1,79,0,0.0937112,"\int \frac{\sin (a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Sin[a + b*x]/(d*Tan[a + b*x])^(3/2),x]","\frac{\sin (a+b x)}{b d \sqrt{d \tan (a+b x)}}+\frac{\sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b d \sqrt{d \tan (a+b x)}}","\frac{\sin (a+b x)}{b d \sqrt{d \tan (a+b x)}}+\frac{\sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b d \sqrt{d \tan (a+b x)}}",1,"Sin[a + b*x]/(b*d*Sqrt[d*Tan[a + b*x]]) + (EllipticF[a - Pi/4 + b*x, 2]*Sec[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(2*b*d*Sqrt[d*Tan[a + b*x]])","A",4,4,19,0.2105,1,"{2602, 2569, 2573, 2641}"
101,1,82,0,0.1040053,"\int \frac{\csc (a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Csc[a + b*x]/(d*Tan[a + b*x])^(3/2),x]","-\frac{\sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{3 b d^2}-\frac{2 \csc (a+b x)}{3 b d \sqrt{d \tan (a+b x)}}","-\frac{\sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{3 b d^2}-\frac{2 \csc (a+b x)}{3 b d \sqrt{d \tan (a+b x)}}",1,"(-2*Csc[a + b*x])/(3*b*d*Sqrt[d*Tan[a + b*x]]) - (Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/(3*b*d^2)","A",4,4,19,0.2105,1,"{2597, 2601, 2573, 2641}"
102,1,112,0,0.1459287,"\int \frac{\csc ^3(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Csc[a + b*x]^3/(d*Tan[a + b*x])^(3/2),x]","-\frac{2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{21 b d^2}-\frac{2 \csc ^3(a+b x)}{7 b d \sqrt{d \tan (a+b x)}}+\frac{2 \csc (a+b x)}{21 b d \sqrt{d \tan (a+b x)}}","-\frac{2 \sqrt{\sin (2 a+2 b x)} \csc (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{21 b d^2}-\frac{2 \csc ^3(a+b x)}{7 b d \sqrt{d \tan (a+b x)}}+\frac{2 \csc (a+b x)}{21 b d \sqrt{d \tan (a+b x)}}",1,"(2*Csc[a + b*x])/(21*b*d*Sqrt[d*Tan[a + b*x]]) - (2*Csc[a + b*x]^3)/(7*b*d*Sqrt[d*Tan[a + b*x]]) - (2*Csc[a + b*x]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])/(21*b*d^2)","A",5,5,21,0.2381,1,"{2597, 2599, 2601, 2573, 2641}"
103,1,257,0,0.1764547,"\int \frac{\sin ^4(a+b x)}{(d \tan (a+b x))^{5/2}} \, dx","Int[Sin[a + b*x]^4/(d*Tan[a + b*x])^(5/2),x]","-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{32 \sqrt{2} b d^{5/2}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} b d^{5/2}}-\frac{3 \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b d^{5/2}}+\frac{3 \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b d^{5/2}}-\frac{\cos ^4(a+b x) \sqrt{d \tan (a+b x)}}{4 b d^3}+\frac{\cos ^2(a+b x) \sqrt{d \tan (a+b x)}}{16 b d^3}","-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{32 \sqrt{2} b d^{5/2}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} b d^{5/2}}-\frac{3 \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b d^{5/2}}+\frac{3 \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{64 \sqrt{2} b d^{5/2}}-\frac{\cos ^4(a+b x) \sqrt{d \tan (a+b x)}}{4 b d^3}+\frac{\cos ^2(a+b x) \sqrt{d \tan (a+b x)}}{16 b d^3}",1,"(-3*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(32*Sqrt[2]*b*d^(5/2)) + (3*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(32*Sqrt[2]*b*d^(5/2)) - (3*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(64*Sqrt[2]*b*d^(5/2)) + (3*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(64*Sqrt[2]*b*d^(5/2)) + (Cos[a + b*x]^2*Sqrt[d*Tan[a + b*x]])/(16*b*d^3) - (Cos[a + b*x]^4*Sqrt[d*Tan[a + b*x]])/(4*b*d^3)","A",13,10,21,0.4762,1,"{2591, 288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
104,1,227,0,0.1623451,"\int \frac{\sin ^2(a+b x)}{(d \tan (a+b x))^{5/2}} \, dx","Int[Sin[a + b*x]^2/(d*Tan[a + b*x])^(5/2),x]","-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b d^{5/2}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b d^{5/2}}-\frac{3 \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b d^{5/2}}+\frac{3 \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b d^{5/2}}+\frac{\cos ^2(a+b x) \sqrt{d \tan (a+b x)}}{2 b d^3}","-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b d^{5/2}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b d^{5/2}}-\frac{3 \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b d^{5/2}}+\frac{3 \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b d^{5/2}}+\frac{\cos ^2(a+b x) \sqrt{d \tan (a+b x)}}{2 b d^3}",1,"(-3*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(4*Sqrt[2]*b*d^(5/2)) + (3*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(4*Sqrt[2]*b*d^(5/2)) - (3*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(8*Sqrt[2]*b*d^(5/2)) + (3*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(8*Sqrt[2]*b*d^(5/2)) + (Cos[a + b*x]^2*Sqrt[d*Tan[a + b*x]])/(2*b*d^3)","A",12,9,21,0.4286,1,"{2591, 290, 329, 211, 1165, 628, 1162, 617, 204}"
105,1,20,0,0.0428568,"\int \frac{\csc ^2(a+b x)}{(d \tan (a+b x))^{5/2}} \, dx","Int[Csc[a + b*x]^2/(d*Tan[a + b*x])^(5/2),x]","-\frac{2 d}{7 b (d \tan (a+b x))^{7/2}}","-\frac{2 d}{7 b (d \tan (a+b x))^{7/2}}",1,"(-2*d)/(7*b*(d*Tan[a + b*x])^(7/2))","A",2,2,21,0.09524,1,"{2591, 30}"
106,1,43,0,0.0496892,"\int \frac{\csc ^4(a+b x)}{(d \tan (a+b x))^{5/2}} \, dx","Int[Csc[a + b*x]^4/(d*Tan[a + b*x])^(5/2),x]","-\frac{2 d^3}{11 b (d \tan (a+b x))^{11/2}}-\frac{2 d}{7 b (d \tan (a+b x))^{7/2}}","-\frac{2 d^3}{11 b (d \tan (a+b x))^{11/2}}-\frac{2 d}{7 b (d \tan (a+b x))^{7/2}}",1,"(-2*d^3)/(11*b*(d*Tan[a + b*x])^(11/2)) - (2*d)/(7*b*(d*Tan[a + b*x])^(7/2))","A",3,2,21,0.09524,1,"{2591, 14}"
107,1,65,0,0.0562098,"\int \frac{\csc ^6(a+b x)}{(d \tan (a+b x))^{5/2}} \, dx","Int[Csc[a + b*x]^6/(d*Tan[a + b*x])^(5/2),x]","-\frac{2 d^5}{15 b (d \tan (a+b x))^{15/2}}-\frac{4 d^3}{11 b (d \tan (a+b x))^{11/2}}-\frac{2 d}{7 b (d \tan (a+b x))^{7/2}}","-\frac{2 d^5}{15 b (d \tan (a+b x))^{15/2}}-\frac{4 d^3}{11 b (d \tan (a+b x))^{11/2}}-\frac{2 d}{7 b (d \tan (a+b x))^{7/2}}",1,"(-2*d^5)/(15*b*(d*Tan[a + b*x])^(15/2)) - (4*d^3)/(11*b*(d*Tan[a + b*x])^(11/2)) - (2*d)/(7*b*(d*Tan[a + b*x])^(7/2))","A",3,2,21,0.09524,1,"{2591, 270}"
108,1,144,0,0.1862407,"\int \frac{\sin ^7(a+b x)}{(d \tan (a+b x))^{5/2}} \, dx","Int[Sin[a + b*x]^7/(d*Tan[a + b*x])^(5/2),x]","\frac{3 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{40 b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}+\frac{\sin ^7(a+b x)}{7 b d (d \tan (a+b x))^{3/2}}-\frac{3 \sin ^5(a+b x)}{70 b d (d \tan (a+b x))^{3/2}}-\frac{\sin ^3(a+b x)}{20 b d (d \tan (a+b x))^{3/2}}","\frac{3 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{40 b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}+\frac{\sin ^7(a+b x)}{7 b d (d \tan (a+b x))^{3/2}}-\frac{3 \sin ^5(a+b x)}{70 b d (d \tan (a+b x))^{3/2}}-\frac{\sin ^3(a+b x)}{20 b d (d \tan (a+b x))^{3/2}}",1,"-Sin[a + b*x]^3/(20*b*d*(d*Tan[a + b*x])^(3/2)) - (3*Sin[a + b*x]^5)/(70*b*d*(d*Tan[a + b*x])^(3/2)) + Sin[a + b*x]^7/(7*b*d*(d*Tan[a + b*x])^(3/2)) + (3*EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(40*b*d^2*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])","A",6,5,21,0.2381,1,"{2596, 2598, 2601, 2572, 2639}"
109,1,114,0,0.1425713,"\int \frac{\sin ^5(a+b x)}{(d \tan (a+b x))^{5/2}} \, dx","Int[Sin[a + b*x]^5/(d*Tan[a + b*x])^(5/2),x]","\frac{3 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{20 b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}+\frac{\sin ^5(a+b x)}{5 b d (d \tan (a+b x))^{3/2}}-\frac{\sin ^3(a+b x)}{10 b d (d \tan (a+b x))^{3/2}}","\frac{3 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{20 b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}+\frac{\sin ^5(a+b x)}{5 b d (d \tan (a+b x))^{3/2}}-\frac{\sin ^3(a+b x)}{10 b d (d \tan (a+b x))^{3/2}}",1,"-Sin[a + b*x]^3/(10*b*d*(d*Tan[a + b*x])^(3/2)) + Sin[a + b*x]^5/(5*b*d*(d*Tan[a + b*x])^(3/2)) + (3*EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(20*b*d^2*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])","A",5,5,21,0.2381,1,"{2596, 2598, 2601, 2572, 2639}"
110,1,84,0,0.1024875,"\int \frac{\sin ^3(a+b x)}{(d \tan (a+b x))^{5/2}} \, dx","Int[Sin[a + b*x]^3/(d*Tan[a + b*x])^(5/2),x]","\frac{\sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}+\frac{\sin ^3(a+b x)}{3 b d (d \tan (a+b x))^{3/2}}","\frac{\sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}+\frac{\sin ^3(a+b x)}{3 b d (d \tan (a+b x))^{3/2}}",1,"Sin[a + b*x]^3/(3*b*d*(d*Tan[a + b*x])^(3/2)) + (EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(2*b*d^2*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])","A",4,4,21,0.1905,1,"{2596, 2601, 2572, 2639}"
111,1,78,0,0.0865126,"\int \frac{\sin (a+b x)}{(d \tan (a+b x))^{5/2}} \, dx","Int[Sin[a + b*x]/(d*Tan[a + b*x])^(5/2),x]","-\frac{3 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}-\frac{2 \sin (a+b x)}{b d (d \tan (a+b x))^{3/2}}","-\frac{3 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}-\frac{2 \sin (a+b x)}{b d (d \tan (a+b x))^{3/2}}",1,"(-2*Sin[a + b*x])/(b*d*(d*Tan[a + b*x])^(3/2)) - (3*EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(b*d^2*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])","A",4,4,19,0.2105,1,"{2597, 2601, 2572, 2639}"
112,1,110,0,0.1361722,"\int \frac{\csc (a+b x)}{(d \tan (a+b x))^{5/2}} \, dx","Int[Csc[a + b*x]/(d*Tan[a + b*x])^(5/2),x]","\frac{6 \cos (a+b x)}{5 b d^2 \sqrt{d \tan (a+b x)}}+\frac{6 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}-\frac{2 \csc (a+b x)}{5 b d (d \tan (a+b x))^{3/2}}","\frac{6 \cos (a+b x)}{5 b d^2 \sqrt{d \tan (a+b x)}}+\frac{6 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}-\frac{2 \csc (a+b x)}{5 b d (d \tan (a+b x))^{3/2}}",1,"(-2*Csc[a + b*x])/(5*b*d*(d*Tan[a + b*x])^(3/2)) + (6*Cos[a + b*x])/(5*b*d^2*Sqrt[d*Tan[a + b*x]]) + (6*EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(5*b*d^2*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])","A",5,5,19,0.2632,1,"{2597, 2601, 2570, 2572, 2639}"
113,1,140,0,0.183669,"\int \frac{\csc ^3(a+b x)}{(d \tan (a+b x))^{5/2}} \, dx","Int[Csc[a + b*x]^3/(d*Tan[a + b*x])^(5/2),x]","\frac{4 \cos (a+b x)}{15 b d^2 \sqrt{d \tan (a+b x)}}+\frac{4 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{15 b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}-\frac{2 \csc ^3(a+b x)}{9 b d (d \tan (a+b x))^{3/2}}+\frac{2 \csc (a+b x)}{15 b d (d \tan (a+b x))^{3/2}}","\frac{4 \cos (a+b x)}{15 b d^2 \sqrt{d \tan (a+b x)}}+\frac{4 \sin (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{15 b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{d \tan (a+b x)}}-\frac{2 \csc ^3(a+b x)}{9 b d (d \tan (a+b x))^{3/2}}+\frac{2 \csc (a+b x)}{15 b d (d \tan (a+b x))^{3/2}}",1,"(2*Csc[a + b*x])/(15*b*d*(d*Tan[a + b*x])^(3/2)) - (2*Csc[a + b*x]^3)/(9*b*d*(d*Tan[a + b*x])^(3/2)) + (4*Cos[a + b*x])/(15*b*d^2*Sqrt[d*Tan[a + b*x]]) + (4*EllipticE[a - Pi/4 + b*x, 2]*Sin[a + b*x])/(15*b*d^2*Sqrt[Sin[2*a + 2*b*x]]*Sqrt[d*Tan[a + b*x]])","A",6,6,21,0.2857,1,"{2597, 2599, 2601, 2570, 2572, 2639}"
114,1,68,0,0.0901038,"\int (a \sin (e+f x))^{5/2} \sqrt{b \tan (e+f x)} \, dx","Int[(a*Sin[e + f*x])^(5/2)*Sqrt[b*Tan[e + f*x]],x]","-\frac{8 a^2 b \sqrt{a \sin (e+f x)}}{5 f \sqrt{b \tan (e+f x)}}-\frac{2 b (a \sin (e+f x))^{5/2}}{5 f \sqrt{b \tan (e+f x)}}","-\frac{8 a^2 b \sqrt{a \sin (e+f x)}}{5 f \sqrt{b \tan (e+f x)}}-\frac{2 b (a \sin (e+f x))^{5/2}}{5 f \sqrt{b \tan (e+f x)}}",1,"(-8*a^2*b*Sqrt[a*Sin[e + f*x]])/(5*f*Sqrt[b*Tan[e + f*x]]) - (2*b*(a*Sin[e + f*x])^(5/2))/(5*f*Sqrt[b*Tan[e + f*x]])","A",2,2,25,0.08000,1,"{2598, 2589}"
115,1,88,0,0.105774,"\int (a \sin (e+f x))^{3/2} \sqrt{b \tan (e+f x)} \, dx","Int[(a*Sin[e + f*x])^(3/2)*Sqrt[b*Tan[e + f*x]],x]","\frac{4 a^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{3 f \sqrt{a \sin (e+f x)}}-\frac{2 b (a \sin (e+f x))^{3/2}}{3 f \sqrt{b \tan (e+f x)}}","\frac{4 a^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{3 f \sqrt{a \sin (e+f x)}}-\frac{2 b (a \sin (e+f x))^{3/2}}{3 f \sqrt{b \tan (e+f x)}}",1,"(-2*b*(a*Sin[e + f*x])^(3/2))/(3*f*Sqrt[b*Tan[e + f*x]]) + (4*a^2*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(3*f*Sqrt[a*Sin[e + f*x]])","A",3,3,25,0.1200,1,"{2598, 2601, 2641}"
116,1,30,0,0.041555,"\int \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)} \, dx","Int[Sqrt[a*Sin[e + f*x]]*Sqrt[b*Tan[e + f*x]],x]","-\frac{2 b \sqrt{a \sin (e+f x)}}{f \sqrt{b \tan (e+f x)}}","-\frac{2 b \sqrt{a \sin (e+f x)}}{f \sqrt{b \tan (e+f x)}}",1,"(-2*b*Sqrt[a*Sin[e + f*x]])/(f*Sqrt[b*Tan[e + f*x]])","A",1,1,25,0.04000,1,"{2589}"
117,1,50,0,0.0528332,"\int \frac{\sqrt{b \tan (e+f x)}}{\sqrt{a \sin (e+f x)}} \, dx","Int[Sqrt[b*Tan[e + f*x]]/Sqrt[a*Sin[e + f*x]],x]","\frac{2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{f \sqrt{a \sin (e+f x)}}","\frac{2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{f \sqrt{a \sin (e+f x)}}",1,"(2*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(f*Sqrt[a*Sin[e + f*x]])","A",2,2,25,0.08000,1,"{2601, 2641}"
118,1,107,0,0.0875813,"\int \frac{\sqrt{b \tan (e+f x)}}{(a \sin (e+f x))^{3/2}} \, dx","Int[Sqrt[b*Tan[e + f*x]]/(a*Sin[e + f*x])^(3/2),x]","-\frac{\sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{a f \sqrt{a \sin (e+f x)}}-\frac{\sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{a f \sqrt{a \sin (e+f x)}}","-\frac{\sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{a f \sqrt{a \sin (e+f x)}}-\frac{\sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{a f \sqrt{a \sin (e+f x)}}",1,"-((ArcTan[Sqrt[Cos[e + f*x]]]*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]])/(a*f*Sqrt[a*Sin[e + f*x]])) - (ArcTanh[Sqrt[Cos[e + f*x]]]*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]])/(a*f*Sqrt[a*Sin[e + f*x]])","A",7,7,25,0.2800,1,"{2601, 12, 2565, 329, 212, 206, 203}"
119,1,86,0,0.1033918,"\int \frac{\sqrt{b \tan (e+f x)}}{(a \sin (e+f x))^{5/2}} \, dx","Int[Sqrt[b*Tan[e + f*x]]/(a*Sin[e + f*x])^(5/2),x]","\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{a^2 f \sqrt{a \sin (e+f x)}}-\frac{b}{a^2 f \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}","\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{a^2 f \sqrt{a \sin (e+f x)}}-\frac{b}{a^2 f \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}",1,"-(b/(a^2*f*Sqrt[a*Sin[e + f*x]]*Sqrt[b*Tan[e + f*x]])) + (Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(a^2*f*Sqrt[a*Sin[e + f*x]])","A",3,3,25,0.1200,1,"{2599, 2601, 2641}"
120,1,126,0,0.1690582,"\int (a \sin (e+f x))^{5/2} (b \tan (e+f x))^{3/2} \, dx","Int[(a*Sin[e + f*x])^(5/2)*(b*Tan[e + f*x])^(3/2),x]","-\frac{24 a^2 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{5 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}+\frac{12 a^2 b \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}{5 f}-\frac{2 b (a \sin (e+f x))^{5/2} \sqrt{b \tan (e+f x)}}{5 f}","-\frac{24 a^2 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{5 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}+\frac{12 a^2 b \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}{5 f}-\frac{2 b (a \sin (e+f x))^{5/2} \sqrt{b \tan (e+f x)}}{5 f}",1,"(-24*a^2*b^2*EllipticE[(e + f*x)/2, 2]*Sqrt[a*Sin[e + f*x]])/(5*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]]) + (12*a^2*b*Sqrt[a*Sin[e + f*x]]*Sqrt[b*Tan[e + f*x]])/(5*f) - (2*b*(a*Sin[e + f*x])^(5/2)*Sqrt[b*Tan[e + f*x]])/(5*f)","A",4,4,25,0.1600,1,"{2598, 2594, 2601, 2639}"
121,1,68,0,0.1045624,"\int (a \sin (e+f x))^{3/2} (b \tan (e+f x))^{3/2} \, dx","Int[(a*Sin[e + f*x])^(3/2)*(b*Tan[e + f*x])^(3/2),x]","\frac{8 a^2 b \sqrt{b \tan (e+f x)}}{3 f \sqrt{a \sin (e+f x)}}-\frac{2 b (a \sin (e+f x))^{3/2} \sqrt{b \tan (e+f x)}}{3 f}","\frac{8 a^2 b \sqrt{b \tan (e+f x)}}{3 f \sqrt{a \sin (e+f x)}}-\frac{2 b (a \sin (e+f x))^{3/2} \sqrt{b \tan (e+f x)}}{3 f}",1,"(8*a^2*b*Sqrt[b*Tan[e + f*x]])/(3*f*Sqrt[a*Sin[e + f*x]]) - (2*b*(a*Sin[e + f*x])^(3/2)*Sqrt[b*Tan[e + f*x]])/(3*f)","A",2,2,25,0.08000,1,"{2598, 2589}"
122,1,84,0,0.1012867,"\int \sqrt{a \sin (e+f x)} (b \tan (e+f x))^{3/2} \, dx","Int[Sqrt[a*Sin[e + f*x]]*(b*Tan[e + f*x])^(3/2),x]","\frac{2 b \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}{f}-\frac{4 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}","\frac{2 b \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}{f}-\frac{4 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}",1,"(-4*b^2*EllipticE[(e + f*x)/2, 2]*Sqrt[a*Sin[e + f*x]])/(f*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]]) + (2*b*Sqrt[a*Sin[e + f*x]]*Sqrt[b*Tan[e + f*x]])/f","A",3,3,25,0.1200,1,"{2594, 2601, 2639}"
123,1,30,0,0.0487723,"\int \frac{(b \tan (e+f x))^{3/2}}{\sqrt{a \sin (e+f x)}} \, dx","Int[(b*Tan[e + f*x])^(3/2)/Sqrt[a*Sin[e + f*x]],x]","\frac{2 b \sqrt{b \tan (e+f x)}}{f \sqrt{a \sin (e+f x)}}","\frac{2 b \sqrt{b \tan (e+f x)}}{f \sqrt{a \sin (e+f x)}}",1,"(2*b*Sqrt[b*Tan[e + f*x]])/(f*Sqrt[a*Sin[e + f*x]])","A",1,1,25,0.04000,1,"{2589}"
124,1,90,0,0.1112411,"\int \frac{(b \tan (e+f x))^{3/2}}{(a \sin (e+f x))^{3/2}} \, dx","Int[(b*Tan[e + f*x])^(3/2)/(a*Sin[e + f*x])^(3/2),x]","\frac{2 b \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}{a^2 f}-\frac{2 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{a^2 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}","\frac{2 b \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}{a^2 f}-\frac{2 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{a^2 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}",1,"(-2*b^2*EllipticE[(e + f*x)/2, 2]*Sqrt[a*Sin[e + f*x]])/(a^2*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]]) + (2*b*Sqrt[a*Sin[e + f*x]]*Sqrt[b*Tan[e + f*x]])/(a^2*f)","A",3,3,25,0.1200,1,"{2593, 2601, 2639}"
125,1,145,0,0.1501685,"\int \frac{(b \tan (e+f x))^{3/2}}{(a \sin (e+f x))^{5/2}} \, dx","Int[(b*Tan[e + f*x])^(3/2)/(a*Sin[e + f*x])^(5/2),x]","\frac{b^2 \sqrt{a \sin (e+f x)} \tan ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{a^3 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}-\frac{b^2 \sqrt{a \sin (e+f x)} \tanh ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{a^3 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}+\frac{2 b \sqrt{b \tan (e+f x)}}{a^2 f \sqrt{a \sin (e+f x)}}","\frac{b^2 \sqrt{a \sin (e+f x)} \tan ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{a^3 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}-\frac{b^2 \sqrt{a \sin (e+f x)} \tanh ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{a^3 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}+\frac{2 b \sqrt{b \tan (e+f x)}}{a^2 f \sqrt{a \sin (e+f x)}}",1,"(b^2*ArcTan[Sqrt[Cos[e + f*x]]]*Sqrt[a*Sin[e + f*x]])/(a^3*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]]) - (b^2*ArcTanh[Sqrt[Cos[e + f*x]]]*Sqrt[a*Sin[e + f*x]])/(a^3*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]]) + (2*b*Sqrt[b*Tan[e + f*x]])/(a^2*f*Sqrt[a*Sin[e + f*x]])","A",8,8,25,0.3200,1,"{2593, 2601, 12, 2565, 329, 298, 203, 206}"
126,1,123,0,0.1615661,"\int \frac{(a \sin (e+f x))^{9/2}}{\sqrt{b \tan (e+f x)}} \, dx","Int[(a*Sin[e + f*x])^(9/2)/Sqrt[b*Tan[e + f*x]],x]","-\frac{4 a^2 b (a \sin (e+f x))^{5/2}}{15 f (b \tan (e+f x))^{3/2}}+\frac{8 a^4 E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{15 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}-\frac{2 b (a \sin (e+f x))^{9/2}}{9 f (b \tan (e+f x))^{3/2}}","-\frac{4 a^2 b (a \sin (e+f x))^{5/2}}{15 f (b \tan (e+f x))^{3/2}}+\frac{8 a^4 E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{15 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}-\frac{2 b (a \sin (e+f x))^{9/2}}{9 f (b \tan (e+f x))^{3/2}}",1,"(-4*a^2*b*(a*Sin[e + f*x])^(5/2))/(15*f*(b*Tan[e + f*x])^(3/2)) - (2*b*(a*Sin[e + f*x])^(9/2))/(9*f*(b*Tan[e + f*x])^(3/2)) + (8*a^4*EllipticE[(e + f*x)/2, 2]*Sqrt[a*Sin[e + f*x]])/(15*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]])","A",4,3,25,0.1200,1,"{2598, 2601, 2639}"
127,1,68,0,0.1017574,"\int \frac{(a \sin (e+f x))^{7/2}}{\sqrt{b \tan (e+f x)}} \, dx","Int[(a*Sin[e + f*x])^(7/2)/Sqrt[b*Tan[e + f*x]],x]","-\frac{8 a^2 b (a \sin (e+f x))^{3/2}}{21 f (b \tan (e+f x))^{3/2}}-\frac{2 b (a \sin (e+f x))^{7/2}}{7 f (b \tan (e+f x))^{3/2}}","-\frac{8 a^2 b (a \sin (e+f x))^{3/2}}{21 f (b \tan (e+f x))^{3/2}}-\frac{2 b (a \sin (e+f x))^{7/2}}{7 f (b \tan (e+f x))^{3/2}}",1,"(-8*a^2*b*(a*Sin[e + f*x])^(3/2))/(21*f*(b*Tan[e + f*x])^(3/2)) - (2*b*(a*Sin[e + f*x])^(7/2))/(7*f*(b*Tan[e + f*x])^(3/2))","A",2,2,25,0.08000,1,"{2598, 2589}"
128,1,88,0,0.1049793,"\int \frac{(a \sin (e+f x))^{5/2}}{\sqrt{b \tan (e+f x)}} \, dx","Int[(a*Sin[e + f*x])^(5/2)/Sqrt[b*Tan[e + f*x]],x]","\frac{4 a^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{5 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}-\frac{2 b (a \sin (e+f x))^{5/2}}{5 f (b \tan (e+f x))^{3/2}}","\frac{4 a^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{5 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}-\frac{2 b (a \sin (e+f x))^{5/2}}{5 f (b \tan (e+f x))^{3/2}}",1,"(-2*b*(a*Sin[e + f*x])^(5/2))/(5*f*(b*Tan[e + f*x])^(3/2)) + (4*a^2*EllipticE[(e + f*x)/2, 2]*Sqrt[a*Sin[e + f*x]])/(5*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]])","A",3,3,25,0.1200,1,"{2598, 2601, 2639}"
129,1,32,0,0.0493257,"\int \frac{(a \sin (e+f x))^{3/2}}{\sqrt{b \tan (e+f x)}} \, dx","Int[(a*Sin[e + f*x])^(3/2)/Sqrt[b*Tan[e + f*x]],x]","-\frac{2 b (a \sin (e+f x))^{3/2}}{3 f (b \tan (e+f x))^{3/2}}","-\frac{2 b (a \sin (e+f x))^{3/2}}{3 f (b \tan (e+f x))^{3/2}}",1,"(-2*b*(a*Sin[e + f*x])^(3/2))/(3*f*(b*Tan[e + f*x])^(3/2))","A",1,1,25,0.04000,1,"{2589}"
130,1,50,0,0.0511875,"\int \frac{\sqrt{a \sin (e+f x)}}{\sqrt{b \tan (e+f x)}} \, dx","Int[Sqrt[a*Sin[e + f*x]]/Sqrt[b*Tan[e + f*x]],x]","\frac{2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}","\frac{2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}",1,"(2*EllipticE[(e + f*x)/2, 2]*Sqrt[a*Sin[e + f*x]])/(f*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]])","A",2,2,25,0.08000,1,"{2601, 2639}"
131,1,106,0,0.0829008,"\int \frac{1}{\sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}} \, dx","Int[1/(Sqrt[a*Sin[e + f*x]]*Sqrt[b*Tan[e + f*x]]),x]","\frac{\sqrt{a \sin (e+f x)} \tan ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{a f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}-\frac{\sqrt{a \sin (e+f x)} \tanh ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{a f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}","\frac{\sqrt{a \sin (e+f x)} \tan ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{a f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}-\frac{\sqrt{a \sin (e+f x)} \tanh ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{a f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}",1,"(ArcTan[Sqrt[Cos[e + f*x]]]*Sqrt[a*Sin[e + f*x]])/(a*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]]) - (ArcTanh[Sqrt[Cos[e + f*x]]]*Sqrt[a*Sin[e + f*x]])/(a*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]])","A",7,7,25,0.2800,1,"{2601, 12, 2565, 329, 298, 203, 206}"
132,1,87,0,0.1053737,"\int \frac{1}{(a \sin (e+f x))^{3/2} \sqrt{b \tan (e+f x)}} \, dx","Int[1/((a*Sin[e + f*x])^(3/2)*Sqrt[b*Tan[e + f*x]]),x]","-\frac{b \sqrt{a \sin (e+f x)}}{a^2 f (b \tan (e+f x))^{3/2}}-\frac{E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{a^2 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}","-\frac{b \sqrt{a \sin (e+f x)}}{a^2 f (b \tan (e+f x))^{3/2}}-\frac{E\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{a \sin (e+f x)}}{a^2 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}",1,"-((b*Sqrt[a*Sin[e + f*x]])/(a^2*f*(b*Tan[e + f*x])^(3/2))) - (EllipticE[(e + f*x)/2, 2]*Sqrt[a*Sin[e + f*x]])/(a^2*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]])","A",3,3,25,0.1200,1,"{2599, 2601, 2639}"
