1,1,92,0,0.070859,"\int \cos ^7(c+d x) \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^7*(A + C*Cos[c + d*x]^2),x]","-\frac{(A+4 C) \sin ^7(c+d x)}{7 d}+\frac{3 (A+2 C) \sin ^5(c+d x)}{5 d}-\frac{(3 A+4 C) \sin ^3(c+d x)}{3 d}+\frac{(A+C) \sin (c+d x)}{d}+\frac{C \sin ^9(c+d x)}{9 d}","-\frac{(A+4 C) \sin ^7(c+d x)}{7 d}+\frac{3 (A+2 C) \sin ^5(c+d x)}{5 d}-\frac{(3 A+4 C) \sin ^3(c+d x)}{3 d}+\frac{(A+C) \sin (c+d x)}{d}+\frac{C \sin ^9(c+d x)}{9 d}",1,"((A + C)*Sin[c + d*x])/d - ((3*A + 4*C)*Sin[c + d*x]^3)/(3*d) + (3*(A + 2*C)*Sin[c + d*x]^5)/(5*d) - ((A + 4*C)*Sin[c + d*x]^7)/(7*d) + (C*Sin[c + d*x]^9)/(9*d)","A",3,2,21,0.09524,1,"{3013, 373}"
2,1,72,0,0.0656366,"\int \cos ^5(c+d x) \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^5*(A + C*Cos[c + d*x]^2),x]","\frac{(A+3 C) \sin ^5(c+d x)}{5 d}-\frac{(2 A+3 C) \sin ^3(c+d x)}{3 d}+\frac{(A+C) \sin (c+d x)}{d}-\frac{C \sin ^7(c+d x)}{7 d}","\frac{(A+3 C) \sin ^5(c+d x)}{5 d}-\frac{(2 A+3 C) \sin ^3(c+d x)}{3 d}+\frac{(A+C) \sin (c+d x)}{d}-\frac{C \sin ^7(c+d x)}{7 d}",1,"((A + C)*Sin[c + d*x])/d - ((2*A + 3*C)*Sin[c + d*x]^3)/(3*d) + ((A + 3*C)*Sin[c + d*x]^5)/(5*d) - (C*Sin[c + d*x]^7)/(7*d)","A",3,2,21,0.09524,1,"{3013, 373}"
3,1,50,0,0.0524978,"\int \cos ^3(c+d x) \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^3*(A + C*Cos[c + d*x]^2),x]","-\frac{(A+2 C) \sin ^3(c+d x)}{3 d}+\frac{(A+C) \sin (c+d x)}{d}+\frac{C \sin ^5(c+d x)}{5 d}","-\frac{(A+2 C) \sin ^3(c+d x)}{3 d}+\frac{(A+C) \sin (c+d x)}{d}+\frac{C \sin ^5(c+d x)}{5 d}",1,"((A + C)*Sin[c + d*x])/d - ((A + 2*C)*Sin[c + d*x]^3)/(3*d) + (C*Sin[c + d*x]^5)/(5*d)","A",3,2,21,0.09524,1,"{3013, 373}"
4,1,30,0,0.0232144,"\int \cos (c+d x) \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(A + C*Cos[c + d*x]^2),x]","\frac{(A+C) \sin (c+d x)}{d}-\frac{C \sin ^3(c+d x)}{3 d}","\frac{(A+C) \sin (c+d x)}{d}-\frac{C \sin ^3(c+d x)}{3 d}",1,"((A + C)*Sin[c + d*x])/d - (C*Sin[c + d*x]^3)/(3*d)","A",2,1,19,0.05263,1,"{3013}"
5,1,24,0,0.0310902,"\int \left(A+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[(A + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","\frac{A \tanh ^{-1}(\sin (c+d x))}{d}+\frac{C \sin (c+d x)}{d}","\frac{A \tanh ^{-1}(\sin (c+d x))}{d}+\frac{C \sin (c+d x)}{d}",1,"(A*ArcTanh[Sin[c + d*x]])/d + (C*Sin[c + d*x])/d","A",2,2,19,0.1053,1,"{3014, 3770}"
6,1,40,0,0.0373045,"\int \left(A+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{(A+2 C) \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{A \tan (c+d x) \sec (c+d x)}{2 d}","\frac{(A+2 C) \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{A \tan (c+d x) \sec (c+d x)}{2 d}",1,"((A + 2*C)*ArcTanh[Sin[c + d*x]])/(2*d) + (A*Sec[c + d*x]*Tan[c + d*x])/(2*d)","A",2,2,21,0.09524,1,"{3012, 3770}"
7,1,70,0,0.0468188,"\int \left(A+C \cos ^2(c+d x)\right) \sec ^5(c+d x) \, dx","Int[(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^5,x]","\frac{(3 A+4 C) \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{(3 A+4 C) \tan (c+d x) \sec (c+d x)}{8 d}+\frac{A \tan (c+d x) \sec ^3(c+d x)}{4 d}","\frac{(3 A+4 C) \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{(3 A+4 C) \tan (c+d x) \sec (c+d x)}{8 d}+\frac{A \tan (c+d x) \sec ^3(c+d x)}{4 d}",1,"((3*A + 4*C)*ArcTanh[Sin[c + d*x]])/(8*d) + ((3*A + 4*C)*Sec[c + d*x]*Tan[c + d*x])/(8*d) + (A*Sec[c + d*x]^3*Tan[c + d*x])/(4*d)","A",3,3,21,0.1429,1,"{3012, 3768, 3770}"
8,1,98,0,0.0601627,"\int \left(A+C \cos ^2(c+d x)\right) \sec ^7(c+d x) \, dx","Int[(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^7,x]","\frac{(5 A+6 C) \tanh ^{-1}(\sin (c+d x))}{16 d}+\frac{(5 A+6 C) \tan (c+d x) \sec ^3(c+d x)}{24 d}+\frac{(5 A+6 C) \tan (c+d x) \sec (c+d x)}{16 d}+\frac{A \tan (c+d x) \sec ^5(c+d x)}{6 d}","\frac{(5 A+6 C) \tanh ^{-1}(\sin (c+d x))}{16 d}+\frac{(5 A+6 C) \tan (c+d x) \sec ^3(c+d x)}{24 d}+\frac{(5 A+6 C) \tan (c+d x) \sec (c+d x)}{16 d}+\frac{A \tan (c+d x) \sec ^5(c+d x)}{6 d}",1,"((5*A + 6*C)*ArcTanh[Sin[c + d*x]])/(16*d) + ((5*A + 6*C)*Sec[c + d*x]*Tan[c + d*x])/(16*d) + ((5*A + 6*C)*Sec[c + d*x]^3*Tan[c + d*x])/(24*d) + (A*Sec[c + d*x]^5*Tan[c + d*x])/(6*d)","A",4,3,21,0.1429,1,"{3012, 3768, 3770}"
9,1,117,0,0.0670029,"\int \cos ^6(c+d x) \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^6*(A + C*Cos[c + d*x]^2),x]","\frac{(8 A+7 C) \sin (c+d x) \cos ^5(c+d x)}{48 d}+\frac{5 (8 A+7 C) \sin (c+d x) \cos ^3(c+d x)}{192 d}+\frac{5 (8 A+7 C) \sin (c+d x) \cos (c+d x)}{128 d}+\frac{5}{128} x (8 A+7 C)+\frac{C \sin (c+d x) \cos ^7(c+d x)}{8 d}","\frac{(8 A+7 C) \sin (c+d x) \cos ^5(c+d x)}{48 d}+\frac{5 (8 A+7 C) \sin (c+d x) \cos ^3(c+d x)}{192 d}+\frac{5 (8 A+7 C) \sin (c+d x) \cos (c+d x)}{128 d}+\frac{5}{128} x (8 A+7 C)+\frac{C \sin (c+d x) \cos ^7(c+d x)}{8 d}",1,"(5*(8*A + 7*C)*x)/128 + (5*(8*A + 7*C)*Cos[c + d*x]*Sin[c + d*x])/(128*d) + (5*(8*A + 7*C)*Cos[c + d*x]^3*Sin[c + d*x])/(192*d) + ((8*A + 7*C)*Cos[c + d*x]^5*Sin[c + d*x])/(48*d) + (C*Cos[c + d*x]^7*Sin[c + d*x])/(8*d)","A",5,3,21,0.1429,1,"{3014, 2635, 8}"
10,1,89,0,0.0532344,"\int \cos ^4(c+d x) \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^4*(A + C*Cos[c + d*x]^2),x]","\frac{(6 A+5 C) \sin (c+d x) \cos ^3(c+d x)}{24 d}+\frac{(6 A+5 C) \sin (c+d x) \cos (c+d x)}{16 d}+\frac{1}{16} x (6 A+5 C)+\frac{C \sin (c+d x) \cos ^5(c+d x)}{6 d}","\frac{(6 A+5 C) \sin (c+d x) \cos ^3(c+d x)}{24 d}+\frac{(6 A+5 C) \sin (c+d x) \cos (c+d x)}{16 d}+\frac{1}{16} x (6 A+5 C)+\frac{C \sin (c+d x) \cos ^5(c+d x)}{6 d}",1,"((6*A + 5*C)*x)/16 + ((6*A + 5*C)*Cos[c + d*x]*Sin[c + d*x])/(16*d) + ((6*A + 5*C)*Cos[c + d*x]^3*Sin[c + d*x])/(24*d) + (C*Cos[c + d*x]^5*Sin[c + d*x])/(6*d)","A",4,3,21,0.1429,1,"{3014, 2635, 8}"
11,1,61,0,0.0412907,"\int \cos ^2(c+d x) \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^2*(A + C*Cos[c + d*x]^2),x]","\frac{(4 A+3 C) \sin (c+d x) \cos (c+d x)}{8 d}+\frac{1}{8} x (4 A+3 C)+\frac{C \sin (c+d x) \cos ^3(c+d x)}{4 d}","\frac{(4 A+3 C) \sin (c+d x) \cos (c+d x)}{8 d}+\frac{1}{8} x (4 A+3 C)+\frac{C \sin (c+d x) \cos ^3(c+d x)}{4 d}",1,"((4*A + 3*C)*x)/8 + ((4*A + 3*C)*Cos[c + d*x]*Sin[c + d*x])/(8*d) + (C*Cos[c + d*x]^3*Sin[c + d*x])/(4*d)","A",3,3,21,0.1429,1,"{3014, 2635, 8}"
12,1,15,0,0.0244259,"\int \left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","\frac{A \tan (c+d x)}{d}+C x","\frac{A \tan (c+d x)}{d}+C x",1,"C*x + (A*Tan[c + d*x])/d","A",2,2,21,0.09524,1,"{3012, 8}"
13,1,43,0,0.0375058,"\int \left(A+C \cos ^2(c+d x)\right) \sec ^4(c+d x) \, dx","Int[(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^4,x]","\frac{(2 A+3 C) \tan (c+d x)}{3 d}+\frac{A \tan (c+d x) \sec ^2(c+d x)}{3 d}","\frac{(2 A+3 C) \tan (c+d x)}{3 d}+\frac{A \tan (c+d x) \sec ^2(c+d x)}{3 d}",1,"((2*A + 3*C)*Tan[c + d*x])/(3*d) + (A*Sec[c + d*x]^2*Tan[c + d*x])/(3*d)","A",3,3,21,0.1429,1,"{3012, 3767, 8}"
14,1,65,0,0.0435946,"\int \left(A+C \cos ^2(c+d x)\right) \sec ^6(c+d x) \, dx","Int[(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^6,x]","\frac{(4 A+5 C) \tan ^3(c+d x)}{15 d}+\frac{(4 A+5 C) \tan (c+d x)}{5 d}+\frac{A \tan (c+d x) \sec ^4(c+d x)}{5 d}","\frac{(4 A+5 C) \tan ^3(c+d x)}{15 d}+\frac{(4 A+5 C) \tan (c+d x)}{5 d}+\frac{A \tan (c+d x) \sec ^4(c+d x)}{5 d}",1,"((4*A + 5*C)*Tan[c + d*x])/(5*d) + (A*Sec[c + d*x]^4*Tan[c + d*x])/(5*d) + ((4*A + 5*C)*Tan[c + d*x]^3)/(15*d)","A",3,2,21,0.09524,1,"{3012, 3767}"
15,1,87,0,0.0496711,"\int \left(A+C \cos ^2(c+d x)\right) \sec ^8(c+d x) \, dx","Int[(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^8,x]","\frac{(6 A+7 C) \tan ^5(c+d x)}{35 d}+\frac{2 (6 A+7 C) \tan ^3(c+d x)}{21 d}+\frac{(6 A+7 C) \tan (c+d x)}{7 d}+\frac{A \tan (c+d x) \sec ^6(c+d x)}{7 d}","\frac{(6 A+7 C) \tan ^5(c+d x)}{35 d}+\frac{2 (6 A+7 C) \tan ^3(c+d x)}{21 d}+\frac{(6 A+7 C) \tan (c+d x)}{7 d}+\frac{A \tan (c+d x) \sec ^6(c+d x)}{7 d}",1,"((6*A + 7*C)*Tan[c + d*x])/(7*d) + (A*Sec[c + d*x]^6*Tan[c + d*x])/(7*d) + (2*(6*A + 7*C)*Tan[c + d*x]^3)/(21*d) + ((6*A + 7*C)*Tan[c + d*x]^5)/(35*d)","A",3,2,21,0.09524,1,"{3012, 3767}"
16,1,113,0,0.0822025,"\int (b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2),x]","\frac{2 b^2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{2 b (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b d}","\frac{2 b^2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{2 b (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b d}",1,"(2*b^2*(9*A + 7*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]) + (2*b*(9*A + 7*C)*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*d) + (2*C*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b*d)","A",4,4,25,0.1600,1,"{3014, 2635, 2640, 2639}"
17,1,113,0,0.0832329,"\int (b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2),x]","\frac{2 b^2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 b (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b d}","\frac{2 b^2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 b (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b d}",1,"(2*b^2*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*b*(7*A + 5*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*C*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b*d)","A",4,4,25,0.1600,1,"{3014, 2635, 2642, 2641}"
18,1,77,0,0.060222,"\int \sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2),x]","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b d}","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b d}",1,"(2*(5*A + 3*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*C*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b*d)","A",3,3,25,0.1200,1,"{3014, 2640, 2639}"
19,1,75,0,0.0572765,"\int \frac{A+C \cos ^2(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(A + C*Cos[c + d*x]^2)/Sqrt[b*Cos[c + d*x]],x]","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b d}","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b d}",1,"(2*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*b*d)","A",3,3,25,0.1200,1,"{3014, 2642, 2641}"
20,1,74,0,0.0619689,"\int \frac{A+C \cos ^2(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(3/2),x]","\frac{2 A \sin (c+d x)}{b d \sqrt{b \cos (c+d x)}}-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^2 d \sqrt{\cos (c+d x)}}","\frac{2 A \sin (c+d x)}{b d \sqrt{b \cos (c+d x)}}-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^2 d \sqrt{\cos (c+d x)}}",1,"(-2*(A - C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b^2*d*Sqrt[Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(b*d*Sqrt[b*Cos[c + d*x]])","A",3,3,25,0.1200,1,"{3012, 2640, 2639}"
21,1,78,0,0.0638188,"\int \frac{A+C \cos ^2(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{3 b d (b \cos (c+d x))^{3/2}}","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{3 b d (b \cos (c+d x))^{3/2}}",1,"(2*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(3*b*d*(b*Cos[c + d*x])^(3/2))","A",3,3,25,0.1200,1,"{3012, 2642, 2641}"
22,1,115,0,0.0866652,"\int \frac{A+C \cos ^2(c+d x)}{(b \cos (c+d x))^{7/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(7/2),x]","\frac{2 (3 A+5 C) \sin (c+d x)}{5 b^3 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^4 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{5 b d (b \cos (c+d x))^{5/2}}","\frac{2 (3 A+5 C) \sin (c+d x)}{5 b^3 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^4 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{5 b d (b \cos (c+d x))^{5/2}}",1,"(-2*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^4*d*Sqrt[Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(5*b*d*(b*Cos[c + d*x])^(5/2)) + (2*(3*A + 5*C)*Sin[c + d*x])/(5*b^3*d*Sqrt[b*Cos[c + d*x]])","A",4,4,25,0.1600,1,"{3012, 2636, 2640, 2639}"
23,1,115,0,0.0896272,"\int \frac{A+C \cos ^2(c+d x)}{(b \cos (c+d x))^{9/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(9/2),x]","\frac{2 (5 A+7 C) \sin (c+d x)}{21 b^3 d (b \cos (c+d x))^{3/2}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^4 d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{7 b d (b \cos (c+d x))^{7/2}}","\frac{2 (5 A+7 C) \sin (c+d x)}{21 b^3 d (b \cos (c+d x))^{3/2}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^4 d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{7 b d (b \cos (c+d x))^{7/2}}",1,"(2*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b^4*d*Sqrt[b*Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(7*b*d*(b*Cos[c + d*x])^(7/2)) + (2*(5*A + 7*C)*Sin[c + d*x])/(21*b^3*d*(b*Cos[c + d*x])^(3/2))","A",4,4,25,0.1600,1,"{3012, 2636, 2642, 2641}"
24,1,21,0,0.0228646,"\int \sqrt{\cos (c+d x)} \left(3-5 \cos ^2(c+d x)\right) \, dx","Int[Sqrt[Cos[c + d*x]]*(3 - 5*Cos[c + d*x]^2),x]","-\frac{2 \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{d}","-\frac{2 \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{d}",1,"(-2*Cos[c + d*x]^(3/2)*Sin[c + d*x])/d","A",1,1,23,0.04348,1,"{3011}"
25,1,21,0,0.0227313,"\int \frac{1-3 \cos ^2(c+d x)}{\sqrt{\cos (c+d x)}} \, dx","Int[(1 - 3*Cos[c + d*x]^2)/Sqrt[Cos[c + d*x]],x]","-\frac{2 \sin (c+d x) \sqrt{\cos (c+d x)}}{d}","-\frac{2 \sin (c+d x) \sqrt{\cos (c+d x)}}{d}",1,"(-2*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/d","A",1,1,23,0.04348,1,"{3011}"
26,1,115,0,0.1245619,"\int \left(A+C \cos ^2(c+d x)\right) (b \sec (c+d x))^{9/2} \, dx","Int[(A + C*Cos[c + d*x]^2)*(b*Sec[c + d*x])^(9/2),x]","\frac{2 b^3 (5 A+7 C) \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 d}+\frac{2 b^4 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 d}+\frac{2 A b^2 \tan (c+d x) (b \sec (c+d x))^{5/2}}{7 d}","\frac{2 b^3 (5 A+7 C) \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 d}+\frac{2 b^4 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 d}+\frac{2 A b^2 \tan (c+d x) (b \sec (c+d x))^{5/2}}{7 d}",1,"(2*b^4*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*d) + (2*b^3*(5*A + 7*C)*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(21*d) + (2*A*b^2*(b*Sec[c + d*x])^(5/2)*Tan[c + d*x])/(7*d)","A",5,5,25,0.2000,1,"{3238, 4046, 3768, 3771, 2641}"
27,1,115,0,0.1336202,"\int \left(A+C \cos ^2(c+d x)\right) (b \sec (c+d x))^{7/2} \, dx","Int[(A + C*Cos[c + d*x]^2)*(b*Sec[c + d*x])^(7/2),x]","\frac{2 b^3 (3 A+5 C) \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}-\frac{2 b^4 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 A b^2 \tan (c+d x) (b \sec (c+d x))^{3/2}}{5 d}","\frac{2 b^3 (3 A+5 C) \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}-\frac{2 b^4 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 A b^2 \tan (c+d x) (b \sec (c+d x))^{3/2}}{5 d}",1,"(-2*b^4*(3*A + 5*C)*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b^3*(3*A + 5*C)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(5*d) + (2*A*b^2*(b*Sec[c + d*x])^(3/2)*Tan[c + d*x])/(5*d)","A",5,5,25,0.2000,1,"{3238, 4046, 3768, 3771, 2639}"
28,1,78,0,0.0957784,"\int \left(A+C \cos ^2(c+d x)\right) (b \sec (c+d x))^{5/2} \, dx","Int[(A + C*Cos[c + d*x]^2)*(b*Sec[c + d*x])^(5/2),x]","\frac{2 b^2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}+\frac{2 A b^2 \tan (c+d x) \sqrt{b \sec (c+d x)}}{3 d}","\frac{2 b^2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}+\frac{2 A b^2 \tan (c+d x) \sqrt{b \sec (c+d x)}}{3 d}",1,"(2*b^2*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*d) + (2*A*b^2*Sqrt[b*Sec[c + d*x]]*Tan[c + d*x])/(3*d)","A",4,4,25,0.1600,1,"{3238, 4046, 3771, 2641}"
29,1,74,0,0.0964418,"\int \left(A+C \cos ^2(c+d x)\right) (b \sec (c+d x))^{3/2} \, dx","Int[(A + C*Cos[c + d*x]^2)*(b*Sec[c + d*x])^(3/2),x]","\frac{2 A b^2 \tan (c+d x)}{d \sqrt{b \sec (c+d x)}}-\frac{2 b^2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 A b^2 \tan (c+d x)}{d \sqrt{b \sec (c+d x)}}-\frac{2 b^2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(-2*b^2*(A - C)*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*A*b^2*Tan[c + d*x])/(d*Sqrt[b*Sec[c + d*x]])","A",4,4,25,0.1600,1,"{3238, 4046, 3771, 2639}"
30,1,75,0,0.0995225,"\int \left(A+C \cos ^2(c+d x)\right) \sqrt{b \sec (c+d x)} \, dx","Int[(A + C*Cos[c + d*x]^2)*Sqrt[b*Sec[c + d*x]],x]","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}+\frac{2 b^2 C \tan (c+d x)}{3 d (b \sec (c+d x))^{3/2}}","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}+\frac{2 b^2 C \tan (c+d x)}{3 d (b \sec (c+d x))^{3/2}}",1,"(2*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*d) + (2*b^2*C*Tan[c + d*x])/(3*d*(b*Sec[c + d*x])^(3/2))","A",4,4,25,0.1600,1,"{3238, 4045, 3771, 2641}"
31,1,77,0,0.0991752,"\int \frac{A+C \cos ^2(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[(A + C*Cos[c + d*x]^2)/Sqrt[b*Sec[c + d*x]],x]","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 b^2 C \tan (c+d x)}{5 d (b \sec (c+d x))^{5/2}}","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 b^2 C \tan (c+d x)}{5 d (b \sec (c+d x))^{5/2}}",1,"(2*(5*A + 3*C)*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b^2*C*Tan[c + d*x])/(5*d*(b*Sec[c + d*x])^(5/2))","A",4,4,25,0.1600,1,"{3238, 4045, 3771, 2639}"
32,1,115,0,0.1330465,"\int \frac{A+C \cos ^2(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(b*Sec[c + d*x])^(3/2),x]","\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b^2 d}+\frac{2 (7 A+5 C) \sin (c+d x)}{21 b d \sqrt{b \sec (c+d x)}}+\frac{2 b^2 C \tan (c+d x)}{7 d (b \sec (c+d x))^{7/2}}","\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b^2 d}+\frac{2 (7 A+5 C) \sin (c+d x)}{21 b d \sqrt{b \sec (c+d x)}}+\frac{2 b^2 C \tan (c+d x)}{7 d (b \sec (c+d x))^{7/2}}",1,"(2*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*b^2*d) + (2*(7*A + 5*C)*Sin[c + d*x])/(21*b*d*Sqrt[b*Sec[c + d*x]]) + (2*b^2*C*Tan[c + d*x])/(7*d*(b*Sec[c + d*x])^(7/2))","A",5,5,25,0.2000,1,"{3238, 4045, 3769, 3771, 2641}"
33,1,115,0,0.1277481,"\int \frac{A+C \cos ^2(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(b*Sec[c + d*x])^(5/2),x]","\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 (9 A+7 C) \sin (c+d x)}{45 b d (b \sec (c+d x))^{3/2}}+\frac{2 b^2 C \tan (c+d x)}{9 d (b \sec (c+d x))^{9/2}}","\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 (9 A+7 C) \sin (c+d x)}{45 b d (b \sec (c+d x))^{3/2}}+\frac{2 b^2 C \tan (c+d x)}{9 d (b \sec (c+d x))^{9/2}}",1,"(2*(9*A + 7*C)*EllipticE[(c + d*x)/2, 2])/(15*b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*(9*A + 7*C)*Sin[c + d*x])/(45*b*d*(b*Sec[c + d*x])^(3/2)) + (2*b^2*C*Tan[c + d*x])/(9*d*(b*Sec[c + d*x])^(9/2))","A",5,5,25,0.2000,1,"{3238, 4045, 3769, 3771, 2639}"
34,1,117,0,0.0721987,"\int (b \cos (c+d x))^m \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^m*(A + C*Cos[c + d*x]^2),x]","\frac{C \sin (c+d x) (b \cos (c+d x))^{m+1}}{b d (m+2)}-\frac{(A (m+2)+C (m+1)) \sin (c+d x) (b \cos (c+d x))^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(c+d x)\right)}{b d (m+1) (m+2) \sqrt{\sin ^2(c+d x)}}","\frac{C \sin (c+d x) (b \cos (c+d x))^{m+1}}{b d (m+2)}-\frac{(A (m+2)+C (m+1)) \sin (c+d x) (b \cos (c+d x))^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(c+d x)\right)}{b d (m+1) (m+2) \sqrt{\sin ^2(c+d x)}}",1,"(C*(b*Cos[c + d*x])^(1 + m)*Sin[c + d*x])/(b*d*(2 + m)) - ((C*(1 + m) + A*(2 + m))*(b*Cos[c + d*x])^(1 + m)*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(1 + m)*(2 + m)*Sqrt[Sin[c + d*x]^2])","A",2,2,23,0.08696,1,"{3014, 2643}"
35,1,31,0,0.0416858,"\int (b \cos (c+d x))^m \left(-\frac{C (1+m)}{2+m}+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^m*(-((C*(1 + m))/(2 + m)) + C*Cos[c + d*x]^2),x]","\frac{C \sin (c+d x) (b \cos (c+d x))^{m+1}}{b d (m+2)}","\frac{C \sin (c+d x) (b \cos (c+d x))^{m+1}}{b d (m+2)}",1,"(C*(b*Cos[c + d*x])^(1 + m)*Sin[c + d*x])/(b*d*(2 + m))","A",1,1,33,0.03030,1,"{3011}"
36,1,32,0,0.0499524,"\int (b \cos (c+d x))^m \left(A-\frac{A (2+m) \cos ^2(c+d x)}{1+m}\right) \, dx","Int[(b*Cos[c + d*x])^m*(A - (A*(2 + m)*Cos[c + d*x]^2)/(1 + m)),x]","-\frac{A \sin (c+d x) (b \cos (c+d x))^{m+1}}{b d (m+1)}","-\frac{A \sin (c+d x) (b \cos (c+d x))^{m+1}}{b d (m+1)}",1,"-((A*(b*Cos[c + d*x])^(1 + m)*Sin[c + d*x])/(b*d*(1 + m)))","A",1,1,32,0.03125,1,"{3011}"
37,1,112,0,0.0988935,"\int \cos ^2(c+d x) \sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^2*Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2),x]","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^3 d}","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^3 d}",1,"(2*(9*A + 7*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]) + (2*(9*A + 7*C)*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*b*d) + (2*C*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^3*d)","A",5,5,33,0.1515,1,"{16, 3014, 2635, 2640, 2639}"
38,1,110,0,0.0919654,"\int \cos (c+d x) \sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2),x]","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 b (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^2 d}","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 b (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^2 d}",1,"(2*b*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*(7*A + 5*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*C*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^2*d)","A",5,5,31,0.1613,1,"{16, 3014, 2635, 2642, 2641}"
39,1,77,0,0.0554759,"\int \sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2),x]","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b d}","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b d}",1,"(2*(5*A + 3*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*C*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b*d)","A",3,3,25,0.1200,1,"{3014, 2640, 2639}"
40,1,73,0,0.0726957,"\int \sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","\frac{2 b (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}","\frac{2 b (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}",1,"(2*b*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",4,4,31,0.1290,1,"{16, 3014, 2642, 2641}"
41,1,69,0,0.0880731,"\int \sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","\frac{2 A b \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{2 A b \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(-2*(A - C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*A*b*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",4,4,33,0.1212,1,"{16, 3012, 2640, 2639}"
42,1,76,0,0.0892076,"\int \sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{2 A b^2 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}","\frac{2 A b^2 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}",1,"(2*b*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^2*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2))","A",4,4,33,0.1212,1,"{16, 3012, 2642, 2641}"
43,1,110,0,0.1135973,"\int \sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \sec ^4(c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^4,x]","\frac{2 A b^3 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 b (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}","\frac{2 A b^3 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 b (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"(-2*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*A*b^3*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*b*(3*A + 5*C)*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",5,5,33,0.1515,1,"{16, 3012, 2636, 2640, 2639}"
44,1,113,0,0.1136608,"\int \sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \sec ^5(c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^5,x]","\frac{2 b^2 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 A b^4 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 b (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}","\frac{2 b^2 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 A b^4 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 b (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}",1,"(2*b*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^4*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (2*b^2*(5*A + 7*C)*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2))","A",5,5,33,0.1515,1,"{16, 3012, 2636, 2642, 2641}"
45,1,110,0,0.0934267,"\int \cos (c+d x) (b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2),x]","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 d}+\frac{2 b (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^2 d}","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 d}+\frac{2 b (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^2 d}",1,"(2*b*(9*A + 7*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]) + (2*(9*A + 7*C)*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*d) + (2*C*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^2*d)","A",5,5,31,0.1613,1,"{16, 3014, 2635, 2640, 2639}"
46,1,113,0,0.0812235,"\int (b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2),x]","\frac{2 b^2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 b (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b d}","\frac{2 b^2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 b (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b d}",1,"(2*b^2*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*b*(7*A + 5*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*C*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b*d)","A",4,4,25,0.1600,1,"{3014, 2635, 2642, 2641}"
47,1,75,0,0.0800262,"\int (b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","\frac{2 b (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}","\frac{2 b (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}",1,"(2*b*(5*A + 3*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*C*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*d)","A",4,4,31,0.1290,1,"{16, 3014, 2640, 2639}"
48,1,76,0,0.1048689,"\int (b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","\frac{2 b^2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}","\frac{2 b^2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}",1,"(2*b^2*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*b*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",4,4,33,0.1212,1,"{16, 3014, 2642, 2641}"
49,1,72,0,0.0984745,"\int (b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{2 A b^2 \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 b (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{2 A b^2 \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 b (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(-2*b*(A - C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*A*b^2*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",4,4,33,0.1212,1,"{16, 3012, 2640, 2639}"
50,1,78,0,0.0990916,"\int (b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right) \sec ^4(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^4,x]","\frac{2 b^2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^3 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}","\frac{2 b^2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^3 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}",1,"(2*b^2*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^3*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2))","A",4,4,33,0.1212,1,"{16, 3012, 2642, 2641}"
51,1,113,0,0.1269732,"\int (b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right) \sec ^5(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^5,x]","\frac{2 b^2 (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^4 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}-\frac{2 b (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}","\frac{2 b^2 (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^4 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}-\frac{2 b (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"(-2*b*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*A*b^4*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*b^2*(3*A + 5*C)*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",5,5,33,0.1515,1,"{16, 3012, 2636, 2640, 2639}"
52,1,115,0,0.1230823,"\int (b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right) \sec ^6(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^6,x]","\frac{2 b^3 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 b^2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^5 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}","\frac{2 b^3 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 b^2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^5 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}",1,"(2*b^2*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^5*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (2*b^3*(5*A + 7*C)*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2))","A",5,5,33,0.1515,1,"{16, 3012, 2636, 2642, 2641}"
53,1,113,0,0.0804051,"\int (b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2),x]","\frac{2 b^2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{2 b (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b d}","\frac{2 b^2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{2 b (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b d}",1,"(2*b^2*(9*A + 7*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]) + (2*b*(9*A + 7*C)*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*d) + (2*C*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b*d)","A",4,4,25,0.1600,1,"{3014, 2635, 2640, 2639}"
54,1,112,0,0.1085954,"\int (b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","\frac{2 b^2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 b^3 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 d}","\frac{2 b^2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 b^3 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 d}",1,"(2*b^3*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*b^2*(7*A + 5*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*C*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*d)","A",5,5,31,0.1613,1,"{16, 3014, 2635, 2642, 2641}"
55,1,78,0,0.0961418,"\int (b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","\frac{2 b^2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 b C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}","\frac{2 b^2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 b C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}",1,"(2*b^2*(5*A + 3*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b*C*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*d)","A",4,4,33,0.1212,1,"{16, 3014, 2640, 2639}"
56,1,78,0,0.0920315,"\int (b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{2 b^3 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b^2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}","\frac{2 b^3 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b^2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}",1,"(2*b^3*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*b^2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",4,4,33,0.1212,1,"{16, 3014, 2642, 2641}"
57,1,74,0,0.0974184,"\int (b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right) \sec ^4(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^4,x]","\frac{2 A b^3 \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 b^2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{2 A b^3 \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 b^2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(-2*b^2*(A - C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*A*b^3*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",4,4,33,0.1212,1,"{16, 3012, 2640, 2639}"
58,1,78,0,0.0974828,"\int (b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right) \sec ^5(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^5,x]","\frac{2 b^3 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^4 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}","\frac{2 b^3 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^4 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}",1,"(2*b^3*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^4*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2))","A",4,4,33,0.1212,1,"{16, 3012, 2642, 2641}"
59,1,115,0,0.1208563,"\int (b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right) \sec ^6(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^6,x]","\frac{2 b^3 (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{2 b^2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 A b^5 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}","\frac{2 b^3 (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{2 b^2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 A b^5 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}",1,"(-2*b^2*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*A*b^5*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*b^3*(3*A + 5*C)*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",5,5,33,0.1515,1,"{16, 3012, 2636, 2640, 2639}"
60,1,115,0,0.1265892,"\int (b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right) \sec ^7(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^7,x]","\frac{2 b^4 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 b^3 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^6 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}","\frac{2 b^4 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 b^3 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^6 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}",1,"(2*b^3*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^6*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (2*b^4*(5*A + 7*C)*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2))","A",5,5,33,0.1515,1,"{16, 3012, 2636, 2642, 2641}"
61,1,147,0,0.1263365,"\int \frac{\cos ^4(c+d x) \left(A+C \cos ^2(c+d x)\right)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^4*(A + C*Cos[c + d*x]^2))/Sqrt[b*Cos[c + d*x]],x]","\frac{2 (11 A+9 C) \sin (c+d x) (b \cos (c+d x))^{5/2}}{77 b^3 d}+\frac{10 (11 A+9 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{231 b d}+\frac{10 (11 A+9 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{231 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{9/2}}{11 b^5 d}","\frac{2 (11 A+9 C) \sin (c+d x) (b \cos (c+d x))^{5/2}}{77 b^3 d}+\frac{10 (11 A+9 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{231 b d}+\frac{10 (11 A+9 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{231 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{9/2}}{11 b^5 d}",1,"(10*(11*A + 9*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(231*d*Sqrt[b*Cos[c + d*x]]) + (10*(11*A + 9*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(231*b*d) + (2*(11*A + 9*C)*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(77*b^3*d) + (2*C*(b*Cos[c + d*x])^(9/2)*Sin[c + d*x])/(11*b^5*d)","A",6,5,33,0.1515,1,"{16, 3014, 2635, 2642, 2641}"
62,1,115,0,0.0931476,"\int \frac{\cos ^3(c+d x) \left(A+C \cos ^2(c+d x)\right)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^3*(A + C*Cos[c + d*x]^2))/Sqrt[b*Cos[c + d*x]],x]","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^2 d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^4 d}","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^2 d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^4 d}",1,"(2*(9*A + 7*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*b*d*Sqrt[Cos[c + d*x]]) + (2*(9*A + 7*C)*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*b^2*d) + (2*C*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^4*d)","A",5,5,33,0.1515,1,"{16, 3014, 2635, 2640, 2639}"
63,1,112,0,0.0888171,"\int \frac{\cos ^2(c+d x) \left(A+C \cos ^2(c+d x)\right)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^2*(A + C*Cos[c + d*x]^2))/Sqrt[b*Cos[c + d*x]],x]","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b d}+\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^3 d}","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b d}+\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^3 d}",1,"(2*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*(7*A + 5*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*b*d) + (2*C*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^3*d)","A",5,5,33,0.1515,1,"{16, 3014, 2635, 2642, 2641}"
64,1,80,0,0.0630443,"\int \frac{\cos (c+d x) \left(A+C \cos ^2(c+d x)\right)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]*(A + C*Cos[c + d*x]^2))/Sqrt[b*Cos[c + d*x]],x]","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^2 d}","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^2 d}",1,"(2*(5*A + 3*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b*d*Sqrt[Cos[c + d*x]]) + (2*C*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b^2*d)","A",4,4,31,0.1290,1,"{16, 3014, 2640, 2639}"
65,1,75,0,0.0540866,"\int \frac{A+C \cos ^2(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(A + C*Cos[c + d*x]^2)/Sqrt[b*Cos[c + d*x]],x]","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b d}","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b d}",1,"(2*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*b*d)","A",3,3,25,0.1200,1,"{3014, 2642, 2641}"
66,1,71,0,0.0763436,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec (c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x])/Sqrt[b*Cos[c + d*x]],x]","\frac{2 A \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b d \sqrt{\cos (c+d x)}}","\frac{2 A \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b d \sqrt{\cos (c+d x)}}",1,"(-2*(A - C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b*d*Sqrt[Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",4,4,31,0.1290,1,"{16, 3012, 2640, 2639}"
67,1,73,0,0.0893228,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2)/Sqrt[b*Cos[c + d*x]],x]","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 A b \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 A b \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}",1,"(2*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2))","A",4,4,33,0.1212,1,"{16, 3012, 2642, 2641}"
68,1,112,0,0.1124194,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec ^3(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x]^3)/Sqrt[b*Cos[c + d*x]],x]","\frac{2 A b^2 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}","\frac{2 A b^2 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}",1,"(-2*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b*d*Sqrt[Cos[c + d*x]]) + (2*A*b^2*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*(3*A + 5*C)*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",5,5,33,0.1515,1,"{16, 3012, 2636, 2640, 2639}"
69,1,110,0,0.1225423,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec ^4(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x]^4)/Sqrt[b*Cos[c + d*x]],x]","\frac{2 A b^3 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 b (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}","\frac{2 A b^3 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 b (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}",1,"(2*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^3*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (2*b*(5*A + 7*C)*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2))","A",5,5,33,0.1515,1,"{16, 3012, 2636, 2642, 2641}"
70,1,147,0,0.1506537,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec ^5(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x]^5)/Sqrt[b*Cos[c + d*x]],x]","\frac{2 b^2 (7 A+9 C) \sin (c+d x)}{45 d (b \cos (c+d x))^{5/2}}+\frac{2 A b^4 \sin (c+d x)}{9 d (b \cos (c+d x))^{9/2}}+\frac{2 (7 A+9 C) \sin (c+d x)}{15 d \sqrt{b \cos (c+d x)}}-\frac{2 (7 A+9 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b d \sqrt{\cos (c+d x)}}","\frac{2 b^2 (7 A+9 C) \sin (c+d x)}{45 d (b \cos (c+d x))^{5/2}}+\frac{2 A b^4 \sin (c+d x)}{9 d (b \cos (c+d x))^{9/2}}+\frac{2 (7 A+9 C) \sin (c+d x)}{15 d \sqrt{b \cos (c+d x)}}-\frac{2 (7 A+9 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b d \sqrt{\cos (c+d x)}}",1,"(-2*(7*A + 9*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*b*d*Sqrt[Cos[c + d*x]]) + (2*A*b^4*Sin[c + d*x])/(9*d*(b*Cos[c + d*x])^(9/2)) + (2*b^2*(7*A + 9*C)*Sin[c + d*x])/(45*d*(b*Cos[c + d*x])^(5/2)) + (2*(7*A + 9*C)*Sin[c + d*x])/(15*d*Sqrt[b*Cos[c + d*x]])","A",6,5,33,0.1515,1,"{16, 3012, 2636, 2640, 2639}"
71,1,115,0,0.091136,"\int \frac{\cos ^4(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]^4*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^3 d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^5 d}","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^3 d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^5 d}",1,"(2*(9*A + 7*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*b^2*d*Sqrt[Cos[c + d*x]]) + (2*(9*A + 7*C)*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*b^3*d) + (2*C*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^5*d)","A",5,5,33,0.1515,1,"{16, 3014, 2635, 2640, 2639}"
72,1,115,0,0.0882239,"\int \frac{\cos ^3(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]^3*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^2 d}+\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^4 d}","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^2 d}+\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^4 d}",1,"(2*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b*d*Sqrt[b*Cos[c + d*x]]) + (2*(7*A + 5*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*b^2*d) + (2*C*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^4*d)","A",5,5,33,0.1515,1,"{16, 3014, 2635, 2642, 2641}"
73,1,80,0,0.0714687,"\int \frac{\cos ^2(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]^2*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^3 d}","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^3 d}",1,"(2*(5*A + 3*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^2*d*Sqrt[Cos[c + d*x]]) + (2*C*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b^3*d)","A",4,4,33,0.1212,1,"{16, 3014, 2640, 2639}"