133,1,146,0,0.1416957,"\int \frac{1}{(a \sin (e+f x))^{5/2} \sqrt{b \tan (e+f x)}} \, dx","Int[1/((a*Sin[e + f*x])^(5/2)*Sqrt[b*Tan[e + f*x]]),x]","-\frac{b}{2 a^2 f \sqrt{a \sin (e+f x)} (b \tan (e+f x))^{3/2}}+\frac{\sqrt{a \sin (e+f x)} \tan ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{4 a^3 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}-\frac{\sqrt{a \sin (e+f x)} \tanh ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{4 a^3 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}","-\frac{b}{2 a^2 f \sqrt{a \sin (e+f x)} (b \tan (e+f x))^{3/2}}+\frac{\sqrt{a \sin (e+f x)} \tan ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{4 a^3 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}-\frac{\sqrt{a \sin (e+f x)} \tanh ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{4 a^3 f \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)}}",1,"-b/(2*a^2*f*Sqrt[a*Sin[e + f*x]]*(b*Tan[e + f*x])^(3/2)) + (ArcTan[Sqrt[Cos[e + f*x]]]*Sqrt[a*Sin[e + f*x]])/(4*a^3*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]]) - (ArcTanh[Sqrt[Cos[e + f*x]]]*Sqrt[a*Sin[e + f*x]])/(4*a^3*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]])","A",8,8,25,0.3200,1,"{2599, 2601, 12, 2565, 329, 298, 203, 206}"
134,1,146,0,0.2067201,"\int \frac{(a \sin (e+f x))^{13/2}}{(b \tan (e+f x))^{3/2}} \, dx","Int[(a*Sin[e + f*x])^(13/2)/(b*Tan[e + f*x])^(3/2),x]","-\frac{2 a^2 (a \sin (e+f x))^{9/2}}{117 b f \sqrt{b \tan (e+f x)}}-\frac{16 a^4 (a \sin (e+f x))^{5/2}}{585 b f \sqrt{b \tan (e+f x)}}-\frac{64 a^6 \sqrt{a \sin (e+f x)}}{585 b f \sqrt{b \tan (e+f x)}}+\frac{2 (a \sin (e+f x))^{13/2}}{13 b f \sqrt{b \tan (e+f x)}}","-\frac{2 a^2 (a \sin (e+f x))^{9/2}}{117 b f \sqrt{b \tan (e+f x)}}-\frac{16 a^4 (a \sin (e+f x))^{5/2}}{585 b f \sqrt{b \tan (e+f x)}}-\frac{64 a^6 \sqrt{a \sin (e+f x)}}{585 b f \sqrt{b \tan (e+f x)}}+\frac{2 (a \sin (e+f x))^{13/2}}{13 b f \sqrt{b \tan (e+f x)}}",1,"(-64*a^6*Sqrt[a*Sin[e + f*x]])/(585*b*f*Sqrt[b*Tan[e + f*x]]) - (16*a^4*(a*Sin[e + f*x])^(5/2))/(585*b*f*Sqrt[b*Tan[e + f*x]]) - (2*a^2*(a*Sin[e + f*x])^(9/2))/(117*b*f*Sqrt[b*Tan[e + f*x]]) + (2*(a*Sin[e + f*x])^(13/2))/(13*b*f*Sqrt[b*Tan[e + f*x]])","A",4,3,25,0.1200,1,"{2596, 2598, 2589}"
135,1,109,0,0.1508269,"\int \frac{(a \sin (e+f x))^{9/2}}{(b \tan (e+f x))^{3/2}} \, dx","Int[(a*Sin[e + f*x])^(9/2)/(b*Tan[e + f*x])^(3/2),x]","-\frac{2 a^2 (a \sin (e+f x))^{5/2}}{45 b f \sqrt{b \tan (e+f x)}}-\frac{8 a^4 \sqrt{a \sin (e+f x)}}{45 b f \sqrt{b \tan (e+f x)}}+\frac{2 (a \sin (e+f x))^{9/2}}{9 b f \sqrt{b \tan (e+f x)}}","-\frac{2 a^2 (a \sin (e+f x))^{5/2}}{45 b f \sqrt{b \tan (e+f x)}}-\frac{8 a^4 \sqrt{a \sin (e+f x)}}{45 b f \sqrt{b \tan (e+f x)}}+\frac{2 (a \sin (e+f x))^{9/2}}{9 b f \sqrt{b \tan (e+f x)}}",1,"(-8*a^4*Sqrt[a*Sin[e + f*x]])/(45*b*f*Sqrt[b*Tan[e + f*x]]) - (2*a^2*(a*Sin[e + f*x])^(5/2))/(45*b*f*Sqrt[b*Tan[e + f*x]]) + (2*(a*Sin[e + f*x])^(9/2))/(9*b*f*Sqrt[b*Tan[e + f*x]])","A",3,3,25,0.1200,1,"{2596, 2598, 2589}"
136,1,32,0,0.0547281,"\int \frac{(a \sin (e+f x))^{5/2}}{(b \tan (e+f x))^{3/2}} \, dx","Int[(a*Sin[e + f*x])^(5/2)/(b*Tan[e + f*x])^(3/2),x]","-\frac{2 b (a \sin (e+f x))^{5/2}}{5 f (b \tan (e+f x))^{5/2}}","-\frac{2 b (a \sin (e+f x))^{5/2}}{5 f (b \tan (e+f x))^{5/2}}",1,"(-2*b*(a*Sin[e + f*x])^(5/2))/(5*f*(b*Tan[e + f*x])^(5/2))","A",1,1,25,0.04000,1,"{2589}"
137,1,141,0,0.1433148,"\int \frac{\sqrt{a \sin (e+f x)}}{(b \tan (e+f x))^{3/2}} \, dx","Int[Sqrt[a*Sin[e + f*x]]/(b*Tan[e + f*x])^(3/2),x]","-\frac{a \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{b^2 f \sqrt{a \sin (e+f x)}}-\frac{a \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{b^2 f \sqrt{a \sin (e+f x)}}+\frac{2 \sqrt{a \sin (e+f x)}}{b f \sqrt{b \tan (e+f x)}}","-\frac{a \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{b^2 f \sqrt{a \sin (e+f x)}}-\frac{a \sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{b^2 f \sqrt{a \sin (e+f x)}}+\frac{2 \sqrt{a \sin (e+f x)}}{b f \sqrt{b \tan (e+f x)}}",1,"(2*Sqrt[a*Sin[e + f*x]])/(b*f*Sqrt[b*Tan[e + f*x]]) - (a*ArcTan[Sqrt[Cos[e + f*x]]]*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]])/(b^2*f*Sqrt[a*Sin[e + f*x]]) - (a*ArcTanh[Sqrt[Cos[e + f*x]]]*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]])/(b^2*f*Sqrt[a*Sin[e + f*x]])","A",8,8,25,0.3200,1,"{2595, 2601, 12, 2565, 329, 212, 206, 203}"
138,1,151,0,0.1549784,"\int \frac{1}{(a \sin (e+f x))^{3/2} (b \tan (e+f x))^{3/2}} \, dx","Int[1/((a*Sin[e + f*x])^(3/2)*(b*Tan[e + f*x])^(3/2)),x]","\frac{\sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{4 a b^2 f \sqrt{a \sin (e+f x)}}+\frac{\sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{4 a b^2 f \sqrt{a \sin (e+f x)}}-\frac{1}{2 b f (a \sin (e+f x))^{3/2} \sqrt{b \tan (e+f x)}}","\frac{\sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{4 a b^2 f \sqrt{a \sin (e+f x)}}+\frac{\sqrt{\cos (e+f x)} \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\sqrt{\cos (e+f x)}\right)}{4 a b^2 f \sqrt{a \sin (e+f x)}}-\frac{1}{2 b f (a \sin (e+f x))^{3/2} \sqrt{b \tan (e+f x)}}",1,"-1/(2*b*f*(a*Sin[e + f*x])^(3/2)*Sqrt[b*Tan[e + f*x]]) + (ArcTan[Sqrt[Cos[e + f*x]]]*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]])/(4*a*b^2*f*Sqrt[a*Sin[e + f*x]]) + (ArcTanh[Sqrt[Cos[e + f*x]]]*Sqrt[Cos[e + f*x]]*Sqrt[b*Tan[e + f*x]])/(4*a*b^2*f*Sqrt[a*Sin[e + f*x]])","A",8,8,25,0.3200,1,"{2597, 2601, 12, 2565, 329, 212, 206, 203}"
139,1,167,0,0.2269366,"\int \frac{(a \sin (e+f x))^{11/2}}{(b \tan (e+f x))^{3/2}} \, dx","Int[(a*Sin[e + f*x])^(11/2)/(b*Tan[e + f*x])^(3/2),x]","\frac{8 a^6 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{77 b^2 f \sqrt{a \sin (e+f x)}}-\frac{4 a^4 (a \sin (e+f x))^{3/2}}{77 b f \sqrt{b \tan (e+f x)}}-\frac{2 a^2 (a \sin (e+f x))^{7/2}}{77 b f \sqrt{b \tan (e+f x)}}+\frac{2 (a \sin (e+f x))^{11/2}}{11 b f \sqrt{b \tan (e+f x)}}","\frac{8 a^6 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{77 b^2 f \sqrt{a \sin (e+f x)}}-\frac{4 a^4 (a \sin (e+f x))^{3/2}}{77 b f \sqrt{b \tan (e+f x)}}-\frac{2 a^2 (a \sin (e+f x))^{7/2}}{77 b f \sqrt{b \tan (e+f x)}}+\frac{2 (a \sin (e+f x))^{11/2}}{11 b f \sqrt{b \tan (e+f x)}}",1,"(-4*a^4*(a*Sin[e + f*x])^(3/2))/(77*b*f*Sqrt[b*Tan[e + f*x]]) - (2*a^2*(a*Sin[e + f*x])^(7/2))/(77*b*f*Sqrt[b*Tan[e + f*x]]) + (2*(a*Sin[e + f*x])^(11/2))/(11*b*f*Sqrt[b*Tan[e + f*x]]) + (8*a^6*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(77*b^2*f*Sqrt[a*Sin[e + f*x]])","A",5,4,25,0.1600,1,"{2596, 2598, 2601, 2641}"
140,1,130,0,0.1672867,"\int \frac{(a \sin (e+f x))^{7/2}}{(b \tan (e+f x))^{3/2}} \, dx","Int[(a*Sin[e + f*x])^(7/2)/(b*Tan[e + f*x])^(3/2),x]","\frac{4 a^4 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{21 b^2 f \sqrt{a \sin (e+f x)}}-\frac{2 a^2 (a \sin (e+f x))^{3/2}}{21 b f \sqrt{b \tan (e+f x)}}+\frac{2 (a \sin (e+f x))^{7/2}}{7 b f \sqrt{b \tan (e+f x)}}","\frac{4 a^4 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{21 b^2 f \sqrt{a \sin (e+f x)}}-\frac{2 a^2 (a \sin (e+f x))^{3/2}}{21 b f \sqrt{b \tan (e+f x)}}+\frac{2 (a \sin (e+f x))^{7/2}}{7 b f \sqrt{b \tan (e+f x)}}",1,"(-2*a^2*(a*Sin[e + f*x])^(3/2))/(21*b*f*Sqrt[b*Tan[e + f*x]]) + (2*(a*Sin[e + f*x])^(7/2))/(7*b*f*Sqrt[b*Tan[e + f*x]]) + (4*a^4*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(21*b^2*f*Sqrt[a*Sin[e + f*x]])","A",4,4,25,0.1600,1,"{2596, 2598, 2601, 2641}"
141,1,93,0,0.1124466,"\int \frac{(a \sin (e+f x))^{3/2}}{(b \tan (e+f x))^{3/2}} \, dx","Int[(a*Sin[e + f*x])^(3/2)/(b*Tan[e + f*x])^(3/2),x]","\frac{2 a^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{3 b^2 f \sqrt{a \sin (e+f x)}}+\frac{2 (a \sin (e+f x))^{3/2}}{3 b f \sqrt{b \tan (e+f x)}}","\frac{2 a^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{3 b^2 f \sqrt{a \sin (e+f x)}}+\frac{2 (a \sin (e+f x))^{3/2}}{3 b f \sqrt{b \tan (e+f x)}}",1,"(2*(a*Sin[e + f*x])^(3/2))/(3*b*f*Sqrt[b*Tan[e + f*x]]) + (2*a^2*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(3*b^2*f*Sqrt[a*Sin[e + f*x]])","A",3,3,25,0.1200,1,"{2596, 2601, 2641}"
142,1,86,0,0.1044789,"\int \frac{1}{\sqrt{a \sin (e+f x)} (b \tan (e+f x))^{3/2}} \, dx","Int[1/(Sqrt[a*Sin[e + f*x]]*(b*Tan[e + f*x])^(3/2)),x]","-\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{b^2 f \sqrt{a \sin (e+f x)}}-\frac{1}{b f \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}","-\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{b^2 f \sqrt{a \sin (e+f x)}}-\frac{1}{b f \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}",1,"-(1/(b*f*Sqrt[a*Sin[e + f*x]]*Sqrt[b*Tan[e + f*x]])) - (Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(b^2*f*Sqrt[a*Sin[e + f*x]])","A",3,3,25,0.1200,1,"{2597, 2601, 2641}"
143,1,130,0,0.1685321,"\int \frac{1}{(a \sin (e+f x))^{5/2} (b \tan (e+f x))^{3/2}} \, dx","Int[1/((a*Sin[e + f*x])^(5/2)*(b*Tan[e + f*x])^(3/2)),x]","-\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{6 a^2 b^2 f \sqrt{a \sin (e+f x)}}+\frac{1}{6 a^2 b f \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}-\frac{1}{3 b f (a \sin (e+f x))^{5/2} \sqrt{b \tan (e+f x)}}","-\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{6 a^2 b^2 f \sqrt{a \sin (e+f x)}}+\frac{1}{6 a^2 b f \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}-\frac{1}{3 b f (a \sin (e+f x))^{5/2} \sqrt{b \tan (e+f x)}}",1,"-1/(3*b*f*(a*Sin[e + f*x])^(5/2)*Sqrt[b*Tan[e + f*x]]) + 1/(6*a^2*b*f*Sqrt[a*Sin[e + f*x]]*Sqrt[b*Tan[e + f*x]]) - (Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(6*a^2*b^2*f*Sqrt[a*Sin[e + f*x]])","A",4,4,25,0.1600,1,"{2597, 2599, 2601, 2641}"
144,1,167,0,0.2330633,"\int \frac{1}{(a \sin (e+f x))^{9/2} (b \tan (e+f x))^{3/2}} \, dx","Int[1/((a*Sin[e + f*x])^(9/2)*(b*Tan[e + f*x])^(3/2)),x]","-\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{12 a^4 b^2 f \sqrt{a \sin (e+f x)}}+\frac{1}{12 a^4 b f \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}+\frac{1}{30 a^2 b f (a \sin (e+f x))^{5/2} \sqrt{b \tan (e+f x)}}-\frac{1}{5 b f (a \sin (e+f x))^{9/2} \sqrt{b \tan (e+f x)}}","-\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \tan (e+f x)}}{12 a^4 b^2 f \sqrt{a \sin (e+f x)}}+\frac{1}{12 a^4 b f \sqrt{a \sin (e+f x)} \sqrt{b \tan (e+f x)}}+\frac{1}{30 a^2 b f (a \sin (e+f x))^{5/2} \sqrt{b \tan (e+f x)}}-\frac{1}{5 b f (a \sin (e+f x))^{9/2} \sqrt{b \tan (e+f x)}}",1,"-1/(5*b*f*(a*Sin[e + f*x])^(9/2)*Sqrt[b*Tan[e + f*x]]) + 1/(30*a^2*b*f*(a*Sin[e + f*x])^(5/2)*Sqrt[b*Tan[e + f*x]]) + 1/(12*a^4*b*f*Sqrt[a*Sin[e + f*x]]*Sqrt[b*Tan[e + f*x]]) - (Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(12*a^4*b^2*f*Sqrt[a*Sin[e + f*x]])","A",5,4,25,0.1600,1,"{2597, 2599, 2601, 2641}"
145,1,64,0,0.0951208,"\int (b \sin (e+f x))^{4/3} \sqrt{d \tan (e+f x)} \, dx","Int[(b*Sin[e + f*x])^(4/3)*Sqrt[d*Tan[e + f*x]],x]","\frac{6 \cos ^2(e+f x)^{3/4} (b \sin (e+f x))^{4/3} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{3}{4},\frac{17}{12};\frac{29}{12};\sin ^2(e+f x)\right)}{17 d f}","\frac{6 \cos ^2(e+f x)^{3/4} (b \sin (e+f x))^{4/3} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{3}{4},\frac{17}{12};\frac{29}{12};\sin ^2(e+f x)\right)}{17 d f}",1,"(6*(Cos[e + f*x]^2)^(3/4)*Hypergeometric2F1[3/4, 17/12, 29/12, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(4/3)*(d*Tan[e + f*x])^(3/2))/(17*d*f)","A",2,2,25,0.08000,1,"{2602, 2577}"
146,1,64,0,0.0886116,"\int \sqrt[3]{b \sin (e+f x)} \sqrt{d \tan (e+f x)} \, dx","Int[(b*Sin[e + f*x])^(1/3)*Sqrt[d*Tan[e + f*x]],x]","\frac{6 \cos ^2(e+f x)^{3/4} \sqrt[3]{b \sin (e+f x)} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{3}{4},\frac{11}{12};\frac{23}{12};\sin ^2(e+f x)\right)}{11 d f}","\frac{6 \cos ^2(e+f x)^{3/4} \sqrt[3]{b \sin (e+f x)} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{3}{4},\frac{11}{12};\frac{23}{12};\sin ^2(e+f x)\right)}{11 d f}",1,"(6*(Cos[e + f*x]^2)^(3/4)*Hypergeometric2F1[3/4, 11/12, 23/12, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(1/3)*(d*Tan[e + f*x])^(3/2))/(11*d*f)","A",2,2,25,0.08000,1,"{2602, 2577}"
147,1,64,0,0.082222,"\int \frac{\sqrt{d \tan (e+f x)}}{\sqrt[3]{b \sin (e+f x)}} \, dx","Int[Sqrt[d*Tan[e + f*x]]/(b*Sin[e + f*x])^(1/3),x]","\frac{6 \cos ^2(e+f x)^{3/4} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{7}{12},\frac{3}{4};\frac{19}{12};\sin ^2(e+f x)\right)}{7 d f \sqrt[3]{b \sin (e+f x)}}","\frac{6 \cos ^2(e+f x)^{3/4} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{7}{12},\frac{3}{4};\frac{19}{12};\sin ^2(e+f x)\right)}{7 d f \sqrt[3]{b \sin (e+f x)}}",1,"(6*(Cos[e + f*x]^2)^(3/4)*Hypergeometric2F1[7/12, 3/4, 19/12, Sin[e + f*x]^2]*(d*Tan[e + f*x])^(3/2))/(7*d*f*(b*Sin[e + f*x])^(1/3))","A",2,2,25,0.08000,1,"{2602, 2577}"
148,1,62,0,0.0971231,"\int \frac{\sqrt{d \tan (e+f x)}}{(b \sin (e+f x))^{4/3}} \, dx","Int[Sqrt[d*Tan[e + f*x]]/(b*Sin[e + f*x])^(4/3),x]","\frac{6 \cos ^2(e+f x)^{3/4} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{1}{12},\frac{3}{4};\frac{13}{12};\sin ^2(e+f x)\right)}{d f (b \sin (e+f x))^{4/3}}","\frac{6 \cos ^2(e+f x)^{3/4} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{1}{12},\frac{3}{4};\frac{13}{12};\sin ^2(e+f x)\right)}{d f (b \sin (e+f x))^{4/3}}",1,"(6*(Cos[e + f*x]^2)^(3/4)*Hypergeometric2F1[1/12, 3/4, 13/12, Sin[e + f*x]^2]*(d*Tan[e + f*x])^(3/2))/(d*f*(b*Sin[e + f*x])^(4/3))","A",2,2,25,0.08000,1,"{2602, 2577}"
149,1,64,0,0.0992829,"\int (b \sin (e+f x))^{4/3} (d \tan (e+f x))^{3/2} \, dx","Int[(b*Sin[e + f*x])^(4/3)*(d*Tan[e + f*x])^(3/2),x]","\frac{6 \cos ^2(e+f x)^{5/4} (b \sin (e+f x))^{4/3} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{5}{4},\frac{23}{12};\frac{35}{12};\sin ^2(e+f x)\right)}{23 d f}","\frac{6 \cos ^2(e+f x)^{5/4} (b \sin (e+f x))^{4/3} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{5}{4},\frac{23}{12};\frac{35}{12};\sin ^2(e+f x)\right)}{23 d f}",1,"(6*(Cos[e + f*x]^2)^(5/4)*Hypergeometric2F1[5/4, 23/12, 35/12, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(4/3)*(d*Tan[e + f*x])^(5/2))/(23*d*f)","A",2,2,25,0.08000,1,"{2602, 2577}"
150,1,64,0,0.0944806,"\int \sqrt[3]{b \sin (e+f x)} (d \tan (e+f x))^{3/2} \, dx","Int[(b*Sin[e + f*x])^(1/3)*(d*Tan[e + f*x])^(3/2),x]","\frac{6 \cos ^2(e+f x)^{5/4} \sqrt[3]{b \sin (e+f x)} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{5}{4},\frac{17}{12};\frac{29}{12};\sin ^2(e+f x)\right)}{17 d f}","\frac{6 \cos ^2(e+f x)^{5/4} \sqrt[3]{b \sin (e+f x)} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{5}{4},\frac{17}{12};\frac{29}{12};\sin ^2(e+f x)\right)}{17 d f}",1,"(6*(Cos[e + f*x]^2)^(5/4)*Hypergeometric2F1[5/4, 17/12, 29/12, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(1/3)*(d*Tan[e + f*x])^(5/2))/(17*d*f)","A",2,2,25,0.08000,1,"{2602, 2577}"
151,1,64,0,0.0960796,"\int \frac{(d \tan (e+f x))^{3/2}}{\sqrt[3]{b \sin (e+f x)}} \, dx","Int[(d*Tan[e + f*x])^(3/2)/(b*Sin[e + f*x])^(1/3),x]","\frac{6 \cos ^2(e+f x)^{5/4} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{13}{12},\frac{5}{4};\frac{25}{12};\sin ^2(e+f x)\right)}{13 d f \sqrt[3]{b \sin (e+f x)}}","\frac{6 \cos ^2(e+f x)^{5/4} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{13}{12},\frac{5}{4};\frac{25}{12};\sin ^2(e+f x)\right)}{13 d f \sqrt[3]{b \sin (e+f x)}}",1,"(6*(Cos[e + f*x]^2)^(5/4)*Hypergeometric2F1[13/12, 5/4, 25/12, Sin[e + f*x]^2]*(d*Tan[e + f*x])^(5/2))/(13*d*f*(b*Sin[e + f*x])^(1/3))","A",2,2,25,0.08000,1,"{2602, 2577}"
152,1,64,0,0.0941235,"\int \frac{(d \tan (e+f x))^{3/2}}{(b \sin (e+f x))^{4/3}} \, dx","Int[(d*Tan[e + f*x])^(3/2)/(b*Sin[e + f*x])^(4/3),x]","\frac{6 \cos ^2(e+f x)^{5/4} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{7}{12},\frac{5}{4};\frac{19}{12};\sin ^2(e+f x)\right)}{7 d f (b \sin (e+f x))^{4/3}}","\frac{6 \cos ^2(e+f x)^{5/4} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{7}{12},\frac{5}{4};\frac{19}{12};\sin ^2(e+f x)\right)}{7 d f (b \sin (e+f x))^{4/3}}",1,"(6*(Cos[e + f*x]^2)^(5/4)*Hypergeometric2F1[7/12, 5/4, 19/12, Sin[e + f*x]^2]*(d*Tan[e + f*x])^(5/2))/(7*d*f*(b*Sin[e + f*x])^(4/3))","A",2,2,25,0.08000,1,"{2602, 2577}"
153,1,64,0,0.0926452,"\int \sqrt{b \sin (e+f x)} (d \tan (e+f x))^{4/3} \, dx","Int[Sqrt[b*Sin[e + f*x]]*(d*Tan[e + f*x])^(4/3),x]","\frac{6 \cos ^2(e+f x)^{7/6} \sqrt{b \sin (e+f x)} (d \tan (e+f x))^{7/3} \, _2F_1\left(\frac{7}{6},\frac{17}{12};\frac{29}{12};\sin ^2(e+f x)\right)}{17 d f}","\frac{6 \cos ^2(e+f x)^{7/6} \sqrt{b \sin (e+f x)} (d \tan (e+f x))^{7/3} \, _2F_1\left(\frac{7}{6},\frac{17}{12};\frac{29}{12};\sin ^2(e+f x)\right)}{17 d f}",1,"(6*(Cos[e + f*x]^2)^(7/6)*Hypergeometric2F1[7/6, 17/12, 29/12, Sin[e + f*x]^2]*Sqrt[b*Sin[e + f*x]]*(d*Tan[e + f*x])^(7/3))/(17*d*f)","A",2,2,25,0.08000,1,"{2602, 2577}"
154,1,64,0,0.0865125,"\int \sqrt{b \sin (e+f x)} \sqrt[3]{d \tan (e+f x)} \, dx","Int[Sqrt[b*Sin[e + f*x]]*(d*Tan[e + f*x])^(1/3),x]","\frac{6 \cos ^2(e+f x)^{2/3} \sqrt{b \sin (e+f x)} (d \tan (e+f x))^{4/3} \, _2F_1\left(\frac{2}{3},\frac{11}{12};\frac{23}{12};\sin ^2(e+f x)\right)}{11 d f}","\frac{6 \cos ^2(e+f x)^{2/3} \sqrt{b \sin (e+f x)} (d \tan (e+f x))^{4/3} \, _2F_1\left(\frac{2}{3},\frac{11}{12};\frac{23}{12};\sin ^2(e+f x)\right)}{11 d f}",1,"(6*(Cos[e + f*x]^2)^(2/3)*Hypergeometric2F1[2/3, 11/12, 23/12, Sin[e + f*x]^2]*Sqrt[b*Sin[e + f*x]]*(d*Tan[e + f*x])^(4/3))/(11*d*f)","A",2,2,25,0.08000,1,"{2602, 2577}"
155,1,64,0,0.0830445,"\int \frac{\sqrt{b \sin (e+f x)}}{\sqrt[3]{d \tan (e+f x)}} \, dx","Int[Sqrt[b*Sin[e + f*x]]/(d*Tan[e + f*x])^(1/3),x]","\frac{6 \sqrt[3]{\cos ^2(e+f x)} \sqrt{b \sin (e+f x)} (d \tan (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{7}{12};\frac{19}{12};\sin ^2(e+f x)\right)}{7 d f}","\frac{6 \sqrt[3]{\cos ^2(e+f x)} \sqrt{b \sin (e+f x)} (d \tan (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{7}{12};\frac{19}{12};\sin ^2(e+f x)\right)}{7 d f}",1,"(6*(Cos[e + f*x]^2)^(1/3)*Hypergeometric2F1[1/3, 7/12, 19/12, Sin[e + f*x]^2]*Sqrt[b*Sin[e + f*x]]*(d*Tan[e + f*x])^(2/3))/(7*d*f)","A",2,2,25,0.08000,1,"{2602, 2577}"
156,1,62,0,0.0959553,"\int \frac{\sqrt{b \sin (e+f x)}}{(d \tan (e+f x))^{4/3}} \, dx","Int[Sqrt[b*Sin[e + f*x]]/(d*Tan[e + f*x])^(4/3),x]","\frac{6 \sqrt{b \sin (e+f x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{12};\frac{13}{12};\sin ^2(e+f x)\right)}{d f \sqrt[6]{\cos ^2(e+f x)} \sqrt[3]{d \tan (e+f x)}}","\frac{6 \sqrt{b \sin (e+f x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{12};\frac{13}{12};\sin ^2(e+f x)\right)}{d f \sqrt[6]{\cos ^2(e+f x)} \sqrt[3]{d \tan (e+f x)}}",1,"(6*Hypergeometric2F1[-1/6, 1/12, 13/12, Sin[e + f*x]^2]*Sqrt[b*Sin[e + f*x]])/(d*f*(Cos[e + f*x]^2)^(1/6)*(d*Tan[e + f*x])^(1/3))","A",2,2,25,0.08000,1,"{2602, 2577}"
157,1,64,0,0.0986516,"\int (b \sin (e+f x))^{3/2} (d \tan (e+f x))^{4/3} \, dx","Int[(b*Sin[e + f*x])^(3/2)*(d*Tan[e + f*x])^(4/3),x]","\frac{6 \cos ^2(e+f x)^{7/6} (b \sin (e+f x))^{3/2} (d \tan (e+f x))^{7/3} \, _2F_1\left(\frac{7}{6},\frac{23}{12};\frac{35}{12};\sin ^2(e+f x)\right)}{23 d f}","\frac{6 \cos ^2(e+f x)^{7/6} (b \sin (e+f x))^{3/2} (d \tan (e+f x))^{7/3} \, _2F_1\left(\frac{7}{6},\frac{23}{12};\frac{35}{12};\sin ^2(e+f x)\right)}{23 d f}",1,"(6*(Cos[e + f*x]^2)^(7/6)*Hypergeometric2F1[7/6, 23/12, 35/12, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(3/2)*(d*Tan[e + f*x])^(7/3))/(23*d*f)","A",2,2,25,0.08000,1,"{2602, 2577}"
158,1,64,0,0.0919098,"\int (b \sin (e+f x))^{3/2} \sqrt[3]{d \tan (e+f x)} \, dx","Int[(b*Sin[e + f*x])^(3/2)*(d*Tan[e + f*x])^(1/3),x]","\frac{6 \cos ^2(e+f x)^{2/3} (b \sin (e+f x))^{3/2} (d \tan (e+f x))^{4/3} \, _2F_1\left(\frac{2}{3},\frac{17}{12};\frac{29}{12};\sin ^2(e+f x)\right)}{17 d f}","\frac{6 \cos ^2(e+f x)^{2/3} (b \sin (e+f x))^{3/2} (d \tan (e+f x))^{4/3} \, _2F_1\left(\frac{2}{3},\frac{17}{12};\frac{29}{12};\sin ^2(e+f x)\right)}{17 d f}",1,"(6*(Cos[e + f*x]^2)^(2/3)*Hypergeometric2F1[2/3, 17/12, 29/12, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(3/2)*(d*Tan[e + f*x])^(4/3))/(17*d*f)","A",2,2,25,0.08000,1,"{2602, 2577}"
159,1,64,0,0.0943887,"\int \frac{(b \sin (e+f x))^{3/2}}{\sqrt[3]{d \tan (e+f x)}} \, dx","Int[(b*Sin[e + f*x])^(3/2)/(d*Tan[e + f*x])^(1/3),x]","\frac{6 \sqrt[3]{\cos ^2(e+f x)} (b \sin (e+f x))^{3/2} (d \tan (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{13}{12};\frac{25}{12};\sin ^2(e+f x)\right)}{13 d f}","\frac{6 \sqrt[3]{\cos ^2(e+f x)} (b \sin (e+f x))^{3/2} (d \tan (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{13}{12};\frac{25}{12};\sin ^2(e+f x)\right)}{13 d f}",1,"(6*(Cos[e + f*x]^2)^(1/3)*Hypergeometric2F1[1/3, 13/12, 25/12, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(3/2)*(d*Tan[e + f*x])^(2/3))/(13*d*f)","A",2,2,25,0.08000,1,"{2602, 2577}"
160,1,64,0,0.0934154,"\int \frac{(b \sin (e+f x))^{3/2}}{(d \tan (e+f x))^{4/3}} \, dx","Int[(b*Sin[e + f*x])^(3/2)/(d*Tan[e + f*x])^(4/3),x]","\frac{6 (b \sin (e+f x))^{3/2} \, _2F_1\left(-\frac{1}{6},\frac{7}{12};\frac{19}{12};\sin ^2(e+f x)\right)}{7 d f \sqrt[6]{\cos ^2(e+f x)} \sqrt[3]{d \tan (e+f x)}}","\frac{6 (b \sin (e+f x))^{3/2} \, _2F_1\left(-\frac{1}{6},\frac{7}{12};\frac{19}{12};\sin ^2(e+f x)\right)}{7 d f \sqrt[6]{\cos ^2(e+f x)} \sqrt[3]{d \tan (e+f x)}}",1,"(6*Hypergeometric2F1[-1/6, 7/12, 19/12, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(3/2))/(7*d*f*(Cos[e + f*x]^2)^(1/6)*(d*Tan[e + f*x])^(1/3))","A",2,2,25,0.08000,1,"{2602, 2577}"
161,1,48,0,0.0487703,"\int (a \sin (e+f x))^m \tan ^3(e+f x) \, dx","Int[(a*Sin[e + f*x])^m*Tan[e + f*x]^3,x]","\frac{(a \sin (e+f x))^{m+4} \, _2F_1\left(2,\frac{m+4}{2};\frac{m+6}{2};\sin ^2(e+f x)\right)}{a^4 f (m+4)}","\frac{(a \sin (e+f x))^{m+4} \, _2F_1\left(2,\frac{m+4}{2};\frac{m+6}{2};\sin ^2(e+f x)\right)}{a^4 f (m+4)}",1,"(Hypergeometric2F1[2, (4 + m)/2, (6 + m)/2, Sin[e + f*x]^2]*(a*Sin[e + f*x])^(4 + m))/(a^4*f*(4 + m))","A",2,2,19,0.1053,1,"{2592, 364}"
162,1,48,0,0.0348985,"\int (a \sin (e+f x))^m \tan (e+f x) \, dx","Int[(a*Sin[e + f*x])^m*Tan[e + f*x],x]","\frac{(a \sin (e+f x))^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};\sin ^2(e+f x)\right)}{a^2 f (m+2)}","\frac{(a \sin (e+f x))^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};\sin ^2(e+f x)\right)}{a^2 f (m+2)}",1,"(Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, Sin[e + f*x]^2]*(a*Sin[e + f*x])^(2 + m))/(a^2*f*(2 + m))","A",2,2,17,0.1176,1,"{2592, 364}"
163,1,17,0,0.0286763,"\int \cot (e+f x) (a \sin (e+f x))^m \, dx","Int[Cot[e + f*x]*(a*Sin[e + f*x])^m,x]","\frac{(a \sin (e+f x))^m}{f m}","\frac{(a \sin (e+f x))^m}{f m}",1,"(a*Sin[e + f*x])^m/(f*m)","A",2,2,17,0.1176,1,"{2592, 30}"
164,1,46,0,0.0500821,"\int \cot ^3(e+f x) (a \sin (e+f x))^m \, dx","Int[Cot[e + f*x]^3*(a*Sin[e + f*x])^m,x]","-\frac{a^2 (a \sin (e+f x))^{m-2}}{f (2-m)}-\frac{(a \sin (e+f x))^m}{f m}","-\frac{a^2 (a \sin (e+f x))^{m-2}}{f (2-m)}-\frac{(a \sin (e+f x))^m}{f m}",1,"-((a^2*(a*Sin[e + f*x])^(-2 + m))/(f*(2 - m))) - (a*Sin[e + f*x])^m/(f*m)","A",3,2,19,0.1053,1,"{2592, 14}"
165,1,72,0,0.0609768,"\int \cot ^5(e+f x) (a \sin (e+f x))^m \, dx","Int[Cot[e + f*x]^5*(a*Sin[e + f*x])^m,x]","-\frac{a^4 (a \sin (e+f x))^{m-4}}{f (4-m)}+\frac{2 a^2 (a \sin (e+f x))^{m-2}}{f (2-m)}+\frac{(a \sin (e+f x))^m}{f m}","-\frac{a^4 (a \sin (e+f x))^{m-4}}{f (4-m)}+\frac{2 a^2 (a \sin (e+f x))^{m-2}}{f (2-m)}+\frac{(a \sin (e+f x))^m}{f m}",1,"-((a^4*(a*Sin[e + f*x])^(-4 + m))/(f*(4 - m))) + (2*a^2*(a*Sin[e + f*x])^(-2 + m))/(f*(2 - m)) + (a*Sin[e + f*x])^m/(f*m)","A",3,2,19,0.1053,1,"{2592, 270}"
166,1,68,0,0.0897263,"\int (a \sin (e+f x))^m \tan ^4(e+f x) \, dx","Int[(a*Sin[e + f*x])^m*Tan[e + f*x]^4,x]","\frac{\sqrt{\cos ^2(e+f x)} \sec (e+f x) (a \sin (e+f x))^{m+5} \, _2F_1\left(\frac{5}{2},\frac{m+5}{2};\frac{m+7}{2};\sin ^2(e+f x)\right)}{a^5 f (m+5)}","\frac{\sqrt{\cos ^2(e+f x)} \sec (e+f x) (a \sin (e+f x))^{m+5} \, _2F_1\left(\frac{5}{2},\frac{m+5}{2};\frac{m+7}{2};\sin ^2(e+f x)\right)}{a^5 f (m+5)}",1,"(Sqrt[Cos[e + f*x]^2]*Hypergeometric2F1[5/2, (5 + m)/2, (7 + m)/2, Sin[e + f*x]^2]*Sec[e + f*x]*(a*Sin[e + f*x])^(5 + m))/(a^5*f*(5 + m))","A",2,2,19,0.1053,1,"{2600, 2577}"
167,1,68,0,0.0888997,"\int (a \sin (e+f x))^m \tan ^2(e+f x) \, dx","Int[(a*Sin[e + f*x])^m*Tan[e + f*x]^2,x]","\frac{\sqrt{\cos ^2(e+f x)} \sec (e+f x) (a \sin (e+f x))^{m+3} \, _2F_1\left(\frac{3}{2},\frac{m+3}{2};\frac{m+5}{2};\sin ^2(e+f x)\right)}{a^3 f (m+3)}","\frac{\sqrt{\cos ^2(e+f x)} \sec (e+f x) (a \sin (e+f x))^{m+3} \, _2F_1\left(\frac{3}{2},\frac{m+3}{2};\frac{m+5}{2};\sin ^2(e+f x)\right)}{a^3 f (m+3)}",1,"(Sqrt[Cos[e + f*x]^2]*Hypergeometric2F1[3/2, (3 + m)/2, (5 + m)/2, Sin[e + f*x]^2]*Sec[e + f*x]*(a*Sin[e + f*x])^(3 + m))/(a^3*f*(3 + m))","A",2,2,19,0.1053,1,"{2600, 2577}"
168,1,69,0,0.0921402,"\int \cot ^2(e+f x) (a \sin (e+f x))^m \, dx","Int[Cot[e + f*x]^2*(a*Sin[e + f*x])^m,x]","-\frac{a \cos (e+f x) (a \sin (e+f x))^{m-1} \, _2F_1\left(-\frac{1}{2},\frac{m-1}{2};\frac{m+1}{2};\sin ^2(e+f x)\right)}{f (1-m) \sqrt{\cos ^2(e+f x)}}","-\frac{a \cos (e+f x) (a \sin (e+f x))^{m-1} \, _2F_1\left(-\frac{1}{2},\frac{m-1}{2};\frac{m+1}{2};\sin ^2(e+f x)\right)}{f (1-m) \sqrt{\cos ^2(e+f x)}}",1,"-((a*Cos[e + f*x]*Hypergeometric2F1[-1/2, (-1 + m)/2, (1 + m)/2, Sin[e + f*x]^2]*(a*Sin[e + f*x])^(-1 + m))/(f*(1 - m)*Sqrt[Cos[e + f*x]^2]))","A",2,2,19,0.1053,1,"{2600, 2577}"
169,1,71,0,0.0882018,"\int \cot ^4(e+f x) (a \sin (e+f x))^m \, dx","Int[Cot[e + f*x]^4*(a*Sin[e + f*x])^m,x]","-\frac{a^3 \cos (e+f x) (a \sin (e+f x))^{m-3} \, _2F_1\left(-\frac{3}{2},\frac{m-3}{2};\frac{m-1}{2};\sin ^2(e+f x)\right)}{f (3-m) \sqrt{\cos ^2(e+f x)}}","-\frac{a^3 \cos (e+f x) (a \sin (e+f x))^{m-3} \, _2F_1\left(-\frac{3}{2},\frac{m-3}{2};\frac{m-1}{2};\sin ^2(e+f x)\right)}{f (3-m) \sqrt{\cos ^2(e+f x)}}",1,"-((a^3*Cos[e + f*x]*Hypergeometric2F1[-3/2, (-3 + m)/2, (-1 + m)/2, Sin[e + f*x]^2]*(a*Sin[e + f*x])^(-3 + m))/(f*(3 - m)*Sqrt[Cos[e + f*x]^2]))","A",2,2,19,0.1053,1,"{2600, 2577}"
170,1,79,0,0.115703,"\int (a \sin (e+f x))^m (b \tan (e+f x))^{3/2} \, dx","Int[(a*Sin[e + f*x])^m*(b*Tan[e + f*x])^(3/2),x]","\frac{2 \cos ^2(e+f x)^{5/4} (b \tan (e+f x))^{5/2} (a \sin (e+f x))^m \, _2F_1\left(\frac{5}{4},\frac{1}{4} (2 m+5);\frac{1}{4} (2 m+9);\sin ^2(e+f x)\right)}{b f (2 m+5)}","\frac{2 \cos ^2(e+f x)^{5/4} (b \tan (e+f x))^{5/2} (a \sin (e+f x))^m \, _2F_1\left(\frac{5}{4},\frac{1}{4} (2 m+5);\frac{1}{4} (2 m+9);\sin ^2(e+f x)\right)}{b f (2 m+5)}",1,"(2*(Cos[e + f*x]^2)^(5/4)*Hypergeometric2F1[5/4, (5 + 2*m)/4, (9 + 2*m)/4, Sin[e + f*x]^2]*(a*Sin[e + f*x])^m*(b*Tan[e + f*x])^(5/2))/(b*f*(5 + 2*m))","A",2,2,23,0.08696,1,"{2602, 2577}"
171,1,79,0,0.1037513,"\int (a \sin (e+f x))^m \sqrt{b \tan (e+f x)} \, dx","Int[(a*Sin[e + f*x])^m*Sqrt[b*Tan[e + f*x]],x]","\frac{2 \cos ^2(e+f x)^{3/4} (b \tan (e+f x))^{3/2} (a \sin (e+f x))^m \, _2F_1\left(\frac{3}{4},\frac{1}{4} (2 m+3);\frac{1}{4} (2 m+7);\sin ^2(e+f x)\right)}{b f (2 m+3)}","\frac{2 \cos ^2(e+f x)^{3/4} (b \tan (e+f x))^{3/2} (a \sin (e+f x))^m \, _2F_1\left(\frac{3}{4},\frac{1}{4} (2 m+3);\frac{1}{4} (2 m+7);\sin ^2(e+f x)\right)}{b f (2 m+3)}",1,"(2*(Cos[e + f*x]^2)^(3/4)*Hypergeometric2F1[3/4, (3 + 2*m)/4, (7 + 2*m)/4, Sin[e + f*x]^2]*(a*Sin[e + f*x])^m*(b*Tan[e + f*x])^(3/2))/(b*f*(3 + 2*m))","A",2,2,23,0.08696,1,"{2602, 2577}"
172,1,79,0,0.102909,"\int \frac{(a \sin (e+f x))^m}{\sqrt{b \tan (e+f x)}} \, dx","Int[(a*Sin[e + f*x])^m/Sqrt[b*Tan[e + f*x]],x]","\frac{2 \sqrt[4]{\cos ^2(e+f x)} \sqrt{b \tan (e+f x)} (a \sin (e+f x))^m \, _2F_1\left(\frac{1}{4},\frac{1}{4} (2 m+1);\frac{1}{4} (2 m+5);\sin ^2(e+f x)\right)}{b f (2 m+1)}","\frac{2 \sqrt[4]{\cos ^2(e+f x)} \sqrt{b \tan (e+f x)} (a \sin (e+f x))^m \, _2F_1\left(\frac{1}{4},\frac{1}{4} (2 m+1);\frac{1}{4} (2 m+5);\sin ^2(e+f x)\right)}{b f (2 m+1)}",1,"(2*(Cos[e + f*x]^2)^(1/4)*Hypergeometric2F1[1/4, (1 + 2*m)/4, (5 + 2*m)/4, Sin[e + f*x]^2]*(a*Sin[e + f*x])^m*Sqrt[b*Tan[e + f*x]])/(b*f*(1 + 2*m))","A",2,2,23,0.08696,1,"{2602, 2577}"
173,1,79,0,0.1197771,"\int \frac{(a \sin (e+f x))^m}{(b \tan (e+f x))^{3/2}} \, dx","Int[(a*Sin[e + f*x])^m/(b*Tan[e + f*x])^(3/2),x]","-\frac{2 (a \sin (e+f x))^m \, _2F_1\left(-\frac{1}{4},\frac{1}{4} (2 m-1);\frac{1}{4} (2 m+3);\sin ^2(e+f x)\right)}{b f (1-2 m) \sqrt[4]{\cos ^2(e+f x)} \sqrt{b \tan (e+f x)}}","-\frac{2 (a \sin (e+f x))^m \, _2F_1\left(-\frac{1}{4},\frac{1}{4} (2 m-1);\frac{1}{4} (2 m+3);\sin ^2(e+f x)\right)}{b f (1-2 m) \sqrt[4]{\cos ^2(e+f x)} \sqrt{b \tan (e+f x)}}",1,"(-2*Hypergeometric2F1[-1/4, (-1 + 2*m)/4, (3 + 2*m)/4, Sin[e + f*x]^2]*(a*Sin[e + f*x])^m)/(b*f*(1 - 2*m)*(Cos[e + f*x]^2)^(1/4)*Sqrt[b*Tan[e + f*x]])","A",2,2,23,0.08696,1,"{2602, 2577}"
174,1,83,0,0.1028355,"\int (a \sin (e+f x))^m (b \tan (e+f x))^n \, dx","Int[(a*Sin[e + f*x])^m*(b*Tan[e + f*x])^n,x]","\frac{\cos ^2(e+f x)^{\frac{n+1}{2}} (a \sin (e+f x))^m (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);\sin ^2(e+f x)\right)}{b f (m+n+1)}","\frac{\cos ^2(e+f x)^{\frac{n+1}{2}} (a \sin (e+f x))^m (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);\sin ^2(e+f x)\right)}{b f (m+n+1)}",1,"((Cos[e + f*x]^2)^((1 + n)/2)*Hypergeometric2F1[(1 + n)/2, (1 + m + n)/2, (3 + m + n)/2, Sin[e + f*x]^2]*(a*Sin[e + f*x])^m*(b*Tan[e + f*x])^(1 + n))/(b*f*(1 + m + n))","A",2,2,21,0.09524,1,"{2602, 2577}"
175,1,50,0,0.0572467,"\int \sin ^4(e+f x) (b \tan (e+f x))^n \, dx","Int[Sin[e + f*x]^4*(b*Tan[e + f*x])^n,x]","\frac{(b \tan (e+f x))^{n+5} \, _2F_1\left(3,\frac{n+5}{2};\frac{n+7}{2};-\tan ^2(e+f x)\right)}{b^5 f (n+5)}","\frac{(b \tan (e+f x))^{n+5} \, _2F_1\left(3,\frac{n+5}{2};\frac{n+7}{2};-\tan ^2(e+f x)\right)}{b^5 f (n+5)}",1,"(Hypergeometric2F1[3, (5 + n)/2, (7 + n)/2, -Tan[e + f*x]^2]*(b*Tan[e + f*x])^(5 + n))/(b^5*f*(5 + n))","A",2,2,19,0.1053,1,"{2591, 364}"
176,1,50,0,0.0531362,"\int \sin ^2(e+f x) (b \tan (e+f x))^n \, dx","Int[Sin[e + f*x]^2*(b*Tan[e + f*x])^n,x]","\frac{(b \tan (e+f x))^{n+3} \, _2F_1\left(2,\frac{n+3}{2};\frac{n+5}{2};-\tan ^2(e+f x)\right)}{b^3 f (n+3)}","\frac{(b \tan (e+f x))^{n+3} \, _2F_1\left(2,\frac{n+3}{2};\frac{n+5}{2};-\tan ^2(e+f x)\right)}{b^3 f (n+3)}",1,"(Hypergeometric2F1[2, (3 + n)/2, (5 + n)/2, -Tan[e + f*x]^2]*(b*Tan[e + f*x])^(3 + n))/(b^3*f*(3 + n))","A",2,2,19,0.1053,1,"{2591, 364}"
177,1,25,0,0.0424143,"\int \csc ^2(e+f x) (b \tan (e+f x))^n \, dx","Int[Csc[e + f*x]^2*(b*Tan[e + f*x])^n,x]","-\frac{b (b \tan (e+f x))^{n-1}}{f (1-n)}","-\frac{b (b \tan (e+f x))^{n-1}}{f (1-n)}",1,"-((b*(b*Tan[e + f*x])^(-1 + n))/(f*(1 - n)))","A",2,2,19,0.1053,1,"{2591, 30}"
178,1,53,0,0.0550273,"\int \csc ^4(e+f x) (b \tan (e+f x))^n \, dx","Int[Csc[e + f*x]^4*(b*Tan[e + f*x])^n,x]","-\frac{b^3 (b \tan (e+f x))^{n-3}}{f (3-n)}-\frac{b (b \tan (e+f x))^{n-1}}{f (1-n)}","-\frac{b^3 (b \tan (e+f x))^{n-3}}{f (3-n)}-\frac{b (b \tan (e+f x))^{n-1}}{f (1-n)}",1,"-((b^3*(b*Tan[e + f*x])^(-3 + n))/(f*(3 - n))) - (b*(b*Tan[e + f*x])^(-1 + n))/(f*(1 - n))","A",3,2,19,0.1053,1,"{2591, 14}"
179,1,80,0,0.063032,"\int \csc ^6(e+f x) (b \tan (e+f x))^n \, dx","Int[Csc[e + f*x]^6*(b*Tan[e + f*x])^n,x]","-\frac{b^5 (b \tan (e+f x))^{n-5}}{f (5-n)}-\frac{2 b^3 (b \tan (e+f x))^{n-3}}{f (3-n)}-\frac{b (b \tan (e+f x))^{n-1}}{f (1-n)}","-\frac{b^5 (b \tan (e+f x))^{n-5}}{f (5-n)}-\frac{2 b^3 (b \tan (e+f x))^{n-3}}{f (3-n)}-\frac{b (b \tan (e+f x))^{n-1}}{f (1-n)}",1,"-((b^5*(b*Tan[e + f*x])^(-5 + n))/(f*(5 - n))) - (2*b^3*(b*Tan[e + f*x])^(-3 + n))/(f*(3 - n)) - (b*(b*Tan[e + f*x])^(-1 + n))/(f*(1 - n))","A",3,2,19,0.1053,1,"{2591, 270}"
180,1,78,0,0.084357,"\int \sin ^3(e+f x) (b \tan (e+f x))^n \, dx","Int[Sin[e + f*x]^3*(b*Tan[e + f*x])^n,x]","\frac{\sin ^3(e+f x) \cos ^2(e+f x)^{\frac{n+1}{2}} (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+4}{2};\frac{n+6}{2};\sin ^2(e+f x)\right)}{b f (n+4)}","\frac{\sin ^3(e+f x) \cos ^2(e+f x)^{\frac{n+1}{2}} (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+4}{2};\frac{n+6}{2};\sin ^2(e+f x)\right)}{b f (n+4)}",1,"((Cos[e + f*x]^2)^((1 + n)/2)*Hypergeometric2F1[(1 + n)/2, (4 + n)/2, (6 + n)/2, Sin[e + f*x]^2]*Sin[e + f*x]^3*(b*Tan[e + f*x])^(1 + n))/(b*f*(4 + n))","A",2,2,19,0.1053,1,"{2602, 2577}"
181,1,76,0,0.0702338,"\int \sin (e+f x) (b \tan (e+f x))^n \, dx","Int[Sin[e + f*x]*(b*Tan[e + f*x])^n,x]","\frac{\sin (e+f x) \cos ^2(e+f x)^{\frac{n+1}{2}} (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{b f (n+2)}","\frac{\sin (e+f x) \cos ^2(e+f x)^{\frac{n+1}{2}} (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{b f (n+2)}",1,"((Cos[e + f*x]^2)^((1 + n)/2)*Hypergeometric2F1[(1 + n)/2, (2 + n)/2, (4 + n)/2, Sin[e + f*x]^2]*Sin[e + f*x]*(b*Tan[e + f*x])^(1 + n))/(b*f*(2 + n))","A",2,2,17,0.1176,1,"{2602, 2577}"
182,1,78,0,0.0782896,"\int \csc (e+f x) (b \tan (e+f x))^n \, dx","Int[Csc[e + f*x]*(b*Tan[e + f*x])^n,x]","-\frac{\cos (e+f x) \sin ^2(e+f x)^{-n/2} (b \tan (e+f x))^n \, _2F_1\left(\frac{1-n}{2},\frac{2-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}","-\frac{\cos (e+f x) \sin ^2(e+f x)^{-n/2} (b \tan (e+f x))^n \, _2F_1\left(\frac{1-n}{2},\frac{2-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}",1,"-((Cos[e + f*x]*Hypergeometric2F1[(1 - n)/2, (2 - n)/2, (3 - n)/2, Cos[e + f*x]^2]*(b*Tan[e + f*x])^n)/(f*(1 - n)*(Sin[e + f*x]^2)^(n/2)))","A",2,2,17,0.1176,1,"{2601, 2576}"
183,1,78,0,0.0818814,"\int \csc ^3(e+f x) (b \tan (e+f x))^n \, dx","Int[Csc[e + f*x]^3*(b*Tan[e + f*x])^n,x]","-\frac{\cos (e+f x) \sin ^2(e+f x)^{-n/2} (b \tan (e+f x))^n \, _2F_1\left(\frac{1-n}{2},\frac{4-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}","-\frac{\cos (e+f x) \sin ^2(e+f x)^{-n/2} (b \tan (e+f x))^n \, _2F_1\left(\frac{1-n}{2},\frac{4-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}",1,"-((Cos[e + f*x]*Hypergeometric2F1[(1 - n)/2, (4 - n)/2, (3 - n)/2, Cos[e + f*x]^2]*(b*Tan[e + f*x])^n)/(f*(1 - n)*(Sin[e + f*x]^2)^(n/2)))","A",2,2,19,0.1053,1,"{2601, 2576}"
184,1,78,0,0.082808,"\int \csc ^5(e+f x) (b \tan (e+f x))^n \, dx","Int[Csc[e + f*x]^5*(b*Tan[e + f*x])^n,x]","-\frac{\cos (e+f x) \sin ^2(e+f x)^{-n/2} (b \tan (e+f x))^n \, _2F_1\left(\frac{1-n}{2},\frac{6-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}","-\frac{\cos (e+f x) \sin ^2(e+f x)^{-n/2} (b \tan (e+f x))^n \, _2F_1\left(\frac{1-n}{2},\frac{6-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}",1,"-((Cos[e + f*x]*Hypergeometric2F1[(1 - n)/2, (6 - n)/2, (3 - n)/2, Cos[e + f*x]^2]*(b*Tan[e + f*x])^n)/(f*(1 - n)*(Sin[e + f*x]^2)^(n/2)))","A",2,2,19,0.1053,1,"{2601, 2576}"
185,1,89,0,0.1207633,"\int (a \sin (e+f x))^{3/2} (b \tan (e+f x))^n \, dx","Int[(a*Sin[e + f*x])^(3/2)*(b*Tan[e + f*x])^n,x]","\frac{2 (a \sin (e+f x))^{3/2} \cos ^2(e+f x)^{\frac{n+1}{2}} (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{4} (2 n+5);\frac{1}{4} (2 n+9);\sin ^2(e+f x)\right)}{b f (2 n+5)}","\frac{2 (a \sin (e+f x))^{3/2} \cos ^2(e+f x)^{\frac{n+1}{2}} (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{4} (2 n+5);\frac{1}{4} (2 n+9);\sin ^2(e+f x)\right)}{b f (2 n+5)}",1,"(2*(Cos[e + f*x]^2)^((1 + n)/2)*Hypergeometric2F1[(1 + n)/2, (5 + 2*n)/4, (9 + 2*n)/4, Sin[e + f*x]^2]*(a*Sin[e + f*x])^(3/2)*(b*Tan[e + f*x])^(1 + n))/(b*f*(5 + 2*n))","A",2,2,23,0.08696,1,"{2602, 2577}"
186,1,89,0,0.1065813,"\int \sqrt{a \sin (e+f x)} (b \tan (e+f x))^n \, dx","Int[Sqrt[a*Sin[e + f*x]]*(b*Tan[e + f*x])^n,x]","\frac{2 \sqrt{a \sin (e+f x)} \cos ^2(e+f x)^{\frac{n+1}{2}} (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\sin ^2(e+f x)\right)}{b f (2 n+3)}","\frac{2 \sqrt{a \sin (e+f x)} \cos ^2(e+f x)^{\frac{n+1}{2}} (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\sin ^2(e+f x)\right)}{b f (2 n+3)}",1,"(2*(Cos[e + f*x]^2)^((1 + n)/2)*Hypergeometric2F1[(1 + n)/2, (3 + 2*n)/4, (7 + 2*n)/4, Sin[e + f*x]^2]*Sqrt[a*Sin[e + f*x]]*(b*Tan[e + f*x])^(1 + n))/(b*f*(3 + 2*n))","A",2,2,23,0.08696,1,"{2602, 2577}"
187,1,89,0,0.1066942,"\int \frac{(b \tan (e+f x))^n}{\sqrt{a \sin (e+f x)}} \, dx","Int[(b*Tan[e + f*x])^n/Sqrt[a*Sin[e + f*x]],x]","\frac{2 \cos ^2(e+f x)^{\frac{n+1}{2}} (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\sin ^2(e+f x)\right)}{b f (2 n+1) \sqrt{a \sin (e+f x)}}","\frac{2 \cos ^2(e+f x)^{\frac{n+1}{2}} (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\sin ^2(e+f x)\right)}{b f (2 n+1) \sqrt{a \sin (e+f x)}}",1,"(2*(Cos[e + f*x]^2)^((1 + n)/2)*Hypergeometric2F1[(1 + n)/2, (1 + 2*n)/4, (5 + 2*n)/4, Sin[e + f*x]^2]*(b*Tan[e + f*x])^(1 + n))/(b*f*(1 + 2*n)*Sqrt[a*Sin[e + f*x]])","A",2,2,23,0.08696,1,"{2602, 2577}"
188,1,89,0,0.1247728,"\int \frac{(b \tan (e+f x))^n}{(a \sin (e+f x))^{3/2}} \, dx","Int[(b*Tan[e + f*x])^n/(a*Sin[e + f*x])^(3/2),x]","-\frac{2 \cos ^2(e+f x)^{\frac{n+1}{2}} (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{4} (2 n-1);\frac{1}{4} (2 n+3);\sin ^2(e+f x)\right)}{b f (1-2 n) (a \sin (e+f x))^{3/2}}","-\frac{2 \cos ^2(e+f x)^{\frac{n+1}{2}} (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{4} (2 n-1);\frac{1}{4} (2 n+3);\sin ^2(e+f x)\right)}{b f (1-2 n) (a \sin (e+f x))^{3/2}}",1,"(-2*(Cos[e + f*x]^2)^((1 + n)/2)*Hypergeometric2F1[(1 + n)/2, (-1 + 2*n)/4, (3 + 2*n)/4, Sin[e + f*x]^2]*(b*Tan[e + f*x])^(1 + n))/(b*f*(1 - 2*n)*(a*Sin[e + f*x])^(3/2))","A",2,2,23,0.08696,1,"{2602, 2577}"
189,1,86,0,0.0954729,"\int (a \cos (e+f x))^m (b \tan (e+f x))^n \, dx","Int[(a*Cos[e + f*x])^m*(b*Tan[e + f*x])^n,x]","\frac{(a \cos (e+f x))^m (b \tan (e+f x))^{n+1} \cos ^2(e+f x)^{\frac{1}{2} (-m+n+1)} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (-m+n+1);\frac{n+3}{2};\sin ^2(e+f x)\right)}{b f (n+1)}","\frac{(a \cos (e+f x))^m (b \tan (e+f x))^{n+1} \cos ^2(e+f x)^{\frac{1}{2} (-m+n+1)} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (-m+n+1);\frac{n+3}{2};\sin ^2(e+f x)\right)}{b f (n+1)}",1,"((a*Cos[e + f*x])^m*(Cos[e + f*x]^2)^((1 - m + n)/2)*Hypergeometric2F1[(1 + n)/2, (1 - m + n)/2, (3 + n)/2, Sin[e + f*x]^2]*(b*Tan[e + f*x])^(1 + n))/(b*f*(1 + n))","A",2,2,21,0.09524,1,"{2603, 2617}"
190,1,63,0,0.0362079,"\int (a \tan (e+f x))^m (b \tan (e+f x))^n \, dx","Int[(a*Tan[e + f*x])^m*(b*Tan[e + f*x])^n,x]","\frac{(a \tan (e+f x))^{m+1} (b \tan (e+f x))^n \, _2F_1\left(1,\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);-\tan ^2(e+f x)\right)}{a f (m+n+1)}","\frac{(a \tan (e+f x))^{m+1} (b \tan (e+f x))^n \, _2F_1\left(1,\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);-\tan ^2(e+f x)\right)}{a f (m+n+1)}",1,"(Hypergeometric2F1[1, (1 + m + n)/2, (3 + m + n)/2, -Tan[e + f*x]^2]*(a*Tan[e + f*x])^(1 + m)*(b*Tan[e + f*x])^n)/(a*f*(1 + m + n))","A",3,3,21,0.1429,1,"{20, 3476, 364}"
191,1,232,0,0.2271333,"\int \sqrt{d \cot (e+f x)} \tan ^4(e+f x) \, dx","Int[Sqrt[d*Cot[e + f*x]]*Tan[e + f*x]^4,x]","\frac{2 d^3}{5 f (d \cot (e+f x))^{5/2}}-\frac{2 d}{f \sqrt{d \cot (e+f x)}}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}","\frac{2 d^3}{5 f (d \cot (e+f x))^{5/2}}-\frac{2 d}{f \sqrt{d \cot (e+f x)}}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}",1,"(Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) + (2*d^3)/(5*f*(d*Cot[e + f*x])^(5/2)) - (2*d)/(f*Sqrt[d*Cot[e + f*x]]) - (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) + (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",14,10,21,0.4762,1,"{16, 3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
192,1,214,0,0.1815167,"\int \sqrt{d \cot (e+f x)} \tan ^3(e+f x) \, dx","Int[Sqrt[d*Cot[e + f*x]]*Tan[e + f*x]^3,x]","\frac{2 d^2}{3 f (d \cot (e+f x))^{3/2}}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}","\frac{2 d^2}{3 f (d \cot (e+f x))^{3/2}}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}",1,"-((Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f)) + (Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) + (2*d^2)/(3*f*(d*Cot[e + f*x])^(3/2)) - (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) + (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",13,10,21,0.4762,1,"{16, 3474, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
193,1,210,0,0.1789922,"\int \sqrt{d \cot (e+f x)} \tan ^2(e+f x) \, dx","Int[Sqrt[d*Cot[e + f*x]]*Tan[e + f*x]^2,x]","\frac{2 d}{f \sqrt{d \cot (e+f x)}}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}","\frac{2 d}{f \sqrt{d \cot (e+f x)}}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}",1,"-((Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f)) + (Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) + (2*d)/(f*Sqrt[d*Cot[e + f*x]]) + (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) - (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",13,10,21,0.4762,1,"{16, 3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
194,1,192,0,0.1378012,"\int \sqrt{d \cot (e+f x)} \tan (e+f x) \, dx","Int[Sqrt[d*Cot[e + f*x]]*Tan[e + f*x],x]","\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}","\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}",1,"(Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) + (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) - (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",12,9,19,0.4737,1,"{16, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
195,1,192,0,0.1171445,"\int \sqrt{d \cot (e+f x)} \, dx","Int[Sqrt[d*Cot[e + f*x]],x]","-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}","-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}",1,"(Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) + (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",11,8,12,0.6667,1,"{3476, 329, 297, 1162, 617, 204, 1165, 628}"
196,1,209,0,0.1650355,"\int \cot (e+f x) \sqrt{d \cot (e+f x)} \, dx","Int[Cot[e + f*x]*Sqrt[d*Cot[e + f*x]],x]","-\frac{2 \sqrt{d \cot (e+f x)}}{f}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}","-\frac{2 \sqrt{d \cot (e+f x)}}{f}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}",1,"-((Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f)) + (Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (2*Sqrt[d*Cot[e + f*x]])/f - (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) + (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",13,10,19,0.5263,1,"{16, 3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
197,1,214,0,0.1616357,"\int \cot ^2(e+f x) \sqrt{d \cot (e+f x)} \, dx","Int[Cot[e + f*x]^2*Sqrt[d*Cot[e + f*x]],x]","-\frac{2 (d \cot (e+f x))^{3/2}}{3 d f}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}","-\frac{2 (d \cot (e+f x))^{3/2}}{3 d f}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}",1,"-((Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f)) + (Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (2*(d*Cot[e + f*x])^(3/2))/(3*d*f) + (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) - (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",13,10,21,0.4762,1,"{16, 3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
198,1,231,0,0.1976844,"\int \cot ^3(e+f x) \sqrt{d \cot (e+f x)} \, dx","Int[Cot[e + f*x]^3*Sqrt[d*Cot[e + f*x]],x]","-\frac{2 (d \cot (e+f x))^{5/2}}{5 d^2 f}+\frac{2 \sqrt{d \cot (e+f x)}}{f}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}","-\frac{2 (d \cot (e+f x))^{5/2}}{5 d^2 f}+\frac{2 \sqrt{d \cot (e+f x)}}{f}+\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}",1,"(Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) + (2*Sqrt[d*Cot[e + f*x]])/f - (2*(d*Cot[e + f*x])^(5/2))/(5*d^2*f) + (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) - (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",14,10,21,0.4762,1,"{16, 3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
199,1,234,0,0.2144653,"\int (d \cot (e+f x))^{3/2} \tan ^5(e+f x) \, dx","Int[(d*Cot[e + f*x])^(3/2)*Tan[e + f*x]^5,x]","\frac{2 d^4}{5 f (d \cot (e+f x))^{5/2}}-\frac{2 d^2}{f \sqrt{d \cot (e+f x)}}-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}","\frac{2 d^4}{5 f (d \cot (e+f x))^{5/2}}-\frac{2 d^2}{f \sqrt{d \cot (e+f x)}}-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}",1,"(d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) + (2*d^4)/(5*f*(d*Cot[e + f*x])^(5/2)) - (2*d^2)/(f*Sqrt[d*Cot[e + f*x]]) - (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) + (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",14,10,21,0.4762,1,"{16, 3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
200,1,214,0,0.1787596,"\int (d \cot (e+f x))^{3/2} \tan ^4(e+f x) \, dx","Int[(d*Cot[e + f*x])^(3/2)*Tan[e + f*x]^4,x]","\frac{2 d^3}{3 f (d \cot (e+f x))^{3/2}}-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}","\frac{2 d^3}{3 f (d \cot (e+f x))^{3/2}}-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}",1,"-((d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f)) + (d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) + (2*d^3)/(3*f*(d*Cot[e + f*x])^(3/2)) - (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) + (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",13,10,21,0.4762,1,"{16, 3474, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
201,1,212,0,0.1738382,"\int (d \cot (e+f x))^{3/2} \tan ^3(e+f x) \, dx","Int[(d*Cot[e + f*x])^(3/2)*Tan[e + f*x]^3,x]","\frac{2 d^2}{f \sqrt{d \cot (e+f x)}}+\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}","\frac{2 d^2}{f \sqrt{d \cot (e+f x)}}+\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}",1,"-((d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f)) + (d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) + (2*d^2)/(f*Sqrt[d*Cot[e + f*x]]) + (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) - (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",13,10,21,0.4762,1,"{16, 3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
202,1,192,0,0.1466971,"\int (d \cot (e+f x))^{3/2} \tan ^2(e+f x) \, dx","Int[(d*Cot[e + f*x])^(3/2)*Tan[e + f*x]^2,x]","\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}","\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}",1,"(d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) + (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) - (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",12,9,21,0.4286,1,"{16, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
203,1,192,0,0.1379587,"\int (d \cot (e+f x))^{3/2} \tan (e+f x) \, dx","Int[(d*Cot[e + f*x])^(3/2)*Tan[e + f*x],x]","-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}","-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}",1,"(d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) + (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",12,9,19,0.4737,1,"{16, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
204,1,210,0,0.1443091,"\int (d \cot (e+f x))^{3/2} \, dx","Int[(d*Cot[e + f*x])^(3/2),x]","-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}-\frac{2 d \sqrt{d \cot (e+f x)}}{f}","-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}-\frac{2 d \sqrt{d \cot (e+f x)}}{f}",1,"-((d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f)) + (d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (2*d*Sqrt[d*Cot[e + f*x]])/f - (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) + (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",12,9,12,0.7500,1,"{3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
205,1,211,0,0.1573279,"\int \cot (e+f x) (d \cot (e+f x))^{3/2} \, dx","Int[Cot[e + f*x]*(d*Cot[e + f*x])^(3/2),x]","\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}-\frac{2 (d \cot (e+f x))^{3/2}}{3 f}","\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}-\frac{2 (d \cot (e+f x))^{3/2}}{3 f}",1,"-((d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f)) + (d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (2*(d*Cot[e + f*x])^(3/2))/(3*f) + (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) - (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",13,10,19,0.5263,1,"{16, 3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
206,1,232,0,0.1960811,"\int \cot ^2(e+f x) (d \cot (e+f x))^{3/2} \, dx","Int[Cot[e + f*x]^2*(d*Cot[e + f*x])^(3/2),x]","\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}-\frac{2 (d \cot (e+f x))^{5/2}}{5 d f}+\frac{2 d \sqrt{d \cot (e+f x)}}{f}","\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{d^{3/2} \log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}-\frac{2 (d \cot (e+f x))^{5/2}}{5 d f}+\frac{2 d \sqrt{d \cot (e+f x)}}{f}",1,"(d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) + (2*d*Sqrt[d*Cot[e + f*x]])/f - (2*(d*Cot[e + f*x])^(5/2))/(5*d*f) + (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f) - (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]])/(2*Sqrt[2]*f)","A",14,10,21,0.4762,1,"{16, 3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