74,1,78,0,0.0676145,"\int \frac{\cos (c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^2 d}","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^2 d}",1,"(2*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b*d*Sqrt[b*Cos[c + d*x]]) + (2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*b^2*d)","A",4,4,31,0.1290,1,"{16, 3014, 2642, 2641}"
75,1,74,0,0.0882502,"\int \frac{A+C \cos ^2(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(3/2),x]","\frac{2 A \sin (c+d x)}{b d \sqrt{b \cos (c+d x)}}-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^2 d \sqrt{\cos (c+d x)}}","\frac{2 A \sin (c+d x)}{b d \sqrt{b \cos (c+d x)}}-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^2 d \sqrt{\cos (c+d x)}}",1,"(-2*(A - C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b^2*d*Sqrt[Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(b*d*Sqrt[b*Cos[c + d*x]])","A",3,3,25,0.1200,1,"{3012, 2640, 2639}"
76,1,75,0,0.0844471,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec (c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x])/(b*Cos[c + d*x])^(3/2),x]","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}",1,"(2*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b*d*Sqrt[b*Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2))","A",4,4,31,0.1290,1,"{16, 3012, 2642, 2641}"
77,1,113,0,0.1315592,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2)/(b*Cos[c + d*x])^(3/2),x]","-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 (3 A+5 C) \sin (c+d x)}{5 b d \sqrt{b \cos (c+d x)}}+\frac{2 A b \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}","-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 (3 A+5 C) \sin (c+d x)}{5 b d \sqrt{b \cos (c+d x)}}+\frac{2 A b \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}",1,"(-2*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^2*d*Sqrt[Cos[c + d*x]]) + (2*A*b*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*(3*A + 5*C)*Sin[c + d*x])/(5*b*d*Sqrt[b*Cos[c + d*x]])","A",5,5,33,0.1515,1,"{16, 3012, 2636, 2640, 2639}"
78,1,112,0,0.1478842,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec ^3(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x]^3)/(b*Cos[c + d*x])^(3/2),x]","\frac{2 A b^2 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b d \sqrt{b \cos (c+d x)}}","\frac{2 A b^2 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b d \sqrt{b \cos (c+d x)}}",1,"(2*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^2*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (2*(5*A + 7*C)*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2))","A",5,5,33,0.1515,1,"{16, 3012, 2636, 2642, 2641}"
79,1,115,0,0.1122269,"\int \frac{\cos ^5(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^5*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^4 d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^6 d}","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^4 d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^6 d}",1,"(2*(9*A + 7*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*b^3*d*Sqrt[Cos[c + d*x]]) + (2*(9*A + 7*C)*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*b^4*d) + (2*C*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^6*d)","A",5,5,33,0.1515,1,"{16, 3014, 2635, 2640, 2639}"
80,1,115,0,0.1029947,"\int \frac{\cos ^4(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^4*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^3 d}+\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^5 d}","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^3 d}+\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^5 d}",1,"(2*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*(7*A + 5*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*b^3*d) + (2*C*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^5*d)","A",5,5,33,0.1515,1,"{16, 3014, 2635, 2642, 2641}"
81,1,80,0,0.0703028,"\int \frac{\cos ^3(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^3*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^4 d}","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^4 d}",1,"(2*(5*A + 3*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^3*d*Sqrt[Cos[c + d*x]]) + (2*C*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b^4*d)","A",4,4,33,0.1212,1,"{16, 3014, 2640, 2639}"
82,1,78,0,0.0659925,"\int \frac{\cos ^2(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^2*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^3 d}","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^3 d}",1,"(2*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*b^3*d)","A",4,4,33,0.1212,1,"{16, 3014, 2642, 2641}"
83,1,74,0,0.0706919,"\int \frac{\cos (c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{2 A \sin (c+d x)}{b^2 d \sqrt{b \cos (c+d x)}}-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^3 d \sqrt{\cos (c+d x)}}","\frac{2 A \sin (c+d x)}{b^2 d \sqrt{b \cos (c+d x)}}-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^3 d \sqrt{\cos (c+d x)}}",1,"(-2*(A - C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b^3*d*Sqrt[Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(b^2*d*Sqrt[b*Cos[c + d*x]])","A",4,4,31,0.1290,1,"{16, 3012, 2640, 2639}"
84,1,78,0,0.0660394,"\int \frac{A+C \cos ^2(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{3 b d (b \cos (c+d x))^{3/2}}","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{3 b d (b \cos (c+d x))^{3/2}}",1,"(2*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(3*b*d*(b*Cos[c + d*x])^(3/2))","A",3,3,25,0.1200,1,"{3012, 2642, 2641}"
85,1,112,0,0.107227,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec (c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x])/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (3 A+5 C) \sin (c+d x)}{5 b^2 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}","\frac{2 (3 A+5 C) \sin (c+d x)}{5 b^2 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}",1,"(-2*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^3*d*Sqrt[Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*(3*A + 5*C)*Sin[c + d*x])/(5*b^2*d*Sqrt[b*Cos[c + d*x]])","A",5,5,31,0.1613,1,"{16, 3012, 2636, 2640, 2639}"
86,1,113,0,0.1223829,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2)/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 (5 A+7 C) \sin (c+d x)}{21 b d (b \cos (c+d x))^{3/2}}+\frac{2 A b \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}","\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 (5 A+7 C) \sin (c+d x)}{21 b d (b \cos (c+d x))^{3/2}}+\frac{2 A b \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}",1,"(2*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (2*(5*A + 7*C)*Sin[c + d*x])/(21*b*d*(b*Cos[c + d*x])^(3/2))","A",5,5,33,0.1515,1,"{16, 3012, 2636, 2642, 2641}"
87,1,115,0,0.0917528,"\int \frac{A+C \cos ^2(c+d x)}{(b \cos (c+d x))^{7/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(7/2),x]","\frac{2 (3 A+5 C) \sin (c+d x)}{5 b^3 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^4 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{5 b d (b \cos (c+d x))^{5/2}}","\frac{2 (3 A+5 C) \sin (c+d x)}{5 b^3 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^4 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{5 b d (b \cos (c+d x))^{5/2}}",1,"(-2*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^4*d*Sqrt[Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(5*b*d*(b*Cos[c + d*x])^(5/2)) + (2*(3*A + 5*C)*Sin[c + d*x])/(5*b^3*d*Sqrt[b*Cos[c + d*x]])","A",4,4,25,0.1600,1,"{3012, 2636, 2640, 2639}"
88,1,115,0,0.1164773,"\int \frac{A+C \cos ^2(c+d x)}{(b \cos (c+d x))^{9/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(9/2),x]","\frac{2 (5 A+7 C) \sin (c+d x)}{21 b^3 d (b \cos (c+d x))^{3/2}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^4 d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{7 b d (b \cos (c+d x))^{7/2}}","\frac{2 (5 A+7 C) \sin (c+d x)}{21 b^3 d (b \cos (c+d x))^{3/2}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^4 d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{7 b d (b \cos (c+d x))^{7/2}}",1,"(2*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b^4*d*Sqrt[b*Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(7*b*d*(b*Cos[c + d*x])^(7/2)) + (2*(5*A + 7*C)*Sin[c + d*x])/(21*b^3*d*(b*Cos[c + d*x])^(3/2))","A",4,4,25,0.1600,1,"{3012, 2636, 2642, 2641}"
89,1,116,0,0.0589568,"\int \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2),x]","-\frac{(A+2 C) \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{(A+C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{C \sin ^5(c+d x) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}","-\frac{(A+2 C) \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{(A+C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{C \sin ^5(c+d x) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"((A + C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) - ((A + 2*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Cos[c + d*x]]) + (C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^5)/(5*d*Sqrt[Cos[c + d*x]])","A",4,3,35,0.08571,1,"{17, 3013, 373}"
90,1,113,0,0.072712,"\int \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2),x]","\frac{x (4 A+3 C) \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}+\frac{C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}","\frac{x (4 A+3 C) \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}+\frac{C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}",1,"((4*A + 3*C)*x*Sqrt[b*Cos[c + d*x]])/(8*Sqrt[Cos[c + d*x]]) + ((4*A + 3*C)*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d) + (C*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d)","A",4,4,35,0.1143,1,"{17, 3014, 2635, 8}"
91,1,74,0,0.0375622,"\int \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2),x]","\frac{(A+C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}-\frac{C \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}","\frac{(A+C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}-\frac{C \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}",1,"((A + C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) - (C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Cos[c + d*x]])","A",3,2,35,0.05714,1,"{17, 3013}"
92,1,90,0,0.0231953,"\int \frac{\sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right)}{\sqrt{\cos (c+d x)}} \, dx","Int[(Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2))/Sqrt[Cos[c + d*x]],x]","\frac{A x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{C x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}","\frac{A x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{C x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}",1,"(A*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (C*x*Sqrt[b*Cos[c + d*x]])/(2*Sqrt[Cos[c + d*x]]) + (C*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d)","A",4,3,35,0.08571,1,"{17, 2635, 8}"
93,1,68,0,0.0389626,"\int \frac{\sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Int[(Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(3/2),x]","\frac{A \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{A \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(A*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(d*Sqrt[Cos[c + d*x]]) + (C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]])","A",3,3,35,0.08571,1,"{17, 3014, 3770}"
94,1,59,0,0.0311298,"\int \frac{\sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Int[(Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(5/2),x]","\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}+\frac{C x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}","\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}+\frac{C x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}",1,"(C*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (A*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2))","A",3,3,35,0.08571,1,"{17, 3012, 8}"
95,1,78,0,0.043072,"\int \frac{\sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Int[(Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(7/2),x]","\frac{(A+2 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}+\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}","\frac{(A+2 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}+\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}",1,"((A + 2*C)*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(2*d*Sqrt[Cos[c + d*x]]) + (A*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d*Cos[c + d*x]^(5/2))","A",3,3,35,0.08571,1,"{17, 3012, 3770}"
96,1,79,0,0.0442948,"\int \frac{\sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Int[(Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(9/2),x]","\frac{(2 A+3 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}","\frac{(2 A+3 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}",1,"(A*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Cos[c + d*x]^(7/2)) + ((2*A + 3*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Cos[c + d*x]^(3/2))","A",4,4,35,0.1143,1,"{17, 3012, 3767, 8}"
97,1,122,0,0.0647402,"\int \frac{\sqrt{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{11}{2}}(c+d x)} \, dx","Int[(Sqrt[b*Cos[c + d*x]]*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(11/2),x]","\frac{(3 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{(3 A+4 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}+\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}","\frac{(3 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{(3 A+4 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}+\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}",1,"((3*A + 4*C)*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(8*d*Sqrt[Cos[c + d*x]]) + (A*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d*Cos[c + d*x]^(9/2)) + ((3*A + 4*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d*Cos[c + d*x]^(5/2))","A",4,4,35,0.1143,1,"{17, 3012, 3768, 3770}"
98,1,119,0,0.0575295,"\int \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2),x]","-\frac{b (A+2 C) \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{b (A+C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{b C \sin ^5(c+d x) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}","-\frac{b (A+2 C) \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{b (A+C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{b C \sin ^5(c+d x) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"(b*(A + C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) - (b*(A + 2*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Cos[c + d*x]]) + (b*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^5)/(5*d*Sqrt[Cos[c + d*x]])","A",4,3,35,0.08571,1,"{17, 3013, 373}"
99,1,116,0,0.0566941,"\int \sqrt{\cos (c+d x)} (b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2),x]","\frac{b x (4 A+3 C) \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b (4 A+3 C) \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}+\frac{b C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}","\frac{b x (4 A+3 C) \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b (4 A+3 C) \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}+\frac{b C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}",1,"(b*(4*A + 3*C)*x*Sqrt[b*Cos[c + d*x]])/(8*Sqrt[Cos[c + d*x]]) + (b*(4*A + 3*C)*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d) + (b*C*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d)","A",4,4,35,0.1143,1,"{17, 3014, 2635, 8}"
100,1,76,0,0.0326561,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right)}{\sqrt{\cos (c+d x)}} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2))/Sqrt[Cos[c + d*x]],x]","\frac{b (A+C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}-\frac{b C \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}","\frac{b (A+C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}-\frac{b C \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}",1,"(b*(A + C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) - (b*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Cos[c + d*x]])","A",3,2,35,0.05714,1,"{17, 3013}"
101,1,93,0,0.0304866,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(3/2),x]","\frac{A b x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{b C x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b C \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}","\frac{A b x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{b C x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b C \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}",1,"(A*b*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (b*C*x*Sqrt[b*Cos[c + d*x]])/(2*Sqrt[Cos[c + d*x]]) + (b*C*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d)","A",4,3,35,0.08571,1,"{17, 2635, 8}"
102,1,70,0,0.0328485,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(5/2),x]","\frac{A b \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{b C \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{A b \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{b C \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(A*b*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(d*Sqrt[Cos[c + d*x]]) + (b*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]])","A",3,3,35,0.08571,1,"{17, 3014, 3770}"
103,1,61,0,0.0322901,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(7/2),x]","\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}+\frac{b C x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}","\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}+\frac{b C x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}",1,"(b*C*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (A*b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2))","A",3,3,35,0.08571,1,"{17, 3012, 8}"
104,1,80,0,0.0401435,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(9/2),x]","\frac{b (A+2 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}+\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}","\frac{b (A+2 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}+\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}",1,"(b*(A + 2*C)*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(2*d*Sqrt[Cos[c + d*x]]) + (A*b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d*Cos[c + d*x]^(5/2))","A",3,3,35,0.08571,1,"{17, 3012, 3770}"
105,1,81,0,0.0476186,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{11}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(11/2),x]","\frac{b (2 A+3 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}","\frac{b (2 A+3 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}",1,"(A*b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Cos[c + d*x]^(7/2)) + (b*(2*A + 3*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Cos[c + d*x]^(3/2))","A",4,4,35,0.1143,1,"{17, 3012, 3767, 8}"
106,1,125,0,0.0623372,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{13}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(13/2),x]","\frac{b (3 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b (3 A+4 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}+\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}","\frac{b (3 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b (3 A+4 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}+\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}",1,"(b*(3*A + 4*C)*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(8*d*Sqrt[Cos[c + d*x]]) + (A*b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d*Cos[c + d*x]^(9/2)) + (b*(3*A + 4*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d*Cos[c + d*x]^(5/2))","A",4,4,35,0.1143,1,"{17, 3012, 3768, 3770}"
107,1,125,0,0.0620607,"\int \sqrt{\cos (c+d x)} (b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2),x]","-\frac{b^2 (A+2 C) \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{b^2 (A+C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{b^2 C \sin ^5(c+d x) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}","-\frac{b^2 (A+2 C) \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{b^2 (A+C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{b^2 C \sin ^5(c+d x) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"(b^2*(A + C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) - (b^2*(A + 2*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Cos[c + d*x]]) + (b^2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^5)/(5*d*Sqrt[Cos[c + d*x]])","A",4,3,35,0.08571,1,"{17, 3013, 373}"
108,1,122,0,0.0537611,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right)}{\sqrt{\cos (c+d x)}} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2))/Sqrt[Cos[c + d*x]],x]","\frac{b^2 x (4 A+3 C) \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b^2 (4 A+3 C) \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}+\frac{b^2 C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}","\frac{b^2 x (4 A+3 C) \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b^2 (4 A+3 C) \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}+\frac{b^2 C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}",1,"(b^2*(4*A + 3*C)*x*Sqrt[b*Cos[c + d*x]])/(8*Sqrt[Cos[c + d*x]]) + (b^2*(4*A + 3*C)*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d) + (b^2*C*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d)","A",4,4,35,0.1143,1,"{17, 3014, 2635, 8}"