207,1,231,0,0.206992,"\int \frac{\tan ^3(e+f x)}{\sqrt{d \cot (e+f x)}} \, dx","Int[Tan[e + f*x]^3/Sqrt[d*Cot[e + f*x]],x]","\frac{2 d^2}{5 f (d \cot (e+f x))^{5/2}}-\frac{2}{f \sqrt{d \cot (e+f x)}}-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}","\frac{2 d^2}{5 f (d \cot (e+f x))^{5/2}}-\frac{2}{f \sqrt{d \cot (e+f x)}}-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f) - ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f) + (2*d^2)/(5*f*(d*Cot[e + f*x])^(5/2)) - 2/(f*Sqrt[d*Cot[e + f*x]]) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f)","A",14,10,21,0.4762,1,"{16, 3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
208,1,212,0,0.1705402,"\int \frac{\tan ^2(e+f x)}{\sqrt{d \cot (e+f x)}} \, dx","Int[Tan[e + f*x]^2/Sqrt[d*Cot[e + f*x]],x]","\frac{2 d}{3 f (d \cot (e+f x))^{3/2}}-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}","\frac{2 d}{3 f (d \cot (e+f x))^{3/2}}-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f)) + ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f) + (2*d)/(3*f*(d*Cot[e + f*x])^(3/2)) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f)","A",13,10,21,0.4762,1,"{16, 3474, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
209,1,209,0,0.1644057,"\int \frac{\tan (e+f x)}{\sqrt{d \cot (e+f x)}} \, dx","Int[Tan[e + f*x]/Sqrt[d*Cot[e + f*x]],x]","\frac{2}{f \sqrt{d \cot (e+f x)}}+\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}","\frac{2}{f \sqrt{d \cot (e+f x)}}+\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f)) + ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f) + 2/(f*Sqrt[d*Cot[e + f*x]]) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f)","A",13,10,19,0.5263,1,"{16, 3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
210,1,192,0,0.1114567,"\int \frac{1}{\sqrt{d \cot (e+f x)}} \, dx","Int[1/Sqrt[d*Cot[e + f*x]],x]","\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}","\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f) - ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f)","A",11,8,12,0.6667,1,"{3476, 329, 211, 1165, 628, 1162, 617, 204}"
211,1,192,0,0.1299086,"\int \frac{\cot (e+f x)}{\sqrt{d \cot (e+f x)}} \, dx","Int[Cot[e + f*x]/Sqrt[d*Cot[e + f*x]],x]","-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}","-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f) - ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f)","A",12,9,19,0.4737,1,"{16, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
212,1,212,0,0.1625751,"\int \frac{\cot ^2(e+f x)}{\sqrt{d \cot (e+f x)}} \, dx","Int[Cot[e + f*x]^2/Sqrt[d*Cot[e + f*x]],x]","-\frac{2 \sqrt{d \cot (e+f x)}}{d f}-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}","-\frac{2 \sqrt{d \cot (e+f x)}}{d f}-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f)) + ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f) - (2*Sqrt[d*Cot[e + f*x]])/(d*f) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f)","A",13,10,21,0.4762,1,"{16, 3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
213,1,214,0,0.1598535,"\int \frac{\cot ^3(e+f x)}{\sqrt{d \cot (e+f x)}} \, dx","Int[Cot[e + f*x]^3/Sqrt[d*Cot[e + f*x]],x]","-\frac{2 (d \cot (e+f x))^{3/2}}{3 d^2 f}+\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}","-\frac{2 (d \cot (e+f x))^{3/2}}{3 d^2 f}+\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} \sqrt{d} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} f}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f)) + ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*f) - (2*(d*Cot[e + f*x])^(3/2))/(3*d^2*f) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*Sqrt[d]*f)","A",13,10,21,0.4762,1,"{16, 3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
214,1,232,0,0.2092842,"\int \frac{\tan ^2(e+f x)}{(d \cot (e+f x))^{3/2}} \, dx","Int[Tan[e + f*x]^2/(d*Cot[e + f*x])^(3/2),x]","-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}+\frac{2 d}{5 f (d \cot (e+f x))^{5/2}}-\frac{2}{d f \sqrt{d \cot (e+f x)}}","-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}+\frac{2 d}{5 f (d \cot (e+f x))^{5/2}}-\frac{2}{d f \sqrt{d \cot (e+f x)}}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f) - ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f) + (2*d)/(5*f*(d*Cot[e + f*x])^(5/2)) - 2/(d*f*Sqrt[d*Cot[e + f*x]]) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f)","A",14,10,21,0.4762,1,"{16, 3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
215,1,211,0,0.1735289,"\int \frac{\tan (e+f x)}{(d \cot (e+f x))^{3/2}} \, dx","Int[Tan[e + f*x]/(d*Cot[e + f*x])^(3/2),x]","-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}+\frac{2}{3 f (d \cot (e+f x))^{3/2}}","-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}+\frac{2}{3 f (d \cot (e+f x))^{3/2}}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f)) + ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f) + 2/(3*f*(d*Cot[e + f*x])^(3/2)) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f)","A",13,10,19,0.5263,1,"{16, 3474, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
216,1,212,0,0.1424893,"\int \frac{1}{(d \cot (e+f x))^{3/2}} \, dx","Int[(d*Cot[e + f*x])^(-3/2),x]","\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}+\frac{2}{d f \sqrt{d \cot (e+f x)}}","\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}+\frac{2}{d f \sqrt{d \cot (e+f x)}}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f)) + ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f) + 2/(d*f*Sqrt[d*Cot[e + f*x]]) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f)","A",12,9,12,0.7500,1,"{3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
217,1,192,0,0.1323797,"\int \frac{\cot (e+f x)}{(d \cot (e+f x))^{3/2}} \, dx","Int[Cot[e + f*x]/(d*Cot[e + f*x])^(3/2),x]","\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}","\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f) - ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f)","A",12,9,19,0.4737,1,"{16, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
218,1,192,0,0.1316904,"\int \frac{\cot ^2(e+f x)}{(d \cot (e+f x))^{3/2}} \, dx","Int[Cot[e + f*x]^2/(d*Cot[e + f*x])^(3/2),x]","-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}","-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f) - ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f)","A",12,9,21,0.4286,1,"{16, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
219,1,212,0,0.1619772,"\int \frac{\cot ^3(e+f x)}{(d \cot (e+f x))^{3/2}} \, dx","Int[Cot[e + f*x]^3/(d*Cot[e + f*x])^(3/2),x]","-\frac{2 \sqrt{d \cot (e+f x)}}{d^2 f}-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}","-\frac{2 \sqrt{d \cot (e+f x)}}{d^2 f}-\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f)) + ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f) - (2*Sqrt[d*Cot[e + f*x]])/(d^2*f) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f)","A",13,10,21,0.4762,1,"{16, 3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
220,1,214,0,0.1613155,"\int \frac{\cot ^4(e+f x)}{(d \cot (e+f x))^{3/2}} \, dx","Int[Cot[e + f*x]^4/(d*Cot[e + f*x])^(3/2),x]","-\frac{2 (d \cot (e+f x))^{3/2}}{3 d^3 f}+\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}","-\frac{2 (d \cot (e+f x))^{3/2}}{3 d^3 f}+\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f)) + ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f) - (2*(d*Cot[e + f*x])^(3/2))/(3*d^3*f) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f)","A",13,10,21,0.4762,1,"{16, 3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
221,1,234,0,0.1884223,"\int \frac{\cot ^5(e+f x)}{(d \cot (e+f x))^{3/2}} \, dx","Int[Cot[e + f*x]^5/(d*Cot[e + f*x])^(3/2),x]","-\frac{2 (d \cot (e+f x))^{5/2}}{5 d^4 f}+\frac{2 \sqrt{d \cot (e+f x)}}{d^2 f}+\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}","-\frac{2 (d \cot (e+f x))^{5/2}}{5 d^4 f}+\frac{2 \sqrt{d \cot (e+f x)}}{d^2 f}+\frac{\log \left(\sqrt{d} \cot (e+f x)-\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}-\frac{\log \left(\sqrt{d} \cot (e+f x)+\sqrt{2} \sqrt{d \cot (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} d^{3/2} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} d^{3/2} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \cot (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} d^{3/2} f}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f) - ArcTan[1 + (Sqrt[2]*Sqrt[d*Cot[e + f*x]])/Sqrt[d]]/(Sqrt[2]*d^(3/2)*f) + (2*Sqrt[d*Cot[e + f*x]])/(d^2*f) - (2*(d*Cot[e + f*x])^(5/2))/(5*d^4*f) + Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] - Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f) - Log[Sqrt[d] + Sqrt[d]*Cot[e + f*x] + Sqrt[2]*Sqrt[d*Cot[e + f*x]]]/(2*Sqrt[2]*d^(3/2)*f)","A",14,10,21,0.4762,1,"{16, 3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
222,1,62,0,0.0582763,"\int \cot ^m(e+f x) \tan ^n(e+f x) \, dx","Int[Cot[e + f*x]^m*Tan[e + f*x]^n,x]","\frac{\cot ^m(e+f x) \tan ^{n+1}(e+f x) \, _2F_1\left(1,\frac{1}{2} (-m+n+1);\frac{1}{2} (-m+n+3);-\tan ^2(e+f x)\right)}{f (-m+n+1)}","\frac{\cot ^m(e+f x) \tan ^{n+1}(e+f x) \, _2F_1\left(1,\frac{1}{2} (-m+n+1);\frac{1}{2} (-m+n+3);-\tan ^2(e+f x)\right)}{f (-m+n+1)}",1,"(Cot[e + f*x]^m*Hypergeometric2F1[1, (1 - m + n)/2, (3 - m + n)/2, -Tan[e + f*x]^2]*Tan[e + f*x]^(1 + n))/(f*(1 - m + n))","A",3,3,17,0.1765,1,"{2604, 3476, 364}"
223,1,67,0,0.067043,"\int \cot ^m(e+f x) (b \tan (e+f x))^n \, dx","Int[Cot[e + f*x]^m*(b*Tan[e + f*x])^n,x]","\frac{\cot ^m(e+f x) (b \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{1}{2} (-m+n+1);\frac{1}{2} (-m+n+3);-\tan ^2(e+f x)\right)}{b f (-m+n+1)}","\frac{\cot ^m(e+f x) (b \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{1}{2} (-m+n+1);\frac{1}{2} (-m+n+3);-\tan ^2(e+f x)\right)}{b f (-m+n+1)}",1,"(Cot[e + f*x]^m*Hypergeometric2F1[1, (1 - m + n)/2, (3 - m + n)/2, -Tan[e + f*x]^2]*(b*Tan[e + f*x])^(1 + n))/(b*f*(1 - m + n))","A",3,3,19,0.1579,1,"{2604, 3476, 364}"
224,1,64,0,0.059477,"\int (a \cot (e+f x))^m \tan ^n(e+f x) \, dx","Int[(a*Cot[e + f*x])^m*Tan[e + f*x]^n,x]","\frac{\tan ^{n+1}(e+f x) (a \cot (e+f x))^m \, _2F_1\left(1,\frac{1}{2} (-m+n+1);\frac{1}{2} (-m+n+3);-\tan ^2(e+f x)\right)}{f (-m+n+1)}","\frac{\tan ^{n+1}(e+f x) (a \cot (e+f x))^m \, _2F_1\left(1,\frac{1}{2} (-m+n+1);\frac{1}{2} (-m+n+3);-\tan ^2(e+f x)\right)}{f (-m+n+1)}",1,"((a*Cot[e + f*x])^m*Hypergeometric2F1[1, (1 - m + n)/2, (3 - m + n)/2, -Tan[e + f*x]^2]*Tan[e + f*x]^(1 + n))/(f*(1 - m + n))","A",3,3,19,0.1579,1,"{2604, 3476, 364}"
225,1,69,0,0.0687408,"\int (a \cot (e+f x))^m (b \tan (e+f x))^n \, dx","Int[(a*Cot[e + f*x])^m*(b*Tan[e + f*x])^n,x]","\frac{(a \cot (e+f x))^m (b \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{1}{2} (-m+n+1);\frac{1}{2} (-m+n+3);-\tan ^2(e+f x)\right)}{b f (-m+n+1)}","\frac{(a \cot (e+f x))^m (b \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{1}{2} (-m+n+1);\frac{1}{2} (-m+n+3);-\tan ^2(e+f x)\right)}{b f (-m+n+1)}",1,"((a*Cot[e + f*x])^m*Hypergeometric2F1[1, (1 - m + n)/2, (3 - m + n)/2, -Tan[e + f*x]^2]*(b*Tan[e + f*x])^(1 + n))/(b*f*(1 - m + n))","A",3,3,21,0.1429,1,"{2604, 3476, 364}"
226,1,67,0,0.0538728,"\int \sec ^6(e+f x) \sqrt{d \tan (e+f x)} \, dx","Int[Sec[e + f*x]^6*Sqrt[d*Tan[e + f*x]],x]","\frac{2 (d \tan (e+f x))^{11/2}}{11 d^5 f}+\frac{4 (d \tan (e+f x))^{7/2}}{7 d^3 f}+\frac{2 (d \tan (e+f x))^{3/2}}{3 d f}","\frac{2 (d \tan (e+f x))^{11/2}}{11 d^5 f}+\frac{4 (d \tan (e+f x))^{7/2}}{7 d^3 f}+\frac{2 (d \tan (e+f x))^{3/2}}{3 d f}",1,"(2*(d*Tan[e + f*x])^(3/2))/(3*d*f) + (4*(d*Tan[e + f*x])^(7/2))/(7*d^3*f) + (2*(d*Tan[e + f*x])^(11/2))/(11*d^5*f)","A",3,2,21,0.09524,1,"{2607, 270}"
227,1,45,0,0.0449009,"\int \sec ^4(e+f x) \sqrt{d \tan (e+f x)} \, dx","Int[Sec[e + f*x]^4*Sqrt[d*Tan[e + f*x]],x]","\frac{2 (d \tan (e+f x))^{7/2}}{7 d^3 f}+\frac{2 (d \tan (e+f x))^{3/2}}{3 d f}","\frac{2 (d \tan (e+f x))^{7/2}}{7 d^3 f}+\frac{2 (d \tan (e+f x))^{3/2}}{3 d f}",1,"(2*(d*Tan[e + f*x])^(3/2))/(3*d*f) + (2*(d*Tan[e + f*x])^(7/2))/(7*d^3*f)","A",3,2,21,0.09524,1,"{2607, 14}"
228,1,22,0,0.0371223,"\int \sec ^2(e+f x) \sqrt{d \tan (e+f x)} \, dx","Int[Sec[e + f*x]^2*Sqrt[d*Tan[e + f*x]],x]","\frac{2 (d \tan (e+f x))^{3/2}}{3 d f}","\frac{2 (d \tan (e+f x))^{3/2}}{3 d f}",1,"(2*(d*Tan[e + f*x])^(3/2))/(3*d*f)","A",2,2,21,0.09524,1,"{2607, 32}"
229,1,192,0,0.1106246,"\int \sqrt{d \tan (e+f x)} \, dx","Int[Sqrt[d*Tan[e + f*x]],x]","-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}+\frac{\sqrt{d} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}","-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}+\frac{\sqrt{d} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}-\frac{\sqrt{d} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}",1,"-((Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f)) + (Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) + (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(2*Sqrt[2]*f) - (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(2*Sqrt[2]*f)","A",11,8,12,0.6667,1,"{3476, 329, 297, 1162, 617, 204, 1165, 628}"
230,1,227,0,0.1697223,"\int \cos ^2(e+f x) \sqrt{d \tan (e+f x)} \, dx","Int[Cos[e + f*x]^2*Sqrt[d*Tan[e + f*x]],x]","-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{4 \sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} f}+\frac{\sqrt{d} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{8 \sqrt{2} f}-\frac{\sqrt{d} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{8 \sqrt{2} f}+\frac{\cos ^2(e+f x) (d \tan (e+f x))^{3/2}}{2 d f}","-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{4 \sqrt{2} f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} f}+\frac{\sqrt{d} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{8 \sqrt{2} f}-\frac{\sqrt{d} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{8 \sqrt{2} f}+\frac{\cos ^2(e+f x) (d \tan (e+f x))^{3/2}}{2 d f}",1,"-(Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(4*Sqrt[2]*f) + (Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(4*Sqrt[2]*f) + (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(8*Sqrt[2]*f) - (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(8*Sqrt[2]*f) + (Cos[e + f*x]^2*(d*Tan[e + f*x])^(3/2))/(2*d*f)","A",12,9,21,0.4286,1,"{2607, 290, 329, 297, 1162, 617, 204, 1165, 628}"
231,1,107,0,0.1291661,"\int \sec ^3(e+f x) \sqrt{d \tan (e+f x)} \, dx","Int[Sec[e + f*x]^3*Sqrt[d*Tan[e + f*x]],x]","\frac{4 \cos (e+f x) (d \tan (e+f x))^{3/2}}{5 d f}+\frac{2 \sec (e+f x) (d \tan (e+f x))^{3/2}}{5 d f}-\frac{4 \cos (e+f x) E\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (e+f x)}}{5 f \sqrt{\sin (2 e+2 f x)}}","\frac{4 \cos (e+f x) (d \tan (e+f x))^{3/2}}{5 d f}+\frac{2 \sec (e+f x) (d \tan (e+f x))^{3/2}}{5 d f}-\frac{4 \cos (e+f x) E\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (e+f x)}}{5 f \sqrt{\sin (2 e+2 f x)}}",1,"(-4*Cos[e + f*x]*EllipticE[e - Pi/4 + f*x, 2]*Sqrt[d*Tan[e + f*x]])/(5*f*Sqrt[Sin[2*e + 2*f*x]]) + (4*Cos[e + f*x]*(d*Tan[e + f*x])^(3/2))/(5*d*f) + (2*Sec[e + f*x]*(d*Tan[e + f*x])^(3/2))/(5*d*f)","A",5,4,21,0.1905,1,"{2613, 2615, 2572, 2639}"
232,1,75,0,0.0899136,"\int \sec (e+f x) \sqrt{d \tan (e+f x)} \, dx","Int[Sec[e + f*x]*Sqrt[d*Tan[e + f*x]],x]","\frac{2 \cos (e+f x) (d \tan (e+f x))^{3/2}}{d f}-\frac{2 \cos (e+f x) E\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (e+f x)}}{f \sqrt{\sin (2 e+2 f x)}}","\frac{2 \cos (e+f x) (d \tan (e+f x))^{3/2}}{d f}-\frac{2 \cos (e+f x) E\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (e+f x)}}{f \sqrt{\sin (2 e+2 f x)}}",1,"(-2*Cos[e + f*x]*EllipticE[e - Pi/4 + f*x, 2]*Sqrt[d*Tan[e + f*x]])/(f*Sqrt[Sin[2*e + 2*f*x]]) + (2*Cos[e + f*x]*(d*Tan[e + f*x])^(3/2))/(d*f)","A",4,4,19,0.2105,1,"{2613, 2615, 2572, 2639}"
233,1,47,0,0.0649298,"\int \cos (e+f x) \sqrt{d \tan (e+f x)} \, dx","Int[Cos[e + f*x]*Sqrt[d*Tan[e + f*x]],x]","\frac{\cos (e+f x) E\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (e+f x)}}{f \sqrt{\sin (2 e+2 f x)}}","\frac{\cos (e+f x) E\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (e+f x)}}{f \sqrt{\sin (2 e+2 f x)}}",1,"(Cos[e + f*x]*EllipticE[e - Pi/4 + f*x, 2]*Sqrt[d*Tan[e + f*x]])/(f*Sqrt[Sin[2*e + 2*f*x]])","A",3,3,19,0.1579,1,"{2615, 2572, 2639}"
234,1,81,0,0.1017962,"\int \cos ^3(e+f x) \sqrt{d \tan (e+f x)} \, dx","Int[Cos[e + f*x]^3*Sqrt[d*Tan[e + f*x]],x]","\frac{\cos ^3(e+f x) (d \tan (e+f x))^{3/2}}{3 d f}+\frac{\cos (e+f x) E\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (e+f x)}}{2 f \sqrt{\sin (2 e+2 f x)}}","\frac{\cos ^3(e+f x) (d \tan (e+f x))^{3/2}}{3 d f}+\frac{\cos (e+f x) E\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (e+f x)}}{2 f \sqrt{\sin (2 e+2 f x)}}",1,"(Cos[e + f*x]*EllipticE[e - Pi/4 + f*x, 2]*Sqrt[d*Tan[e + f*x]])/(2*f*Sqrt[Sin[2*e + 2*f*x]]) + (Cos[e + f*x]^3*(d*Tan[e + f*x])^(3/2))/(3*d*f)","A",4,4,21,0.1905,1,"{2612, 2615, 2572, 2639}"
235,1,111,0,0.139029,"\int \cos ^5(e+f x) \sqrt{d \tan (e+f x)} \, dx","Int[Cos[e + f*x]^5*Sqrt[d*Tan[e + f*x]],x]","\frac{\cos ^5(e+f x) (d \tan (e+f x))^{3/2}}{5 d f}+\frac{7 \cos ^3(e+f x) (d \tan (e+f x))^{3/2}}{30 d f}+\frac{7 \cos (e+f x) E\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (e+f x)}}{20 f \sqrt{\sin (2 e+2 f x)}}","\frac{\cos ^5(e+f x) (d \tan (e+f x))^{3/2}}{5 d f}+\frac{7 \cos ^3(e+f x) (d \tan (e+f x))^{3/2}}{30 d f}+\frac{7 \cos (e+f x) E\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (e+f x)}}{20 f \sqrt{\sin (2 e+2 f x)}}",1,"(7*Cos[e + f*x]*EllipticE[e - Pi/4 + f*x, 2]*Sqrt[d*Tan[e + f*x]])/(20*f*Sqrt[Sin[2*e + 2*f*x]]) + (7*Cos[e + f*x]^3*(d*Tan[e + f*x])^(3/2))/(30*d*f) + (Cos[e + f*x]^5*(d*Tan[e + f*x])^(3/2))/(5*d*f)","A",5,4,21,0.1905,1,"{2612, 2615, 2572, 2639}"
236,1,67,0,0.0579711,"\int \sec ^6(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Sec[a + b*x]^6*(d*Tan[a + b*x])^(3/2),x]","\frac{2 (d \tan (a+b x))^{13/2}}{13 b d^5}+\frac{4 (d \tan (a+b x))^{9/2}}{9 b d^3}+\frac{2 (d \tan (a+b x))^{5/2}}{5 b d}","\frac{2 (d \tan (a+b x))^{13/2}}{13 b d^5}+\frac{4 (d \tan (a+b x))^{9/2}}{9 b d^3}+\frac{2 (d \tan (a+b x))^{5/2}}{5 b d}",1,"(2*(d*Tan[a + b*x])^(5/2))/(5*b*d) + (4*(d*Tan[a + b*x])^(9/2))/(9*b*d^3) + (2*(d*Tan[a + b*x])^(13/2))/(13*b*d^5)","A",3,2,21,0.09524,1,"{2607, 270}"
237,1,45,0,0.0526398,"\int \sec ^4(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Sec[a + b*x]^4*(d*Tan[a + b*x])^(3/2),x]","\frac{2 (d \tan (a+b x))^{9/2}}{9 b d^3}+\frac{2 (d \tan (a+b x))^{5/2}}{5 b d}","\frac{2 (d \tan (a+b x))^{9/2}}{9 b d^3}+\frac{2 (d \tan (a+b x))^{5/2}}{5 b d}",1,"(2*(d*Tan[a + b*x])^(5/2))/(5*b*d) + (2*(d*Tan[a + b*x])^(9/2))/(9*b*d^3)","A",3,2,21,0.09524,1,"{2607, 14}"
238,1,22,0,0.0432917,"\int \sec ^2(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Sec[a + b*x]^2*(d*Tan[a + b*x])^(3/2),x]","\frac{2 (d \tan (a+b x))^{5/2}}{5 b d}","\frac{2 (d \tan (a+b x))^{5/2}}{5 b d}",1,"(2*(d*Tan[a + b*x])^(5/2))/(5*b*d)","A",2,2,21,0.09524,1,"{2607, 32}"
239,1,210,0,0.1415728,"\int (d \tan (a+b x))^{3/2} \, dx","Int[(d*Tan[a + b*x])^(3/2),x]","\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{\sqrt{2} b}-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{\sqrt{2} b}+\frac{d^{3/2} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{2 \sqrt{2} b}-\frac{d^{3/2} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{2 \sqrt{2} b}+\frac{2 d \sqrt{d \tan (a+b x)}}{b}","\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{\sqrt{2} b}-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{\sqrt{2} b}+\frac{d^{3/2} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{2 \sqrt{2} b}-\frac{d^{3/2} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{2 \sqrt{2} b}+\frac{2 d \sqrt{d \tan (a+b x)}}{b}",1,"(d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(Sqrt[2]*b) - (d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(Sqrt[2]*b) + (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(2*Sqrt[2]*b) - (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(2*Sqrt[2]*b) + (2*d*Sqrt[d*Tan[a + b*x]])/b","A",12,9,12,0.7500,1,"{3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
240,1,225,0,0.162636,"\int \cos ^2(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Cos[a + b*x]^2*(d*Tan[a + b*x])^(3/2),x]","-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b}-\frac{d^{3/2} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}+\frac{d^{3/2} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}-\frac{d \cos ^2(a+b x) \sqrt{d \tan (a+b x)}}{2 b}","-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b}-\frac{d^{3/2} \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}+\frac{d^{3/2} \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b}-\frac{d \cos ^2(a+b x) \sqrt{d \tan (a+b x)}}{2 b}",1,"-(d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(4*Sqrt[2]*b) + (d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(4*Sqrt[2]*b) - (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(8*Sqrt[2]*b) + (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(8*Sqrt[2]*b) - (d*Cos[a + b*x]^2*Sqrt[d*Tan[a + b*x]])/(2*b)","A",12,9,21,0.4286,1,"{2607, 288, 329, 211, 1165, 628, 1162, 617, 204}"
241,1,136,0,0.1834552,"\int \sec ^5(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Sec[a + b*x]^5*(d*Tan[a + b*x])^(3/2),x]","-\frac{4 d^2 \sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{77 b \sqrt{d \tan (a+b x)}}+\frac{2 d \sec ^5(a+b x) \sqrt{d \tan (a+b x)}}{11 b}-\frac{2 d \sec ^3(a+b x) \sqrt{d \tan (a+b x)}}{77 b}-\frac{4 d \sec (a+b x) \sqrt{d \tan (a+b x)}}{77 b}","-\frac{4 d^2 \sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{77 b \sqrt{d \tan (a+b x)}}+\frac{2 d \sec ^5(a+b x) \sqrt{d \tan (a+b x)}}{11 b}-\frac{2 d \sec ^3(a+b x) \sqrt{d \tan (a+b x)}}{77 b}-\frac{4 d \sec (a+b x) \sqrt{d \tan (a+b x)}}{77 b}",1,"(-4*d^2*EllipticF[a - Pi/4 + b*x, 2]*Sec[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(77*b*Sqrt[d*Tan[a + b*x]]) - (4*d*Sec[a + b*x]*Sqrt[d*Tan[a + b*x]])/(77*b) - (2*d*Sec[a + b*x]^3*Sqrt[d*Tan[a + b*x]])/(77*b) + (2*d*Sec[a + b*x]^5*Sqrt[d*Tan[a + b*x]])/(11*b)","A",6,5,21,0.2381,1,"{2611, 2613, 2614, 2573, 2641}"
242,1,108,0,0.1448403,"\int \sec ^3(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Sec[a + b*x]^3*(d*Tan[a + b*x])^(3/2),x]","-\frac{2 d^2 \sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{21 b \sqrt{d \tan (a+b x)}}+\frac{2 d \sec ^3(a+b x) \sqrt{d \tan (a+b x)}}{7 b}-\frac{2 d \sec (a+b x) \sqrt{d \tan (a+b x)}}{21 b}","-\frac{2 d^2 \sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{21 b \sqrt{d \tan (a+b x)}}+\frac{2 d \sec ^3(a+b x) \sqrt{d \tan (a+b x)}}{7 b}-\frac{2 d \sec (a+b x) \sqrt{d \tan (a+b x)}}{21 b}",1,"(-2*d^2*EllipticF[a - Pi/4 + b*x, 2]*Sec[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(21*b*Sqrt[d*Tan[a + b*x]]) - (2*d*Sec[a + b*x]*Sqrt[d*Tan[a + b*x]])/(21*b) + (2*d*Sec[a + b*x]^3*Sqrt[d*Tan[a + b*x]])/(7*b)","A",5,5,21,0.2381,1,"{2611, 2613, 2614, 2573, 2641}"
243,1,80,0,0.0845474,"\int \sec (a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Sec[a + b*x]*(d*Tan[a + b*x])^(3/2),x]","\frac{2 d \sec (a+b x) \sqrt{d \tan (a+b x)}}{3 b}-\frac{d^2 \sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{3 b \sqrt{d \tan (a+b x)}}","\frac{2 d \sec (a+b x) \sqrt{d \tan (a+b x)}}{3 b}-\frac{d^2 \sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{3 b \sqrt{d \tan (a+b x)}}",1,"-(d^2*EllipticF[a - Pi/4 + b*x, 2]*Sec[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(3*b*Sqrt[d*Tan[a + b*x]]) + (2*d*Sec[a + b*x]*Sqrt[d*Tan[a + b*x]])/(3*b)","A",4,4,19,0.2105,1,"{2611, 2614, 2573, 2641}"
244,1,78,0,0.0951669,"\int \cos (a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Cos[a + b*x]*(d*Tan[a + b*x])^(3/2),x]","\frac{d^2 \sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b \sqrt{d \tan (a+b x)}}-\frac{d \cos (a+b x) \sqrt{d \tan (a+b x)}}{b}","\frac{d^2 \sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b \sqrt{d \tan (a+b x)}}-\frac{d \cos (a+b x) \sqrt{d \tan (a+b x)}}{b}",1,"(d^2*EllipticF[a - Pi/4 + b*x, 2]*Sec[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(2*b*Sqrt[d*Tan[a + b*x]]) - (d*Cos[a + b*x]*Sqrt[d*Tan[a + b*x]])/b","A",4,4,19,0.2105,1,"{2610, 2614, 2573, 2641}"
245,1,108,0,0.1335093,"\int \cos ^3(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Cos[a + b*x]^3*(d*Tan[a + b*x])^(3/2),x]","\frac{d^2 \sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{12 b \sqrt{d \tan (a+b x)}}-\frac{d \cos ^3(a+b x) \sqrt{d \tan (a+b x)}}{3 b}+\frac{d \cos (a+b x) \sqrt{d \tan (a+b x)}}{6 b}","\frac{d^2 \sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{12 b \sqrt{d \tan (a+b x)}}-\frac{d \cos ^3(a+b x) \sqrt{d \tan (a+b x)}}{3 b}+\frac{d \cos (a+b x) \sqrt{d \tan (a+b x)}}{6 b}",1,"(d^2*EllipticF[a - Pi/4 + b*x, 2]*Sec[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(12*b*Sqrt[d*Tan[a + b*x]]) + (d*Cos[a + b*x]*Sqrt[d*Tan[a + b*x]])/(6*b) - (d*Cos[a + b*x]^3*Sqrt[d*Tan[a + b*x]])/(3*b)","A",5,5,21,0.2381,1,"{2610, 2612, 2614, 2573, 2641}"
246,1,136,0,0.1741812,"\int \cos ^5(a+b x) (d \tan (a+b x))^{3/2} \, dx","Int[Cos[a + b*x]^5*(d*Tan[a + b*x])^(3/2),x]","\frac{d^2 \sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{24 b \sqrt{d \tan (a+b x)}}-\frac{d \cos ^5(a+b x) \sqrt{d \tan (a+b x)}}{5 b}+\frac{d \cos ^3(a+b x) \sqrt{d \tan (a+b x)}}{30 b}+\frac{d \cos (a+b x) \sqrt{d \tan (a+b x)}}{12 b}","\frac{d^2 \sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{24 b \sqrt{d \tan (a+b x)}}-\frac{d \cos ^5(a+b x) \sqrt{d \tan (a+b x)}}{5 b}+\frac{d \cos ^3(a+b x) \sqrt{d \tan (a+b x)}}{30 b}+\frac{d \cos (a+b x) \sqrt{d \tan (a+b x)}}{12 b}",1,"(d^2*EllipticF[a - Pi/4 + b*x, 2]*Sec[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(24*b*Sqrt[d*Tan[a + b*x]]) + (d*Cos[a + b*x]*Sqrt[d*Tan[a + b*x]])/(12*b) + (d*Cos[a + b*x]^3*Sqrt[d*Tan[a + b*x]])/(30*b) - (d*Cos[a + b*x]^5*Sqrt[d*Tan[a + b*x]])/(5*b)","A",6,5,21,0.2381,1,"{2610, 2612, 2614, 2573, 2641}"
247,1,67,0,0.0584089,"\int \sec ^6(e+f x) (d \tan (e+f x))^{5/2} \, dx","Int[Sec[e + f*x]^6*(d*Tan[e + f*x])^(5/2),x]","\frac{2 (d \tan (e+f x))^{15/2}}{15 d^5 f}+\frac{4 (d \tan (e+f x))^{11/2}}{11 d^3 f}+\frac{2 (d \tan (e+f x))^{7/2}}{7 d f}","\frac{2 (d \tan (e+f x))^{15/2}}{15 d^5 f}+\frac{4 (d \tan (e+f x))^{11/2}}{11 d^3 f}+\frac{2 (d \tan (e+f x))^{7/2}}{7 d f}",1,"(2*(d*Tan[e + f*x])^(7/2))/(7*d*f) + (4*(d*Tan[e + f*x])^(11/2))/(11*d^3*f) + (2*(d*Tan[e + f*x])^(15/2))/(15*d^5*f)","A",3,2,21,0.09524,1,"{2607, 270}"
248,1,45,0,0.0503122,"\int \sec ^4(e+f x) (d \tan (e+f x))^{5/2} \, dx","Int[Sec[e + f*x]^4*(d*Tan[e + f*x])^(5/2),x]","\frac{2 (d \tan (e+f x))^{11/2}}{11 d^3 f}+\frac{2 (d \tan (e+f x))^{7/2}}{7 d f}","\frac{2 (d \tan (e+f x))^{11/2}}{11 d^3 f}+\frac{2 (d \tan (e+f x))^{7/2}}{7 d f}",1,"(2*(d*Tan[e + f*x])^(7/2))/(7*d*f) + (2*(d*Tan[e + f*x])^(11/2))/(11*d^3*f)","A",3,2,21,0.09524,1,"{2607, 14}"
249,1,22,0,0.0427842,"\int \sec ^2(e+f x) (d \tan (e+f x))^{5/2} \, dx","Int[Sec[e + f*x]^2*(d*Tan[e + f*x])^(5/2),x]","\frac{2 (d \tan (e+f x))^{7/2}}{7 d f}","\frac{2 (d \tan (e+f x))^{7/2}}{7 d f}",1,"(2*(d*Tan[e + f*x])^(7/2))/(7*d*f)","A",2,2,21,0.09524,1,"{2607, 32}"
250,1,212,0,0.1422499,"\int (d \tan (e+f x))^{5/2} \, dx","Int[(d*Tan[e + f*x])^(5/2),x]","\frac{d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}-\frac{d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{2 d (d \tan (e+f x))^{3/2}}{3 f}","\frac{d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} f}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} f}-\frac{d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{2 \sqrt{2} f}+\frac{2 d (d \tan (e+f x))^{3/2}}{3 f}",1,"(d^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (d^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*f) - (d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(2*Sqrt[2]*f) + (d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(2*Sqrt[2]*f) + (2*d*(d*Tan[e + f*x])^(3/2))/(3*f)","A",12,9,12,0.7500,1,"{3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
251,1,225,0,0.1628246,"\int \cos ^2(e+f x) (d \tan (e+f x))^{5/2} \, dx","Int[Cos[e + f*x]^2*(d*Tan[e + f*x])^(5/2),x]","-\frac{3 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{4 \sqrt{2} f}+\frac{3 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} f}+\frac{3 d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{8 \sqrt{2} f}-\frac{3 d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{8 \sqrt{2} f}-\frac{d \cos ^2(e+f x) (d \tan (e+f x))^{3/2}}{2 f}","-\frac{3 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{4 \sqrt{2} f}+\frac{3 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} f}+\frac{3 d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{8 \sqrt{2} f}-\frac{3 d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{8 \sqrt{2} f}-\frac{d \cos ^2(e+f x) (d \tan (e+f x))^{3/2}}{2 f}",1,"(-3*d^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(4*Sqrt[2]*f) + (3*d^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(4*Sqrt[2]*f) + (3*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(8*Sqrt[2]*f) - (3*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(8*Sqrt[2]*f) - (d*Cos[e + f*x]^2*(d*Tan[e + f*x])^(3/2))/(2*f)","A",12,9,21,0.4286,1,"{2607, 288, 329, 297, 1162, 617, 204, 1165, 628}"
252,1,253,0,0.1798715,"\int \cos ^4(e+f x) (d \tan (e+f x))^{5/2} \, dx","Int[Cos[e + f*x]^4*(d*Tan[e + f*x])^(5/2),x]","-\frac{3 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{32 \sqrt{2} f}+\frac{3 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} f}+\frac{3 d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{64 \sqrt{2} f}-\frac{3 d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{64 \sqrt{2} f}-\frac{d \cos ^4(e+f x) (d \tan (e+f x))^{3/2}}{4 f}+\frac{3 d \cos ^2(e+f x) (d \tan (e+f x))^{3/2}}{16 f}","-\frac{3 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{32 \sqrt{2} f}+\frac{3 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{32 \sqrt{2} f}+\frac{3 d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{64 \sqrt{2} f}-\frac{3 d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{64 \sqrt{2} f}-\frac{d \cos ^4(e+f x) (d \tan (e+f x))^{3/2}}{4 f}+\frac{3 d \cos ^2(e+f x) (d \tan (e+f x))^{3/2}}{16 f}",1,"(-3*d^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(32*Sqrt[2]*f) + (3*d^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(32*Sqrt[2]*f) + (3*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(64*Sqrt[2]*f) - (3*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(64*Sqrt[2]*f) + (3*d*Cos[e + f*x]^2*(d*Tan[e + f*x])^(3/2))/(16*f) - (d*Cos[e + f*x]^4*(d*Tan[e + f*x])^(3/2))/(4*f)","A",13,10,21,0.4762,1,"{2607, 288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
253,1,109,0,0.1369326,"\int \frac{\sec ^5(e+f x)}{\sqrt{d \tan (e+f x)}} \, dx","Int[Sec[e + f*x]^5/Sqrt[d*Tan[e + f*x]],x]","\frac{2 \sec ^3(e+f x) \sqrt{d \tan (e+f x)}}{7 d f}+\frac{4 \sec (e+f x) \sqrt{d \tan (e+f x)}}{7 d f}+\frac{4 \sqrt{\sin (2 e+2 f x)} \sec (e+f x) F\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{7 f \sqrt{d \tan (e+f x)}}","\frac{2 \sec ^3(e+f x) \sqrt{d \tan (e+f x)}}{7 d f}+\frac{4 \sec (e+f x) \sqrt{d \tan (e+f x)}}{7 d f}+\frac{4 \sqrt{\sin (2 e+2 f x)} \sec (e+f x) F\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{7 f \sqrt{d \tan (e+f x)}}",1,"(4*EllipticF[e - Pi/4 + f*x, 2]*Sec[e + f*x]*Sqrt[Sin[2*e + 2*f*x]])/(7*f*Sqrt[d*Tan[e + f*x]]) + (4*Sec[e + f*x]*Sqrt[d*Tan[e + f*x]])/(7*d*f) + (2*Sec[e + f*x]^3*Sqrt[d*Tan[e + f*x]])/(7*d*f)","A",5,4,21,0.1905,1,"{2613, 2614, 2573, 2641}"
254,1,79,0,0.0959896,"\int \frac{\sec ^3(e+f x)}{\sqrt{d \tan (e+f x)}} \, dx","Int[Sec[e + f*x]^3/Sqrt[d*Tan[e + f*x]],x]","\frac{2 \sec (e+f x) \sqrt{d \tan (e+f x)}}{3 d f}+\frac{2 \sqrt{\sin (2 e+2 f x)} \sec (e+f x) F\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{3 f \sqrt{d \tan (e+f x)}}","\frac{2 \sec (e+f x) \sqrt{d \tan (e+f x)}}{3 d f}+\frac{2 \sqrt{\sin (2 e+2 f x)} \sec (e+f x) F\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{3 f \sqrt{d \tan (e+f x)}}",1,"(2*EllipticF[e - Pi/4 + f*x, 2]*Sec[e + f*x]*Sqrt[Sin[2*e + 2*f*x]])/(3*f*Sqrt[d*Tan[e + f*x]]) + (2*Sec[e + f*x]*Sqrt[d*Tan[e + f*x]])/(3*d*f)","A",4,4,21,0.1905,1,"{2613, 2614, 2573, 2641}"
255,1,47,0,0.0587222,"\int \frac{\sec (e+f x)}{\sqrt{d \tan (e+f x)}} \, dx","Int[Sec[e + f*x]/Sqrt[d*Tan[e + f*x]],x]","\frac{\sqrt{\sin (2 e+2 f x)} \sec (e+f x) F\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{f \sqrt{d \tan (e+f x)}}","\frac{\sqrt{\sin (2 e+2 f x)} \sec (e+f x) F\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{f \sqrt{d \tan (e+f x)}}",1,"(EllipticF[e - Pi/4 + f*x, 2]*Sec[e + f*x]*Sqrt[Sin[2*e + 2*f*x]])/(f*Sqrt[d*Tan[e + f*x]])","A",3,3,19,0.1579,1,"{2614, 2573, 2641}"
256,1,76,0,0.0932574,"\int \frac{\cos (e+f x)}{\sqrt{d \tan (e+f x)}} \, dx","Int[Cos[e + f*x]/Sqrt[d*Tan[e + f*x]],x]","\frac{\cos (e+f x) \sqrt{d \tan (e+f x)}}{d f}+\frac{\sqrt{\sin (2 e+2 f x)} \sec (e+f x) F\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{2 f \sqrt{d \tan (e+f x)}}","\frac{\cos (e+f x) \sqrt{d \tan (e+f x)}}{d f}+\frac{\sqrt{\sin (2 e+2 f x)} \sec (e+f x) F\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{2 f \sqrt{d \tan (e+f x)}}",1,"(EllipticF[e - Pi/4 + f*x, 2]*Sec[e + f*x]*Sqrt[Sin[2*e + 2*f*x]])/(2*f*Sqrt[d*Tan[e + f*x]]) + (Cos[e + f*x]*Sqrt[d*Tan[e + f*x]])/(d*f)","A",4,4,19,0.2105,1,"{2612, 2614, 2573, 2641}"
257,1,109,0,0.1273416,"\int \frac{\cos ^3(e+f x)}{\sqrt{d \tan (e+f x)}} \, dx","Int[Cos[e + f*x]^3/Sqrt[d*Tan[e + f*x]],x]","\frac{\cos ^3(e+f x) \sqrt{d \tan (e+f x)}}{3 d f}+\frac{5 \cos (e+f x) \sqrt{d \tan (e+f x)}}{6 d f}+\frac{5 \sqrt{\sin (2 e+2 f x)} \sec (e+f x) F\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{12 f \sqrt{d \tan (e+f x)}}","\frac{\cos ^3(e+f x) \sqrt{d \tan (e+f x)}}{3 d f}+\frac{5 \cos (e+f x) \sqrt{d \tan (e+f x)}}{6 d f}+\frac{5 \sqrt{\sin (2 e+2 f x)} \sec (e+f x) F\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{12 f \sqrt{d \tan (e+f x)}}",1,"(5*EllipticF[e - Pi/4 + f*x, 2]*Sec[e + f*x]*Sqrt[Sin[2*e + 2*f*x]])/(12*f*Sqrt[d*Tan[e + f*x]]) + (5*Cos[e + f*x]*Sqrt[d*Tan[e + f*x]])/(6*d*f) + (Cos[e + f*x]^3*Sqrt[d*Tan[e + f*x]])/(3*d*f)","A",5,4,21,0.1905,1,"{2612, 2614, 2573, 2641}"
258,1,65,0,0.0598842,"\int \frac{\sec ^6(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Sec[a + b*x]^6/(d*Tan[a + b*x])^(3/2),x]","\frac{2 (d \tan (a+b x))^{7/2}}{7 b d^5}+\frac{4 (d \tan (a+b x))^{3/2}}{3 b d^3}-\frac{2}{b d \sqrt{d \tan (a+b x)}}","\frac{2 (d \tan (a+b x))^{7/2}}{7 b d^5}+\frac{4 (d \tan (a+b x))^{3/2}}{3 b d^3}-\frac{2}{b d \sqrt{d \tan (a+b x)}}",1,"-2/(b*d*Sqrt[d*Tan[a + b*x]]) + (4*(d*Tan[a + b*x])^(3/2))/(3*b*d^3) + (2*(d*Tan[a + b*x])^(7/2))/(7*b*d^5)","A",3,2,21,0.09524,1,"{2607, 270}"
259,1,43,0,0.0522945,"\int \frac{\sec ^4(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Sec[a + b*x]^4/(d*Tan[a + b*x])^(3/2),x]","\frac{2 (d \tan (a+b x))^{3/2}}{3 b d^3}-\frac{2}{b d \sqrt{d \tan (a+b x)}}","\frac{2 (d \tan (a+b x))^{3/2}}{3 b d^3}-\frac{2}{b d \sqrt{d \tan (a+b x)}}",1,"-2/(b*d*Sqrt[d*Tan[a + b*x]]) + (2*(d*Tan[a + b*x])^(3/2))/(3*b*d^3)","A",3,2,21,0.09524,1,"{2607, 14}"
260,1,20,0,0.0434227,"\int \frac{\sec ^2(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Sec[a + b*x]^2/(d*Tan[a + b*x])^(3/2),x]","-\frac{2}{b d \sqrt{d \tan (a+b x)}}","-\frac{2}{b d \sqrt{d \tan (a+b x)}}",1,"-2/(b*d*Sqrt[d*Tan[a + b*x]])","A",2,2,21,0.09524,1,"{2607, 32}"
261,1,212,0,0.141506,"\int \frac{1}{(d \tan (a+b x))^{3/2}} \, dx","Int[(d*Tan[a + b*x])^(-3/2),x]","\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{\sqrt{2} b d^{3/2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{\sqrt{2} b d^{3/2}}-\frac{\log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{2 \sqrt{2} b d^{3/2}}+\frac{\log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{2 \sqrt{2} b d^{3/2}}-\frac{2}{b d \sqrt{d \tan (a+b x)}}","\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{\sqrt{2} b d^{3/2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{\sqrt{2} b d^{3/2}}-\frac{\log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{2 \sqrt{2} b d^{3/2}}+\frac{\log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{2 \sqrt{2} b d^{3/2}}-\frac{2}{b d \sqrt{d \tan (a+b x)}}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]]/(Sqrt[2]*b*d^(3/2)) - ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]]/(Sqrt[2]*b*d^(3/2)) - Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]]/(2*Sqrt[2]*b*d^(3/2)) + Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]]/(2*Sqrt[2]*b*d^(3/2)) - 2/(b*d*Sqrt[d*Tan[a + b*x]])","A",12,9,12,0.7500,1,"{3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
262,1,249,0,0.1832141,"\int \frac{\cos ^2(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Cos[a + b*x]^2/(d*Tan[a + b*x])^(3/2),x]","\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b d^{3/2}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b d^{3/2}}-\frac{5 \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b d^{3/2}}+\frac{5 \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b d^{3/2}}-\frac{5}{2 b d \sqrt{d \tan (a+b x)}}+\frac{\cos ^2(a+b x)}{2 b d \sqrt{d \tan (a+b x)}}","\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}\right)}{4 \sqrt{2} b d^{3/2}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (a+b x)}}{\sqrt{d}}+1\right)}{4 \sqrt{2} b d^{3/2}}-\frac{5 \log \left(\sqrt{d} \tan (a+b x)-\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b d^{3/2}}+\frac{5 \log \left(\sqrt{d} \tan (a+b x)+\sqrt{2} \sqrt{d \tan (a+b x)}+\sqrt{d}\right)}{8 \sqrt{2} b d^{3/2}}-\frac{5}{2 b d \sqrt{d \tan (a+b x)}}+\frac{\cos ^2(a+b x)}{2 b d \sqrt{d \tan (a+b x)}}",1,"(5*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(4*Sqrt[2]*b*d^(3/2)) - (5*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[a + b*x]])/Sqrt[d]])/(4*Sqrt[2]*b*d^(3/2)) - (5*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] - Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(8*Sqrt[2]*b*d^(3/2)) + (5*Log[Sqrt[d] + Sqrt[d]*Tan[a + b*x] + Sqrt[2]*Sqrt[d*Tan[a + b*x]]])/(8*Sqrt[2]*b*d^(3/2)) - 5/(2*b*d*Sqrt[d*Tan[a + b*x]]) + Cos[a + b*x]^2/(2*b*d*Sqrt[d*Tan[a + b*x]])","A",13,10,21,0.4762,1,"{2607, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
263,1,138,0,0.1741872,"\int \frac{\sec ^5(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Sec[a + b*x]^5/(d*Tan[a + b*x])^(3/2),x]","\frac{24 \cos (a+b x) (d \tan (a+b x))^{3/2}}{5 b d^3}+\frac{12 \sec (a+b x) (d \tan (a+b x))^{3/2}}{5 b d^3}-\frac{24 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{5 b d^2 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \sec ^3(a+b x)}{b d \sqrt{d \tan (a+b x)}}","\frac{24 \cos (a+b x) (d \tan (a+b x))^{3/2}}{5 b d^3}+\frac{12 \sec (a+b x) (d \tan (a+b x))^{3/2}}{5 b d^3}-\frac{24 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{5 b d^2 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \sec ^3(a+b x)}{b d \sqrt{d \tan (a+b x)}}",1,"(-2*Sec[a + b*x]^3)/(b*d*Sqrt[d*Tan[a + b*x]]) - (24*Cos[a + b*x]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[d*Tan[a + b*x]])/(5*b*d^2*Sqrt[Sin[2*a + 2*b*x]]) + (24*Cos[a + b*x]*(d*Tan[a + b*x])^(3/2))/(5*b*d^3) + (12*Sec[a + b*x]*(d*Tan[a + b*x])^(3/2))/(5*b*d^3)","A",6,5,21,0.2381,1,"{2608, 2613, 2615, 2572, 2639}"
264,1,104,0,0.1337492,"\int \frac{\sec ^3(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Sec[a + b*x]^3/(d*Tan[a + b*x])^(3/2),x]","\frac{4 \cos (a+b x) (d \tan (a+b x))^{3/2}}{b d^3}-\frac{4 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{b d^2 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \sec (a+b x)}{b d \sqrt{d \tan (a+b x)}}","\frac{4 \cos (a+b x) (d \tan (a+b x))^{3/2}}{b d^3}-\frac{4 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{b d^2 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \sec (a+b x)}{b d \sqrt{d \tan (a+b x)}}",1,"(-2*Sec[a + b*x])/(b*d*Sqrt[d*Tan[a + b*x]]) - (4*Cos[a + b*x]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[d*Tan[a + b*x]])/(b*d^2*Sqrt[Sin[2*a + 2*b*x]]) + (4*Cos[a + b*x]*(d*Tan[a + b*x])^(3/2))/(b*d^3)","A",5,5,21,0.2381,1,"{2608, 2613, 2615, 2572, 2639}"
265,1,78,0,0.0919042,"\int \frac{\sec (a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Sec[a + b*x]/(d*Tan[a + b*x])^(3/2),x]","-\frac{2 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{b d^2 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \cos (a+b x)}{b d \sqrt{d \tan (a+b x)}}","-\frac{2 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{b d^2 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \cos (a+b x)}{b d \sqrt{d \tan (a+b x)}}",1,"(-2*Cos[a + b*x])/(b*d*Sqrt[d*Tan[a + b*x]]) - (2*Cos[a + b*x]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[d*Tan[a + b*x]])/(b*d^2*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,19,0.2105,1,"{2608, 2615, 2572, 2639}"
266,1,78,0,0.0982776,"\int \frac{\cos (a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Cos[a + b*x]/(d*Tan[a + b*x])^(3/2),x]","-\frac{3 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{b d^2 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \cos (a+b x)}{b d \sqrt{d \tan (a+b x)}}","-\frac{3 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{b d^2 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \cos (a+b x)}{b d \sqrt{d \tan (a+b x)}}",1,"(-2*Cos[a + b*x])/(b*d*Sqrt[d*Tan[a + b*x]]) - (3*Cos[a + b*x]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[d*Tan[a + b*x]])/(b*d^2*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,19,0.2105,1,"{2609, 2615, 2572, 2639}"
267,1,112,0,0.1493107,"\int \frac{\cos ^3(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Cos[a + b*x]^3/(d*Tan[a + b*x])^(3/2),x]","-\frac{7 \cos ^3(a+b x) (d \tan (a+b x))^{3/2}}{3 b d^3}-\frac{7 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{2 b d^2 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \cos ^3(a+b x)}{b d \sqrt{d \tan (a+b x)}}","-\frac{7 \cos ^3(a+b x) (d \tan (a+b x))^{3/2}}{3 b d^3}-\frac{7 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{2 b d^2 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \cos ^3(a+b x)}{b d \sqrt{d \tan (a+b x)}}",1,"(-2*Cos[a + b*x]^3)/(b*d*Sqrt[d*Tan[a + b*x]]) - (7*Cos[a + b*x]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[d*Tan[a + b*x]])/(2*b*d^2*Sqrt[Sin[2*a + 2*b*x]]) - (7*Cos[a + b*x]^3*(d*Tan[a + b*x])^(3/2))/(3*b*d^3)","A",5,5,21,0.2381,1,"{2609, 2612, 2615, 2572, 2639}"
268,1,142,0,0.1870951,"\int \frac{\cos ^5(a+b x)}{(d \tan (a+b x))^{3/2}} \, dx","Int[Cos[a + b*x]^5/(d*Tan[a + b*x])^(3/2),x]","-\frac{11 \cos ^5(a+b x) (d \tan (a+b x))^{3/2}}{5 b d^3}-\frac{77 \cos ^3(a+b x) (d \tan (a+b x))^{3/2}}{30 b d^3}-\frac{77 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{20 b d^2 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \cos ^5(a+b x)}{b d \sqrt{d \tan (a+b x)}}","-\frac{11 \cos ^5(a+b x) (d \tan (a+b x))^{3/2}}{5 b d^3}-\frac{77 \cos ^3(a+b x) (d \tan (a+b x))^{3/2}}{30 b d^3}-\frac{77 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{20 b d^2 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \cos ^5(a+b x)}{b d \sqrt{d \tan (a+b x)}}",1,"(-2*Cos[a + b*x]^5)/(b*d*Sqrt[d*Tan[a + b*x]]) - (77*Cos[a + b*x]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[d*Tan[a + b*x]])/(20*b*d^2*Sqrt[Sin[2*a + 2*b*x]]) - (77*Cos[a + b*x]^3*(d*Tan[a + b*x])^(3/2))/(30*b*d^3) - (11*Cos[a + b*x]^5*(d*Tan[a + b*x])^(3/2))/(5*b*d^3)","A",6,5,21,0.2381,1,"{2609, 2612, 2615, 2572, 2639}"
269,1,82,0,0.0873308,"\int \frac{\sec (a+b x)}{(d \tan (a+b x))^{5/2}} \, dx","Int[Sec[a + b*x]/(d*Tan[a + b*x])^(5/2),x]","-\frac{\sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{3 b d^2 \sqrt{d \tan (a+b x)}}-\frac{2 \sec (a+b x)}{3 b d (d \tan (a+b x))^{3/2}}","-\frac{\sqrt{\sin (2 a+2 b x)} \sec (a+b x) F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{3 b d^2 \sqrt{d \tan (a+b x)}}-\frac{2 \sec (a+b x)}{3 b d (d \tan (a+b x))^{3/2}}",1,"(-2*Sec[a + b*x])/(3*b*d*(d*Tan[a + b*x])^(3/2)) - (EllipticF[a - Pi/4 + b*x, 2]*Sec[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(3*b*d^2*Sqrt[d*Tan[a + b*x]])","A",4,4,19,0.2105,1,"{2609, 2614, 2573, 2641}"
270,1,110,0,0.1373945,"\int \frac{\sec ^3(a+b x)}{(d \tan (a+b x))^{7/2}} \, dx","Int[Sec[a + b*x]^3/(d*Tan[a + b*x])^(7/2),x]","-\frac{4 \cos (a+b x)}{5 b d^3 \sqrt{d \tan (a+b x)}}-\frac{4 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{5 b d^4 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \sec (a+b x)}{5 b d (d \tan (a+b x))^{5/2}}","-\frac{4 \cos (a+b x)}{5 b d^3 \sqrt{d \tan (a+b x)}}-\frac{4 \cos (a+b x) E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{d \tan (a+b x)}}{5 b d^4 \sqrt{\sin (2 a+2 b x)}}-\frac{2 \sec (a+b x)}{5 b d (d \tan (a+b x))^{5/2}}",1,"(-2*Sec[a + b*x])/(5*b*d*(d*Tan[a + b*x])^(5/2)) - (4*Cos[a + b*x])/(5*b*d^3*Sqrt[d*Tan[a + b*x]]) - (4*Cos[a + b*x]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[d*Tan[a + b*x]])/(5*b*d^4*Sqrt[Sin[2*a + 2*b*x]])","A",5,4,21,0.1905,1,"{2608, 2615, 2572, 2639}"
271,1,53,0,0.058961,"\int \sec ^{\frac{10}{3}}(e+f x) \sin ^2(e+f x) \, dx","Int[Sec[e + f*x]^(10/3)*Sin[e + f*x]^2,x]","\frac{3 \sin (e+f x) \sec ^{\frac{7}{3}}(e+f x) \, _2F_1\left(-\frac{7}{6},-\frac{1}{2};-\frac{1}{6};\cos ^2(e+f x)\right)}{7 f \sqrt{\sin ^2(e+f x)}}","\frac{3 \sin (e+f x) \sec ^{\frac{7}{3}}(e+f x) \, _2F_1\left(-\frac{7}{6},-\frac{1}{2};-\frac{1}{6};\cos ^2(e+f x)\right)}{7 f \sqrt{\sin ^2(e+f x)}}",1,"(3*Hypergeometric2F1[-7/6, -1/2, -1/6, Cos[e + f*x]^2]*Sec[e + f*x]^(7/3)*Sin[e + f*x])/(7*f*Sqrt[Sin[e + f*x]^2])","A",2,2,19,0.1053,1,"{2632, 2576}"
272,1,53,0,0.0588771,"\int \sec ^{\frac{8}{3}}(e+f x) \sin ^2(e+f x) \, dx","Int[Sec[e + f*x]^(8/3)*Sin[e + f*x]^2,x]","\frac{3 \sin (e+f x) \sec ^{\frac{5}{3}}(e+f x) \, _2F_1\left(-\frac{5}{6},-\frac{1}{2};\frac{1}{6};\cos ^2(e+f x)\right)}{5 f \sqrt{\sin ^2(e+f x)}}","\frac{3 \sin (e+f x) \sec ^{\frac{5}{3}}(e+f x) \, _2F_1\left(-\frac{5}{6},-\frac{1}{2};\frac{1}{6};\cos ^2(e+f x)\right)}{5 f \sqrt{\sin ^2(e+f x)}}",1,"(3*Hypergeometric2F1[-5/6, -1/2, 1/6, Cos[e + f*x]^2]*Sec[e + f*x]^(5/3)*Sin[e + f*x])/(5*f*Sqrt[Sin[e + f*x]^2])","A",2,2,19,0.1053,1,"{2632, 2576}"
273,1,53,0,0.0581687,"\int \sec ^{\frac{7}{3}}(e+f x) \sin ^2(e+f x) \, dx","Int[Sec[e + f*x]^(7/3)*Sin[e + f*x]^2,x]","\frac{3 \sin (e+f x) \sec ^{\frac{4}{3}}(e+f x) \, _2F_1\left(-\frac{2}{3},-\frac{1}{2};\frac{1}{3};\cos ^2(e+f x)\right)}{4 f \sqrt{\sin ^2(e+f x)}}","\frac{3 \sin (e+f x) \sec ^{\frac{4}{3}}(e+f x) \, _2F_1\left(-\frac{2}{3},-\frac{1}{2};\frac{1}{3};\cos ^2(e+f x)\right)}{4 f \sqrt{\sin ^2(e+f x)}}",1,"(3*Hypergeometric2F1[-2/3, -1/2, 1/3, Cos[e + f*x]^2]*Sec[e + f*x]^(4/3)*Sin[e + f*x])/(4*f*Sqrt[Sin[e + f*x]^2])","A",2,2,19,0.1053,1,"{2632, 2576}"
274,1,53,0,0.0579557,"\int \sec ^{\frac{5}{3}}(e+f x) \sin ^2(e+f x) \, dx","Int[Sec[e + f*x]^(5/3)*Sin[e + f*x]^2,x]","\frac{3 \sin (e+f x) \sec ^{\frac{2}{3}}(e+f x) \, _2F_1\left(-\frac{1}{2},-\frac{1}{3};\frac{2}{3};\cos ^2(e+f x)\right)}{2 f \sqrt{\sin ^2(e+f x)}}","\frac{3 \sin (e+f x) \sec ^{\frac{2}{3}}(e+f x) \, _2F_1\left(-\frac{1}{2},-\frac{1}{3};\frac{2}{3};\cos ^2(e+f x)\right)}{2 f \sqrt{\sin ^2(e+f x)}}",1,"(3*Hypergeometric2F1[-1/2, -1/3, 2/3, Cos[e + f*x]^2]*Sec[e + f*x]^(2/3)*Sin[e + f*x])/(2*f*Sqrt[Sin[e + f*x]^2])","A",2,2,19,0.1053,1,"{2632, 2576}"
275,1,51,0,0.0581419,"\int \sec ^{\frac{4}{3}}(e+f x) \sin ^2(e+f x) \, dx","Int[Sec[e + f*x]^(4/3)*Sin[e + f*x]^2,x]","\frac{3 \sin (e+f x) \sqrt[3]{\sec (e+f x)} \, _2F_1\left(-\frac{1}{2},-\frac{1}{6};\frac{5}{6};\cos ^2(e+f x)\right)}{f \sqrt{\sin ^2(e+f x)}}","\frac{3 \sin (e+f x) \sqrt[3]{\sec (e+f x)} \, _2F_1\left(-\frac{1}{2},-\frac{1}{6};\frac{5}{6};\cos ^2(e+f x)\right)}{f \sqrt{\sin ^2(e+f x)}}",1,"(3*Hypergeometric2F1[-1/2, -1/6, 5/6, Cos[e + f*x]^2]*Sec[e + f*x]^(1/3)*Sin[e + f*x])/(f*Sqrt[Sin[e + f*x]^2])","A",2,2,19,0.1053,1,"{2632, 2576}"