109,1,80,0,0.0340368,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(3/2),x]","\frac{b^2 (A+C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}-\frac{b^2 C \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}","\frac{b^2 (A+C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}-\frac{b^2 C \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}",1,"(b^2*(A + C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) - (b^2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Cos[c + d*x]])","A",3,2,35,0.05714,1,"{17, 3013}"
110,1,99,0,0.0262921,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(5/2),x]","\frac{A b^2 x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{b^2 C x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b^2 C \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}","\frac{A b^2 x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{b^2 C x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b^2 C \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}",1,"(A*b^2*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (b^2*C*x*Sqrt[b*Cos[c + d*x]])/(2*Sqrt[Cos[c + d*x]]) + (b^2*C*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d)","A",4,3,35,0.08571,1,"{17, 2635, 8}"
111,1,74,0,0.0369129,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(7/2),x]","\frac{A b^2 \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{b^2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{A b^2 \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{b^2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(A*b^2*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(d*Sqrt[Cos[c + d*x]]) + (b^2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]])","A",3,3,35,0.08571,1,"{17, 3014, 3770}"
112,1,65,0,0.0334339,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(9/2),x]","\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}+\frac{b^2 C x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}","\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}+\frac{b^2 C x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}",1,"(b^2*C*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (A*b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2))","A",3,3,35,0.08571,1,"{17, 3012, 8}"
113,1,84,0,0.04534,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{11}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(11/2),x]","\frac{b^2 (A+2 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}+\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}","\frac{b^2 (A+2 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}+\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}",1,"(b^2*(A + 2*C)*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(2*d*Sqrt[Cos[c + d*x]]) + (A*b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d*Cos[c + d*x]^(5/2))","A",3,3,35,0.08571,1,"{17, 3012, 3770}"
114,1,85,0,0.0520294,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{13}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(13/2),x]","\frac{b^2 (2 A+3 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}","\frac{b^2 (2 A+3 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}",1,"(A*b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Cos[c + d*x]^(7/2)) + (b^2*(2*A + 3*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Cos[c + d*x]^(3/2))","A",4,4,35,0.1143,1,"{17, 3012, 3767, 8}"
115,1,131,0,0.0636691,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{15}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(15/2),x]","\frac{b^2 (3 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b^2 (3 A+4 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}+\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}","\frac{b^2 (3 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b^2 (3 A+4 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}+\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}",1,"(b^2*(3*A + 4*C)*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(8*d*Sqrt[Cos[c + d*x]]) + (A*b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d*Cos[c + d*x]^(9/2)) + (b^2*(3*A + 4*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d*Cos[c + d*x]^(5/2))","A",4,4,35,0.1143,1,"{17, 3012, 3768, 3770}"
116,1,113,0,0.0593178,"\int \frac{\cos ^{\frac{5}{2}}(c+d x) \left(A+C \cos ^2(c+d x)\right)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^(5/2)*(A + C*Cos[c + d*x]^2))/Sqrt[b*Cos[c + d*x]],x]","\frac{x (4 A+3 C) \sqrt{\cos (c+d x)}}{8 \sqrt{b \cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 d \sqrt{b \cos (c+d x)}}","\frac{x (4 A+3 C) \sqrt{\cos (c+d x)}}{8 \sqrt{b \cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 d \sqrt{b \cos (c+d x)}}",1,"((4*A + 3*C)*x*Sqrt[Cos[c + d*x]])/(8*Sqrt[b*Cos[c + d*x]]) + ((4*A + 3*C)*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(8*d*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(7/2)*Sin[c + d*x])/(4*d*Sqrt[b*Cos[c + d*x]])","A",4,4,35,0.1143,1,"{17, 3014, 2635, 8}"
117,1,74,0,0.0321965,"\int \frac{\cos ^{\frac{3}{2}}(c+d x) \left(A+C \cos ^2(c+d x)\right)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^(3/2)*(A + C*Cos[c + d*x]^2))/Sqrt[b*Cos[c + d*x]],x]","\frac{(A+C) \sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}-\frac{C \sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 d \sqrt{b \cos (c+d x)}}","\frac{(A+C) \sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}-\frac{C \sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 d \sqrt{b \cos (c+d x)}}",1,"((A + C)*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]]) - (C*Sqrt[Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[b*Cos[c + d*x]])","A",3,2,35,0.05714,1,"{17, 3013}"
118,1,90,0,0.0249023,"\int \frac{\sqrt{\cos (c+d x)} \left(A+C \cos ^2(c+d x)\right)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(Sqrt[Cos[c + d*x]]*(A + C*Cos[c + d*x]^2))/Sqrt[b*Cos[c + d*x]],x]","\frac{A x \sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{2 \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 d \sqrt{b \cos (c+d x)}}","\frac{A x \sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{2 \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 d \sqrt{b \cos (c+d x)}}",1,"(A*x*Sqrt[Cos[c + d*x]])/Sqrt[b*Cos[c + d*x]] + (C*x*Sqrt[Cos[c + d*x]])/(2*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(2*d*Sqrt[b*Cos[c + d*x]])","A",4,3,35,0.08571,1,"{17, 2635, 8}"
119,1,68,0,0.0353761,"\int \frac{A+C \cos ^2(c+d x)}{\sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]),x]","\frac{A \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}","\frac{A \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}",1,"(A*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(d*Sqrt[b*Cos[c + d*x]]) + (C*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",3,3,35,0.08571,1,"{18, 3014, 3770}"
120,1,59,0,0.035275,"\int \frac{A+C \cos ^2(c+d x)}{\cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]),x]","\frac{A \sin (c+d x)}{d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}}","\frac{A \sin (c+d x)}{d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}}",1,"(C*x*Sqrt[Cos[c + d*x]])/Sqrt[b*Cos[c + d*x]] + (A*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",3,3,35,0.08571,1,"{18, 3012, 8}"
121,1,78,0,0.0467411,"\int \frac{A+C \cos ^2(c+d x)}{\cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]),x]","\frac{(A+2 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}","\frac{(A+2 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}",1,"((A + 2*C)*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(2*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(2*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]])","A",3,3,35,0.08571,1,"{18, 3012, 3770}"
122,1,79,0,0.0608861,"\int \frac{A+C \cos ^2(c+d x)}{\cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]),x]","\frac{(2 A+3 C) \sin (c+d x)}{3 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{3 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}","\frac{(2 A+3 C) \sin (c+d x)}{3 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{3 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}",1,"(A*Sin[c + d*x])/(3*d*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]) + ((2*A + 3*C)*Sin[c + d*x])/(3*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",4,4,35,0.1143,1,"{18, 3012, 3767, 8}"
123,1,122,0,0.0701011,"\int \frac{A+C \cos ^2(c+d x)}{\cos ^{\frac{9}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(9/2)*Sqrt[b*Cos[c + d*x]]),x]","\frac{(3 A+4 C) \sin (c+d x)}{8 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{(3 A+4 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{4 d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}","\frac{(3 A+4 C) \sin (c+d x)}{8 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{(3 A+4 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{4 d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}",1,"((3*A + 4*C)*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(8*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(4*d*Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]) + ((3*A + 4*C)*Sin[c + d*x])/(8*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]])","A",4,4,35,0.1143,1,"{18, 3012, 3768, 3770}"
124,1,122,0,0.0592297,"\int \frac{\cos ^{\frac{7}{2}}(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]^(7/2)*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{x (4 A+3 C) \sqrt{\cos (c+d x)}}{8 b \sqrt{b \cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 b d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 b d \sqrt{b \cos (c+d x)}}","\frac{x (4 A+3 C) \sqrt{\cos (c+d x)}}{8 b \sqrt{b \cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 b d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 b d \sqrt{b \cos (c+d x)}}",1,"((4*A + 3*C)*x*Sqrt[Cos[c + d*x]])/(8*b*Sqrt[b*Cos[c + d*x]]) + ((4*A + 3*C)*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(8*b*d*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(7/2)*Sin[c + d*x])/(4*b*d*Sqrt[b*Cos[c + d*x]])","A",4,4,35,0.1143,1,"{17, 3014, 2635, 8}"
125,1,80,0,0.0335879,"\int \frac{\cos ^{\frac{5}{2}}(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]^(5/2)*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{(A+C) \sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}-\frac{C \sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 b d \sqrt{b \cos (c+d x)}}","\frac{(A+C) \sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}-\frac{C \sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 b d \sqrt{b \cos (c+d x)}}",1,"((A + C)*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(b*d*Sqrt[b*Cos[c + d*x]]) - (C*Sqrt[Cos[c + d*x]]*Sin[c + d*x]^3)/(3*b*d*Sqrt[b*Cos[c + d*x]])","A",3,2,35,0.05714,1,"{17, 3013}"
126,1,99,0,0.0283984,"\int \frac{\cos ^{\frac{3}{2}}(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]^(3/2)*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{A x \sqrt{\cos (c+d x)}}{b \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{2 b \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b d \sqrt{b \cos (c+d x)}}","\frac{A x \sqrt{\cos (c+d x)}}{b \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{2 b \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b d \sqrt{b \cos (c+d x)}}",1,"(A*x*Sqrt[Cos[c + d*x]])/(b*Sqrt[b*Cos[c + d*x]]) + (C*x*Sqrt[Cos[c + d*x]])/(2*b*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(2*b*d*Sqrt[b*Cos[c + d*x]])","A",4,3,35,0.08571,1,"{17, 2635, 8}"
127,1,74,0,0.0392348,"\int \frac{\sqrt{\cos (c+d x)} \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Sqrt[Cos[c + d*x]]*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{A \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}","\frac{A \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}",1,"(A*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(b*d*Sqrt[b*Cos[c + d*x]]) + (C*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(b*d*Sqrt[b*Cos[c + d*x]])","A",3,3,35,0.08571,1,"{17, 3014, 3770}"
128,1,65,0,0.0332848,"\int \frac{A+C \cos ^2(c+d x)}{\sqrt{\cos (c+d x)} (b \cos (c+d x))^{3/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(3/2)),x]","\frac{A \sin (c+d x)}{b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{b \sqrt{b \cos (c+d x)}}","\frac{A \sin (c+d x)}{b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{b \sqrt{b \cos (c+d x)}}",1,"(C*x*Sqrt[Cos[c + d*x]])/(b*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",3,3,35,0.08571,1,"{18, 3012, 8}"
129,1,84,0,0.0447938,"\int \frac{A+C \cos ^2(c+d x)}{\cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(3/2)),x]","\frac{(A+2 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{2 b d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}","\frac{(A+2 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{2 b d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}",1,"((A + 2*C)*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(2*b*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(2*b*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]])","A",3,3,35,0.08571,1,"{18, 3012, 3770}"
130,1,85,0,0.0539444,"\int \frac{A+C \cos ^2(c+d x)}{\cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^(3/2)),x]","\frac{(2 A+3 C) \sin (c+d x)}{3 b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{3 b d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}","\frac{(2 A+3 C) \sin (c+d x)}{3 b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{3 b d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}",1,"(A*Sin[c + d*x])/(3*b*d*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]) + ((2*A + 3*C)*Sin[c + d*x])/(3*b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",4,4,35,0.1143,1,"{18, 3012, 3767, 8}"
131,1,131,0,0.0673471,"\int \frac{A+C \cos ^2(c+d x)}{\cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(7/2)*(b*Cos[c + d*x])^(3/2)),x]","\frac{(3 A+4 C) \sin (c+d x)}{8 b d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{(3 A+4 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 b d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{4 b d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}","\frac{(3 A+4 C) \sin (c+d x)}{8 b d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{(3 A+4 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 b d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{4 b d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}",1,"((3*A + 4*C)*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(8*b*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(4*b*d*Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]) + ((3*A + 4*C)*Sin[c + d*x])/(8*b*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]])","A",4,4,35,0.1143,1,"{18, 3012, 3768, 3770}"
132,1,122,0,0.0642664,"\int \frac{\cos ^{\frac{9}{2}}(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^(9/2)*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{x (4 A+3 C) \sqrt{\cos (c+d x)}}{8 b^2 \sqrt{b \cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 b^2 d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 b^2 d \sqrt{b \cos (c+d x)}}","\frac{x (4 A+3 C) \sqrt{\cos (c+d x)}}{8 b^2 \sqrt{b \cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 b^2 d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 b^2 d \sqrt{b \cos (c+d x)}}",1,"((4*A + 3*C)*x*Sqrt[Cos[c + d*x]])/(8*b^2*Sqrt[b*Cos[c + d*x]]) + ((4*A + 3*C)*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(8*b^2*d*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(7/2)*Sin[c + d*x])/(4*b^2*d*Sqrt[b*Cos[c + d*x]])","A",4,4,35,0.1143,1,"{17, 3014, 2635, 8}"
133,1,80,0,0.0328293,"\int \frac{\cos ^{\frac{7}{2}}(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^(7/2)*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{(A+C) \sin (c+d x) \sqrt{\cos (c+d x)}}{b^2 d \sqrt{b \cos (c+d x)}}-\frac{C \sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 b^2 d \sqrt{b \cos (c+d x)}}","\frac{(A+C) \sin (c+d x) \sqrt{\cos (c+d x)}}{b^2 d \sqrt{b \cos (c+d x)}}-\frac{C \sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 b^2 d \sqrt{b \cos (c+d x)}}",1,"((A + C)*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(b^2*d*Sqrt[b*Cos[c + d*x]]) - (C*Sqrt[Cos[c + d*x]]*Sin[c + d*x]^3)/(3*b^2*d*Sqrt[b*Cos[c + d*x]])","A",3,2,35,0.05714,1,"{17, 3013}"
134,1,99,0,0.0268343,"\int \frac{\cos ^{\frac{5}{2}}(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^(5/2)*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{A x \sqrt{\cos (c+d x)}}{b^2 \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{2 b^2 \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b^2 d \sqrt{b \cos (c+d x)}}","\frac{A x \sqrt{\cos (c+d x)}}{b^2 \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{2 b^2 \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b^2 d \sqrt{b \cos (c+d x)}}",1,"(A*x*Sqrt[Cos[c + d*x]])/(b^2*Sqrt[b*Cos[c + d*x]]) + (C*x*Sqrt[Cos[c + d*x]])/(2*b^2*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(2*b^2*d*Sqrt[b*Cos[c + d*x]])","A",4,3,35,0.08571,1,"{17, 2635, 8}"
135,1,74,0,0.0345567,"\int \frac{\cos ^{\frac{3}{2}}(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^(3/2)*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{A \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b^2 d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)}}{b^2 d \sqrt{b \cos (c+d x)}}","\frac{A \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b^2 d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)}}{b^2 d \sqrt{b \cos (c+d x)}}",1,"(A*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(b^2*d*Sqrt[b*Cos[c + d*x]]) + (C*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(b^2*d*Sqrt[b*Cos[c + d*x]])","A",3,3,35,0.08571,1,"{17, 3014, 3770}"
136,1,65,0,0.0326107,"\int \frac{\sqrt{\cos (c+d x)} \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Sqrt[Cos[c + d*x]]*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{A \sin (c+d x)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{b^2 \sqrt{b \cos (c+d x)}}","\frac{A \sin (c+d x)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{b^2 \sqrt{b \cos (c+d x)}}",1,"(C*x*Sqrt[Cos[c + d*x]])/(b^2*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",3,3,35,0.08571,1,"{17, 3012, 8}"
137,1,84,0,0.041872,"\int \frac{A+C \cos ^2(c+d x)}{\sqrt{\cos (c+d x)} (b \cos (c+d x))^{5/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(5/2)),x]","\frac{(A+2 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b^2 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{2 b^2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}","\frac{(A+2 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b^2 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{2 b^2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}",1,"((A + 2*C)*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(2*b^2*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(2*b^2*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]])","A",3,3,35,0.08571,1,"{18, 3012, 3770}"
138,1,85,0,0.0469938,"\int \frac{A+C \cos ^2(c+d x)}{\cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{5/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(5/2)),x]","\frac{(2 A+3 C) \sin (c+d x)}{3 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{3 b^2 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}","\frac{(2 A+3 C) \sin (c+d x)}{3 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{3 b^2 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}",1,"(A*Sin[c + d*x])/(3*b^2*d*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]) + ((2*A + 3*C)*Sin[c + d*x])/(3*b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",4,4,35,0.1143,1,"{18, 3012, 3767, 8}"
139,1,131,0,0.0624157,"\int \frac{A+C \cos ^2(c+d x)}{\cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^{5/2}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^(5/2)),x]","\frac{(3 A+4 C) \sin (c+d x)}{8 b^2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{(3 A+4 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 b^2 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{4 b^2 d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}","\frac{(3 A+4 C) \sin (c+d x)}{8 b^2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{(3 A+4 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 b^2 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{4 b^2 d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}",1,"((3*A + 4*C)*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(8*b^2*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(4*b^2*d*Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]) + ((3*A + 4*C)*Sin[c + d*x])/(8*b^2*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]])","A",4,4,35,0.1143,1,"{18, 3012, 3768, 3770}"