276,1,53,0,0.0594236,"\int \sec ^{\frac{16}{3}}(e+f x) \sin ^4(e+f x) \, dx","Int[Sec[e + f*x]^(16/3)*Sin[e + f*x]^4,x]","\frac{3 \sin (e+f x) \sec ^{\frac{13}{3}}(e+f x) \, _2F_1\left(-\frac{13}{6},-\frac{3}{2};-\frac{7}{6};\cos ^2(e+f x)\right)}{13 f \sqrt{\sin ^2(e+f x)}}","\frac{3 \sin (e+f x) \sec ^{\frac{13}{3}}(e+f x) \, _2F_1\left(-\frac{13}{6},-\frac{3}{2};-\frac{7}{6};\cos ^2(e+f x)\right)}{13 f \sqrt{\sin ^2(e+f x)}}",1,"(3*Hypergeometric2F1[-13/6, -3/2, -7/6, Cos[e + f*x]^2]*Sec[e + f*x]^(13/3)*Sin[e + f*x])/(13*f*Sqrt[Sin[e + f*x]^2])","A",2,2,19,0.1053,1,"{2632, 2576}"
277,1,53,0,0.05791,"\int \sec ^{\frac{14}{3}}(e+f x) \sin ^4(e+f x) \, dx","Int[Sec[e + f*x]^(14/3)*Sin[e + f*x]^4,x]","\frac{3 \sin (e+f x) \sec ^{\frac{11}{3}}(e+f x) \, _2F_1\left(-\frac{11}{6},-\frac{3}{2};-\frac{5}{6};\cos ^2(e+f x)\right)}{11 f \sqrt{\sin ^2(e+f x)}}","\frac{3 \sin (e+f x) \sec ^{\frac{11}{3}}(e+f x) \, _2F_1\left(-\frac{11}{6},-\frac{3}{2};-\frac{5}{6};\cos ^2(e+f x)\right)}{11 f \sqrt{\sin ^2(e+f x)}}",1,"(3*Hypergeometric2F1[-11/6, -3/2, -5/6, Cos[e + f*x]^2]*Sec[e + f*x]^(11/3)*Sin[e + f*x])/(11*f*Sqrt[Sin[e + f*x]^2])","A",2,2,19,0.1053,1,"{2632, 2576}"
278,1,53,0,0.0572237,"\int \sec ^{\frac{13}{3}}(e+f x) \sin ^4(e+f x) \, dx","Int[Sec[e + f*x]^(13/3)*Sin[e + f*x]^4,x]","\frac{3 \sin (e+f x) \sec ^{\frac{10}{3}}(e+f x) \, _2F_1\left(-\frac{5}{3},-\frac{3}{2};-\frac{2}{3};\cos ^2(e+f x)\right)}{10 f \sqrt{\sin ^2(e+f x)}}","\frac{3 \sin (e+f x) \sec ^{\frac{10}{3}}(e+f x) \, _2F_1\left(-\frac{5}{3},-\frac{3}{2};-\frac{2}{3};\cos ^2(e+f x)\right)}{10 f \sqrt{\sin ^2(e+f x)}}",1,"(3*Hypergeometric2F1[-5/3, -3/2, -2/3, Cos[e + f*x]^2]*Sec[e + f*x]^(10/3)*Sin[e + f*x])/(10*f*Sqrt[Sin[e + f*x]^2])","A",2,2,19,0.1053,1,"{2632, 2576}"
279,1,53,0,0.0602202,"\int \sec ^{\frac{11}{3}}(e+f x) \sin ^4(e+f x) \, dx","Int[Sec[e + f*x]^(11/3)*Sin[e + f*x]^4,x]","\frac{3 \sin (e+f x) \sec ^{\frac{8}{3}}(e+f x) \, _2F_1\left(-\frac{3}{2},-\frac{4}{3};-\frac{1}{3};\cos ^2(e+f x)\right)}{8 f \sqrt{\sin ^2(e+f x)}}","\frac{3 \sin (e+f x) \sec ^{\frac{8}{3}}(e+f x) \, _2F_1\left(-\frac{3}{2},-\frac{4}{3};-\frac{1}{3};\cos ^2(e+f x)\right)}{8 f \sqrt{\sin ^2(e+f x)}}",1,"(3*Hypergeometric2F1[-3/2, -4/3, -1/3, Cos[e + f*x]^2]*Sec[e + f*x]^(8/3)*Sin[e + f*x])/(8*f*Sqrt[Sin[e + f*x]^2])","A",2,2,19,0.1053,1,"{2632, 2576}"
280,1,53,0,0.0585169,"\int \sec ^{\frac{10}{3}}(e+f x) \sin ^4(e+f x) \, dx","Int[Sec[e + f*x]^(10/3)*Sin[e + f*x]^4,x]","\frac{3 \sin (e+f x) \sec ^{\frac{7}{3}}(e+f x) \, _2F_1\left(-\frac{3}{2},-\frac{7}{6};-\frac{1}{6};\cos ^2(e+f x)\right)}{7 f \sqrt{\sin ^2(e+f x)}}","\frac{3 \sin (e+f x) \sec ^{\frac{7}{3}}(e+f x) \, _2F_1\left(-\frac{3}{2},-\frac{7}{6};-\frac{1}{6};\cos ^2(e+f x)\right)}{7 f \sqrt{\sin ^2(e+f x)}}",1,"(3*Hypergeometric2F1[-3/2, -7/6, -1/6, Cos[e + f*x]^2]*Sec[e + f*x]^(7/3)*Sin[e + f*x])/(7*f*Sqrt[Sin[e + f*x]^2])","A",2,2,19,0.1053,1,"{2632, 2576}"
281,1,57,0,0.043448,"\int (d \sec (e+f x))^{4/3} \tan ^2(e+f x) \, dx","Int[(d*Sec[e + f*x])^(4/3)*Tan[e + f*x]^2,x]","\frac{\cos ^2(e+f x)^{13/6} \tan ^3(e+f x) (d \sec (e+f x))^{4/3} \, _2F_1\left(\frac{3}{2},\frac{13}{6};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f}","\frac{\cos ^2(e+f x)^{13/6} \tan ^3(e+f x) (d \sec (e+f x))^{4/3} \, _2F_1\left(\frac{3}{2},\frac{13}{6};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f}",1,"((Cos[e + f*x]^2)^(13/6)*Hypergeometric2F1[3/2, 13/6, 5/2, Sin[e + f*x]^2]*(d*Sec[e + f*x])^(4/3)*Tan[e + f*x]^3)/(3*f)","A",1,1,21,0.04762,1,"{2617}"
282,1,57,0,0.0421866,"\int (d \sec (e+f x))^{2/3} \tan ^2(e+f x) \, dx","Int[(d*Sec[e + f*x])^(2/3)*Tan[e + f*x]^2,x]","\frac{\cos ^2(e+f x)^{11/6} \tan ^3(e+f x) (d \sec (e+f x))^{2/3} \, _2F_1\left(\frac{3}{2},\frac{11}{6};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f}","\frac{\cos ^2(e+f x)^{11/6} \tan ^3(e+f x) (d \sec (e+f x))^{2/3} \, _2F_1\left(\frac{3}{2},\frac{11}{6};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f}",1,"((Cos[e + f*x]^2)^(11/6)*Hypergeometric2F1[3/2, 11/6, 5/2, Sin[e + f*x]^2]*(d*Sec[e + f*x])^(2/3)*Tan[e + f*x]^3)/(3*f)","A",1,1,21,0.04762,1,"{2617}"
283,1,57,0,0.0364821,"\int \sqrt[3]{d \sec (e+f x)} \tan ^2(e+f x) \, dx","Int[(d*Sec[e + f*x])^(1/3)*Tan[e + f*x]^2,x]","\frac{\cos ^2(e+f x)^{5/3} \tan ^3(e+f x) \sqrt[3]{d \sec (e+f x)} \, _2F_1\left(\frac{3}{2},\frac{5}{3};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f}","\frac{\cos ^2(e+f x)^{5/3} \tan ^3(e+f x) \sqrt[3]{d \sec (e+f x)} \, _2F_1\left(\frac{3}{2},\frac{5}{3};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f}",1,"((Cos[e + f*x]^2)^(5/3)*Hypergeometric2F1[3/2, 5/3, 5/2, Sin[e + f*x]^2]*(d*Sec[e + f*x])^(1/3)*Tan[e + f*x]^3)/(3*f)","A",1,1,21,0.04762,1,"{2617}"
284,1,57,0,0.0425088,"\int \frac{\tan ^2(e+f x)}{\sqrt[3]{d \sec (e+f x)}} \, dx","Int[Tan[e + f*x]^2/(d*Sec[e + f*x])^(1/3),x]","\frac{\cos ^2(e+f x)^{4/3} \tan ^3(e+f x) \, _2F_1\left(\frac{4}{3},\frac{3}{2};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f \sqrt[3]{d \sec (e+f x)}}","\frac{\cos ^2(e+f x)^{4/3} \tan ^3(e+f x) \, _2F_1\left(\frac{4}{3},\frac{3}{2};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f \sqrt[3]{d \sec (e+f x)}}",1,"((Cos[e + f*x]^2)^(4/3)*Hypergeometric2F1[4/3, 3/2, 5/2, Sin[e + f*x]^2]*Tan[e + f*x]^3)/(3*f*(d*Sec[e + f*x])^(1/3))","A",1,1,21,0.04762,1,"{2617}"
285,1,57,0,0.0444188,"\int \frac{\tan ^2(e+f x)}{(d \sec (e+f x))^{2/3}} \, dx","Int[Tan[e + f*x]^2/(d*Sec[e + f*x])^(2/3),x]","\frac{\cos ^2(e+f x)^{7/6} \tan ^3(e+f x) \, _2F_1\left(\frac{7}{6},\frac{3}{2};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f (d \sec (e+f x))^{2/3}}","\frac{\cos ^2(e+f x)^{7/6} \tan ^3(e+f x) \, _2F_1\left(\frac{7}{6},\frac{3}{2};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f (d \sec (e+f x))^{2/3}}",1,"((Cos[e + f*x]^2)^(7/6)*Hypergeometric2F1[7/6, 3/2, 5/2, Sin[e + f*x]^2]*Tan[e + f*x]^3)/(3*f*(d*Sec[e + f*x])^(2/3))","A",1,1,21,0.04762,1,"{2617}"
286,1,57,0,0.04203,"\int (d \sec (e+f x))^{4/3} \tan ^4(e+f x) \, dx","Int[(d*Sec[e + f*x])^(4/3)*Tan[e + f*x]^4,x]","\frac{\cos ^2(e+f x)^{19/6} \tan ^5(e+f x) (d \sec (e+f x))^{4/3} \, _2F_1\left(\frac{5}{2},\frac{19}{6};\frac{7}{2};\sin ^2(e+f x)\right)}{5 f}","\frac{\cos ^2(e+f x)^{19/6} \tan ^5(e+f x) (d \sec (e+f x))^{4/3} \, _2F_1\left(\frac{5}{2},\frac{19}{6};\frac{7}{2};\sin ^2(e+f x)\right)}{5 f}",1,"((Cos[e + f*x]^2)^(19/6)*Hypergeometric2F1[5/2, 19/6, 7/2, Sin[e + f*x]^2]*(d*Sec[e + f*x])^(4/3)*Tan[e + f*x]^5)/(5*f)","A",1,1,21,0.04762,1,"{2617}"
287,1,57,0,0.0434981,"\int (d \sec (e+f x))^{2/3} \tan ^4(e+f x) \, dx","Int[(d*Sec[e + f*x])^(2/3)*Tan[e + f*x]^4,x]","\frac{\cos ^2(e+f x)^{17/6} \tan ^5(e+f x) (d \sec (e+f x))^{2/3} \, _2F_1\left(\frac{5}{2},\frac{17}{6};\frac{7}{2};\sin ^2(e+f x)\right)}{5 f}","\frac{\cos ^2(e+f x)^{17/6} \tan ^5(e+f x) (d \sec (e+f x))^{2/3} \, _2F_1\left(\frac{5}{2},\frac{17}{6};\frac{7}{2};\sin ^2(e+f x)\right)}{5 f}",1,"((Cos[e + f*x]^2)^(17/6)*Hypergeometric2F1[5/2, 17/6, 7/2, Sin[e + f*x]^2]*(d*Sec[e + f*x])^(2/3)*Tan[e + f*x]^5)/(5*f)","A",1,1,21,0.04762,1,"{2617}"
288,1,57,0,0.0374419,"\int \sqrt[3]{d \sec (e+f x)} \tan ^4(e+f x) \, dx","Int[(d*Sec[e + f*x])^(1/3)*Tan[e + f*x]^4,x]","\frac{\cos ^2(e+f x)^{8/3} \tan ^5(e+f x) \sqrt[3]{d \sec (e+f x)} \, _2F_1\left(\frac{5}{2},\frac{8}{3};\frac{7}{2};\sin ^2(e+f x)\right)}{5 f}","\frac{\cos ^2(e+f x)^{8/3} \tan ^5(e+f x) \sqrt[3]{d \sec (e+f x)} \, _2F_1\left(\frac{5}{2},\frac{8}{3};\frac{7}{2};\sin ^2(e+f x)\right)}{5 f}",1,"((Cos[e + f*x]^2)^(8/3)*Hypergeometric2F1[5/2, 8/3, 7/2, Sin[e + f*x]^2]*(d*Sec[e + f*x])^(1/3)*Tan[e + f*x]^5)/(5*f)","A",1,1,21,0.04762,1,"{2617}"
289,1,57,0,0.0386355,"\int \frac{\tan ^4(e+f x)}{\sqrt[3]{d \sec (e+f x)}} \, dx","Int[Tan[e + f*x]^4/(d*Sec[e + f*x])^(1/3),x]","\frac{\cos ^2(e+f x)^{7/3} \tan ^5(e+f x) \, _2F_1\left(\frac{7}{3},\frac{5}{2};\frac{7}{2};\sin ^2(e+f x)\right)}{5 f \sqrt[3]{d \sec (e+f x)}}","\frac{\cos ^2(e+f x)^{7/3} \tan ^5(e+f x) \, _2F_1\left(\frac{7}{3},\frac{5}{2};\frac{7}{2};\sin ^2(e+f x)\right)}{5 f \sqrt[3]{d \sec (e+f x)}}",1,"((Cos[e + f*x]^2)^(7/3)*Hypergeometric2F1[7/3, 5/2, 7/2, Sin[e + f*x]^2]*Tan[e + f*x]^5)/(5*f*(d*Sec[e + f*x])^(1/3))","A",1,1,21,0.04762,1,"{2617}"
290,1,57,0,0.0446449,"\int \frac{\tan ^4(e+f x)}{(d \sec (e+f x))^{2/3}} \, dx","Int[Tan[e + f*x]^4/(d*Sec[e + f*x])^(2/3),x]","\frac{\cos ^2(e+f x)^{13/6} \tan ^5(e+f x) \, _2F_1\left(\frac{13}{6},\frac{5}{2};\frac{7}{2};\sin ^2(e+f x)\right)}{5 f (d \sec (e+f x))^{2/3}}","\frac{\cos ^2(e+f x)^{13/6} \tan ^5(e+f x) \, _2F_1\left(\frac{13}{6},\frac{5}{2};\frac{7}{2};\sin ^2(e+f x)\right)}{5 f (d \sec (e+f x))^{2/3}}",1,"((Cos[e + f*x]^2)^(13/6)*Hypergeometric2F1[13/6, 5/2, 7/2, Sin[e + f*x]^2]*Tan[e + f*x]^5)/(5*f*(d*Sec[e + f*x])^(2/3))","A",1,1,21,0.04762,1,"{2617}"
291,1,178,0,0.1621232,"\int (d \sec (e+f x))^{5/2} \sqrt{b \tan (e+f x)} \, dx","Int[(d*Sec[e + f*x])^(5/2)*Sqrt[b*Tan[e + f*x]],x]","\frac{d^2 (b \tan (e+f x))^{3/2} \sqrt{d \sec (e+f x)}}{2 b f}-\frac{\sqrt{b} d^3 \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{\sqrt{b} d^3 \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}","\frac{d^2 (b \tan (e+f x))^{3/2} \sqrt{d \sec (e+f x)}}{2 b f}-\frac{\sqrt{b} d^3 \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{\sqrt{b} d^3 \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}",1,"-(Sqrt[b]*d^3*ArcTan[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[b*Tan[e + f*x]])/(4*f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]]) + (Sqrt[b]*d^3*ArcTanh[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[b*Tan[e + f*x]])/(4*f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]]) + (d^2*Sqrt[d*Sec[e + f*x]]*(b*Tan[e + f*x])^(3/2))/(2*b*f)","A",7,7,25,0.2800,1,"{2613, 2616, 2564, 329, 298, 203, 206}"
292,1,93,0,0.1116899,"\int (d \sec (e+f x))^{3/2} \sqrt{b \tan (e+f x)} \, dx","Int[(d*Sec[e + f*x])^(3/2)*Sqrt[b*Tan[e + f*x]],x]","\frac{d^2 (b \tan (e+f x))^{3/2}}{b f \sqrt{d \sec (e+f x)}}-\frac{d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}","\frac{d^2 (b \tan (e+f x))^{3/2}}{b f \sqrt{d \sec (e+f x)}}-\frac{d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}",1,"-((d^2*EllipticE[(e - Pi/2 + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(f*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])) + (d^2*(b*Tan[e + f*x])^(3/2))/(b*f*Sqrt[d*Sec[e + f*x]])","A",4,4,25,0.1600,1,"{2613, 2616, 2640, 2639}"
293,1,132,0,0.0979791,"\int \sqrt{d \sec (e+f x)} \sqrt{b \tan (e+f x)} \, dx","Int[Sqrt[d*Sec[e + f*x]]*Sqrt[b*Tan[e + f*x]],x]","\frac{\sqrt{b} d \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{\sqrt{b} d \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}","\frac{\sqrt{b} d \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{\sqrt{b} d \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}",1,"-((Sqrt[b]*d*ArcTan[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[b*Tan[e + f*x]])/(f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]])) + (Sqrt[b]*d*ArcTanh[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[b*Tan[e + f*x]])/(f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]])","A",6,6,25,0.2400,1,"{2616, 2564, 329, 298, 203, 206}"
294,1,55,0,0.061064,"\int \frac{\sqrt{b \tan (e+f x)}}{\sqrt{d \sec (e+f x)}} \, dx","Int[Sqrt[b*Tan[e + f*x]]/Sqrt[d*Sec[e + f*x]],x]","\frac{2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}","\frac{2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}",1,"(2*EllipticE[(e - Pi/2 + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(f*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])","A",3,3,25,0.1200,1,"{2616, 2640, 2639}"
295,1,34,0,0.0510625,"\int \frac{\sqrt{b \tan (e+f x)}}{(d \sec (e+f x))^{3/2}} \, dx","Int[Sqrt[b*Tan[e + f*x]]/(d*Sec[e + f*x])^(3/2),x]","\frac{2 (b \tan (e+f x))^{3/2}}{3 b f (d \sec (e+f x))^{3/2}}","\frac{2 (b \tan (e+f x))^{3/2}}{3 b f (d \sec (e+f x))^{3/2}}",1,"(2*(b*Tan[e + f*x])^(3/2))/(3*b*f*(d*Sec[e + f*x])^(3/2))","A",1,1,25,0.04000,1,"{2605}"
296,1,95,0,0.113922,"\int \frac{\sqrt{b \tan (e+f x)}}{(d \sec (e+f x))^{5/2}} \, dx","Int[Sqrt[b*Tan[e + f*x]]/(d*Sec[e + f*x])^(5/2),x]","\frac{4 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{5 d^2 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 (b \tan (e+f x))^{3/2}}{5 b f (d \sec (e+f x))^{5/2}}","\frac{4 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{5 d^2 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 (b \tan (e+f x))^{3/2}}{5 b f (d \sec (e+f x))^{5/2}}",1,"(4*EllipticE[(e - Pi/2 + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(5*d^2*f*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]]) + (2*(b*Tan[e + f*x])^(3/2))/(5*b*f*(d*Sec[e + f*x])^(5/2))","A",4,4,25,0.1600,1,"{2612, 2616, 2640, 2639}"
297,1,72,0,0.1033738,"\int \frac{\sqrt{b \tan (e+f x)}}{(d \sec (e+f x))^{7/2}} \, dx","Int[Sqrt[b*Tan[e + f*x]]/(d*Sec[e + f*x])^(7/2),x]","\frac{8 (b \tan (e+f x))^{3/2}}{21 b d^2 f (d \sec (e+f x))^{3/2}}+\frac{2 (b \tan (e+f x))^{3/2}}{7 b f (d \sec (e+f x))^{7/2}}","\frac{8 (b \tan (e+f x))^{3/2}}{21 b d^2 f (d \sec (e+f x))^{3/2}}+\frac{2 (b \tan (e+f x))^{3/2}}{7 b f (d \sec (e+f x))^{7/2}}",1,"(2*(b*Tan[e + f*x])^(3/2))/(7*b*f*(d*Sec[e + f*x])^(7/2)) + (8*(b*Tan[e + f*x])^(3/2))/(21*b*d^2*f*(d*Sec[e + f*x])^(3/2))","A",2,2,25,0.08000,1,"{2612, 2605}"
298,1,132,0,0.167954,"\int \frac{\sqrt{b \tan (e+f x)}}{(d \sec (e+f x))^{9/2}} \, dx","Int[Sqrt[b*Tan[e + f*x]]/(d*Sec[e + f*x])^(9/2),x]","\frac{4 (b \tan (e+f x))^{3/2}}{15 b d^2 f (d \sec (e+f x))^{5/2}}+\frac{8 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{15 d^4 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 (b \tan (e+f x))^{3/2}}{9 b f (d \sec (e+f x))^{9/2}}","\frac{4 (b \tan (e+f x))^{3/2}}{15 b d^2 f (d \sec (e+f x))^{5/2}}+\frac{8 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{15 d^4 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 (b \tan (e+f x))^{3/2}}{9 b f (d \sec (e+f x))^{9/2}}",1,"(8*EllipticE[(e - Pi/2 + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(15*d^4*f*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]]) + (2*(b*Tan[e + f*x])^(3/2))/(9*b*f*(d*Sec[e + f*x])^(9/2)) + (4*(b*Tan[e + f*x])^(3/2))/(15*b*d^2*f*(d*Sec[e + f*x])^(5/2))","A",5,4,25,0.1600,1,"{2612, 2616, 2640, 2639}"
299,1,131,0,0.1764895,"\int (d \sec (e+f x))^{5/2} (b \tan (e+f x))^{3/2} \, dx","Int[(d*Sec[e + f*x])^(5/2)*(b*Tan[e + f*x])^(3/2),x]","-\frac{b^2 d^2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{6 f \sqrt{b \tan (e+f x)}}-\frac{b d^2 \sqrt{b \tan (e+f x)} \sqrt{d \sec (e+f x)}}{6 f}+\frac{b \sqrt{b \tan (e+f x)} (d \sec (e+f x))^{5/2}}{3 f}","-\frac{b^2 d^2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{6 f \sqrt{b \tan (e+f x)}}-\frac{b d^2 \sqrt{b \tan (e+f x)} \sqrt{d \sec (e+f x)}}{6 f}+\frac{b \sqrt{b \tan (e+f x)} (d \sec (e+f x))^{5/2}}{3 f}",1,"-(b^2*d^2*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])/(6*f*Sqrt[b*Tan[e + f*x]]) - (b*d^2*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Tan[e + f*x]])/(6*f) + (b*(d*Sec[e + f*x])^(5/2)*Sqrt[b*Tan[e + f*x]])/(3*f)","A",5,5,25,0.2000,1,"{2611, 2613, 2616, 2642, 2641}"
300,1,169,0,0.1737372,"\int (d \sec (e+f x))^{3/2} (b \tan (e+f x))^{3/2} \, dx","Int[(d*Sec[e + f*x])^(3/2)*(b*Tan[e + f*x])^(3/2),x]","-\frac{b^{3/2} d \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 f \sqrt{b \tan (e+f x)}}-\frac{b^{3/2} d \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 f \sqrt{b \tan (e+f x)}}+\frac{b \sqrt{b \tan (e+f x)} (d \sec (e+f x))^{3/2}}{2 f}","-\frac{b^{3/2} d \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 f \sqrt{b \tan (e+f x)}}-\frac{b^{3/2} d \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 f \sqrt{b \tan (e+f x)}}+\frac{b \sqrt{b \tan (e+f x)} (d \sec (e+f x))^{3/2}}{2 f}",1,"-(b^(3/2)*d*ArcTan[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]])/(4*f*Sqrt[b*Tan[e + f*x]]) - (b^(3/2)*d*ArcTanh[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]])/(4*f*Sqrt[b*Tan[e + f*x]]) + (b*(d*Sec[e + f*x])^(3/2)*Sqrt[b*Tan[e + f*x]])/(2*f)","A",7,7,25,0.2800,1,"{2611, 2616, 2564, 329, 212, 206, 203}"
301,1,88,0,0.1154615,"\int \sqrt{d \sec (e+f x)} (b \tan (e+f x))^{3/2} \, dx","Int[Sqrt[d*Sec[e + f*x]]*(b*Tan[e + f*x])^(3/2),x]","\frac{b \sqrt{b \tan (e+f x)} \sqrt{d \sec (e+f x)}}{f}-\frac{b^2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{f \sqrt{b \tan (e+f x)}}","\frac{b \sqrt{b \tan (e+f x)} \sqrt{d \sec (e+f x)}}{f}-\frac{b^2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{f \sqrt{b \tan (e+f x)}}",1,"-((b^2*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])/(f*Sqrt[b*Tan[e + f*x]])) + (b*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Tan[e + f*x]])/f","A",4,4,25,0.1600,1,"{2611, 2616, 2642, 2641}"
302,1,167,0,0.1253622,"\int \frac{(b \tan (e+f x))^{3/2}}{\sqrt{d \sec (e+f x)}} \, dx","Int[(b*Tan[e + f*x])^(3/2)/Sqrt[d*Sec[e + f*x]],x]","\frac{b^{3/2} d (b \tan (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{f (b \sin (e+f x))^{3/2} (d \sec (e+f x))^{3/2}}+\frac{b^{3/2} d (b \tan (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{f (b \sin (e+f x))^{3/2} (d \sec (e+f x))^{3/2}}-\frac{2 d \csc (e+f x) (b \tan (e+f x))^{3/2}}{f (d \sec (e+f x))^{3/2}}","\frac{b^{3/2} d (b \tan (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{f (b \sin (e+f x))^{3/2} (d \sec (e+f x))^{3/2}}+\frac{b^{3/2} d (b \tan (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{f (b \sin (e+f x))^{3/2} (d \sec (e+f x))^{3/2}}-\frac{2 d \csc (e+f x) (b \tan (e+f x))^{3/2}}{f (d \sec (e+f x))^{3/2}}",1,"(-2*d*Csc[e + f*x]*(b*Tan[e + f*x])^(3/2))/(f*(d*Sec[e + f*x])^(3/2)) + (b^(3/2)*d*ArcTan[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*(b*Tan[e + f*x])^(3/2))/(f*(d*Sec[e + f*x])^(3/2)*(b*Sin[e + f*x])^(3/2)) + (b^(3/2)*d*ArcTanh[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*(b*Tan[e + f*x])^(3/2))/(f*(d*Sec[e + f*x])^(3/2)*(b*Sin[e + f*x])^(3/2))","A",7,7,25,0.2800,1,"{2616, 2564, 321, 329, 212, 206, 203}"
303,1,96,0,0.1211396,"\int \frac{(b \tan (e+f x))^{3/2}}{(d \sec (e+f x))^{3/2}} \, dx","Int[(b*Tan[e + f*x])^(3/2)/(d*Sec[e + f*x])^(3/2),x]","\frac{2 b^2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{3 d^2 f \sqrt{b \tan (e+f x)}}-\frac{2 b \sqrt{b \tan (e+f x)}}{3 f (d \sec (e+f x))^{3/2}}","\frac{2 b^2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{3 d^2 f \sqrt{b \tan (e+f x)}}-\frac{2 b \sqrt{b \tan (e+f x)}}{3 f (d \sec (e+f x))^{3/2}}",1,"(2*b^2*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])/(3*d^2*f*Sqrt[b*Tan[e + f*x]]) - (2*b*Sqrt[b*Tan[e + f*x]])/(3*f*(d*Sec[e + f*x])^(3/2))","A",4,4,25,0.1600,1,"{2610, 2616, 2642, 2641}"
304,1,34,0,0.0570212,"\int \frac{(b \tan (e+f x))^{3/2}}{(d \sec (e+f x))^{5/2}} \, dx","Int[(b*Tan[e + f*x])^(3/2)/(d*Sec[e + f*x])^(5/2),x]","\frac{2 (b \tan (e+f x))^{5/2}}{5 b f (d \sec (e+f x))^{5/2}}","\frac{2 (b \tan (e+f x))^{5/2}}{5 b f (d \sec (e+f x))^{5/2}}",1,"(2*(b*Tan[e + f*x])^(5/2))/(5*b*f*(d*Sec[e + f*x])^(5/2))","A",1,1,25,0.04000,1,"{2605}"
305,1,131,0,0.1795606,"\int \frac{(b \tan (e+f x))^{3/2}}{(d \sec (e+f x))^{7/2}} \, dx","Int[(b*Tan[e + f*x])^(3/2)/(d*Sec[e + f*x])^(7/2),x]","\frac{4 b^2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{21 d^4 f \sqrt{b \tan (e+f x)}}+\frac{2 b \sqrt{b \tan (e+f x)}}{21 d^2 f (d \sec (e+f x))^{3/2}}-\frac{2 b \sqrt{b \tan (e+f x)}}{7 f (d \sec (e+f x))^{7/2}}","\frac{4 b^2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{21 d^4 f \sqrt{b \tan (e+f x)}}+\frac{2 b \sqrt{b \tan (e+f x)}}{21 d^2 f (d \sec (e+f x))^{3/2}}-\frac{2 b \sqrt{b \tan (e+f x)}}{7 f (d \sec (e+f x))^{7/2}}",1,"(4*b^2*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])/(21*d^4*f*Sqrt[b*Tan[e + f*x]]) - (2*b*Sqrt[b*Tan[e + f*x]])/(7*f*(d*Sec[e + f*x])^(7/2)) + (2*b*Sqrt[b*Tan[e + f*x]])/(21*d^2*f*(d*Sec[e + f*x])^(3/2))","A",5,5,25,0.2000,1,"{2610, 2612, 2616, 2642, 2641}"
306,1,103,0,0.1629036,"\int \frac{(b \tan (e+f x))^{3/2}}{(d \sec (e+f x))^{9/2}} \, dx","Int[(b*Tan[e + f*x])^(3/2)/(d*Sec[e + f*x])^(9/2),x]","\frac{8 b \sqrt{b \tan (e+f x)}}{45 d^4 f \sqrt{d \sec (e+f x)}}+\frac{2 b \sqrt{b \tan (e+f x)}}{45 d^2 f (d \sec (e+f x))^{5/2}}-\frac{2 b \sqrt{b \tan (e+f x)}}{9 f (d \sec (e+f x))^{9/2}}","\frac{8 b \sqrt{b \tan (e+f x)}}{45 d^4 f \sqrt{d \sec (e+f x)}}+\frac{2 b \sqrt{b \tan (e+f x)}}{45 d^2 f (d \sec (e+f x))^{5/2}}-\frac{2 b \sqrt{b \tan (e+f x)}}{9 f (d \sec (e+f x))^{9/2}}",1,"(-2*b*Sqrt[b*Tan[e + f*x]])/(9*f*(d*Sec[e + f*x])^(9/2)) + (2*b*Sqrt[b*Tan[e + f*x]])/(45*d^2*f*(d*Sec[e + f*x])^(5/2)) + (8*b*Sqrt[b*Tan[e + f*x]])/(45*d^4*f*Sqrt[d*Sec[e + f*x]])","A",3,3,25,0.1200,1,"{2610, 2612, 2605}"
307,1,208,0,0.2280344,"\int (d \sec (e+f x))^{5/2} (b \tan (e+f x))^{5/2} \, dx","Int[(d*Sec[e + f*x])^(5/2)*(b*Tan[e + f*x])^(5/2),x]","\frac{3 b^{5/2} d^3 \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{32 f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{3 b^{5/2} d^3 \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{32 f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{3 b d^2 (b \tan (e+f x))^{3/2} \sqrt{d \sec (e+f x)}}{16 f}+\frac{b (b \tan (e+f x))^{3/2} (d \sec (e+f x))^{5/2}}{4 f}","\frac{3 b^{5/2} d^3 \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{32 f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{3 b^{5/2} d^3 \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{32 f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{3 b d^2 (b \tan (e+f x))^{3/2} \sqrt{d \sec (e+f x)}}{16 f}+\frac{b (b \tan (e+f x))^{3/2} (d \sec (e+f x))^{5/2}}{4 f}",1,"(3*b^(5/2)*d^3*ArcTan[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[b*Tan[e + f*x]])/(32*f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]]) - (3*b^(5/2)*d^3*ArcTanh[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[b*Tan[e + f*x]])/(32*f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]]) - (3*b*d^2*Sqrt[d*Sec[e + f*x]]*(b*Tan[e + f*x])^(3/2))/(16*f) + (b*(d*Sec[e + f*x])^(5/2)*(b*Tan[e + f*x])^(3/2))/(4*f)","A",8,8,25,0.3200,1,"{2611, 2613, 2616, 2564, 329, 298, 203, 206}"
308,1,131,0,0.1732009,"\int (d \sec (e+f x))^{3/2} (b \tan (e+f x))^{5/2} \, dx","Int[(d*Sec[e + f*x])^(3/2)*(b*Tan[e + f*x])^(5/2),x]","\frac{b^2 d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{2 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{b d^2 (b \tan (e+f x))^{3/2}}{2 f \sqrt{d \sec (e+f x)}}+\frac{b (b \tan (e+f x))^{3/2} (d \sec (e+f x))^{3/2}}{3 f}","\frac{b^2 d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{2 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{b d^2 (b \tan (e+f x))^{3/2}}{2 f \sqrt{d \sec (e+f x)}}+\frac{b (b \tan (e+f x))^{3/2} (d \sec (e+f x))^{3/2}}{3 f}",1,"(b^2*d^2*EllipticE[(e - Pi/2 + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(2*f*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]]) - (b*d^2*(b*Tan[e + f*x])^(3/2))/(2*f*Sqrt[d*Sec[e + f*x]]) + (b*(d*Sec[e + f*x])^(3/2)*(b*Tan[e + f*x])^(3/2))/(3*f)","A",5,5,25,0.2000,1,"{2611, 2613, 2616, 2640, 2639}"
309,1,169,0,0.1529338,"\int \sqrt{d \sec (e+f x)} (b \tan (e+f x))^{5/2} \, dx","Int[Sqrt[d*Sec[e + f*x]]*(b*Tan[e + f*x])^(5/2),x]","\frac{3 b^{5/2} d \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{3 b^{5/2} d \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{b (b \tan (e+f x))^{3/2} \sqrt{d \sec (e+f x)}}{2 f}","\frac{3 b^{5/2} d \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{3 b^{5/2} d \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{b (b \tan (e+f x))^{3/2} \sqrt{d \sec (e+f x)}}{2 f}",1,"(3*b^(5/2)*d*ArcTan[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[b*Tan[e + f*x]])/(4*f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]]) - (3*b^(5/2)*d*ArcTanh[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[b*Tan[e + f*x]])/(4*f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]]) + (b*Sqrt[d*Sec[e + f*x]]*(b*Tan[e + f*x])^(3/2))/(2*f)","A",7,7,25,0.2800,1,"{2611, 2616, 2564, 329, 298, 203, 206}"