140,1,95,0,0.0709075,"\int \cos ^2(c+d x) \sqrt[3]{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^2*(b*Cos[c + d*x])^(1/3)*(A + C*Cos[c + d*x]^2),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{10/3}}{13 b^3 d}-\frac{3 (13 A+10 C) \sin (c+d x) (b \cos (c+d x))^{10/3} \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{130 b^3 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{10/3}}{13 b^3 d}-\frac{3 (13 A+10 C) \sin (c+d x) (b \cos (c+d x))^{10/3} \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{130 b^3 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(10/3)*Sin[c + d*x])/(13*b^3*d) - (3*(13*A + 10*C)*(b*Cos[c + d*x])^(10/3)*Hypergeometric2F1[1/2, 5/3, 8/3, Cos[c + d*x]^2]*Sin[c + d*x])/(130*b^3*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3014, 2643}"
141,1,95,0,0.0716823,"\int \cos (c+d x) \sqrt[3]{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^(1/3)*(A + C*Cos[c + d*x]^2),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{7/3}}{10 b^2 d}-\frac{3 (10 A+7 C) \sin (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{70 b^2 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{7/3}}{10 b^2 d}-\frac{3 (10 A+7 C) \sin (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{70 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(7/3)*Sin[c + d*x])/(10*b^2*d) - (3*(10*A + 7*C)*(b*Cos[c + d*x])^(7/3)*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[c + d*x]^2]*Sin[c + d*x])/(70*b^2*d*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3014, 2643}"
142,1,95,0,0.0563284,"\int \sqrt[3]{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^(1/3)*(A + C*Cos[c + d*x]^2),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{4/3}}{7 b d}-\frac{3 (7 A+4 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{28 b d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{4/3}}{7 b d}-\frac{3 (7 A+4 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{28 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(4/3)*Sin[c + d*x])/(7*b*d) - (3*(7*A + 4*C)*(b*Cos[c + d*x])^(4/3)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(28*b*d*Sqrt[Sin[c + d*x]^2])","A",2,2,25,0.08000,1,"{3014, 2643}"
143,1,87,0,0.0758734,"\int \sqrt[3]{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^(1/3)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","\frac{3 C \sin (c+d x) \sqrt[3]{b \cos (c+d x)}}{4 d}-\frac{3 (4 A+C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) \sqrt[3]{b \cos (c+d x)}}{4 d}-\frac{3 (4 A+C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(4*d) - (3*(4*A + C)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sin[c + d*x])/(4*d*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3014, 2643}"
144,1,91,0,0.0933749,"\int \sqrt[3]{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^(1/3)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","\frac{3 (A-2 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{8 b d \sqrt{\sin ^2(c+d x)}}+\frac{3 A b \sin (c+d x)}{2 d (b \cos (c+d x))^{2/3}}","\frac{3 (A-2 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{8 b d \sqrt{\sin ^2(c+d x)}}+\frac{3 A b \sin (c+d x)}{2 d (b \cos (c+d x))^{2/3}}",1,"(3*A*b*Sin[c + d*x])/(2*d*(b*Cos[c + d*x])^(2/3)) + (3*(A - 2*C)*(b*Cos[c + d*x])^(4/3)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*b*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3012, 2643}"
145,1,92,0,0.0952027,"\int \sqrt[3]{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(1/3)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{3 A b^2 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/3}}-\frac{3 (2 A+5 C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{5 d \sqrt{\sin ^2(c+d x)}}","\frac{3 A b^2 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/3}}-\frac{3 (2 A+5 C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{5 d \sqrt{\sin ^2(c+d x)}}",1,"(3*A*b^2*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/3)) - (3*(2*A + 5*C)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3012, 2643}"
146,1,95,0,0.0698885,"\int \cos ^2(c+d x) (b \cos (c+d x))^{2/3} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^2*(b*Cos[c + d*x])^(2/3)*(A + C*Cos[c + d*x]^2),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{11/3}}{14 b^3 d}-\frac{3 (14 A+11 C) \sin (c+d x) (b \cos (c+d x))^{11/3} \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{17}{6};\cos ^2(c+d x)\right)}{154 b^3 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{11/3}}{14 b^3 d}-\frac{3 (14 A+11 C) \sin (c+d x) (b \cos (c+d x))^{11/3} \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{17}{6};\cos ^2(c+d x)\right)}{154 b^3 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(11/3)*Sin[c + d*x])/(14*b^3*d) - (3*(14*A + 11*C)*(b*Cos[c + d*x])^(11/3)*Hypergeometric2F1[1/2, 11/6, 17/6, Cos[c + d*x]^2]*Sin[c + d*x])/(154*b^3*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3014, 2643}"
147,1,95,0,0.0700274,"\int \cos (c+d x) (b \cos (c+d x))^{2/3} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^(2/3)*(A + C*Cos[c + d*x]^2),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{8/3}}{11 b^2 d}-\frac{3 (11 A+8 C) \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{88 b^2 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{8/3}}{11 b^2 d}-\frac{3 (11 A+8 C) \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{88 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(8/3)*Sin[c + d*x])/(11*b^2*d) - (3*(11*A + 8*C)*(b*Cos[c + d*x])^(8/3)*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[c + d*x]^2]*Sin[c + d*x])/(88*b^2*d*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3014, 2643}"
148,1,95,0,0.0576242,"\int (b \cos (c+d x))^{2/3} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^(2/3)*(A + C*Cos[c + d*x]^2),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{5/3}}{8 b d}-\frac{3 (8 A+5 C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{40 b d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{5/3}}{8 b d}-\frac{3 (8 A+5 C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{40 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(5/3)*Sin[c + d*x])/(8*b*d) - (3*(8*A + 5*C)*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(40*b*d*Sqrt[Sin[c + d*x]^2])","A",2,2,25,0.08000,1,"{3014, 2643}"
149,1,89,0,0.0905986,"\int (b \cos (c+d x))^{2/3} \left(A+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^(2/3)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3}}{5 d}-\frac{3 (5 A+2 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{10 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3}}{5 d}-\frac{3 (5 A+2 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{10 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*d) - (3*(5*A + 2*C)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(10*d*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3014, 2643}"
150,1,91,0,0.1045745,"\int (b \cos (c+d x))^{2/3} \left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^(2/3)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","\frac{3 (2 A-C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b d \sqrt{\sin ^2(c+d x)}}+\frac{3 A b \sin (c+d x)}{d \sqrt[3]{b \cos (c+d x)}}","\frac{3 (2 A-C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b d \sqrt{\sin ^2(c+d x)}}+\frac{3 A b \sin (c+d x)}{d \sqrt[3]{b \cos (c+d x)}}",1,"(3*A*b*Sin[c + d*x])/(d*(b*Cos[c + d*x])^(1/3)) + (3*(2*A - C)*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*b*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3012, 2643}"
151,1,90,0,0.1004009,"\int (b \cos (c+d x))^{2/3} \left(A+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(2/3)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{3 A b^2 \sin (c+d x)}{4 d (b \cos (c+d x))^{4/3}}-\frac{3 (A+4 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{8 d \sqrt{\sin ^2(c+d x)}}","\frac{3 A b^2 \sin (c+d x)}{4 d (b \cos (c+d x))^{4/3}}-\frac{3 (A+4 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{8 d \sqrt{\sin ^2(c+d x)}}",1,"(3*A*b^2*Sin[c + d*x])/(4*d*(b*Cos[c + d*x])^(4/3)) - (3*(A + 4*C)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3012, 2643}"
152,1,95,0,0.0701794,"\int \cos ^2(c+d x) (b \cos (c+d x))^{4/3} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^2*(b*Cos[c + d*x])^(4/3)*(A + C*Cos[c + d*x]^2),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{13/3}}{16 b^3 d}-\frac{3 (16 A+13 C) \sin (c+d x) (b \cos (c+d x))^{13/3} \, _2F_1\left(\frac{1}{2},\frac{13}{6};\frac{19}{6};\cos ^2(c+d x)\right)}{208 b^3 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{13/3}}{16 b^3 d}-\frac{3 (16 A+13 C) \sin (c+d x) (b \cos (c+d x))^{13/3} \, _2F_1\left(\frac{1}{2},\frac{13}{6};\frac{19}{6};\cos ^2(c+d x)\right)}{208 b^3 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(13/3)*Sin[c + d*x])/(16*b^3*d) - (3*(16*A + 13*C)*(b*Cos[c + d*x])^(13/3)*Hypergeometric2F1[1/2, 13/6, 19/6, Cos[c + d*x]^2]*Sin[c + d*x])/(208*b^3*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3014, 2643}"
153,1,95,0,0.0696035,"\int \cos (c+d x) (b \cos (c+d x))^{4/3} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^(4/3)*(A + C*Cos[c + d*x]^2),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{10/3}}{13 b^2 d}-\frac{3 (13 A+10 C) \sin (c+d x) (b \cos (c+d x))^{10/3} \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{130 b^2 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{10/3}}{13 b^2 d}-\frac{3 (13 A+10 C) \sin (c+d x) (b \cos (c+d x))^{10/3} \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{130 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(10/3)*Sin[c + d*x])/(13*b^2*d) - (3*(13*A + 10*C)*(b*Cos[c + d*x])^(10/3)*Hypergeometric2F1[1/2, 5/3, 8/3, Cos[c + d*x]^2]*Sin[c + d*x])/(130*b^2*d*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3014, 2643}"
154,1,95,0,0.0591191,"\int (b \cos (c+d x))^{4/3} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^(4/3)*(A + C*Cos[c + d*x]^2),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{7/3}}{10 b d}-\frac{3 (10 A+7 C) \sin (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{70 b d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{7/3}}{10 b d}-\frac{3 (10 A+7 C) \sin (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{70 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(7/3)*Sin[c + d*x])/(10*b*d) - (3*(10*A + 7*C)*(b*Cos[c + d*x])^(7/3)*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[c + d*x]^2]*Sin[c + d*x])/(70*b*d*Sqrt[Sin[c + d*x]^2])","A",2,2,25,0.08000,1,"{3014, 2643}"
155,1,89,0,0.0751851,"\int (b \cos (c+d x))^{4/3} \left(A+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^(4/3)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{4/3}}{7 d}-\frac{3 (7 A+4 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{28 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{4/3}}{7 d}-\frac{3 (7 A+4 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{28 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(4/3)*Sin[c + d*x])/(7*d) - (3*(7*A + 4*C)*(b*Cos[c + d*x])^(4/3)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(28*d*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3014, 2643}"
156,1,89,0,0.0949197,"\int (b \cos (c+d x))^{4/3} \left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^(4/3)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","\frac{3 b C \sin (c+d x) \sqrt[3]{b \cos (c+d x)}}{4 d}-\frac{3 b (4 A+C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)}}","\frac{3 b C \sin (c+d x) \sqrt[3]{b \cos (c+d x)}}{4 d}-\frac{3 b (4 A+C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)}}",1,"(3*b*C*(b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(4*d) - (3*b*(4*A + C)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sin[c + d*x])/(4*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3014, 2643}"
157,1,90,0,0.0978578,"\int (b \cos (c+d x))^{4/3} \left(A+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(4/3)*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{3 A b^2 \sin (c+d x)}{2 d (b \cos (c+d x))^{2/3}}+\frac{3 (A-2 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{8 d \sqrt{\sin ^2(c+d x)}}","\frac{3 A b^2 \sin (c+d x)}{2 d (b \cos (c+d x))^{2/3}}+\frac{3 (A-2 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{8 d \sqrt{\sin ^2(c+d x)}}",1,"(3*A*b^2*Sin[c + d*x])/(2*d*(b*Cos[c + d*x])^(2/3)) + (3*(A - 2*C)*(b*Cos[c + d*x])^(4/3)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3012, 2643}"
158,1,95,0,0.068204,"\int \frac{\cos ^2(c+d x) \left(A+C \cos ^2(c+d x)\right)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^2*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(1/3),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{8/3}}{11 b^3 d}-\frac{3 (11 A+8 C) \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{88 b^3 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{8/3}}{11 b^3 d}-\frac{3 (11 A+8 C) \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{88 b^3 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(8/3)*Sin[c + d*x])/(11*b^3*d) - (3*(11*A + 8*C)*(b*Cos[c + d*x])^(8/3)*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[c + d*x]^2]*Sin[c + d*x])/(88*b^3*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3014, 2643}"
159,1,95,0,0.0674989,"\int \frac{\cos (c+d x) \left(A+C \cos ^2(c+d x)\right)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(1/3),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{5/3}}{8 b^2 d}-\frac{3 (8 A+5 C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{40 b^2 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{5/3}}{8 b^2 d}-\frac{3 (8 A+5 C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{40 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(5/3)*Sin[c + d*x])/(8*b^2*d) - (3*(8*A + 5*C)*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(40*b^2*d*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3014, 2643}"
160,1,95,0,0.0547281,"\int \frac{A+C \cos ^2(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(1/3),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3}}{5 b d}-\frac{3 (5 A+2 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{10 b d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3}}{5 b d}-\frac{3 (5 A+2 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{10 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*b*d) - (3*(5*A + 2*C)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(10*b*d*Sqrt[Sin[c + d*x]^2])","A",2,2,25,0.08000,1,"{3014, 2643}"
161,1,90,0,0.0770518,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec (c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x])/(b*Cos[c + d*x])^(1/3),x]","\frac{3 (2 A-C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 A \sin (c+d x)}{d \sqrt[3]{b \cos (c+d x)}}","\frac{3 (2 A-C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 A \sin (c+d x)}{d \sqrt[3]{b \cos (c+d x)}}",1,"(3*A*Sin[c + d*x])/(d*(b*Cos[c + d*x])^(1/3)) + (3*(2*A - C)*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*b^2*d*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3012, 2643}"
162,1,91,0,0.0920171,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2)/(b*Cos[c + d*x])^(1/3),x]","\frac{3 A b \sin (c+d x)}{4 d (b \cos (c+d x))^{4/3}}-\frac{3 (A+4 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{8 b d \sqrt{\sin ^2(c+d x)}}","\frac{3 A b \sin (c+d x)}{4 d (b \cos (c+d x))^{4/3}}-\frac{3 (A+4 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{8 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*A*b*Sin[c + d*x])/(4*d*(b*Cos[c + d*x])^(4/3)) - (3*(A + 4*C)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*b*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3012, 2643}"
163,1,92,0,0.0972061,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec ^3(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x]^3)/(b*Cos[c + d*x])^(1/3),x]","\frac{3 A b^2 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/3}}+\frac{3 (4 A+7 C) \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}","\frac{3 A b^2 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/3}}+\frac{3 (4 A+7 C) \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}",1,"(3*A*b^2*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/3)) + (3*(4*A + 7*C)*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3012, 2643}"
164,1,95,0,0.0684882,"\int \frac{\cos ^2(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{2/3}} \, dx","Int[(Cos[c + d*x]^2*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(2/3),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{7/3}}{10 b^3 d}-\frac{3 (10 A+7 C) \sin (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{70 b^3 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{7/3}}{10 b^3 d}-\frac{3 (10 A+7 C) \sin (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{70 b^3 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(7/3)*Sin[c + d*x])/(10*b^3*d) - (3*(10*A + 7*C)*(b*Cos[c + d*x])^(7/3)*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[c + d*x]^2]*Sin[c + d*x])/(70*b^3*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3014, 2643}"
165,1,95,0,0.0640115,"\int \frac{\cos (c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{2/3}} \, dx","Int[(Cos[c + d*x]*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(2/3),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{4/3}}{7 b^2 d}-\frac{3 (7 A+4 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{28 b^2 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{4/3}}{7 b^2 d}-\frac{3 (7 A+4 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{28 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(4/3)*Sin[c + d*x])/(7*b^2*d) - (3*(7*A + 4*C)*(b*Cos[c + d*x])^(4/3)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(28*b^2*d*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3014, 2643}"
166,1,93,0,0.0614186,"\int \frac{A+C \cos ^2(c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(2/3),x]","\frac{3 C \sin (c+d x) \sqrt[3]{b \cos (c+d x)}}{4 b d}-\frac{3 (4 A+C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{4 b d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) \sqrt[3]{b \cos (c+d x)}}{4 b d}-\frac{3 (4 A+C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{4 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(4*b*d) - (3*(4*A + C)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sin[c + d*x])/(4*b*d*Sqrt[Sin[c + d*x]^2])","A",2,2,25,0.08000,1,"{3014, 2643}"
167,1,90,0,0.0813656,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec (c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x])/(b*Cos[c + d*x])^(2/3),x]","\frac{3 (A-2 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{8 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 A \sin (c+d x)}{2 d (b \cos (c+d x))^{2/3}}","\frac{3 (A-2 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{8 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 A \sin (c+d x)}{2 d (b \cos (c+d x))^{2/3}}",1,"(3*A*Sin[c + d*x])/(2*d*(b*Cos[c + d*x])^(2/3)) + (3*(A - 2*C)*(b*Cos[c + d*x])^(4/3)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*b^2*d*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3012, 2643}"
168,1,93,0,0.1013855,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2)/(b*Cos[c + d*x])^(2/3),x]","\frac{3 A b \sin (c+d x)}{5 d (b \cos (c+d x))^{5/3}}-\frac{3 (2 A+5 C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{5 b d \sqrt{\sin ^2(c+d x)}}","\frac{3 A b \sin (c+d x)}{5 d (b \cos (c+d x))^{5/3}}-\frac{3 (2 A+5 C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{5 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*A*b*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/3)) - (3*(2*A + 5*C)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*b*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3012, 2643}"
169,1,92,0,0.1006135,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec ^3(c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x]^3)/(b*Cos[c + d*x])^(2/3),x]","\frac{3 A b^2 \sin (c+d x)}{8 d (b \cos (c+d x))^{8/3}}+\frac{3 (5 A+8 C) \sin (c+d x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\cos ^2(c+d x)\right)}{16 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}","\frac{3 A b^2 \sin (c+d x)}{8 d (b \cos (c+d x))^{8/3}}+\frac{3 (5 A+8 C) \sin (c+d x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\cos ^2(c+d x)\right)}{16 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}",1,"(3*A*b^2*Sin[c + d*x])/(8*d*(b*Cos[c + d*x])^(8/3)) + (3*(5*A + 8*C)*Hypergeometric2F1[-1/3, 1/2, 2/3, Cos[c + d*x]^2]*Sin[c + d*x])/(16*d*(b*Cos[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3012, 2643}"