310,1,88,0,0.1126273,"\int \frac{(b \tan (e+f x))^{5/2}}{\sqrt{d \sec (e+f x)}} \, dx","Int[(b*Tan[e + f*x])^(5/2)/Sqrt[d*Sec[e + f*x]],x]","\frac{b (b \tan (e+f x))^{3/2}}{f \sqrt{d \sec (e+f x)}}-\frac{3 b^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}","\frac{b (b \tan (e+f x))^{3/2}}{f \sqrt{d \sec (e+f x)}}-\frac{3 b^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}",1,"(-3*b^2*EllipticE[(e - Pi/2 + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(f*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]]) + (b*(b*Tan[e + f*x])^(3/2))/(f*Sqrt[d*Sec[e + f*x]])","A",4,4,25,0.1600,1,"{2611, 2616, 2640, 2639}"
311,1,168,0,0.1653207,"\int \frac{(b \tan (e+f x))^{5/2}}{(d \sec (e+f x))^{3/2}} \, dx","Int[(b*Tan[e + f*x])^(5/2)/(d*Sec[e + f*x])^(3/2),x]","-\frac{b^{5/2} \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{d f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{b^{5/2} \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{d f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{2 b (b \tan (e+f x))^{3/2}}{3 f (d \sec (e+f x))^{3/2}}","-\frac{b^{5/2} \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{d f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{b^{5/2} \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{d f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{2 b (b \tan (e+f x))^{3/2}}{3 f (d \sec (e+f x))^{3/2}}",1,"-((b^(5/2)*ArcTan[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[b*Tan[e + f*x]])/(d*f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]])) + (b^(5/2)*ArcTanh[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[b*Tan[e + f*x]])/(d*f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]]) - (2*b*(b*Tan[e + f*x])^(3/2))/(3*f*(d*Sec[e + f*x])^(3/2))","A",7,7,25,0.2800,1,"{2610, 2616, 2564, 329, 298, 203, 206}"
312,1,96,0,0.1202618,"\int \frac{(b \tan (e+f x))^{5/2}}{(d \sec (e+f x))^{5/2}} \, dx","Int[(b*Tan[e + f*x])^(5/2)/(d*Sec[e + f*x])^(5/2),x]","\frac{6 b^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{5 d^2 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{2 b (b \tan (e+f x))^{3/2}}{5 f (d \sec (e+f x))^{5/2}}","\frac{6 b^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{5 d^2 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{2 b (b \tan (e+f x))^{3/2}}{5 f (d \sec (e+f x))^{5/2}}",1,"(6*b^2*EllipticE[(e - Pi/2 + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(5*d^2*f*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]]) - (2*b*(b*Tan[e + f*x])^(3/2))/(5*f*(d*Sec[e + f*x])^(5/2))","A",4,4,25,0.1600,1,"{2610, 2616, 2640, 2639}"
313,1,34,0,0.0549945,"\int \frac{(b \tan (e+f x))^{5/2}}{(d \sec (e+f x))^{7/2}} \, dx","Int[(b*Tan[e + f*x])^(5/2)/(d*Sec[e + f*x])^(7/2),x]","\frac{2 (b \tan (e+f x))^{7/2}}{7 b f (d \sec (e+f x))^{7/2}}","\frac{2 (b \tan (e+f x))^{7/2}}{7 b f (d \sec (e+f x))^{7/2}}",1,"(2*(b*Tan[e + f*x])^(7/2))/(7*b*f*(d*Sec[e + f*x])^(7/2))","A",1,1,25,0.04000,1,"{2605}"
314,1,131,0,0.1768887,"\int \frac{(b \tan (e+f x))^{5/2}}{(d \sec (e+f x))^{9/2}} \, dx","Int[(b*Tan[e + f*x])^(5/2)/(d*Sec[e + f*x])^(9/2),x]","\frac{4 b^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{15 d^4 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 b (b \tan (e+f x))^{3/2}}{15 d^2 f (d \sec (e+f x))^{5/2}}-\frac{2 b (b \tan (e+f x))^{3/2}}{9 f (d \sec (e+f x))^{9/2}}","\frac{4 b^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{15 d^4 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 b (b \tan (e+f x))^{3/2}}{15 d^2 f (d \sec (e+f x))^{5/2}}-\frac{2 b (b \tan (e+f x))^{3/2}}{9 f (d \sec (e+f x))^{9/2}}",1,"(4*b^2*EllipticE[(e - Pi/2 + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(15*d^4*f*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]]) - (2*b*(b*Tan[e + f*x])^(3/2))/(9*f*(d*Sec[e + f*x])^(9/2)) + (2*b*(b*Tan[e + f*x])^(3/2))/(15*d^2*f*(d*Sec[e + f*x])^(5/2))","A",5,5,25,0.2000,1,"{2610, 2612, 2616, 2640, 2639}"
315,1,178,0,0.1678803,"\int \frac{(d \sec (e+f x))^{7/2}}{\sqrt{b \tan (e+f x)}} \, dx","Int[(d*Sec[e + f*x])^(7/2)/Sqrt[b*Tan[e + f*x]],x]","\frac{d^2 \sqrt{b \tan (e+f x)} (d \sec (e+f x))^{3/2}}{2 b f}+\frac{3 d^3 \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 \sqrt{b} f \sqrt{b \tan (e+f x)}}+\frac{3 d^3 \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 \sqrt{b} f \sqrt{b \tan (e+f x)}}","\frac{d^2 \sqrt{b \tan (e+f x)} (d \sec (e+f x))^{3/2}}{2 b f}+\frac{3 d^3 \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 \sqrt{b} f \sqrt{b \tan (e+f x)}}+\frac{3 d^3 \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{4 \sqrt{b} f \sqrt{b \tan (e+f x)}}",1,"(3*d^3*ArcTan[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]])/(4*Sqrt[b]*f*Sqrt[b*Tan[e + f*x]]) + (3*d^3*ArcTanh[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]])/(4*Sqrt[b]*f*Sqrt[b*Tan[e + f*x]]) + (d^2*(d*Sec[e + f*x])^(3/2)*Sqrt[b*Tan[e + f*x]])/(2*b*f)","A",7,7,25,0.2800,1,"{2613, 2616, 2564, 329, 212, 206, 203}"
316,1,92,0,0.1128052,"\int \frac{(d \sec (e+f x))^{5/2}}{\sqrt{b \tan (e+f x)}} \, dx","Int[(d*Sec[e + f*x])^(5/2)/Sqrt[b*Tan[e + f*x]],x]","\frac{d^2 \sqrt{b \tan (e+f x)} \sqrt{d \sec (e+f x)}}{b f}+\frac{d^2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{f \sqrt{b \tan (e+f x)}}","\frac{d^2 \sqrt{b \tan (e+f x)} \sqrt{d \sec (e+f x)}}{b f}+\frac{d^2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{f \sqrt{b \tan (e+f x)}}",1,"(d^2*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])/(f*Sqrt[b*Tan[e + f*x]]) + (d^2*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Tan[e + f*x]])/(b*f)","A",4,4,25,0.1600,1,"{2613, 2616, 2642, 2641}"
317,1,131,0,0.1064358,"\int \frac{(d \sec (e+f x))^{3/2}}{\sqrt{b \tan (e+f x)}} \, dx","Int[(d*Sec[e + f*x])^(3/2)/Sqrt[b*Tan[e + f*x]],x]","\frac{d \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{\sqrt{b} f \sqrt{b \tan (e+f x)}}+\frac{d \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{\sqrt{b} f \sqrt{b \tan (e+f x)}}","\frac{d \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{\sqrt{b} f \sqrt{b \tan (e+f x)}}+\frac{d \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{\sqrt{b} f \sqrt{b \tan (e+f x)}}",1,"(d*ArcTan[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]])/(Sqrt[b]*f*Sqrt[b*Tan[e + f*x]]) + (d*ArcTanh[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]])/(Sqrt[b]*f*Sqrt[b*Tan[e + f*x]])","A",6,6,25,0.2400,1,"{2616, 2564, 329, 212, 206, 203}"
318,1,55,0,0.061367,"\int \frac{\sqrt{d \sec (e+f x)}}{\sqrt{b \tan (e+f x)}} \, dx","Int[Sqrt[d*Sec[e + f*x]]/Sqrt[b*Tan[e + f*x]],x]","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{f \sqrt{b \tan (e+f x)}}","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{f \sqrt{b \tan (e+f x)}}",1,"(2*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])/(f*Sqrt[b*Tan[e + f*x]])","A",3,3,25,0.1200,1,"{2616, 2642, 2641}"
319,1,32,0,0.045485,"\int \frac{1}{\sqrt{d \sec (e+f x)} \sqrt{b \tan (e+f x)}} \, dx","Int[1/(Sqrt[d*Sec[e + f*x]]*Sqrt[b*Tan[e + f*x]]),x]","\frac{2 \sqrt{b \tan (e+f x)}}{b f \sqrt{d \sec (e+f x)}}","\frac{2 \sqrt{b \tan (e+f x)}}{b f \sqrt{d \sec (e+f x)}}",1,"(2*Sqrt[b*Tan[e + f*x]])/(b*f*Sqrt[d*Sec[e + f*x]])","A",1,1,25,0.04000,1,"{2605}"
320,1,95,0,0.1151067,"\int \frac{1}{(d \sec (e+f x))^{3/2} \sqrt{b \tan (e+f x)}} \, dx","Int[1/((d*Sec[e + f*x])^(3/2)*Sqrt[b*Tan[e + f*x]]),x]","\frac{4 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{3 d^2 f \sqrt{b \tan (e+f x)}}+\frac{2 \sqrt{b \tan (e+f x)}}{3 b f (d \sec (e+f x))^{3/2}}","\frac{4 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{3 d^2 f \sqrt{b \tan (e+f x)}}+\frac{2 \sqrt{b \tan (e+f x)}}{3 b f (d \sec (e+f x))^{3/2}}",1,"(4*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])/(3*d^2*f*Sqrt[b*Tan[e + f*x]]) + (2*Sqrt[b*Tan[e + f*x]])/(3*b*f*(d*Sec[e + f*x])^(3/2))","A",4,4,25,0.1600,1,"{2612, 2616, 2642, 2641}"
321,1,72,0,0.0973784,"\int \frac{1}{(d \sec (e+f x))^{5/2} \sqrt{b \tan (e+f x)}} \, dx","Int[1/((d*Sec[e + f*x])^(5/2)*Sqrt[b*Tan[e + f*x]]),x]","\frac{8 \sqrt{b \tan (e+f x)}}{5 b d^2 f \sqrt{d \sec (e+f x)}}+\frac{2 \sqrt{b \tan (e+f x)}}{5 b f (d \sec (e+f x))^{5/2}}","\frac{8 \sqrt{b \tan (e+f x)}}{5 b d^2 f \sqrt{d \sec (e+f x)}}+\frac{2 \sqrt{b \tan (e+f x)}}{5 b f (d \sec (e+f x))^{5/2}}",1,"(2*Sqrt[b*Tan[e + f*x]])/(5*b*f*(d*Sec[e + f*x])^(5/2)) + (8*Sqrt[b*Tan[e + f*x]])/(5*b*d^2*f*Sqrt[d*Sec[e + f*x]])","A",2,2,25,0.08000,1,"{2612, 2605}"
322,1,171,0,0.1667654,"\int \frac{(d \sec (e+f x))^{5/2}}{(b \tan (e+f x))^{3/2}} \, dx","Int[(d*Sec[e + f*x])^(5/2)/(b*Tan[e + f*x])^(3/2),x]","-\frac{d^3 \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{b^{3/2} f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{d^3 \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{b^{3/2} f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{2 d^2 \sqrt{d \sec (e+f x)}}{b f \sqrt{b \tan (e+f x)}}","-\frac{d^3 \sqrt{b \tan (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{b^{3/2} f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{d^3 \sqrt{b \tan (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{b^{3/2} f \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{2 d^2 \sqrt{d \sec (e+f x)}}{b f \sqrt{b \tan (e+f x)}}",1,"(-2*d^2*Sqrt[d*Sec[e + f*x]])/(b*f*Sqrt[b*Tan[e + f*x]]) - (d^3*ArcTan[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[b*Tan[e + f*x]])/(b^(3/2)*f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]]) + (d^3*ArcTanh[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[b*Tan[e + f*x]])/(b^(3/2)*f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]])","A",7,7,25,0.2800,1,"{2608, 2616, 2564, 329, 298, 203, 206}"
323,1,97,0,0.1225581,"\int \frac{(d \sec (e+f x))^{3/2}}{(b \tan (e+f x))^{3/2}} \, dx","Int[(d*Sec[e + f*x])^(3/2)/(b*Tan[e + f*x])^(3/2),x]","-\frac{2 d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{b^2 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{2 d^2}{b f \sqrt{b \tan (e+f x)} \sqrt{d \sec (e+f x)}}","-\frac{2 d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{b^2 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{2 d^2}{b f \sqrt{b \tan (e+f x)} \sqrt{d \sec (e+f x)}}",1,"(-2*d^2)/(b*f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Tan[e + f*x]]) - (2*d^2*EllipticE[(e - Pi/2 + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(b^2*f*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])","A",4,4,25,0.1600,1,"{2608, 2616, 2640, 2639}"
324,1,32,0,0.0503519,"\int \frac{\sqrt{d \sec (e+f x)}}{(b \tan (e+f x))^{3/2}} \, dx","Int[Sqrt[d*Sec[e + f*x]]/(b*Tan[e + f*x])^(3/2),x]","-\frac{2 \sqrt{d \sec (e+f x)}}{b f \sqrt{b \tan (e+f x)}}","-\frac{2 \sqrt{d \sec (e+f x)}}{b f \sqrt{b \tan (e+f x)}}",1,"(-2*Sqrt[d*Sec[e + f*x]])/(b*f*Sqrt[b*Tan[e + f*x]])","A",1,1,25,0.04000,1,"{2605}"
325,1,91,0,0.1163573,"\int \frac{1}{\sqrt{d \sec (e+f x)} (b \tan (e+f x))^{3/2}} \, dx","Int[1/(Sqrt[d*Sec[e + f*x]]*(b*Tan[e + f*x])^(3/2)),x]","-\frac{4 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{b^2 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{2}{b f \sqrt{b \tan (e+f x)} \sqrt{d \sec (e+f x)}}","-\frac{4 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{b^2 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{2}{b f \sqrt{b \tan (e+f x)} \sqrt{d \sec (e+f x)}}",1,"-2/(b*f*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Tan[e + f*x]]) - (4*EllipticE[(e - Pi/2 + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(b^2*f*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])","A",4,4,25,0.1600,1,"{2609, 2616, 2640, 2639}"
326,1,67,0,0.1084941,"\int \frac{1}{(d \sec (e+f x))^{3/2} (b \tan (e+f x))^{3/2}} \, dx","Int[1/((d*Sec[e + f*x])^(3/2)*(b*Tan[e + f*x])^(3/2)),x]","-\frac{8 (b \tan (e+f x))^{3/2}}{3 b^3 f (d \sec (e+f x))^{3/2}}-\frac{2}{b f \sqrt{b \tan (e+f x)} (d \sec (e+f x))^{3/2}}","\frac{2}{3 b f \sqrt{b \tan (e+f x)} (d \sec (e+f x))^{3/2}}-\frac{8 \sqrt{d \sec (e+f x)}}{3 b d^2 f \sqrt{b \tan (e+f x)}}",1,"-2/(b*f*(d*Sec[e + f*x])^(3/2)*Sqrt[b*Tan[e + f*x]]) - (8*(b*Tan[e + f*x])^(3/2))/(3*b^3*f*(d*Sec[e + f*x])^(3/2))","A",2,2,25,0.08000,1,"{2609, 2605}"
327,1,130,0,0.1863734,"\int \frac{1}{(d \sec (e+f x))^{5/2} (b \tan (e+f x))^{3/2}} \, dx","Int[1/((d*Sec[e + f*x])^(5/2)*(b*Tan[e + f*x])^(3/2)),x]","-\frac{24 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{5 b^2 d^2 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{12 (b \tan (e+f x))^{3/2}}{5 b^3 f (d \sec (e+f x))^{5/2}}-\frac{2}{b f \sqrt{b \tan (e+f x)} (d \sec (e+f x))^{5/2}}","-\frac{24 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \tan (e+f x)}}{5 b^2 d^2 f \sqrt{\sin (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{12 (b \tan (e+f x))^{3/2}}{5 b^3 f (d \sec (e+f x))^{5/2}}-\frac{2}{b f \sqrt{b \tan (e+f x)} (d \sec (e+f x))^{5/2}}",1,"-2/(b*f*(d*Sec[e + f*x])^(5/2)*Sqrt[b*Tan[e + f*x]]) - (24*EllipticE[(e - Pi/2 + f*x)/2, 2]*Sqrt[b*Tan[e + f*x]])/(5*b^2*d^2*f*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]]) - (12*(b*Tan[e + f*x])^(3/2))/(5*b^3*f*(d*Sec[e + f*x])^(5/2))","A",5,5,25,0.2000,1,"{2609, 2612, 2616, 2640, 2639}"
328,1,172,0,0.1803732,"\int \frac{(d \sec (e+f x))^{7/2}}{(b \tan (e+f x))^{5/2}} \, dx","Int[(d*Sec[e + f*x])^(7/2)/(b*Tan[e + f*x])^(5/2),x]","\frac{d^3 \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{b^{5/2} f \sqrt{b \tan (e+f x)}}+\frac{d^3 \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{b^{5/2} f \sqrt{b \tan (e+f x)}}-\frac{2 d^2 (d \sec (e+f x))^{3/2}}{3 b f (b \tan (e+f x))^{3/2}}","\frac{d^3 \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{b^{5/2} f \sqrt{b \tan (e+f x)}}+\frac{d^3 \sqrt{b \sin (e+f x)} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b \sin (e+f x)}}{\sqrt{b}}\right)}{b^{5/2} f \sqrt{b \tan (e+f x)}}-\frac{2 d^2 (d \sec (e+f x))^{3/2}}{3 b f (b \tan (e+f x))^{3/2}}",1,"(-2*d^2*(d*Sec[e + f*x])^(3/2))/(3*b*f*(b*Tan[e + f*x])^(3/2)) + (d^3*ArcTan[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]])/(b^(5/2)*f*Sqrt[b*Tan[e + f*x]]) + (d^3*ArcTanh[Sqrt[b*Sin[e + f*x]]/Sqrt[b]]*Sqrt[d*Sec[e + f*x]]*Sqrt[b*Sin[e + f*x]])/(b^(5/2)*f*Sqrt[b*Tan[e + f*x]])","A",7,7,25,0.2800,1,"{2608, 2616, 2564, 329, 212, 206, 203}"
329,1,101,0,0.1260312,"\int \frac{(d \sec (e+f x))^{5/2}}{(b \tan (e+f x))^{5/2}} \, dx","Int[(d*Sec[e + f*x])^(5/2)/(b*Tan[e + f*x])^(5/2),x]","\frac{2 d^2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{3 b^2 f \sqrt{b \tan (e+f x)}}-\frac{2 d^2 \sqrt{d \sec (e+f x)}}{3 b f (b \tan (e+f x))^{3/2}}","\frac{2 d^2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{3 b^2 f \sqrt{b \tan (e+f x)}}-\frac{2 d^2 \sqrt{d \sec (e+f x)}}{3 b f (b \tan (e+f x))^{3/2}}",1,"(-2*d^2*Sqrt[d*Sec[e + f*x]])/(3*b*f*(b*Tan[e + f*x])^(3/2)) + (2*d^2*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])/(3*b^2*f*Sqrt[b*Tan[e + f*x]])","A",4,4,25,0.1600,1,"{2608, 2616, 2642, 2641}"
330,1,34,0,0.0568758,"\int \frac{(d \sec (e+f x))^{3/2}}{(b \tan (e+f x))^{5/2}} \, dx","Int[(d*Sec[e + f*x])^(3/2)/(b*Tan[e + f*x])^(5/2),x]","-\frac{2 (d \sec (e+f x))^{3/2}}{3 b f (b \tan (e+f x))^{3/2}}","-\frac{2 (d \sec (e+f x))^{3/2}}{3 b f (b \tan (e+f x))^{3/2}}",1,"(-2*(d*Sec[e + f*x])^(3/2))/(3*b*f*(b*Tan[e + f*x])^(3/2))","A",1,1,25,0.04000,1,"{2605}"
331,1,95,0,0.1143013,"\int \frac{\sqrt{d \sec (e+f x)}}{(b \tan (e+f x))^{5/2}} \, dx","Int[Sqrt[d*Sec[e + f*x]]/(b*Tan[e + f*x])^(5/2),x]","-\frac{4 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{3 b^2 f \sqrt{b \tan (e+f x)}}-\frac{2 \sqrt{d \sec (e+f x)}}{3 b f (b \tan (e+f x))^{3/2}}","-\frac{4 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{3 b^2 f \sqrt{b \tan (e+f x)}}-\frac{2 \sqrt{d \sec (e+f x)}}{3 b f (b \tan (e+f x))^{3/2}}",1,"(-2*Sqrt[d*Sec[e + f*x]])/(3*b*f*(b*Tan[e + f*x])^(3/2)) - (4*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])/(3*b^2*f*Sqrt[b*Tan[e + f*x]])","A",4,4,25,0.1600,1,"{2609, 2616, 2642, 2641}"
332,1,69,0,0.1008901,"\int \frac{1}{\sqrt{d \sec (e+f x)} (b \tan (e+f x))^{5/2}} \, dx","Int[1/(Sqrt[d*Sec[e + f*x]]*(b*Tan[e + f*x])^(5/2)),x]","-\frac{8 \sqrt{b \tan (e+f x)}}{3 b^3 f \sqrt{d \sec (e+f x)}}-\frac{2}{3 b f (b \tan (e+f x))^{3/2} \sqrt{d \sec (e+f x)}}","-\frac{8 \sqrt{b \tan (e+f x)}}{3 b^3 f \sqrt{d \sec (e+f x)}}-\frac{2}{3 b f (b \tan (e+f x))^{3/2} \sqrt{d \sec (e+f x)}}",1,"-2/(3*b*f*Sqrt[d*Sec[e + f*x]]*(b*Tan[e + f*x])^(3/2)) - (8*Sqrt[b*Tan[e + f*x]])/(3*b^3*f*Sqrt[d*Sec[e + f*x]])","A",2,2,25,0.08000,1,"{2609, 2605}"
333,1,132,0,0.1843949,"\int \frac{1}{(d \sec (e+f x))^{3/2} (b \tan (e+f x))^{5/2}} \, dx","Int[1/((d*Sec[e + f*x])^(3/2)*(b*Tan[e + f*x])^(5/2)),x]","-\frac{8 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{3 b^2 d^2 f \sqrt{b \tan (e+f x)}}-\frac{4 \sqrt{b \tan (e+f x)}}{3 b^3 f (d \sec (e+f x))^{3/2}}-\frac{2}{3 b f (b \tan (e+f x))^{3/2} (d \sec (e+f x))^{3/2}}","-\frac{8 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \sec (e+f x)}}{3 b^2 d^2 f \sqrt{b \tan (e+f x)}}-\frac{4 \sqrt{b \tan (e+f x)}}{3 b^3 f (d \sec (e+f x))^{3/2}}-\frac{2}{3 b f (b \tan (e+f x))^{3/2} (d \sec (e+f x))^{3/2}}",1,"-2/(3*b*f*(d*Sec[e + f*x])^(3/2)*(b*Tan[e + f*x])^(3/2)) - (8*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]]*Sqrt[Sin[e + f*x]])/(3*b^2*d^2*f*Sqrt[b*Tan[e + f*x]]) - (4*Sqrt[b*Tan[e + f*x]])/(3*b^3*f*(d*Sec[e + f*x])^(3/2))","A",5,5,25,0.2000,1,"{2609, 2612, 2616, 2642, 2641}"
334,1,106,0,0.1657771,"\int \frac{1}{(d \sec (e+f x))^{5/2} (b \tan (e+f x))^{5/2}} \, dx","Int[1/((d*Sec[e + f*x])^(5/2)*(b*Tan[e + f*x])^(5/2)),x]","-\frac{64 \sqrt{b \tan (e+f x)}}{15 b^3 d^2 f \sqrt{d \sec (e+f x)}}-\frac{16 \sqrt{b \tan (e+f x)}}{15 b^3 f (d \sec (e+f x))^{5/2}}-\frac{2}{3 b f (b \tan (e+f x))^{3/2} (d \sec (e+f x))^{5/2}}","-\frac{64 \sqrt{b \tan (e+f x)}}{15 b^3 d^2 f \sqrt{d \sec (e+f x)}}-\frac{16 \sqrt{b \tan (e+f x)}}{15 b^3 f (d \sec (e+f x))^{5/2}}-\frac{2}{3 b f (b \tan (e+f x))^{3/2} (d \sec (e+f x))^{5/2}}",1,"-2/(3*b*f*(d*Sec[e + f*x])^(5/2)*(b*Tan[e + f*x])^(3/2)) - (16*Sqrt[b*Tan[e + f*x]])/(15*b^3*f*(d*Sec[e + f*x])^(5/2)) - (64*Sqrt[b*Tan[e + f*x]])/(15*b^3*d^2*f*Sqrt[d*Sec[e + f*x]])","A",3,3,25,0.1200,1,"{2609, 2612, 2605}"
335,1,64,0,0.0530586,"\int (b \sec (e+f x))^{4/3} \sqrt{d \tan (e+f x)} \, dx","Int[(b*Sec[e + f*x])^(4/3)*Sqrt[d*Tan[e + f*x]],x]","\frac{2 \cos ^2(e+f x)^{17/12} (b \sec (e+f x))^{4/3} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{3}{4},\frac{17}{12};\frac{7}{4};\sin ^2(e+f x)\right)}{3 d f}","\frac{2 \cos ^2(e+f x)^{17/12} (b \sec (e+f x))^{4/3} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{3}{4},\frac{17}{12};\frac{7}{4};\sin ^2(e+f x)\right)}{3 d f}",1,"(2*(Cos[e + f*x]^2)^(17/12)*Hypergeometric2F1[3/4, 17/12, 7/4, Sin[e + f*x]^2]*(b*Sec[e + f*x])^(4/3)*(d*Tan[e + f*x])^(3/2))/(3*d*f)","A",1,1,25,0.04000,1,"{2617}"
336,1,64,0,0.04489,"\int \sqrt[3]{b \sec (e+f x)} \sqrt{d \tan (e+f x)} \, dx","Int[(b*Sec[e + f*x])^(1/3)*Sqrt[d*Tan[e + f*x]],x]","\frac{2 \cos ^2(e+f x)^{11/12} \sqrt[3]{b \sec (e+f x)} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{3}{4},\frac{11}{12};\frac{7}{4};\sin ^2(e+f x)\right)}{3 d f}","\frac{2 \cos ^2(e+f x)^{11/12} \sqrt[3]{b \sec (e+f x)} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{3}{4},\frac{11}{12};\frac{7}{4};\sin ^2(e+f x)\right)}{3 d f}",1,"(2*(Cos[e + f*x]^2)^(11/12)*Hypergeometric2F1[3/4, 11/12, 7/4, Sin[e + f*x]^2]*(b*Sec[e + f*x])^(1/3)*(d*Tan[e + f*x])^(3/2))/(3*d*f)","A",1,1,25,0.04000,1,"{2617}"
337,1,64,0,0.0484381,"\int \frac{\sqrt{d \tan (e+f x)}}{\sqrt[3]{b \sec (e+f x)}} \, dx","Int[Sqrt[d*Tan[e + f*x]]/(b*Sec[e + f*x])^(1/3),x]","\frac{2 \cos ^2(e+f x)^{7/12} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{7}{12},\frac{3}{4};\frac{7}{4};\sin ^2(e+f x)\right)}{3 d f \sqrt[3]{b \sec (e+f x)}}","\frac{2 \cos ^2(e+f x)^{7/12} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{7}{12},\frac{3}{4};\frac{7}{4};\sin ^2(e+f x)\right)}{3 d f \sqrt[3]{b \sec (e+f x)}}",1,"(2*(Cos[e + f*x]^2)^(7/12)*Hypergeometric2F1[7/12, 3/4, 7/4, Sin[e + f*x]^2]*(d*Tan[e + f*x])^(3/2))/(3*d*f*(b*Sec[e + f*x])^(1/3))","A",1,1,25,0.04000,1,"{2617}"
338,1,64,0,0.0541346,"\int \frac{\sqrt{d \tan (e+f x)}}{(b \sec (e+f x))^{4/3}} \, dx","Int[Sqrt[d*Tan[e + f*x]]/(b*Sec[e + f*x])^(4/3),x]","\frac{2 \sqrt[12]{\cos ^2(e+f x)} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{1}{12},\frac{3}{4};\frac{7}{4};\sin ^2(e+f x)\right)}{3 d f (b \sec (e+f x))^{4/3}}","\frac{2 \sqrt[12]{\cos ^2(e+f x)} (d \tan (e+f x))^{3/2} \, _2F_1\left(\frac{1}{12},\frac{3}{4};\frac{7}{4};\sin ^2(e+f x)\right)}{3 d f (b \sec (e+f x))^{4/3}}",1,"(2*(Cos[e + f*x]^2)^(1/12)*Hypergeometric2F1[1/12, 3/4, 7/4, Sin[e + f*x]^2]*(d*Tan[e + f*x])^(3/2))/(3*d*f*(b*Sec[e + f*x])^(4/3))","A",1,1,25,0.04000,1,"{2617}"
339,1,64,0,0.0580486,"\int (b \sec (e+f x))^{4/3} (d \tan (e+f x))^{3/2} \, dx","Int[(b*Sec[e + f*x])^(4/3)*(d*Tan[e + f*x])^(3/2),x]","\frac{2 \cos ^2(e+f x)^{23/12} (b \sec (e+f x))^{4/3} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{5}{4},\frac{23}{12};\frac{9}{4};\sin ^2(e+f x)\right)}{5 d f}","\frac{2 \cos ^2(e+f x)^{23/12} (b \sec (e+f x))^{4/3} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{5}{4},\frac{23}{12};\frac{9}{4};\sin ^2(e+f x)\right)}{5 d f}",1,"(2*(Cos[e + f*x]^2)^(23/12)*Hypergeometric2F1[5/4, 23/12, 9/4, Sin[e + f*x]^2]*(b*Sec[e + f*x])^(4/3)*(d*Tan[e + f*x])^(5/2))/(5*d*f)","A",1,1,25,0.04000,1,"{2617}"
340,1,64,0,0.0511223,"\int \sqrt[3]{b \sec (e+f x)} (d \tan (e+f x))^{3/2} \, dx","Int[(b*Sec[e + f*x])^(1/3)*(d*Tan[e + f*x])^(3/2),x]","\frac{2 \cos ^2(e+f x)^{17/12} \sqrt[3]{b \sec (e+f x)} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{5}{4},\frac{17}{12};\frac{9}{4};\sin ^2(e+f x)\right)}{5 d f}","\frac{2 \cos ^2(e+f x)^{17/12} \sqrt[3]{b \sec (e+f x)} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{5}{4},\frac{17}{12};\frac{9}{4};\sin ^2(e+f x)\right)}{5 d f}",1,"(2*(Cos[e + f*x]^2)^(17/12)*Hypergeometric2F1[5/4, 17/12, 9/4, Sin[e + f*x]^2]*(b*Sec[e + f*x])^(1/3)*(d*Tan[e + f*x])^(5/2))/(5*d*f)","A",1,1,25,0.04000,1,"{2617}"
341,1,64,0,0.0523521,"\int \frac{(d \tan (e+f x))^{3/2}}{\sqrt[3]{b \sec (e+f x)}} \, dx","Int[(d*Tan[e + f*x])^(3/2)/(b*Sec[e + f*x])^(1/3),x]","\frac{2 \cos ^2(e+f x)^{13/12} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{13}{12},\frac{5}{4};\frac{9}{4};\sin ^2(e+f x)\right)}{5 d f \sqrt[3]{b \sec (e+f x)}}","\frac{2 \cos ^2(e+f x)^{13/12} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{13}{12},\frac{5}{4};\frac{9}{4};\sin ^2(e+f x)\right)}{5 d f \sqrt[3]{b \sec (e+f x)}}",1,"(2*(Cos[e + f*x]^2)^(13/12)*Hypergeometric2F1[13/12, 5/4, 9/4, Sin[e + f*x]^2]*(d*Tan[e + f*x])^(5/2))/(5*d*f*(b*Sec[e + f*x])^(1/3))","A",1,1,25,0.04000,1,"{2617}"
342,1,64,0,0.0597472,"\int \frac{(d \tan (e+f x))^{3/2}}{(b \sec (e+f x))^{4/3}} \, dx","Int[(d*Tan[e + f*x])^(3/2)/(b*Sec[e + f*x])^(4/3),x]","\frac{2 \cos ^2(e+f x)^{7/12} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{7}{12},\frac{5}{4};\frac{9}{4};\sin ^2(e+f x)\right)}{5 d f (b \sec (e+f x))^{4/3}}","\frac{2 \cos ^2(e+f x)^{7/12} (d \tan (e+f x))^{5/2} \, _2F_1\left(\frac{7}{12},\frac{5}{4};\frac{9}{4};\sin ^2(e+f x)\right)}{5 d f (b \sec (e+f x))^{4/3}}",1,"(2*(Cos[e + f*x]^2)^(7/12)*Hypergeometric2F1[7/12, 5/4, 9/4, Sin[e + f*x]^2]*(d*Tan[e + f*x])^(5/2))/(5*d*f*(b*Sec[e + f*x])^(4/3))","A",1,1,25,0.04000,1,"{2617}"
343,1,64,0,0.0503131,"\int \sqrt{b \sec (e+f x)} (d \tan (e+f x))^{4/3} \, dx","Int[Sqrt[b*Sec[e + f*x]]*(d*Tan[e + f*x])^(4/3),x]","\frac{3 \cos ^2(e+f x)^{17/12} \sqrt{b \sec (e+f x)} (d \tan (e+f x))^{7/3} \, _2F_1\left(\frac{7}{6},\frac{17}{12};\frac{13}{6};\sin ^2(e+f x)\right)}{7 d f}","\frac{3 \cos ^2(e+f x)^{17/12} \sqrt{b \sec (e+f x)} (d \tan (e+f x))^{7/3} \, _2F_1\left(\frac{7}{6},\frac{17}{12};\frac{13}{6};\sin ^2(e+f x)\right)}{7 d f}",1,"(3*(Cos[e + f*x]^2)^(17/12)*Hypergeometric2F1[7/6, 17/12, 13/6, Sin[e + f*x]^2]*Sqrt[b*Sec[e + f*x]]*(d*Tan[e + f*x])^(7/3))/(7*d*f)","A",1,1,25,0.04000,1,"{2617}"
344,1,64,0,0.042857,"\int \sqrt{b \sec (e+f x)} \sqrt[3]{d \tan (e+f x)} \, dx","Int[Sqrt[b*Sec[e + f*x]]*(d*Tan[e + f*x])^(1/3),x]","\frac{3 \cos ^2(e+f x)^{11/12} \sqrt{b \sec (e+f x)} (d \tan (e+f x))^{4/3} \, _2F_1\left(\frac{2}{3},\frac{11}{12};\frac{5}{3};\sin ^2(e+f x)\right)}{4 d f}","\frac{3 \cos ^2(e+f x)^{11/12} \sqrt{b \sec (e+f x)} (d \tan (e+f x))^{4/3} \, _2F_1\left(\frac{2}{3},\frac{11}{12};\frac{5}{3};\sin ^2(e+f x)\right)}{4 d f}",1,"(3*(Cos[e + f*x]^2)^(11/12)*Hypergeometric2F1[2/3, 11/12, 5/3, Sin[e + f*x]^2]*Sqrt[b*Sec[e + f*x]]*(d*Tan[e + f*x])^(4/3))/(4*d*f)","A",1,1,25,0.04000,1,"{2617}"
345,1,64,0,0.0466348,"\int \frac{\sqrt{b \sec (e+f x)}}{\sqrt[3]{d \tan (e+f x)}} \, dx","Int[Sqrt[b*Sec[e + f*x]]/(d*Tan[e + f*x])^(1/3),x]","\frac{3 \cos ^2(e+f x)^{7/12} \sqrt{b \sec (e+f x)} (d \tan (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{7}{12};\frac{4}{3};\sin ^2(e+f x)\right)}{2 d f}","\frac{3 \cos ^2(e+f x)^{7/12} \sqrt{b \sec (e+f x)} (d \tan (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{7}{12};\frac{4}{3};\sin ^2(e+f x)\right)}{2 d f}",1,"(3*(Cos[e + f*x]^2)^(7/12)*Hypergeometric2F1[1/3, 7/12, 4/3, Sin[e + f*x]^2]*Sqrt[b*Sec[e + f*x]]*(d*Tan[e + f*x])^(2/3))/(2*d*f)","A",1,1,25,0.04000,1,"{2617}"
346,1,62,0,0.0527477,"\int \frac{\sqrt{b \sec (e+f x)}}{(d \tan (e+f x))^{4/3}} \, dx","Int[Sqrt[b*Sec[e + f*x]]/(d*Tan[e + f*x])^(4/3),x]","-\frac{3 \sqrt[12]{\cos ^2(e+f x)} \sqrt{b \sec (e+f x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{12};\frac{5}{6};\sin ^2(e+f x)\right)}{d f \sqrt[3]{d \tan (e+f x)}}","-\frac{3 \sqrt[12]{\cos ^2(e+f x)} \sqrt{b \sec (e+f x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{12};\frac{5}{6};\sin ^2(e+f x)\right)}{d f \sqrt[3]{d \tan (e+f x)}}",1,"(-3*(Cos[e + f*x]^2)^(1/12)*Hypergeometric2F1[-1/6, 1/12, 5/6, Sin[e + f*x]^2]*Sqrt[b*Sec[e + f*x]])/(d*f*(d*Tan[e + f*x])^(1/3))","A",1,1,25,0.04000,1,"{2617}"
347,1,64,0,0.0579168,"\int (b \sec (e+f x))^{3/2} (d \tan (e+f x))^{4/3} \, dx","Int[(b*Sec[e + f*x])^(3/2)*(d*Tan[e + f*x])^(4/3),x]","\frac{3 \cos ^2(e+f x)^{23/12} (b \sec (e+f x))^{3/2} (d \tan (e+f x))^{7/3} \, _2F_1\left(\frac{7}{6},\frac{23}{12};\frac{13}{6};\sin ^2(e+f x)\right)}{7 d f}","\frac{3 \cos ^2(e+f x)^{23/12} (b \sec (e+f x))^{3/2} (d \tan (e+f x))^{7/3} \, _2F_1\left(\frac{7}{6},\frac{23}{12};\frac{13}{6};\sin ^2(e+f x)\right)}{7 d f}",1,"(3*(Cos[e + f*x]^2)^(23/12)*Hypergeometric2F1[7/6, 23/12, 13/6, Sin[e + f*x]^2]*(b*Sec[e + f*x])^(3/2)*(d*Tan[e + f*x])^(7/3))/(7*d*f)","A",1,1,25,0.04000,1,"{2617}"
348,1,64,0,0.0512265,"\int (b \sec (e+f x))^{3/2} \sqrt[3]{d \tan (e+f x)} \, dx","Int[(b*Sec[e + f*x])^(3/2)*(d*Tan[e + f*x])^(1/3),x]","\frac{3 \cos ^2(e+f x)^{17/12} (b \sec (e+f x))^{3/2} (d \tan (e+f x))^{4/3} \, _2F_1\left(\frac{2}{3},\frac{17}{12};\frac{5}{3};\sin ^2(e+f x)\right)}{4 d f}","\frac{3 \cos ^2(e+f x)^{17/12} (b \sec (e+f x))^{3/2} (d \tan (e+f x))^{4/3} \, _2F_1\left(\frac{2}{3},\frac{17}{12};\frac{5}{3};\sin ^2(e+f x)\right)}{4 d f}",1,"(3*(Cos[e + f*x]^2)^(17/12)*Hypergeometric2F1[2/3, 17/12, 5/3, Sin[e + f*x]^2]*(b*Sec[e + f*x])^(3/2)*(d*Tan[e + f*x])^(4/3))/(4*d*f)","A",1,1,25,0.04000,1,"{2617}"
349,1,64,0,0.0551391,"\int \frac{(b \sec (e+f x))^{3/2}}{\sqrt[3]{d \tan (e+f x)}} \, dx","Int[(b*Sec[e + f*x])^(3/2)/(d*Tan[e + f*x])^(1/3),x]","\frac{3 \cos ^2(e+f x)^{13/12} (b \sec (e+f x))^{3/2} (d \tan (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{13}{12};\frac{4}{3};\sin ^2(e+f x)\right)}{2 d f}","\frac{3 \cos ^2(e+f x)^{13/12} (b \sec (e+f x))^{3/2} (d \tan (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{13}{12};\frac{4}{3};\sin ^2(e+f x)\right)}{2 d f}",1,"(3*(Cos[e + f*x]^2)^(13/12)*Hypergeometric2F1[1/3, 13/12, 4/3, Sin[e + f*x]^2]*(b*Sec[e + f*x])^(3/2)*(d*Tan[e + f*x])^(2/3))/(2*d*f)","A",1,1,25,0.04000,1,"{2617}"
350,1,62,0,0.0585234,"\int \frac{(b \sec (e+f x))^{3/2}}{(d \tan (e+f x))^{4/3}} \, dx","Int[(b*Sec[e + f*x])^(3/2)/(d*Tan[e + f*x])^(4/3),x]","-\frac{3 \cos ^2(e+f x)^{7/12} (b \sec (e+f x))^{3/2} \, _2F_1\left(-\frac{1}{6},\frac{7}{12};\frac{5}{6};\sin ^2(e+f x)\right)}{d f \sqrt[3]{d \tan (e+f x)}}","-\frac{3 \cos ^2(e+f x)^{7/12} (b \sec (e+f x))^{3/2} \, _2F_1\left(-\frac{1}{6},\frac{7}{12};\frac{5}{6};\sin ^2(e+f x)\right)}{d f \sqrt[3]{d \tan (e+f x)}}",1,"(-3*(Cos[e + f*x]^2)^(7/12)*Hypergeometric2F1[-1/6, 7/12, 5/6, Sin[e + f*x]^2]*(b*Sec[e + f*x])^(3/2))/(d*f*(d*Tan[e + f*x])^(1/3))","A",1,1,25,0.04000,1,"{2617}"
351,1,67,0,0.0623153,"\int (b \sec (e+f x))^m \tan ^5(e+f x) \, dx","Int[(b*Sec[e + f*x])^m*Tan[e + f*x]^5,x]","-\frac{2 (b \sec (e+f x))^{m+2}}{b^2 f (m+2)}+\frac{(b \sec (e+f x))^{m+4}}{b^4 f (m+4)}+\frac{(b \sec (e+f x))^m}{f m}","-\frac{2 (b \sec (e+f x))^{m+2}}{b^2 f (m+2)}+\frac{(b \sec (e+f x))^{m+4}}{b^4 f (m+4)}+\frac{(b \sec (e+f x))^m}{f m}",1,"(b*Sec[e + f*x])^m/(f*m) - (2*(b*Sec[e + f*x])^(2 + m))/(b^2*f*(2 + m)) + (b*Sec[e + f*x])^(4 + m)/(b^4*f*(4 + m))","A",3,2,19,0.1053,1,"{2606, 270}"
352,1,43,0,0.0488089,"\int (b \sec (e+f x))^m \tan ^3(e+f x) \, dx","Int[(b*Sec[e + f*x])^m*Tan[e + f*x]^3,x]","\frac{(b \sec (e+f x))^{m+2}}{b^2 f (m+2)}-\frac{(b \sec (e+f x))^m}{f m}","\frac{(b \sec (e+f x))^{m+2}}{b^2 f (m+2)}-\frac{(b \sec (e+f x))^m}{f m}",1,"-((b*Sec[e + f*x])^m/(f*m)) + (b*Sec[e + f*x])^(2 + m)/(b^2*f*(2 + m))","A",3,2,19,0.1053,1,"{2606, 14}"
353,1,17,0,0.0210696,"\int (b \sec (e+f x))^m \tan (e+f x) \, dx","Int[(b*Sec[e + f*x])^m*Tan[e + f*x],x]","\frac{(b \sec (e+f x))^m}{f m}","\frac{(b \sec (e+f x))^m}{f m}",1,"(b*Sec[e + f*x])^m/(f*m)","A",2,2,17,0.1176,1,"{2606, 32}"
354,1,40,0,0.0416297,"\int \cot (e+f x) (b \sec (e+f x))^m \, dx","Int[Cot[e + f*x]*(b*Sec[e + f*x])^m,x]","-\frac{(b \sec (e+f x))^m \, _2F_1\left(1,\frac{m}{2};\frac{m+2}{2};\sec ^2(e+f x)\right)}{f m}","-\frac{(b \sec (e+f x))^m \, _2F_1\left(1,\frac{m}{2};\frac{m+2}{2};\sec ^2(e+f x)\right)}{f m}",1,"-((Hypergeometric2F1[1, m/2, (2 + m)/2, Sec[e + f*x]^2]*(b*Sec[e + f*x])^m)/(f*m))","A",2,2,17,0.1176,1,"{2606, 364}"
355,1,39,0,0.0444063,"\int \cot ^3(e+f x) (b \sec (e+f x))^m \, dx","Int[Cot[e + f*x]^3*(b*Sec[e + f*x])^m,x]","\frac{(b \sec (e+f x))^m \, _2F_1\left(2,\frac{m}{2};\frac{m+2}{2};\sec ^2(e+f x)\right)}{f m}","\frac{(b \sec (e+f x))^m \, _2F_1\left(2,\frac{m}{2};\frac{m+2}{2};\sec ^2(e+f x)\right)}{f m}",1,"(Hypergeometric2F1[2, m/2, (2 + m)/2, Sec[e + f*x]^2]*(b*Sec[e + f*x])^m)/(f*m)","A",2,2,19,0.1053,1,"{2606, 364}"
356,1,40,0,0.0439608,"\int \cot ^5(e+f x) (b \sec (e+f x))^m \, dx","Int[Cot[e + f*x]^5*(b*Sec[e + f*x])^m,x]","-\frac{(b \sec (e+f x))^m \, _2F_1\left(3,\frac{m}{2};\frac{m+2}{2};\sec ^2(e+f x)\right)}{f m}","-\frac{(b \sec (e+f x))^m \, _2F_1\left(3,\frac{m}{2};\frac{m+2}{2};\sec ^2(e+f x)\right)}{f m}",1,"-((Hypergeometric2F1[3, m/2, (2 + m)/2, Sec[e + f*x]^2]*(b*Sec[e + f*x])^m)/(f*m))","A",2,2,19,0.1053,1,"{2606, 364}"
357,1,63,0,0.0395067,"\int (b \sec (e+f x))^m \tan ^4(e+f x) \, dx","Int[(b*Sec[e + f*x])^m*Tan[e + f*x]^4,x]","\frac{\tan ^5(e+f x) \cos ^2(e+f x)^{\frac{m+5}{2}} (b \sec (e+f x))^m \, _2F_1\left(\frac{5}{2},\frac{m+5}{2};\frac{7}{2};\sin ^2(e+f x)\right)}{5 f}","\frac{\tan ^5(e+f x) \cos ^2(e+f x)^{\frac{m+5}{2}} (b \sec (e+f x))^m \, _2F_1\left(\frac{5}{2},\frac{m+5}{2};\frac{7}{2};\sin ^2(e+f x)\right)}{5 f}",1,"((Cos[e + f*x]^2)^((5 + m)/2)*Hypergeometric2F1[5/2, (5 + m)/2, 7/2, Sin[e + f*x]^2]*(b*Sec[e + f*x])^m*Tan[e + f*x]^5)/(5*f)","A",1,1,19,0.05263,1,"{2617}"
358,1,63,0,0.0376106,"\int (b \sec (e+f x))^m \tan ^2(e+f x) \, dx","Int[(b*Sec[e + f*x])^m*Tan[e + f*x]^2,x]","\frac{\tan ^3(e+f x) \cos ^2(e+f x)^{\frac{m+3}{2}} (b \sec (e+f x))^m \, _2F_1\left(\frac{3}{2},\frac{m+3}{2};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f}","\frac{\tan ^3(e+f x) \cos ^2(e+f x)^{\frac{m+3}{2}} (b \sec (e+f x))^m \, _2F_1\left(\frac{3}{2},\frac{m+3}{2};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f}",1,"((Cos[e + f*x]^2)^((3 + m)/2)*Hypergeometric2F1[3/2, (3 + m)/2, 5/2, Sin[e + f*x]^2]*(b*Sec[e + f*x])^m*Tan[e + f*x]^3)/(3*f)","A",1,1,19,0.05263,1,"{2617}"
359,1,59,0,0.0370596,"\int \cot ^2(e+f x) (b \sec (e+f x))^m \, dx","Int[Cot[e + f*x]^2*(b*Sec[e + f*x])^m,x]","-\frac{\cot (e+f x) \cos ^2(e+f x)^{\frac{m-1}{2}} (b \sec (e+f x))^m \, _2F_1\left(-\frac{1}{2},\frac{m-1}{2};\frac{1}{2};\sin ^2(e+f x)\right)}{f}","-\frac{\cot (e+f x) \cos ^2(e+f x)^{\frac{m-1}{2}} (b \sec (e+f x))^m \, _2F_1\left(-\frac{1}{2},\frac{m-1}{2};\frac{1}{2};\sin ^2(e+f x)\right)}{f}",1,"-(((Cos[e + f*x]^2)^((-1 + m)/2)*Cot[e + f*x]*Hypergeometric2F1[-1/2, (-1 + m)/2, 1/2, Sin[e + f*x]^2]*(b*Sec[e + f*x])^m)/f)","A",1,1,19,0.05263,1,"{2617}"
360,1,63,0,0.0373571,"\int \cot ^4(e+f x) (b \sec (e+f x))^m \, dx","Int[Cot[e + f*x]^4*(b*Sec[e + f*x])^m,x]","-\frac{\cot ^3(e+f x) \cos ^2(e+f x)^{\frac{m-3}{2}} (b \sec (e+f x))^m \, _2F_1\left(-\frac{3}{2},\frac{m-3}{2};-\frac{1}{2};\sin ^2(e+f x)\right)}{3 f}","-\frac{\cot ^3(e+f x) \cos ^2(e+f x)^{\frac{m-3}{2}} (b \sec (e+f x))^m \, _2F_1\left(-\frac{3}{2},\frac{m-3}{2};-\frac{1}{2};\sin ^2(e+f x)\right)}{3 f}",1,"-((Cos[e + f*x]^2)^((-3 + m)/2)*Cot[e + f*x]^3*Hypergeometric2F1[-3/2, (-3 + m)/2, -1/2, Sin[e + f*x]^2]*(b*Sec[e + f*x])^m)/(3*f)","A",1,1,19,0.05263,1,"{2617}"
361,1,63,0,0.0372654,"\int \cot ^6(e+f x) (b \sec (e+f x))^m \, dx","Int[Cot[e + f*x]^6*(b*Sec[e + f*x])^m,x]","-\frac{\cot ^5(e+f x) \cos ^2(e+f x)^{\frac{m-5}{2}} (b \sec (e+f x))^m \, _2F_1\left(-\frac{5}{2},\frac{m-5}{2};-\frac{3}{2};\sin ^2(e+f x)\right)}{5 f}","-\frac{\cot ^5(e+f x) \cos ^2(e+f x)^{\frac{m-5}{2}} (b \sec (e+f x))^m \, _2F_1\left(-\frac{5}{2},\frac{m-5}{2};-\frac{3}{2};\sin ^2(e+f x)\right)}{5 f}",1,"-((Cos[e + f*x]^2)^((-5 + m)/2)*Cot[e + f*x]^5*Hypergeometric2F1[-5/2, (-5 + m)/2, -3/2, Sin[e + f*x]^2]*(b*Sec[e + f*x])^m)/(5*f)","A",1,1,19,0.05263,1,"{2617}"
362,1,82,0,0.045036,"\int (a \sec (e+f x))^m (b \tan (e+f x))^n \, dx","Int[(a*Sec[e + f*x])^m*(b*Tan[e + f*x])^n,x]","\frac{(a \sec (e+f x))^m (b \tan (e+f x))^{n+1} \cos ^2(e+f x)^{\frac{1}{2} (m+n+1)} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (m+n+1);\frac{n+3}{2};\sin ^2(e+f x)\right)}{b f (n+1)}","\frac{(a \sec (e+f x))^m (b \tan (e+f x))^{n+1} \cos ^2(e+f x)^{\frac{1}{2} (m+n+1)} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (m+n+1);\frac{n+3}{2};\sin ^2(e+f x)\right)}{b f (n+1)}",1,"((Cos[e + f*x]^2)^((1 + m + n)/2)*Hypergeometric2F1[(1 + n)/2, (1 + m + n)/2, (3 + n)/2, Sin[e + f*x]^2]*(a*Sec[e + f*x])^m*(b*Tan[e + f*x])^(1 + n))/(b*f*(1 + n))","A",1,1,21,0.04762,1,"{2617}"
363,1,74,0,0.0660517,"\int \sec ^6(a+b x) (d \tan (a+b x))^n \, dx","Int[Sec[a + b*x]^6*(d*Tan[a + b*x])^n,x]","\frac{2 (d \tan (a+b x))^{n+3}}{b d^3 (n+3)}+\frac{(d \tan (a+b x))^{n+5}}{b d^5 (n+5)}+\frac{(d \tan (a+b x))^{n+1}}{b d (n+1)}","\frac{2 (d \tan (a+b x))^{n+3}}{b d^3 (n+3)}+\frac{(d \tan (a+b x))^{n+5}}{b d^5 (n+5)}+\frac{(d \tan (a+b x))^{n+1}}{b d (n+1)}",1,"(d*Tan[a + b*x])^(1 + n)/(b*d*(1 + n)) + (2*(d*Tan[a + b*x])^(3 + n))/(b*d^3*(3 + n)) + (d*Tan[a + b*x])^(5 + n)/(b*d^5*(5 + n))","A",3,2,19,0.1053,1,"{2607, 270}"
364,1,49,0,0.0511222,"\int \sec ^4(a+b x) (d \tan (a+b x))^n \, dx","Int[Sec[a + b*x]^4*(d*Tan[a + b*x])^n,x]","\frac{(d \tan (a+b x))^{n+3}}{b d^3 (n+3)}+\frac{(d \tan (a+b x))^{n+1}}{b d (n+1)}","\frac{(d \tan (a+b x))^{n+3}}{b d^3 (n+3)}+\frac{(d \tan (a+b x))^{n+1}}{b d (n+1)}",1,"(d*Tan[a + b*x])^(1 + n)/(b*d*(1 + n)) + (d*Tan[a + b*x])^(3 + n)/(b*d^3*(3 + n))","A",3,2,19,0.1053,1,"{2607, 14}"
365,1,24,0,0.0385258,"\int \sec ^2(a+b x) (d \tan (a+b x))^n \, dx","Int[Sec[a + b*x]^2*(d*Tan[a + b*x])^n,x]","\frac{(d \tan (a+b x))^{n+1}}{b d (n+1)}","\frac{(d \tan (a+b x))^{n+1}}{b d (n+1)}",1,"(d*Tan[a + b*x])^(1 + n)/(b*d*(1 + n))","A",2,2,19,0.1053,1,"{2607, 32}"
366,1,50,0,0.0288274,"\int (d \tan (a+b x))^n \, dx","Int[(d*Tan[a + b*x])^n,x]","\frac{(d \tan (a+b x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(a+b x)\right)}{b d (n+1)}","\frac{(d \tan (a+b x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(a+b x)\right)}{b d (n+1)}",1,"(Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Tan[a + b*x]^2]*(d*Tan[a + b*x])^(1 + n))/(b*d*(1 + n))","A",2,2,10,0.2000,1,"{3476, 364}"
367,1,50,0,0.0466357,"\int \cos ^2(a+b x) (d \tan (a+b x))^n \, dx","Int[Cos[a + b*x]^2*(d*Tan[a + b*x])^n,x]","\frac{(d \tan (a+b x))^{n+1} \, _2F_1\left(2,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(a+b x)\right)}{b d (n+1)}","\frac{(d \tan (a+b x))^{n+1} \, _2F_1\left(2,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(a+b x)\right)}{b d (n+1)}",1,"(Hypergeometric2F1[2, (1 + n)/2, (3 + n)/2, -Tan[a + b*x]^2]*(d*Tan[a + b*x])^(1 + n))/(b*d*(1 + n))","A",2,2,19,0.1053,1,"{2607, 364}"
368,1,50,0,0.0445644,"\int \cos ^4(a+b x) (d \tan (a+b x))^n \, dx","Int[Cos[a + b*x]^4*(d*Tan[a + b*x])^n,x]","\frac{(d \tan (a+b x))^{n+1} \, _2F_1\left(3,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(a+b x)\right)}{b d (n+1)}","\frac{(d \tan (a+b x))^{n+1} \, _2F_1\left(3,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(a+b x)\right)}{b d (n+1)}",1,"(Hypergeometric2F1[3, (1 + n)/2, (3 + n)/2, -Tan[a + b*x]^2]*(d*Tan[a + b*x])^(1 + n))/(b*d*(1 + n))","A",2,2,19,0.1053,1,"{2607, 364}"
369,1,78,0,0.0384604,"\int \sec ^5(a+b x) (d \tan (a+b x))^n \, dx","Int[Sec[a + b*x]^5*(d*Tan[a + b*x])^n,x]","\frac{\sec ^5(a+b x) \cos ^2(a+b x)^{\frac{n+6}{2}} (d \tan (a+b x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+6}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b d (n+1)}","\frac{\sec ^5(a+b x) \cos ^2(a+b x)^{\frac{n+6}{2}} (d \tan (a+b x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+6}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b d (n+1)}",1,"((Cos[a + b*x]^2)^((6 + n)/2)*Hypergeometric2F1[(1 + n)/2, (6 + n)/2, (3 + n)/2, Sin[a + b*x]^2]*Sec[a + b*x]^5*(d*Tan[a + b*x])^(1 + n))/(b*d*(1 + n))","A",1,1,19,0.05263,1,"{2617}"
370,1,78,0,0.0384939,"\int \sec ^3(a+b x) (d \tan (a+b x))^n \, dx","Int[Sec[a + b*x]^3*(d*Tan[a + b*x])^n,x]","\frac{\sec ^3(a+b x) \cos ^2(a+b x)^{\frac{n+4}{2}} (d \tan (a+b x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+4}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b d (n+1)}","\frac{\sec ^3(a+b x) \cos ^2(a+b x)^{\frac{n+4}{2}} (d \tan (a+b x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+4}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b d (n+1)}",1,"((Cos[a + b*x]^2)^((4 + n)/2)*Hypergeometric2F1[(1 + n)/2, (4 + n)/2, (3 + n)/2, Sin[a + b*x]^2]*Sec[a + b*x]^3*(d*Tan[a + b*x])^(1 + n))/(b*d*(1 + n))","A",1,1,19,0.05263,1,"{2617}"
371,1,76,0,0.0239285,"\int \sec (a+b x) (d \tan (a+b x))^n \, dx","Int[Sec[a + b*x]*(d*Tan[a + b*x])^n,x]","\frac{\sec (a+b x) \cos ^2(a+b x)^{\frac{n+2}{2}} (d \tan (a+b x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+2}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b d (n+1)}","\frac{\sec (a+b x) \cos ^2(a+b x)^{\frac{n+2}{2}} (d \tan (a+b x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+2}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b d (n+1)}",1,"((Cos[a + b*x]^2)^((2 + n)/2)*Hypergeometric2F1[(1 + n)/2, (2 + n)/2, (3 + n)/2, Sin[a + b*x]^2]*Sec[a + b*x]*(d*Tan[a + b*x])^(1 + n))/(b*d*(1 + n))","A",1,1,17,0.05882,1,"{2617}"
372,1,72,0,0.03143,"\int \cos (a+b x) (d \tan (a+b x))^n \, dx","Int[Cos[a + b*x]*(d*Tan[a + b*x])^n,x]","\frac{\cos (a+b x) \cos ^2(a+b x)^{n/2} (d \tan (a+b x))^{n+1} \, _2F_1\left(\frac{n}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b d (n+1)}","\frac{\cos (a+b x) \cos ^2(a+b x)^{n/2} (d \tan (a+b x))^{n+1} \, _2F_1\left(\frac{n}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b d (n+1)}",1,"(Cos[a + b*x]*(Cos[a + b*x]^2)^(n/2)*Hypergeometric2F1[n/2, (1 + n)/2, (3 + n)/2, Sin[a + b*x]^2]*(d*Tan[a + b*x])^(1 + n))/(b*d*(1 + n))","A",1,1,17,0.05882,1,"{2617}"
373,1,78,0,0.037228,"\int \cos ^3(a+b x) (d \tan (a+b x))^n \, dx","Int[Cos[a + b*x]^3*(d*Tan[a + b*x])^n,x]","\frac{\cos ^3(a+b x) \cos ^2(a+b x)^{\frac{n-2}{2}} (d \tan (a+b x))^{n+1} \, _2F_1\left(\frac{n-2}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b d (n+1)}","\frac{\cos ^3(a+b x) \cos ^2(a+b x)^{\frac{n-2}{2}} (d \tan (a+b x))^{n+1} \, _2F_1\left(\frac{n-2}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b d (n+1)}",1,"(Cos[a + b*x]^3*(Cos[a + b*x]^2)^((-2 + n)/2)*Hypergeometric2F1[(-2 + n)/2, (1 + n)/2, (3 + n)/2, Sin[a + b*x]^2]*(d*Tan[a + b*x])^(1 + n))/(b*d*(1 + n))","A",1,1,19,0.05263,1,"{2617}"
374,1,40,0,0.046136,"\int (b \csc (e+f x))^m \tan ^3(e+f x) \, dx","Int[(b*Csc[e + f*x])^m*Tan[e + f*x]^3,x]","-\frac{(b \csc (e+f x))^m \, _2F_1\left(2,\frac{m}{2};\frac{m+2}{2};\csc ^2(e+f x)\right)}{f m}","-\frac{(b \csc (e+f x))^m \, _2F_1\left(2,\frac{m}{2};\frac{m+2}{2};\csc ^2(e+f x)\right)}{f m}",1,"-(((b*Csc[e + f*x])^m*Hypergeometric2F1[2, m/2, (2 + m)/2, Csc[e + f*x]^2])/(f*m))","A",2,2,19,0.1053,1,"{2606, 364}"
375,1,39,0,0.0357686,"\int (b \csc (e+f x))^m \tan (e+f x) \, dx","Int[(b*Csc[e + f*x])^m*Tan[e + f*x],x]","\frac{(b \csc (e+f x))^m \, _2F_1\left(1,\frac{m}{2};\frac{m+2}{2};\csc ^2(e+f x)\right)}{f m}","\frac{(b \csc (e+f x))^m \, _2F_1\left(1,\frac{m}{2};\frac{m+2}{2};\csc ^2(e+f x)\right)}{f m}",1,"((b*Csc[e + f*x])^m*Hypergeometric2F1[1, m/2, (2 + m)/2, Csc[e + f*x]^2])/(f*m)","A",2,2,17,0.1176,1,"{2606, 364}"
376,1,18,0,0.0214582,"\int \cot (e+f x) (b \csc (e+f x))^m \, dx","Int[Cot[e + f*x]*(b*Csc[e + f*x])^m,x]","-\frac{(b \csc (e+f x))^m}{f m}","-\frac{(b \csc (e+f x))^m}{f m}",1,"-((b*Csc[e + f*x])^m/(f*m))","A",2,2,17,0.1176,1,"{2606, 32}"
377,1,43,0,0.0472561,"\int \cot ^3(e+f x) (b \csc (e+f x))^m \, dx","Int[Cot[e + f*x]^3*(b*Csc[e + f*x])^m,x]","\frac{(b \csc (e+f x))^m}{f m}-\frac{(b \csc (e+f x))^{m+2}}{b^2 f (m+2)}","\frac{(b \csc (e+f x))^m}{f m}-\frac{(b \csc (e+f x))^{m+2}}{b^2 f (m+2)}",1,"(b*Csc[e + f*x])^m/(f*m) - (b*Csc[e + f*x])^(2 + m)/(b^2*f*(2 + m))","A",3,2,19,0.1053,1,"{2606, 14}"
378,1,69,0,0.0604031,"\int \cot ^5(e+f x) (b \csc (e+f x))^m \, dx","Int[Cot[e + f*x]^5*(b*Csc[e + f*x])^m,x]","\frac{2 (b \csc (e+f x))^{m+2}}{b^2 f (m+2)}-\frac{(b \csc (e+f x))^{m+4}}{b^4 f (m+4)}-\frac{(b \csc (e+f x))^m}{f m}","\frac{2 (b \csc (e+f x))^{m+2}}{b^2 f (m+2)}-\frac{(b \csc (e+f x))^{m+4}}{b^4 f (m+4)}-\frac{(b \csc (e+f x))^m}{f m}",1,"-((b*Csc[e + f*x])^m/(f*m)) + (2*(b*Csc[e + f*x])^(2 + m))/(b^2*f*(2 + m)) - (b*Csc[e + f*x])^(4 + m)/(b^4*f*(4 + m))","A",3,2,19,0.1053,1,"{2606, 270}"
379,1,63,0,0.0361783,"\int (b \csc (e+f x))^m \tan ^4(e+f x) \, dx","Int[(b*Csc[e + f*x])^m*Tan[e + f*x]^4,x]","\frac{\tan ^3(e+f x) \sin ^2(e+f x)^{\frac{m-3}{2}} (b \csc (e+f x))^m \, _2F_1\left(-\frac{3}{2},\frac{m-3}{2};-\frac{1}{2};\cos ^2(e+f x)\right)}{3 f}","\frac{\tan ^3(e+f x) \sin ^2(e+f x)^{\frac{m-3}{2}} (b \csc (e+f x))^m \, _2F_1\left(-\frac{3}{2},\frac{m-3}{2};-\frac{1}{2};\cos ^2(e+f x)\right)}{3 f}",1,"((b*Csc[e + f*x])^m*Hypergeometric2F1[-3/2, (-3 + m)/2, -1/2, Cos[e + f*x]^2]*(Sin[e + f*x]^2)^((-3 + m)/2)*Tan[e + f*x]^3)/(3*f)","A",1,1,19,0.05263,1,"{2617}"
380,1,58,0,0.0357518,"\int (b \csc (e+f x))^m \tan ^2(e+f x) \, dx","Int[(b*Csc[e + f*x])^m*Tan[e + f*x]^2,x]","\frac{\tan (e+f x) \sin ^2(e+f x)^{\frac{m-1}{2}} (b \csc (e+f x))^m \, _2F_1\left(-\frac{1}{2},\frac{m-1}{2};\frac{1}{2};\cos ^2(e+f x)\right)}{f}","\frac{\tan (e+f x) \sin ^2(e+f x)^{\frac{m-1}{2}} (b \csc (e+f x))^m \, _2F_1\left(-\frac{1}{2},\frac{m-1}{2};\frac{1}{2};\cos ^2(e+f x)\right)}{f}",1,"((b*Csc[e + f*x])^m*Hypergeometric2F1[-1/2, (-1 + m)/2, 1/2, Cos[e + f*x]^2]*(Sin[e + f*x]^2)^((-1 + m)/2)*Tan[e + f*x])/f","A",1,1,19,0.05263,1,"{2617}"
381,1,63,0,0.0356907,"\int \cot ^2(e+f x) (b \csc (e+f x))^m \, dx","Int[Cot[e + f*x]^2*(b*Csc[e + f*x])^m,x]","-\frac{\cot ^3(e+f x) \sin ^2(e+f x)^{\frac{m+3}{2}} (b \csc (e+f x))^m \, _2F_1\left(\frac{3}{2},\frac{m+3}{2};\frac{5}{2};\cos ^2(e+f x)\right)}{3 f}","-\frac{\cot ^3(e+f x) \sin ^2(e+f x)^{\frac{m+3}{2}} (b \csc (e+f x))^m \, _2F_1\left(\frac{3}{2},\frac{m+3}{2};\frac{5}{2};\cos ^2(e+f x)\right)}{3 f}",1,"-(Cot[e + f*x]^3*(b*Csc[e + f*x])^m*Hypergeometric2F1[3/2, (3 + m)/2, 5/2, Cos[e + f*x]^2]*(Sin[e + f*x]^2)^((3 + m)/2))/(3*f)","A",1,1,19,0.05263,1,"{2617}"
382,1,63,0,0.0364904,"\int \cot ^4(e+f x) (b \csc (e+f x))^m \, dx","Int[Cot[e + f*x]^4*(b*Csc[e + f*x])^m,x]","-\frac{\cot ^5(e+f x) \sin ^2(e+f x)^{\frac{m+5}{2}} (b \csc (e+f x))^m \, _2F_1\left(\frac{5}{2},\frac{m+5}{2};\frac{7}{2};\cos ^2(e+f x)\right)}{5 f}","-\frac{\cot ^5(e+f x) \sin ^2(e+f x)^{\frac{m+5}{2}} (b \csc (e+f x))^m \, _2F_1\left(\frac{5}{2},\frac{m+5}{2};\frac{7}{2};\cos ^2(e+f x)\right)}{5 f}",1,"-(Cot[e + f*x]^5*(b*Csc[e + f*x])^m*Hypergeometric2F1[5/2, (5 + m)/2, 7/2, Cos[e + f*x]^2]*(Sin[e + f*x]^2)^((5 + m)/2))/(5*f)","A",1,1,19,0.05263,1,"{2617}"
383,1,79,0,0.1669968,"\int (b \csc (e+f x))^m (d \tan (e+f x))^{3/2} \, dx","Int[(b*Csc[e + f*x])^m*(d*Tan[e + f*x])^(3/2),x]","\frac{2 \cos ^2(e+f x)^{5/4} (d \tan (e+f x))^{5/2} (b \csc (e+f x))^m \, _2F_1\left(\frac{5}{4},\frac{1}{4} (5-2 m);\frac{1}{4} (9-2 m);\sin ^2(e+f x)\right)}{d f (5-2 m)}","\frac{2 \cos ^2(e+f x)^{5/4} (d \tan (e+f x))^{5/2} (b \csc (e+f x))^m \, _2F_1\left(\frac{5}{4},\frac{1}{4} (5-2 m);\frac{1}{4} (9-2 m);\sin ^2(e+f x)\right)}{d f (5-2 m)}",1,"(2*(Cos[e + f*x]^2)^(5/4)*(b*Csc[e + f*x])^m*Hypergeometric2F1[5/4, (5 - 2*m)/4, (9 - 2*m)/4, Sin[e + f*x]^2]*(d*Tan[e + f*x])^(5/2))/(d*f*(5 - 2*m))","A",3,3,23,0.1304,1,"{2618, 2602, 2577}"
384,1,79,0,0.145495,"\int (b \csc (e+f x))^m \sqrt{d \tan (e+f x)} \, dx","Int[(b*Csc[e + f*x])^m*Sqrt[d*Tan[e + f*x]],x]","\frac{2 \cos ^2(e+f x)^{3/4} (d \tan (e+f x))^{3/2} (b \csc (e+f x))^m \, _2F_1\left(\frac{3}{4},\frac{1}{4} (3-2 m);\frac{1}{4} (7-2 m);\sin ^2(e+f x)\right)}{d f (3-2 m)}","\frac{2 \cos ^2(e+f x)^{3/4} (d \tan (e+f x))^{3/2} (b \csc (e+f x))^m \, _2F_1\left(\frac{3}{4},\frac{1}{4} (3-2 m);\frac{1}{4} (7-2 m);\sin ^2(e+f x)\right)}{d f (3-2 m)}",1,"(2*(Cos[e + f*x]^2)^(3/4)*(b*Csc[e + f*x])^m*Hypergeometric2F1[3/4, (3 - 2*m)/4, (7 - 2*m)/4, Sin[e + f*x]^2]*(d*Tan[e + f*x])^(3/2))/(d*f*(3 - 2*m))","A",3,3,23,0.1304,1,"{2618, 2602, 2577}"
385,1,79,0,0.1505333,"\int \frac{(b \csc (e+f x))^m}{\sqrt{d \tan (e+f x)}} \, dx","Int[(b*Csc[e + f*x])^m/Sqrt[d*Tan[e + f*x]],x]","\frac{2 \sqrt[4]{\cos ^2(e+f x)} \sqrt{d \tan (e+f x)} (b \csc (e+f x))^m \, _2F_1\left(\frac{1}{4},\frac{1}{4} (1-2 m);\frac{1}{4} (5-2 m);\sin ^2(e+f x)\right)}{d f (1-2 m)}","\frac{2 \sqrt[4]{\cos ^2(e+f x)} \sqrt{d \tan (e+f x)} (b \csc (e+f x))^m \, _2F_1\left(\frac{1}{4},\frac{1}{4} (1-2 m);\frac{1}{4} (5-2 m);\sin ^2(e+f x)\right)}{d f (1-2 m)}",1,"(2*(Cos[e + f*x]^2)^(1/4)*(b*Csc[e + f*x])^m*Hypergeometric2F1[1/4, (1 - 2*m)/4, (5 - 2*m)/4, Sin[e + f*x]^2]*Sqrt[d*Tan[e + f*x]])/(d*f*(1 - 2*m))","A",3,3,23,0.1304,1,"{2618, 2602, 2577}"
386,1,79,0,0.173675,"\int \frac{(b \csc (e+f x))^m}{(d \tan (e+f x))^{3/2}} \, dx","Int[(b*Csc[e + f*x])^m/(d*Tan[e + f*x])^(3/2),x]","-\frac{2 (b \csc (e+f x))^m \, _2F_1\left(-\frac{1}{4},\frac{1}{4} (-2 m-1);\frac{1}{4} (3-2 m);\sin ^2(e+f x)\right)}{d f (2 m+1) \sqrt[4]{\cos ^2(e+f x)} \sqrt{d \tan (e+f x)}}","-\frac{2 (b \csc (e+f x))^m \, _2F_1\left(-\frac{1}{4},\frac{1}{4} (-2 m-1);\frac{1}{4} (3-2 m);\sin ^2(e+f x)\right)}{d f (2 m+1) \sqrt[4]{\cos ^2(e+f x)} \sqrt{d \tan (e+f x)}}",1,"(-2*(b*Csc[e + f*x])^m*Hypergeometric2F1[-1/4, (-1 - 2*m)/4, (3 - 2*m)/4, Sin[e + f*x]^2])/(d*f*(1 + 2*m)*(Cos[e + f*x]^2)^(1/4)*Sqrt[d*Tan[e + f*x]])","A",3,3,23,0.1304,1,"{2618, 2602, 2577}"
387,1,89,0,0.1497481,"\int (a \csc (e+f x))^m (b \tan (e+f x))^n \, dx","Int[(a*Csc[e + f*x])^m*(b*Tan[e + f*x])^n,x]","\frac{\cos ^2(e+f x)^{\frac{n+1}{2}} (a \csc (e+f x))^m (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (-m+n+1);\frac{1}{2} (-m+n+3);\sin ^2(e+f x)\right)}{b f (-m+n+1)}","\frac{\cos ^2(e+f x)^{\frac{n+1}{2}} (a \csc (e+f x))^m (b \tan (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (-m+n+1);\frac{1}{2} (-m+n+3);\sin ^2(e+f x)\right)}{b f (-m+n+1)}",1,"((Cos[e + f*x]^2)^((1 + n)/2)*(a*Csc[e + f*x])^m*Hypergeometric2F1[(1 + n)/2, (1 - m + n)/2, (3 - m + n)/2, Sin[e + f*x]^2]*(b*Tan[e + f*x])^(1 + n))/(b*f*(1 - m + n))","A",3,3,21,0.1429,1,"{2618, 2602, 2577}"