170,1,95,0,0.0668854,"\int \frac{\cos ^2(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{4/3}} \, dx","Int[(Cos[c + d*x]^2*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(4/3),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{5/3}}{8 b^3 d}-\frac{3 (8 A+5 C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{40 b^3 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{5/3}}{8 b^3 d}-\frac{3 (8 A+5 C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{40 b^3 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(5/3)*Sin[c + d*x])/(8*b^3*d) - (3*(8*A + 5*C)*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(40*b^3*d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3014, 2643}"
171,1,95,0,0.0658111,"\int \frac{\cos (c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{4/3}} \, dx","Int[(Cos[c + d*x]*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(4/3),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3}}{5 b^2 d}-\frac{3 (5 A+2 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{10 b^2 d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3}}{5 b^2 d}-\frac{3 (5 A+2 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{10 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(3*C*(b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*b^2*d) - (3*(5*A + 2*C)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(10*b^2*d*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3014, 2643}"
172,1,93,0,0.062424,"\int \frac{A+C \cos ^2(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(4/3),x]","\frac{3 (2 A-C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^3 d \sqrt{\sin ^2(c+d x)}}+\frac{3 A \sin (c+d x)}{b d \sqrt[3]{b \cos (c+d x)}}","\frac{3 (2 A-C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^3 d \sqrt{\sin ^2(c+d x)}}+\frac{3 A \sin (c+d x)}{b d \sqrt[3]{b \cos (c+d x)}}",1,"(3*A*Sin[c + d*x])/(b*d*(b*Cos[c + d*x])^(1/3)) + (3*(2*A - C)*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*b^3*d*Sqrt[Sin[c + d*x]^2])","A",2,2,25,0.08000,1,"{3012, 2643}"
173,1,90,0,0.0814465,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec (c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x])/(b*Cos[c + d*x])^(4/3),x]","\frac{3 A \sin (c+d x)}{4 d (b \cos (c+d x))^{4/3}}-\frac{3 (A+4 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{8 b^2 d \sqrt{\sin ^2(c+d x)}}","\frac{3 A \sin (c+d x)}{4 d (b \cos (c+d x))^{4/3}}-\frac{3 (A+4 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{8 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(3*A*Sin[c + d*x])/(4*d*(b*Cos[c + d*x])^(4/3)) - (3*(A + 4*C)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*b^2*d*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3012, 2643}"
174,1,93,0,0.1001245,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2)/(b*Cos[c + d*x])^(4/3),x]","\frac{3 (4 A+7 C) \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{7 b d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}+\frac{3 A b \sin (c+d x)}{7 d (b \cos (c+d x))^{7/3}}","\frac{3 (4 A+7 C) \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{7 b d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}+\frac{3 A b \sin (c+d x)}{7 d (b \cos (c+d x))^{7/3}}",1,"(3*A*b*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/3)) + (3*(4*A + 7*C)*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sin[c + d*x])/(7*b*d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3012, 2643}"
175,1,92,0,0.1049648,"\int \frac{\left(A+C \cos ^2(c+d x)\right) \sec ^3(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Int[((A + C*Cos[c + d*x]^2)*Sec[c + d*x]^3)/(b*Cos[c + d*x])^(4/3),x]","\frac{3 A b^2 \sin (c+d x)}{10 d (b \cos (c+d x))^{10/3}}+\frac{3 (7 A+10 C) \sin (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{40 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{4/3}}","\frac{3 A b^2 \sin (c+d x)}{10 d (b \cos (c+d x))^{10/3}}+\frac{3 (7 A+10 C) \sin (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{40 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{4/3}}",1,"(3*A*b^2*Sin[c + d*x])/(10*d*(b*Cos[c + d*x])^(10/3)) + (3*(7*A + 10*C)*Hypergeometric2F1[-2/3, 1/2, 1/3, Cos[c + d*x]^2]*Sin[c + d*x])/(40*d*(b*Cos[c + d*x])^(4/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{16, 3012, 2643}"
176,1,138,0,0.113143,"\int \cos ^m(c+d x) (b \cos (c+d x))^{4/3} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^m*(b*Cos[c + d*x])^(4/3)*(A + C*Cos[c + d*x]^2),x]","\frac{3 b C \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+2}(c+d x)}{d (3 m+10)}-\frac{3 b \left(\frac{A}{3 m+7}+\frac{C}{3 m+10}\right) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+7);\frac{1}{6} (3 m+13);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}","\frac{3 b C \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+2}(c+d x)}{d (3 m+10)}-\frac{3 b (A (3 m+10)+C (3 m+7)) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+7);\frac{1}{6} (3 m+13);\cos ^2(c+d x)\right)}{d (3 m+7) (3 m+10) \sqrt{\sin ^2(c+d x)}}",1,"(3*b*C*Cos[c + d*x]^(2 + m)*(b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(d*(10 + 3*m)) - (3*b*(A/(7 + 3*m) + C/(10 + 3*m))*Cos[c + d*x]^(2 + m)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/2, (7 + 3*m)/6, (13 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
177,1,136,0,0.1165042,"\int \cos ^m(c+d x) (b \cos (c+d x))^{2/3} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^m*(b*Cos[c + d*x])^(2/3)*(A + C*Cos[c + d*x]^2),x]","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+1}(c+d x)}{d (3 m+8)}-\frac{3 \left(\frac{A}{3 m+5}+\frac{C}{3 m+8}\right) \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+5);\frac{1}{6} (3 m+11);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+1}(c+d x)}{d (3 m+8)}-\frac{3 (A (3 m+8)+C (3 m+5)) \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+5);\frac{1}{6} (3 m+11);\cos ^2(c+d x)\right)}{d (3 m+5) (3 m+8) \sqrt{\sin ^2(c+d x)}}",1,"(3*C*Cos[c + d*x]^(1 + m)*(b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(d*(8 + 3*m)) - (3*(A/(5 + 3*m) + C/(8 + 3*m))*Cos[c + d*x]^(1 + m)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/2, (5 + 3*m)/6, (11 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
178,1,136,0,0.1080957,"\int \cos ^m(c+d x) \sqrt[3]{b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^m*(b*Cos[c + d*x])^(1/3)*(A + C*Cos[c + d*x]^2),x]","\frac{3 C \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+1}(c+d x)}{d (3 m+7)}-\frac{3 \left(\frac{A}{3 m+4}+\frac{C}{3 m+7}\right) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+4);\frac{1}{6} (3 m+10);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}","\frac{3 C \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+1}(c+d x)}{d (3 m+7)}-\frac{3 (A (3 m+7)+C (3 m+4)) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+4);\frac{1}{6} (3 m+10);\cos ^2(c+d x)\right)}{d (3 m+4) (3 m+7) \sqrt{\sin ^2(c+d x)}}",1,"(3*C*Cos[c + d*x]^(1 + m)*(b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(d*(7 + 3*m)) - (3*(A/(4 + 3*m) + C/(7 + 3*m))*Cos[c + d*x]^(1 + m)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/2, (4 + 3*m)/6, (10 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
179,1,136,0,0.1052816,"\int \frac{\cos ^m(c+d x) \left(A+C \cos ^2(c+d x)\right)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^m*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(1/3),x]","\frac{3 C \sin (c+d x) \cos ^{m+1}(c+d x)}{d (3 m+5) \sqrt[3]{b \cos (c+d x)}}-\frac{3 \left(\frac{A}{3 m+2}+\frac{C}{3 m+5}\right) \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+2);\frac{1}{6} (3 m+8);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}","\frac{3 C \sin (c+d x) \cos ^{m+1}(c+d x)}{d (3 m+5) \sqrt[3]{b \cos (c+d x)}}-\frac{3 (A (3 m+5)+C (3 m+2)) \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+2);\frac{1}{6} (3 m+8);\cos ^2(c+d x)\right)}{d (3 m+2) (3 m+5) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}",1,"(3*C*Cos[c + d*x]^(1 + m)*Sin[c + d*x])/(d*(5 + 3*m)*(b*Cos[c + d*x])^(1/3)) - (3*(A/(2 + 3*m) + C/(5 + 3*m))*Cos[c + d*x]^(1 + m)*Hypergeometric2F1[1/2, (2 + 3*m)/6, (8 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
180,1,144,0,0.1039995,"\int \frac{\cos ^m(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{2/3}} \, dx","Int[(Cos[c + d*x]^m*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(2/3),x]","\frac{3 C \sin (c+d x) \cos ^{m+1}(c+d x)}{d (3 m+4) (b \cos (c+d x))^{2/3}}-\frac{3 (A (3 m+4)+3 C m+C) \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+1);\frac{1}{6} (3 m+7);\cos ^2(c+d x)\right)}{d (3 m+1) (3 m+4) \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}","\frac{3 C \sin (c+d x) \cos ^{m+1}(c+d x)}{d (3 m+4) (b \cos (c+d x))^{2/3}}-\frac{3 (A (3 m+4)+3 C m+C) \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+1);\frac{1}{6} (3 m+7);\cos ^2(c+d x)\right)}{d (3 m+1) (3 m+4) \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}",1,"(3*C*Cos[c + d*x]^(1 + m)*Sin[c + d*x])/(d*(4 + 3*m)*(b*Cos[c + d*x])^(2/3)) - (3*(C + 3*C*m + A*(4 + 3*m))*Cos[c + d*x]^(1 + m)*Hypergeometric2F1[1/2, (1 + 3*m)/6, (7 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 + 3*m)*(4 + 3*m)*(b*Cos[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
181,1,139,0,0.122399,"\int \frac{\cos ^m(c+d x) \left(A+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{4/3}} \, dx","Int[(Cos[c + d*x]^m*(A + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(4/3),x]","\frac{3 \left(\frac{A}{1-3 m}-\frac{C}{3 m+2}\right) \sin (c+d x) \cos ^m(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m-1);\frac{1}{6} (3 m+5);\cos ^2(c+d x)\right)}{b d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}+\frac{3 C \sin (c+d x) \cos ^m(c+d x)}{b d (3 m+2) \sqrt[3]{b \cos (c+d x)}}","\frac{3 C \sin (c+d x) \cos ^m(c+d x)}{b d (3 m+2) \sqrt[3]{b \cos (c+d x)}}-\frac{3 (C (1-3 m)-A (3 m+2)) \sin (c+d x) \cos ^m(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m-1);\frac{1}{6} (3 m+5);\cos ^2(c+d x)\right)}{b d (1-3 m) (3 m+2) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}",1,"(3*C*Cos[c + d*x]^m*Sin[c + d*x])/(b*d*(2 + 3*m)*(b*Cos[c + d*x])^(1/3)) + (3*(A/(1 - 3*m) - C/(2 + 3*m))*Cos[c + d*x]^m*Hypergeometric2F1[1/2, (-1 + 3*m)/6, (5 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
182,1,144,0,0.1116336,"\int (a \cos (c+d x))^m (b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(a*Cos[c + d*x])^m*(b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2),x]","\frac{C \sin (c+d x) (a \cos (c+d x))^{m+1} (b \cos (c+d x))^n}{a d (m+n+2)}-\frac{(A (m+n+2)+C (m+n+1)) \sin (c+d x) (a \cos (c+d x))^{m+1} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);\cos ^2(c+d x)\right)}{a d (m+n+1) (m+n+2) \sqrt{\sin ^2(c+d x)}}","\frac{C \sin (c+d x) (a \cos (c+d x))^{m+1} (b \cos (c+d x))^n}{a d (m+n+2)}-\frac{(A (m+n+2)+C (m+n+1)) \sin (c+d x) (a \cos (c+d x))^{m+1} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);\cos ^2(c+d x)\right)}{a d (m+n+1) (m+n+2) \sqrt{\sin ^2(c+d x)}}",1,"(C*(a*Cos[c + d*x])^(1 + m)*(b*Cos[c + d*x])^n*Sin[c + d*x])/(a*d*(2 + m + n)) - ((C*(1 + m + n) + A*(2 + m + n))*(a*Cos[c + d*x])^(1 + m)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (1 + m + n)/2, (3 + m + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(a*d*(1 + m + n)*(2 + m + n)*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
183,1,117,0,0.1051946,"\int \cos ^2(c+d x) (b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^2*(b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2),x]","\frac{C \sin (c+d x) (b \cos (c+d x))^{n+3}}{b^3 d (n+4)}-\frac{(A (n+4)+C (n+3)) \sin (c+d x) (b \cos (c+d x))^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{n+5}{2};\cos ^2(c+d x)\right)}{b^3 d (n+3) (n+4) \sqrt{\sin ^2(c+d x)}}","\frac{C \sin (c+d x) (b \cos (c+d x))^{n+3}}{b^3 d (n+4)}-\frac{(A (n+4)+C (n+3)) \sin (c+d x) (b \cos (c+d x))^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{n+5}{2};\cos ^2(c+d x)\right)}{b^3 d (n+3) (n+4) \sqrt{\sin ^2(c+d x)}}",1,"(C*(b*Cos[c + d*x])^(3 + n)*Sin[c + d*x])/(b^3*d*(4 + n)) - ((C*(3 + n) + A*(4 + n))*(b*Cos[c + d*x])^(3 + n)*Hypergeometric2F1[1/2, (3 + n)/2, (5 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^3*d*(3 + n)*(4 + n)*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3014, 2643}"
184,1,117,0,0.1029899,"\int \cos (c+d x) (b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2),x]","\frac{C \sin (c+d x) (b \cos (c+d x))^{n+2}}{b^2 d (n+3)}-\frac{(A (n+3)+C (n+2)) \sin (c+d x) (b \cos (c+d x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\cos ^2(c+d x)\right)}{b^2 d (n+2) (n+3) \sqrt{\sin ^2(c+d x)}}","\frac{C \sin (c+d x) (b \cos (c+d x))^{n+2}}{b^2 d (n+3)}-\frac{(A (n+3)+C (n+2)) \sin (c+d x) (b \cos (c+d x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\cos ^2(c+d x)\right)}{b^2 d (n+2) (n+3) \sqrt{\sin ^2(c+d x)}}",1,"(C*(b*Cos[c + d*x])^(2 + n)*Sin[c + d*x])/(b^2*d*(3 + n)) - ((C*(2 + n) + A*(3 + n))*(b*Cos[c + d*x])^(2 + n)*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^2*d*(2 + n)*(3 + n)*Sqrt[Sin[c + d*x]^2])","A",3,3,29,0.1034,1,"{16, 3014, 2643}"
185,1,117,0,0.0717034,"\int (b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2),x]","\frac{C \sin (c+d x) (b \cos (c+d x))^{n+1}}{b d (n+2)}-\frac{(A (n+2)+C (n+1)) \sin (c+d x) (b \cos (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(c+d x)\right)}{b d (n+1) (n+2) \sqrt{\sin ^2(c+d x)}}","\frac{C \sin (c+d x) (b \cos (c+d x))^{n+1}}{b d (n+2)}-\frac{(A (n+2)+C (n+1)) \sin (c+d x) (b \cos (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(c+d x)\right)}{b d (n+1) (n+2) \sqrt{\sin ^2(c+d x)}}",1,"(C*(b*Cos[c + d*x])^(1 + n)*Sin[c + d*x])/(b*d*(2 + n)) - ((C*(1 + n) + A*(2 + n))*(b*Cos[c + d*x])^(1 + n)*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(1 + n)*(2 + n)*Sqrt[Sin[c + d*x]^2])","A",2,2,23,0.08696,1,"{3014, 2643}"
186,1,100,0,0.0943137,"\int (b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","\frac{C \sin (c+d x) (b \cos (c+d x))^n}{d (n+1)}-\frac{(A n+A+C n) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\cos ^2(c+d x)\right)}{d n (n+1) \sqrt{\sin ^2(c+d x)}}","\frac{C \sin (c+d x) (b \cos (c+d x))^n}{d (n+1)}-\frac{(A n+A+C n) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\cos ^2(c+d x)\right)}{d n (n+1) \sqrt{\sin ^2(c+d x)}}",1,"(C*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(1 + n)) - ((A + A*n + C*n)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, n/2, (2 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*n*(1 + n)*Sqrt[Sin[c + d*x]^2])","A",3,3,29,0.1034,1,"{16, 3014, 2643}"
187,1,112,0,0.118526,"\int (b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","\frac{b C \sin (c+d x) (b \cos (c+d x))^{n-1}}{d n}-\frac{b (C (1-n)-A n) \sin (c+d x) (b \cos (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n-1}{2};\frac{n+1}{2};\cos ^2(c+d x)\right)}{d (1-n) n \sqrt{\sin ^2(c+d x)}}","\frac{b C \sin (c+d x) (b \cos (c+d x))^{n-1}}{d n}-\frac{b (C (1-n)-A n) \sin (c+d x) (b \cos (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n-1}{2};\frac{n+1}{2};\cos ^2(c+d x)\right)}{d (1-n) n \sqrt{\sin ^2(c+d x)}}",1,"(b*C*(b*Cos[c + d*x])^(-1 + n)*Sin[c + d*x])/(d*n) - (b*(C*(1 - n) - A*n)*(b*Cos[c + d*x])^(-1 + n)*Hypergeometric2F1[1/2, (-1 + n)/2, (1 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - n)*n*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3014, 2643}"
188,1,125,0,0.1324403,"\int (b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{b^2 (A (1-n)+C (2-n)) \sin (c+d x) (b \cos (c+d x))^{n-2} \, _2F_1\left(\frac{1}{2},\frac{n-2}{2};\frac{n}{2};\cos ^2(c+d x)\right)}{d (1-n) (2-n) \sqrt{\sin ^2(c+d x)}}-\frac{b^2 C \sin (c+d x) (b \cos (c+d x))^{n-2}}{d (1-n)}","\frac{b^2 (A (1-n)+C (2-n)) \sin (c+d x) (b \cos (c+d x))^{n-2} \, _2F_1\left(\frac{1}{2},\frac{n-2}{2};\frac{n}{2};\cos ^2(c+d x)\right)}{d (1-n) (2-n) \sqrt{\sin ^2(c+d x)}}-\frac{b^2 C \sin (c+d x) (b \cos (c+d x))^{n-2}}{d (1-n)}",1,"-((b^2*C*(b*Cos[c + d*x])^(-2 + n)*Sin[c + d*x])/(d*(1 - n))) + (b^2*(A*(1 - n) + C*(2 - n))*(b*Cos[c + d*x])^(-2 + n)*Hypergeometric2F1[1/2, (-2 + n)/2, n/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - n)*(2 - n)*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3014, 2643}"
189,1,127,0,0.1256024,"\int (b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right) \sec ^4(c+d x) \, dx","Int[(b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2)*Sec[c + d*x]^4,x]","\frac{b^3 (A (2-n)+C (3-n)) \sin (c+d x) (b \cos (c+d x))^{n-3} \, _2F_1\left(\frac{1}{2},\frac{n-3}{2};\frac{n-1}{2};\cos ^2(c+d x)\right)}{d (2-n) (3-n) \sqrt{\sin ^2(c+d x)}}-\frac{b^3 C \sin (c+d x) (b \cos (c+d x))^{n-3}}{d (2-n)}","\frac{b^3 (A (2-n)+C (3-n)) \sin (c+d x) (b \cos (c+d x))^{n-3} \, _2F_1\left(\frac{1}{2},\frac{n-3}{2};\frac{n-1}{2};\cos ^2(c+d x)\right)}{d (2-n) (3-n) \sqrt{\sin ^2(c+d x)}}-\frac{b^3 C \sin (c+d x) (b \cos (c+d x))^{n-3}}{d (2-n)}",1,"-((b^3*C*(b*Cos[c + d*x])^(-3 + n)*Sin[c + d*x])/(d*(2 - n))) + (b^3*(A*(2 - n) + C*(3 - n))*(b*Cos[c + d*x])^(-3 + n)*Hypergeometric2F1[1/2, (-3 + n)/2, (-1 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(2 - n)*(3 - n)*Sqrt[Sin[c + d*x]^2])","A",3,3,31,0.09677,1,"{16, 3014, 2643}"
190,1,132,0,0.1120713,"\int \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2),x]","\frac{2 C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^n}{d (2 n+9)}-\frac{2 \left(\frac{A}{2 n+7}+\frac{C}{2 n+9}\right) \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+7);\frac{1}{4} (2 n+11);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}","\frac{2 C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^n}{d (2 n+9)}-\frac{2 (A (2 n+9)+C (2 n+7)) \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+7);\frac{1}{4} (2 n+11);\cos ^2(c+d x)\right)}{d (2 n+7) (2 n+9) \sqrt{\sin ^2(c+d x)}}",1,"(2*C*Cos[c + d*x]^(7/2)*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(9 + 2*n)) - (2*(A/(7 + 2*n) + C/(9 + 2*n))*Cos[c + d*x]^(7/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (7 + 2*n)/4, (11 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
191,1,132,0,0.1102449,"\int \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2),x]","\frac{2 C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n}{d (2 n+7)}-\frac{2 \left(\frac{A}{2 n+5}+\frac{C}{2 n+7}\right) \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+5);\frac{1}{4} (2 n+9);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}","\frac{2 C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n}{d (2 n+7)}-\frac{2 (A (2 n+7)+C (2 n+5)) \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+5);\frac{1}{4} (2 n+9);\cos ^2(c+d x)\right)}{d (2 n+5) (2 n+7) \sqrt{\sin ^2(c+d x)}}",1,"(2*C*Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(7 + 2*n)) - (2*(A/(5 + 2*n) + C/(7 + 2*n))*Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (5 + 2*n)/4, (9 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
192,1,132,0,0.1057829,"\int \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right) \, dx","Int[Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2),x]","\frac{2 C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n}{d (2 n+5)}-\frac{2 \left(\frac{A}{2 n+3}+\frac{C}{2 n+5}\right) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}","\frac{2 C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n}{d (2 n+5)}-\frac{2 (A (2 n+5)+C (2 n+3)) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\cos ^2(c+d x)\right)}{d (2 n+3) (2 n+5) \sqrt{\sin ^2(c+d x)}}",1,"(2*C*Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(5 + 2*n)) - (2*(A/(3 + 2*n) + C/(5 + 2*n))*Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (3 + 2*n)/4, (7 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
193,1,140,0,0.1019328,"\int \frac{(b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right)}{\sqrt{\cos (c+d x)}} \, dx","Int[((b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2))/Sqrt[Cos[c + d*x]],x]","\frac{2 C \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n}{d (2 n+3)}-\frac{2 (A (2 n+3)+2 C n+C) \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\cos ^2(c+d x)\right)}{d (2 n+1) (2 n+3) \sqrt{\sin ^2(c+d x)}}","\frac{2 C \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n}{d (2 n+3)}-\frac{2 (A (2 n+3)+2 C n+C) \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\cos ^2(c+d x)\right)}{d (2 n+1) (2 n+3) \sqrt{\sin ^2(c+d x)}}",1,"(2*C*Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(3 + 2*n)) - (2*(C + 2*C*n + A*(3 + 2*n))*Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (1 + 2*n)/4, (5 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 + 2*n)*(3 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
194,1,136,0,0.099564,"\int \frac{(b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(3/2),x]","\frac{2 (2 A n+A-C (1-2 n)) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-1);\frac{1}{4} (2 n+3);\cos ^2(c+d x)\right)}{d \left(1-4 n^2\right) \sqrt{\sin ^2(c+d x)} \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (2 n+1) \sqrt{\cos (c+d x)}}","\frac{2 (2 A n+A-C (1-2 n)) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-1);\frac{1}{4} (2 n+3);\cos ^2(c+d x)\right)}{d \left(1-4 n^2\right) \sqrt{\sin ^2(c+d x)} \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (2 n+1) \sqrt{\cos (c+d x)}}",1,"(2*C*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(1 + 2*n)*Sqrt[Cos[c + d*x]]) + (2*(A - C*(1 - 2*n) + 2*A*n)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-1 + 2*n)/4, (3 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - 4*n^2)*Sqrt[Cos[c + d*x]]*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
195,1,132,0,0.1129087,"\int \frac{(b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(5/2),x]","\frac{2 \left(\frac{A}{3-2 n}+\frac{C}{1-2 n}\right) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-3);\frac{1}{4} (2 n+1);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \cos ^{\frac{3}{2}}(c+d x)}-\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (1-2 n) \cos ^{\frac{3}{2}}(c+d x)}","\frac{2 (-2 A n+A+C (3-2 n)) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-3);\frac{1}{4} (2 n+1);\cos ^2(c+d x)\right)}{d (1-2 n) (3-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{3}{2}}(c+d x)}-\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (1-2 n) \cos ^{\frac{3}{2}}(c+d x)}",1,"(-2*C*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(1 - 2*n)*Cos[c + d*x]^(3/2)) + (2*(C/(1 - 2*n) + A/(3 - 2*n))*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-3 + 2*n)/4, (1 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2)*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
196,1,132,0,0.1153208,"\int \frac{(b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(7/2),x]","\frac{2 \left(\frac{A}{5-2 n}+\frac{C}{3-2 n}\right) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-5);\frac{1}{4} (2 n-1);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \cos ^{\frac{5}{2}}(c+d x)}-\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (3-2 n) \cos ^{\frac{5}{2}}(c+d x)}","\frac{2 (A (3-2 n)+C (5-2 n)) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-5);\frac{1}{4} (2 n-1);\cos ^2(c+d x)\right)}{d (3-2 n) (5-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{5}{2}}(c+d x)}-\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (3-2 n) \cos ^{\frac{5}{2}}(c+d x)}",1,"(-2*C*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(3 - 2*n)*Cos[c + d*x]^(5/2)) + (2*(C/(3 - 2*n) + A/(5 - 2*n))*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-5 + 2*n)/4, (-1 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Cos[c + d*x]^(5/2)*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
197,1,132,0,0.1128235,"\int \frac{(b \cos (c+d x))^n \left(A+C \cos ^2(c+d x)\right)}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^n*(A + C*Cos[c + d*x]^2))/Cos[c + d*x]^(9/2),x]","\frac{2 \left(\frac{A}{7-2 n}+\frac{C}{5-2 n}\right) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-7);\frac{1}{4} (2 n-3);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \cos ^{\frac{7}{2}}(c+d x)}-\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (5-2 n) \cos ^{\frac{7}{2}}(c+d x)}","\frac{2 (A (5-2 n)+C (7-2 n)) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-7);\frac{1}{4} (2 n-3);\cos ^2(c+d x)\right)}{d (5-2 n) (7-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{7}{2}}(c+d x)}-\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (5-2 n) \cos ^{\frac{7}{2}}(c+d x)}",1,"(-2*C*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(5 - 2*n)*Cos[c + d*x]^(7/2)) + (2*(C/(5 - 2*n) + A/(7 - 2*n))*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-7 + 2*n)/4, (-3 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Cos[c + d*x]^(7/2)*Sqrt[Sin[c + d*x]^2])","A",3,3,33,0.09091,1,"{20, 3014, 2643}"
198,1,170,0,0.2086519,"\int (a+a \cos (e+f x))^m \left(A+C \cos ^2(e+f x)\right) \, dx","Int[(a + a*Cos[e + f*x])^m*(A + C*Cos[e + f*x]^2),x]","\frac{2^{m+\frac{1}{2}} \left(A \left(m^2+3 m+2\right)+C \left(m^2+m+1\right)\right) \sin (e+f x) (\cos (e+f x)+1)^{-m-\frac{1}{2}} (a \cos (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x))\right)}{f (m+1) (m+2)}-\frac{C \sin (e+f x) (a \cos (e+f x)+a)^m}{f \left(m^2+3 m+2\right)}+\frac{C \sin (e+f x) (a \cos (e+f x)+a)^{m+1}}{a f (m+2)}","\frac{2^{m+\frac{1}{2}} \left(A \left(m^2+3 m+2\right)+C \left(m^2+m+1\right)\right) \sin (e+f x) (\cos (e+f x)+1)^{-m-\frac{1}{2}} (a \cos (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x))\right)}{f (m+1) (m+2)}-\frac{C \sin (e+f x) (a \cos (e+f x)+a)^m}{f \left(m^2+3 m+2\right)}+\frac{C \sin (e+f x) (a \cos (e+f x)+a)^{m+1}}{a f (m+2)}",1,"-((C*(a + a*Cos[e + f*x])^m*Sin[e + f*x])/(f*(2 + 3*m + m^2))) + (C*(a + a*Cos[e + f*x])^(1 + m)*Sin[e + f*x])/(a*f*(2 + m)) + (2^(1/2 + m)*(C*(1 + m + m^2) + A*(2 + 3*m + m^2))*(1 + Cos[e + f*x])^(-1/2 - m)*(a + a*Cos[e + f*x])^m*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (1 - Cos[e + f*x])/2]*Sin[e + f*x])/(f*(1 + m)*(2 + m))","A",4,4,25,0.1600,1,"{3024, 2751, 2652, 2651}"
199,1,135,0,0.1676836,"\int (a+a \cos (c+d x))^{2/3} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(a + a*Cos[c + d*x])^(2/3)*(A + C*Cos[c + d*x]^2),x]","\frac{(40 A+19 C) \sin (c+d x) (a \cos (c+d x)+a)^{2/3} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{10\ 2^{5/6} d (\cos (c+d x)+1)^{7/6}}+\frac{3 C \sin (c+d x) (a \cos (c+d x)+a)^{5/3}}{8 a d}-\frac{9 C \sin (c+d x) (a \cos (c+d x)+a)^{2/3}}{40 d}","\frac{(40 A+19 C) \sin (c+d x) (a \cos (c+d x)+a)^{2/3} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{10\ 2^{5/6} d (\cos (c+d x)+1)^{7/6}}+\frac{3 C \sin (c+d x) (a \cos (c+d x)+a)^{5/3}}{8 a d}-\frac{9 C \sin (c+d x) (a \cos (c+d x)+a)^{2/3}}{40 d}",1,"(-9*C*(a + a*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(40*d) + (3*C*(a + a*Cos[c + d*x])^(5/3)*Sin[c + d*x])/(8*a*d) + ((40*A + 19*C)*(a + a*Cos[c + d*x])^(2/3)*Hypergeometric2F1[-1/6, 1/2, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(10*2^(5/6)*d*(1 + Cos[c + d*x])^(7/6))","A",4,4,27,0.1481,1,"{3024, 2751, 2652, 2651}"
200,1,135,0,0.1607877,"\int \sqrt[3]{a+a \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(a + a*Cos[c + d*x])^(1/3)*(A + C*Cos[c + d*x]^2),x]","\frac{(28 A+13 C) \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{14 \sqrt[6]{2} d (\cos (c+d x)+1)^{5/6}}+\frac{3 C \sin (c+d x) (a \cos (c+d x)+a)^{4/3}}{7 a d}-\frac{9 C \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a}}{28 d}","\frac{(28 A+13 C) \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{14 \sqrt[6]{2} d (\cos (c+d x)+1)^{5/6}}+\frac{3 C \sin (c+d x) (a \cos (c+d x)+a)^{4/3}}{7 a d}-\frac{9 C \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a}}{28 d}",1,"(-9*C*(a + a*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(28*d) + (3*C*(a + a*Cos[c + d*x])^(4/3)*Sin[c + d*x])/(7*a*d) + ((28*A + 13*C)*(a + a*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(14*2^(1/6)*d*(1 + Cos[c + d*x])^(5/6))","A",4,4,27,0.1481,1,"{3024, 2751, 2652, 2651}"
201,1,135,0,0.1609799,"\int \frac{A+C \cos ^2(c+d x)}{\sqrt[3]{a+a \cos (c+d x)}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(a + a*Cos[c + d*x])^(1/3),x]","\frac{(10 A+7 C) \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{5\ 2^{5/6} d \sqrt[6]{\cos (c+d x)+1} \sqrt[3]{a \cos (c+d x)+a}}+\frac{3 C \sin (c+d x) (a \cos (c+d x)+a)^{2/3}}{5 a d}-\frac{9 C \sin (c+d x)}{10 d \sqrt[3]{a \cos (c+d x)+a}}","\frac{(10 A+7 C) \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{5\ 2^{5/6} d \sqrt[6]{\cos (c+d x)+1} \sqrt[3]{a \cos (c+d x)+a}}+\frac{3 C \sin (c+d x) (a \cos (c+d x)+a)^{2/3}}{5 a d}-\frac{9 C \sin (c+d x)}{10 d \sqrt[3]{a \cos (c+d x)+a}}",1,"(-9*C*Sin[c + d*x])/(10*d*(a + a*Cos[c + d*x])^(1/3)) + (3*C*(a + a*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*a*d) + ((10*A + 7*C)*Hypergeometric2F1[1/2, 5/6, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(5*2^(5/6)*d*(1 + Cos[c + d*x])^(1/6)*(a + a*Cos[c + d*x])^(1/3))","A",4,4,27,0.1481,1,"{3024, 2751, 2652, 2651}"
202,1,138,0,0.1765936,"\int \frac{A+C \cos ^2(c+d x)}{(a+a \cos (c+d x))^{2/3}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(a + a*Cos[c + d*x])^(2/3),x]","-\frac{(4 A+7 C) \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{2 \sqrt[6]{2} a d (\cos (c+d x)+1)^{5/6}}+\frac{3 (A+C) \sin (c+d x)}{d (a \cos (c+d x)+a)^{2/3}}+\frac{3 C \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a}}{4 a d}","-\frac{(4 A+7 C) \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{2 \sqrt[6]{2} a d (\cos (c+d x)+1)^{5/6}}+\frac{3 (A+C) \sin (c+d x)}{d (a \cos (c+d x)+a)^{2/3}}+\frac{3 C \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a}}{4 a d}",1,"(3*(A + C)*Sin[c + d*x])/(d*(a + a*Cos[c + d*x])^(2/3)) + (3*C*(a + a*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(4*a*d) - ((4*A + 7*C)*(a + a*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(2*2^(1/6)*a*d*(1 + Cos[c + d*x])^(5/6))","A",4,4,27,0.1481,1,"{3024, 2750, 2652, 2651}"
203,1,277,0,0.3560949,"\int (a+b \cos (c+d x))^{2/3} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(a + b*Cos[c + d*x])^(2/3)*(A + C*Cos[c + d*x]^2),x]","\frac{\left(3 a^2 C+b^2 (8 A+5 C)\right) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{4 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}-\frac{3 a C (a+b) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{5}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{4 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{5/3}}{8 b d}","\frac{\left(3 a^2 C+b^2 (8 A+5 C)\right) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{4 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}-\frac{3 a C (a+b) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{5}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{4 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{5/3}}{8 b d}",1,"(3*C*(a + b*Cos[c + d*x])^(5/3)*Sin[c + d*x])/(8*b*d) - (3*a*(a + b)*C*AppellF1[1/2, 1/2, -5/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(4*Sqrt[2]*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(2/3)) + ((3*a^2*C + b^2*(8*A + 5*C))*AppellF1[1/2, 1/2, -2/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(4*Sqrt[2]*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(2/3))","A",8,5,27,0.1852,1,"{3024, 2756, 2665, 139, 138}"
204,1,277,0,0.3110466,"\int \sqrt[3]{a+b \cos (c+d x)} \left(A+C \cos ^2(c+d x)\right) \, dx","Int[(a + b*Cos[c + d*x])^(1/3)*(A + C*Cos[c + d*x]^2),x]","\frac{\sqrt{2} \left(3 a^2 C+b^2 (7 A+4 C)\right) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{7 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}-\frac{3 \sqrt{2} a C (a+b) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{7 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{4/3}}{7 b d}","\frac{\sqrt{2} \left(3 a^2 C+b^2 (7 A+4 C)\right) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{7 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}-\frac{3 \sqrt{2} a C (a+b) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{7 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{4/3}}{7 b d}",1,"(3*C*(a + b*Cos[c + d*x])^(4/3)*Sin[c + d*x])/(7*b*d) - (3*Sqrt[2]*a*(a + b)*C*AppellF1[1/2, 1/2, -4/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(7*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(1/3)) + (Sqrt[2]*(3*a^2*C + b^2*(7*A + 4*C))*AppellF1[1/2, 1/2, -1/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(7*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(1/3))","A",8,5,27,0.1852,1,"{3024, 2756, 2665, 139, 138}"
205,1,274,0,0.3097366,"\int \frac{A+C \cos ^2(c+d x)}{\sqrt[3]{a+b \cos (c+d x)}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(a + b*Cos[c + d*x])^(1/3),x]","\frac{\sqrt{2} \left(3 a^2 C+b^2 (5 A+2 C)\right) \sin (c+d x) \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{5 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{a+b \cos (c+d x)}}-\frac{3 \sqrt{2} a C \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{5 b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{2/3}}{5 b d}","\frac{\sqrt{2} \left(3 a^2 C+b^2 (5 A+2 C)\right) \sin (c+d x) \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{5 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{a+b \cos (c+d x)}}-\frac{3 \sqrt{2} a C \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{5 b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{2/3}}{5 b d}",1,"(3*C*(a + b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*b*d) - (3*Sqrt[2]*a*C*AppellF1[1/2, 1/2, -2/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(2/3)) + (Sqrt[2]*(3*a^2*C + b^2*(5*A + 2*C))*AppellF1[1/2, 1/2, 1/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*((a + b*Cos[c + d*x])/(a + b))^(1/3)*Sin[c + d*x])/(5*b^2*d*Sqrt[1 + Cos[c + d*x]]*(a + b*Cos[c + d*x])^(1/3))","A",8,5,27,0.1852,1,"{3024, 2756, 2665, 139, 138}"
206,1,272,0,0.3140452,"\int \frac{A+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^{2/3}} \, dx","Int[(A + C*Cos[c + d*x]^2)/(a + b*Cos[c + d*x])^(2/3),x]","\frac{\left(3 a^2 C+b^2 (4 A+C)\right) \sin (c+d x) \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{2 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} (a+b \cos (c+d x))^{2/3}}-\frac{3 a C \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{2 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{3 C \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)}}{4 b d}","\frac{\left(3 a^2 C+b^2 (4 A+C)\right) \sin (c+d x) \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{2 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} (a+b \cos (c+d x))^{2/3}}-\frac{3 a C \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{2 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{3 C \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)}}{4 b d}",1,"(3*C*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(4*b*d) - (3*a*C*AppellF1[1/2, 1/2, -1/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(2*Sqrt[2]*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(1/3)) + ((3*a^2*C + b^2*(4*A + C))*AppellF1[1/2, 1/2, 2/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*((a + b*Cos[c + d*x])/(a + b))^(2/3)*Sin[c + d*x])/(2*Sqrt[2]*b^2*d*Sqrt[1 + Cos[c + d*x]]*(a + b*Cos[c + d*x])^(2/3))","A",8,5,27,0.1852,1,"{3024, 2756, 2665, 139, 138}"
207,1,211,0,0.2509046,"\int (a+b \cos (e+f x))^m \left(A-A \cos ^2(e+f x)\right) \, dx","Int[(a + b*Cos[e + f*x])^m*(A - A*Cos[e + f*x]^2),x]","\frac{4 \sqrt{2} A \sin (e+f x) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{f \sqrt{\cos (e+f x)+1}}-\frac{4 \sqrt{2} A \sin (e+f x) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{3}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{f \sqrt{\cos (e+f x)+1}}","\frac{4 \sqrt{2} A \sin (e+f x) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{f \sqrt{\cos (e+f x)+1}}-\frac{4 \sqrt{2} A \sin (e+f x) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{3}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{f \sqrt{\cos (e+f x)+1}}",1,"(-4*Sqrt[2]*A*AppellF1[1/2, -3/2, -m, 3/2, (1 - Cos[e + f*x])/2, (b*(1 - Cos[e + f*x]))/(a + b)]*(a + b*Cos[e + f*x])^m*Sin[e + f*x])/(f*Sqrt[1 + Cos[e + f*x]]*((a + b*Cos[e + f*x])/(a + b))^m) + (4*Sqrt[2]*A*AppellF1[1/2, -1/2, -m, 3/2, (1 - Cos[e + f*x])/2, (b*(1 - Cos[e + f*x]))/(a + b)]*(a + b*Cos[e + f*x])^m*Sin[e + f*x])/(f*Sqrt[1 + Cos[e + f*x]]*((a + b*Cos[e + f*x])/(a + b))^m)","A",7,5,26,0.1923,1,"{3018, 2755, 139, 138, 2784}"
208,1,285,0,0.342942,"\int (a+b \cos (e+f x))^m \left(A+C \cos ^2(e+f x)\right) \, dx","Int[(a + b*Cos[e + f*x])^m*(A + C*Cos[e + f*x]^2),x]","\frac{\sqrt{2} \sin (e+f x) \left(a^2 C+b^2 (A (m+2)+C (m+1))\right) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\cos (e+f x)+1}}-\frac{\sqrt{2} a C (a+b) \sin (e+f x) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m-1;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\cos (e+f x)+1}}+\frac{C \sin (e+f x) (a+b \cos (e+f x))^{m+1}}{b f (m+2)}","\frac{\sqrt{2} \sin (e+f x) \left(a^2 C+b^2 (A (m+2)+C (m+1))\right) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\cos (e+f x)+1}}-\frac{\sqrt{2} a C (a+b) \sin (e+f x) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m-1;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\cos (e+f x)+1}}+\frac{C \sin (e+f x) (a+b \cos (e+f x))^{m+1}}{b f (m+2)}",1,"(C*(a + b*Cos[e + f*x])^(1 + m)*Sin[e + f*x])/(b*f*(2 + m)) - (Sqrt[2]*a*(a + b)*C*AppellF1[1/2, 1/2, -1 - m, 3/2, (1 - Cos[e + f*x])/2, (b*(1 - Cos[e + f*x]))/(a + b)]*(a + b*Cos[e + f*x])^m*Sin[e + f*x])/(b^2*f*(2 + m)*Sqrt[1 + Cos[e + f*x]]*((a + b*Cos[e + f*x])/(a + b))^m) + (Sqrt[2]*(a^2*C + b^2*(C*(1 + m) + A*(2 + m)))*AppellF1[1/2, 1/2, -m, 3/2, (1 - Cos[e + f*x])/2, (b*(1 - Cos[e + f*x]))/(a + b)]*(a + b*Cos[e + f*x])^m*Sin[e + f*x])/(b^2*f*(2 + m)*Sqrt[1 + Cos[e + f*x]]*((a + b*Cos[e + f*x])/(a + b))^m)","A",8,5,25,0.2000,1,"{3024, 2756, 2665, 139, 138}"
209,1,141,0,0.1351096,"\int (a \cos (e+f x))^m \left(B \cos (e+f x)+C \cos ^2(e+f x)\right) \, dx","Int[(a*Cos[e + f*x])^m*(B*Cos[e + f*x] + C*Cos[e + f*x]^2),x]","-\frac{B \sin (e+f x) (a \cos (e+f x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};\cos ^2(e+f x)\right)}{a^2 f (m+2) \sqrt{\sin ^2(e+f x)}}-\frac{C \sin (e+f x) (a \cos (e+f x))^{m+3} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};\cos ^2(e+f x)\right)}{a^3 f (m+3) \sqrt{\sin ^2(e+f x)}}","-\frac{B \sin (e+f x) (a \cos (e+f x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};\cos ^2(e+f x)\right)}{a^2 f (m+2) \sqrt{\sin ^2(e+f x)}}-\frac{C \sin (e+f x) (a \cos (e+f x))^{m+3} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};\cos ^2(e+f x)\right)}{a^3 f (m+3) \sqrt{\sin ^2(e+f x)}}",1,"-((B*(a*Cos[e + f*x])^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, Cos[e + f*x]^2]*Sin[e + f*x])/(a^2*f*(2 + m)*Sqrt[Sin[e + f*x]^2])) - (C*(a*Cos[e + f*x])^(3 + m)*Hypergeometric2F1[1/2, (3 + m)/2, (5 + m)/2, Cos[e + f*x]^2]*Sin[e + f*x])/(a^3*f*(3 + m)*Sqrt[Sin[e + f*x]^2])","A",4,3,30,0.1000,1,"{3010, 2748, 2643}"
210,1,167,0,0.1284598,"\int \cos ^m(c+d x) \sqrt[3]{b \cos (c+d x)} \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^m*(b*Cos[c + d*x])^(1/3)*(B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{3 B \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+7);\frac{1}{6} (3 m+13);\cos ^2(c+d x)\right)}{d (3 m+7) \sqrt{\sin ^2(c+d x)}}-\frac{3 C \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+3}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+10);\frac{1}{6} (3 m+16);\cos ^2(c+d x)\right)}{d (3 m+10) \sqrt{\sin ^2(c+d x)}}","-\frac{3 B \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+7);\frac{1}{6} (3 m+13);\cos ^2(c+d x)\right)}{d (3 m+7) \sqrt{\sin ^2(c+d x)}}-\frac{3 C \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+3}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+10);\frac{1}{6} (3 m+16);\cos ^2(c+d x)\right)}{d (3 m+10) \sqrt{\sin ^2(c+d x)}}",1,"(-3*B*Cos[c + d*x]^(2 + m)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/2, (7 + 3*m)/6, (13 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(7 + 3*m)*Sqrt[Sin[c + d*x]^2]) - (3*C*Cos[c + d*x]^(3 + m)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/2, (10 + 3*m)/6, (16 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(10 + 3*m)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
211,1,167,0,0.1322045,"\int \cos ^m(c+d x) (b \cos (c+d x))^{2/3} \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^m*(b*Cos[c + d*x])^(2/3)*(B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+8);\frac{1}{6} (3 m+14);\cos ^2(c+d x)\right)}{d (3 m+8) \sqrt{\sin ^2(c+d x)}}-\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+3}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+11);\frac{1}{6} (3 m+17);\cos ^2(c+d x)\right)}{d (3 m+11) \sqrt{\sin ^2(c+d x)}}","-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+8);\frac{1}{6} (3 m+14);\cos ^2(c+d x)\right)}{d (3 m+8) \sqrt{\sin ^2(c+d x)}}-\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+3}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+11);\frac{1}{6} (3 m+17);\cos ^2(c+d x)\right)}{d (3 m+11) \sqrt{\sin ^2(c+d x)}}",1,"(-3*B*Cos[c + d*x]^(2 + m)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/2, (8 + 3*m)/6, (14 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(8 + 3*m)*Sqrt[Sin[c + d*x]^2]) - (3*C*Cos[c + d*x]^(3 + m)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/2, (11 + 3*m)/6, (17 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(11 + 3*m)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
212,1,169,0,0.1329923,"\int \cos ^m(c+d x) (b \cos (c+d x))^{4/3} \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^m*(b*Cos[c + d*x])^(4/3)*(B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{3 b B \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+3}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+10);\frac{1}{6} (3 m+16);\cos ^2(c+d x)\right)}{d (3 m+10) \sqrt{\sin ^2(c+d x)}}-\frac{3 b C \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+4}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+13);\frac{1}{6} (3 m+19);\cos ^2(c+d x)\right)}{d (3 m+13) \sqrt{\sin ^2(c+d x)}}","-\frac{3 b B \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+3}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+10);\frac{1}{6} (3 m+16);\cos ^2(c+d x)\right)}{d (3 m+10) \sqrt{\sin ^2(c+d x)}}-\frac{3 b C \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+4}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+13);\frac{1}{6} (3 m+19);\cos ^2(c+d x)\right)}{d (3 m+13) \sqrt{\sin ^2(c+d x)}}",1,"(-3*b*B*Cos[c + d*x]^(3 + m)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/2, (10 + 3*m)/6, (16 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(10 + 3*m)*Sqrt[Sin[c + d*x]^2]) - (3*b*C*Cos[c + d*x]^(4 + m)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/2, (13 + 3*m)/6, (19 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(13 + 3*m)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
213,1,167,0,0.1287163,"\int \frac{\cos ^m(c+d x) \left(B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^m*(B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(1/3),x]","-\frac{3 B \sin (c+d x) \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+5);\frac{1}{6} (3 m+11);\cos ^2(c+d x)\right)}{d (3 m+5) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}-\frac{3 C \sin (c+d x) \cos ^{m+3}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+8);\frac{1}{6} (3 m+14);\cos ^2(c+d x)\right)}{d (3 m+8) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}","-\frac{3 B \sin (c+d x) \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+5);\frac{1}{6} (3 m+11);\cos ^2(c+d x)\right)}{d (3 m+5) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}-\frac{3 C \sin (c+d x) \cos ^{m+3}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+8);\frac{1}{6} (3 m+14);\cos ^2(c+d x)\right)}{d (3 m+8) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}",1,"(-3*B*Cos[c + d*x]^(2 + m)*Hypergeometric2F1[1/2, (5 + 3*m)/6, (11 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(5 + 3*m)*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2]) - (3*C*Cos[c + d*x]^(3 + m)*Hypergeometric2F1[1/2, (8 + 3*m)/6, (14 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(8 + 3*m)*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
214,1,167,0,0.1229044,"\int \frac{\cos ^m(c+d x) \left(B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{2/3}} \, dx","Int[(Cos[c + d*x]^m*(B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(2/3),x]","-\frac{3 B \sin (c+d x) \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+4);\frac{1}{6} (3 m+10);\cos ^2(c+d x)\right)}{d (3 m+4) \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}-\frac{3 C \sin (c+d x) \cos ^{m+3}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+7);\frac{1}{6} (3 m+13);\cos ^2(c+d x)\right)}{d (3 m+7) \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}","-\frac{3 B \sin (c+d x) \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+4);\frac{1}{6} (3 m+10);\cos ^2(c+d x)\right)}{d (3 m+4) \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}-\frac{3 C \sin (c+d x) \cos ^{m+3}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+7);\frac{1}{6} (3 m+13);\cos ^2(c+d x)\right)}{d (3 m+7) \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}",1,"(-3*B*Cos[c + d*x]^(2 + m)*Hypergeometric2F1[1/2, (4 + 3*m)/6, (10 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(4 + 3*m)*(b*Cos[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2]) - (3*C*Cos[c + d*x]^(3 + m)*Hypergeometric2F1[1/2, (7 + 3*m)/6, (13 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(7 + 3*m)*(b*Cos[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
215,1,173,0,0.131254,"\int \frac{\cos ^m(c+d x) \left(B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{4/3}} \, dx","Int[(Cos[c + d*x]^m*(B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(4/3),x]","-\frac{3 B \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+2);\frac{1}{6} (3 m+8);\cos ^2(c+d x)\right)}{b d (3 m+2) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}-\frac{3 C \sin (c+d x) \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+5);\frac{1}{6} (3 m+11);\cos ^2(c+d x)\right)}{b d (3 m+5) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}","-\frac{3 B \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+2);\frac{1}{6} (3 m+8);\cos ^2(c+d x)\right)}{b d (3 m+2) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}-\frac{3 C \sin (c+d x) \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+5);\frac{1}{6} (3 m+11);\cos ^2(c+d x)\right)}{b d (3 m+5) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}",1,"(-3*B*Cos[c + d*x]^(1 + m)*Hypergeometric2F1[1/2, (2 + 3*m)/6, (8 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(2 + 3*m)*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2]) - (3*C*Cos[c + d*x]^(2 + m)*Hypergeometric2F1[1/2, (5 + 3*m)/6, (11 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(5 + 3*m)*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
216,1,167,0,0.1637315,"\int (a \cos (c+d x))^m (b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(a*Cos[c + d*x])^m*(b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{B \sin (c+d x) (a \cos (c+d x))^{m+2} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+2);\frac{1}{2} (m+n+4);\cos ^2(c+d x)\right)}{a^2 d (m+n+2) \sqrt{\sin ^2(c+d x)}}-\frac{C \sin (c+d x) (a \cos (c+d x))^{m+3} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+3);\frac{1}{2} (m+n+5);\cos ^2(c+d x)\right)}{a^3 d (m+n+3) \sqrt{\sin ^2(c+d x)}}","-\frac{B \sin (c+d x) (a \cos (c+d x))^{m+2} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+2);\frac{1}{2} (m+n+4);\cos ^2(c+d x)\right)}{a^2 d (m+n+2) \sqrt{\sin ^2(c+d x)}}-\frac{C \sin (c+d x) (a \cos (c+d x))^{m+3} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+3);\frac{1}{2} (m+n+5);\cos ^2(c+d x)\right)}{a^3 d (m+n+3) \sqrt{\sin ^2(c+d x)}}",1,"-((B*(a*Cos[c + d*x])^(2 + m)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (2 + m + n)/2, (4 + m + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(a^2*d*(2 + m + n)*Sqrt[Sin[c + d*x]^2])) - (C*(a*Cos[c + d*x])^(3 + m)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (3 + m + n)/2, (5 + m + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(a^3*d*(3 + m + n)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
217,1,141,0,0.1619287,"\int \cos ^2(c+d x) (b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^2*(b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+4} \, _2F_1\left(\frac{1}{2},\frac{n+4}{2};\frac{n+6}{2};\cos ^2(c+d x)\right)}{b^4 d (n+4) \sqrt{\sin ^2(c+d x)}}-\frac{C \sin (c+d x) (b \cos (c+d x))^{n+5} \, _2F_1\left(\frac{1}{2},\frac{n+5}{2};\frac{n+7}{2};\cos ^2(c+d x)\right)}{b^5 d (n+5) \sqrt{\sin ^2(c+d x)}}","-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+4} \, _2F_1\left(\frac{1}{2},\frac{n+4}{2};\frac{n+6}{2};\cos ^2(c+d x)\right)}{b^4 d (n+4) \sqrt{\sin ^2(c+d x)}}-\frac{C \sin (c+d x) (b \cos (c+d x))^{n+5} \, _2F_1\left(\frac{1}{2},\frac{n+5}{2};\frac{n+7}{2};\cos ^2(c+d x)\right)}{b^5 d (n+5) \sqrt{\sin ^2(c+d x)}}",1,"-((B*(b*Cos[c + d*x])^(4 + n)*Hypergeometric2F1[1/2, (4 + n)/2, (6 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^4*d*(4 + n)*Sqrt[Sin[c + d*x]^2])) - (C*(b*Cos[c + d*x])^(5 + n)*Hypergeometric2F1[1/2, (5 + n)/2, (7 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^5*d*(5 + n)*Sqrt[Sin[c + d*x]^2])","A",5,4,38,0.1053,1,"{16, 3010, 2748, 2643}"
218,1,141,0,0.1550583,"\int \cos (c+d x) (b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{n+5}{2};\cos ^2(c+d x)\right)}{b^3 d (n+3) \sqrt{\sin ^2(c+d x)}}-\frac{C \sin (c+d x) (b \cos (c+d x))^{n+4} \, _2F_1\left(\frac{1}{2},\frac{n+4}{2};\frac{n+6}{2};\cos ^2(c+d x)\right)}{b^4 d (n+4) \sqrt{\sin ^2(c+d x)}}","-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{n+5}{2};\cos ^2(c+d x)\right)}{b^3 d (n+3) \sqrt{\sin ^2(c+d x)}}-\frac{C \sin (c+d x) (b \cos (c+d x))^{n+4} \, _2F_1\left(\frac{1}{2},\frac{n+4}{2};\frac{n+6}{2};\cos ^2(c+d x)\right)}{b^4 d (n+4) \sqrt{\sin ^2(c+d x)}}",1,"-((B*(b*Cos[c + d*x])^(3 + n)*Hypergeometric2F1[1/2, (3 + n)/2, (5 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^3*d*(3 + n)*Sqrt[Sin[c + d*x]^2])) - (C*(b*Cos[c + d*x])^(4 + n)*Hypergeometric2F1[1/2, (4 + n)/2, (6 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^4*d*(4 + n)*Sqrt[Sin[c + d*x]^2])","A",5,4,36,0.1111,1,"{16, 3010, 2748, 2643}"
219,1,141,0,0.1383401,"\int (b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\cos ^2(c+d x)\right)}{b^2 d (n+2) \sqrt{\sin ^2(c+d x)}}-\frac{C \sin (c+d x) (b \cos (c+d x))^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{n+5}{2};\cos ^2(c+d x)\right)}{b^3 d (n+3) \sqrt{\sin ^2(c+d x)}}","-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\cos ^2(c+d x)\right)}{b^2 d (n+2) \sqrt{\sin ^2(c+d x)}}-\frac{C \sin (c+d x) (b \cos (c+d x))^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{n+5}{2};\cos ^2(c+d x)\right)}{b^3 d (n+3) \sqrt{\sin ^2(c+d x)}}",1,"-((B*(b*Cos[c + d*x])^(2 + n)*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^2*d*(2 + n)*Sqrt[Sin[c + d*x]^2])) - (C*(b*Cos[c + d*x])^(3 + n)*Hypergeometric2F1[1/2, (3 + n)/2, (5 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^3*d*(3 + n)*Sqrt[Sin[c + d*x]^2])","A",4,3,30,0.1000,1,"{3010, 2748, 2643}"
220,1,141,0,0.1574931,"\int (b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","-\frac{C \sin (c+d x) (b \cos (c+d x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\cos ^2(c+d x)\right)}{b^2 d (n+2) \sqrt{\sin ^2(c+d x)}}-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(c+d x)\right)}{b d (n+1) \sqrt{\sin ^2(c+d x)}}","-\frac{C \sin (c+d x) (b \cos (c+d x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\cos ^2(c+d x)\right)}{b^2 d (n+2) \sqrt{\sin ^2(c+d x)}}-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(c+d x)\right)}{b d (n+1) \sqrt{\sin ^2(c+d x)}}",1,"-((B*(b*Cos[c + d*x])^(1 + n)*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(1 + n)*Sqrt[Sin[c + d*x]^2])) - (C*(b*Cos[c + d*x])^(2 + n)*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^2*d*(2 + n)*Sqrt[Sin[c + d*x]^2])","A",5,4,36,0.1111,1,"{16, 3010, 2748, 2643}"
221,1,132,0,0.1661469,"\int (b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","-\frac{B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\cos ^2(c+d x)\right)}{d n \sqrt{\sin ^2(c+d x)}}-\frac{C \sin (c+d x) (b \cos (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(c+d x)\right)}{b d (n+1) \sqrt{\sin ^2(c+d x)}}","-\frac{B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\cos ^2(c+d x)\right)}{d n \sqrt{\sin ^2(c+d x)}}-\frac{C \sin (c+d x) (b \cos (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(c+d x)\right)}{b d (n+1) \sqrt{\sin ^2(c+d x)}}",1,"-((B*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, n/2, (2 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*n*Sqrt[Sin[c + d*x]^2])) - (C*(b*Cos[c + d*x])^(1 + n)*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(1 + n)*Sqrt[Sin[c + d*x]^2])","A",5,4,38,0.1053,1,"{16, 3010, 2748, 2643}"
222,1,131,0,0.1714025,"\int (b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{b B \sin (c+d x) (b \cos (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n-1}{2};\frac{n+1}{2};\cos ^2(c+d x)\right)}{d (1-n) \sqrt{\sin ^2(c+d x)}}-\frac{C \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\cos ^2(c+d x)\right)}{d n \sqrt{\sin ^2(c+d x)}}","\frac{b B \sin (c+d x) (b \cos (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n-1}{2};\frac{n+1}{2};\cos ^2(c+d x)\right)}{d (1-n) \sqrt{\sin ^2(c+d x)}}-\frac{C \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\cos ^2(c+d x)\right)}{d n \sqrt{\sin ^2(c+d x)}}",1,"(b*B*(b*Cos[c + d*x])^(-1 + n)*Hypergeometric2F1[1/2, (-1 + n)/2, (1 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - n)*Sqrt[Sin[c + d*x]^2]) - (C*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, n/2, (2 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*n*Sqrt[Sin[c + d*x]^2])","A",5,4,38,0.1053,1,"{16, 3010, 2748, 2643}"
223,1,139,0,0.1825946,"\int (b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^4(c+d x) \, dx","Int[(b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^4,x]","\frac{b^2 B \sin (c+d x) (b \cos (c+d x))^{n-2} \, _2F_1\left(\frac{1}{2},\frac{n-2}{2};\frac{n}{2};\cos ^2(c+d x)\right)}{d (2-n) \sqrt{\sin ^2(c+d x)}}+\frac{b C \sin (c+d x) (b \cos (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n-1}{2};\frac{n+1}{2};\cos ^2(c+d x)\right)}{d (1-n) \sqrt{\sin ^2(c+d x)}}","\frac{b^2 B \sin (c+d x) (b \cos (c+d x))^{n-2} \, _2F_1\left(\frac{1}{2},\frac{n-2}{2};\frac{n}{2};\cos ^2(c+d x)\right)}{d (2-n) \sqrt{\sin ^2(c+d x)}}+\frac{b C \sin (c+d x) (b \cos (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n-1}{2};\frac{n+1}{2};\cos ^2(c+d x)\right)}{d (1-n) \sqrt{\sin ^2(c+d x)}}",1,"(b^2*B*(b*Cos[c + d*x])^(-2 + n)*Hypergeometric2F1[1/2, (-2 + n)/2, n/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(2 - n)*Sqrt[Sin[c + d*x]^2]) + (b*C*(b*Cos[c + d*x])^(-1 + n)*Hypergeometric2F1[1/2, (-1 + n)/2, (1 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - n)*Sqrt[Sin[c + d*x]^2])","A",5,4,38,0.1053,1,"{16, 3010, 2748, 2643}"
224,1,163,0,0.1346884,"\int \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{2 B \sin (c+d x) \cos ^{\frac{9}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+9);\frac{1}{4} (2 n+13);\cos ^2(c+d x)\right)}{d (2 n+9) \sqrt{\sin ^2(c+d x)}}-\frac{2 C \sin (c+d x) \cos ^{\frac{11}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+11);\frac{1}{4} (2 n+15);\cos ^2(c+d x)\right)}{d (2 n+11) \sqrt{\sin ^2(c+d x)}}","-\frac{2 B \sin (c+d x) \cos ^{\frac{9}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+9);\frac{1}{4} (2 n+13);\cos ^2(c+d x)\right)}{d (2 n+9) \sqrt{\sin ^2(c+d x)}}-\frac{2 C \sin (c+d x) \cos ^{\frac{11}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+11);\frac{1}{4} (2 n+15);\cos ^2(c+d x)\right)}{d (2 n+11) \sqrt{\sin ^2(c+d x)}}",1,"(-2*B*Cos[c + d*x]^(9/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (9 + 2*n)/4, (13 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(9 + 2*n)*Sqrt[Sin[c + d*x]^2]) - (2*C*Cos[c + d*x]^(11/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (11 + 2*n)/4, (15 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(11 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
225,1,163,0,0.1281568,"\int \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{2 B \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+7);\frac{1}{4} (2 n+11);\cos ^2(c+d x)\right)}{d (2 n+7) \sqrt{\sin ^2(c+d x)}}-\frac{2 C \sin (c+d x) \cos ^{\frac{9}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+9);\frac{1}{4} (2 n+13);\cos ^2(c+d x)\right)}{d (2 n+9) \sqrt{\sin ^2(c+d x)}}","-\frac{2 B \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+7);\frac{1}{4} (2 n+11);\cos ^2(c+d x)\right)}{d (2 n+7) \sqrt{\sin ^2(c+d x)}}-\frac{2 C \sin (c+d x) \cos ^{\frac{9}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+9);\frac{1}{4} (2 n+13);\cos ^2(c+d x)\right)}{d (2 n+9) \sqrt{\sin ^2(c+d x)}}",1,"(-2*B*Cos[c + d*x]^(7/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (7 + 2*n)/4, (11 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(7 + 2*n)*Sqrt[Sin[c + d*x]^2]) - (2*C*Cos[c + d*x]^(9/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (9 + 2*n)/4, (13 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(9 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
226,1,163,0,0.1243627,"\int \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{2 B \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+5);\frac{1}{4} (2 n+9);\cos ^2(c+d x)\right)}{d (2 n+5) \sqrt{\sin ^2(c+d x)}}-\frac{2 C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+7);\frac{1}{4} (2 n+11);\cos ^2(c+d x)\right)}{d (2 n+7) \sqrt{\sin ^2(c+d x)}}","-\frac{2 B \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+5);\frac{1}{4} (2 n+9);\cos ^2(c+d x)\right)}{d (2 n+5) \sqrt{\sin ^2(c+d x)}}-\frac{2 C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+7);\frac{1}{4} (2 n+11);\cos ^2(c+d x)\right)}{d (2 n+7) \sqrt{\sin ^2(c+d x)}}",1,"(-2*B*Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (5 + 2*n)/4, (9 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(5 + 2*n)*Sqrt[Sin[c + d*x]^2]) - (2*C*Cos[c + d*x]^(7/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (7 + 2*n)/4, (11 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(7 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
227,1,163,0,0.1283193,"\int \frac{(b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt{\cos (c+d x)}} \, dx","Int[((b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Sqrt[Cos[c + d*x]],x]","-\frac{2 B \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\cos ^2(c+d x)\right)}{d (2 n+3) \sqrt{\sin ^2(c+d x)}}-\frac{2 C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+5);\frac{1}{4} (2 n+9);\cos ^2(c+d x)\right)}{d (2 n+5) \sqrt{\sin ^2(c+d x)}}","-\frac{2 B \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\cos ^2(c+d x)\right)}{d (2 n+3) \sqrt{\sin ^2(c+d x)}}-\frac{2 C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+5);\frac{1}{4} (2 n+9);\cos ^2(c+d x)\right)}{d (2 n+5) \sqrt{\sin ^2(c+d x)}}",1,"(-2*B*Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (3 + 2*n)/4, (7 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(3 + 2*n)*Sqrt[Sin[c + d*x]^2]) - (2*C*Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (5 + 2*n)/4, (9 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(5 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
228,1,163,0,0.1301233,"\int \frac{(b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(3/2),x]","-\frac{2 B \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\cos ^2(c+d x)\right)}{d (2 n+1) \sqrt{\sin ^2(c+d x)}}-\frac{2 C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\cos ^2(c+d x)\right)}{d (2 n+3) \sqrt{\sin ^2(c+d x)}}","-\frac{2 B \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\cos ^2(c+d x)\right)}{d (2 n+1) \sqrt{\sin ^2(c+d x)}}-\frac{2 C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\cos ^2(c+d x)\right)}{d (2 n+3) \sqrt{\sin ^2(c+d x)}}",1,"(-2*B*Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (1 + 2*n)/4, (5 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 + 2*n)*Sqrt[Sin[c + d*x]^2]) - (2*C*Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (3 + 2*n)/4, (7 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(3 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
229,1,163,0,0.1330481,"\int \frac{(b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(5/2),x]","\frac{2 B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-1);\frac{1}{4} (2 n+3);\cos ^2(c+d x)\right)}{d (1-2 n) \sqrt{\sin ^2(c+d x)} \sqrt{\cos (c+d x)}}-\frac{2 C \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\cos ^2(c+d x)\right)}{d (2 n+1) \sqrt{\sin ^2(c+d x)}}","\frac{2 B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-1);\frac{1}{4} (2 n+3);\cos ^2(c+d x)\right)}{d (1-2 n) \sqrt{\sin ^2(c+d x)} \sqrt{\cos (c+d x)}}-\frac{2 C \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\cos ^2(c+d x)\right)}{d (2 n+1) \sqrt{\sin ^2(c+d x)}}",1,"(2*B*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-1 + 2*n)/4, (3 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - 2*n)*Sqrt[Cos[c + d*x]]*Sqrt[Sin[c + d*x]^2]) - (2*C*Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (1 + 2*n)/4, (5 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
230,1,163,0,0.1273889,"\int \frac{(b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(7/2),x]","\frac{2 B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-3);\frac{1}{4} (2 n+1);\cos ^2(c+d x)\right)}{d (3-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{3}{2}}(c+d x)}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-1);\frac{1}{4} (2 n+3);\cos ^2(c+d x)\right)}{d (1-2 n) \sqrt{\sin ^2(c+d x)} \sqrt{\cos (c+d x)}}","\frac{2 B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-3);\frac{1}{4} (2 n+1);\cos ^2(c+d x)\right)}{d (3-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{3}{2}}(c+d x)}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-1);\frac{1}{4} (2 n+3);\cos ^2(c+d x)\right)}{d (1-2 n) \sqrt{\sin ^2(c+d x)} \sqrt{\cos (c+d x)}}",1,"(2*B*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-3 + 2*n)/4, (1 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(3 - 2*n)*Cos[c + d*x]^(3/2)*Sqrt[Sin[c + d*x]^2]) + (2*C*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-1 + 2*n)/4, (3 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - 2*n)*Sqrt[Cos[c + d*x]]*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
231,1,163,0,0.1240419,"\int \frac{(b \cos (c+d x))^n \left(B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^n*(B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(9/2),x]","\frac{2 B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-5);\frac{1}{4} (2 n-1);\cos ^2(c+d x)\right)}{d (5-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{5}{2}}(c+d x)}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-3);\frac{1}{4} (2 n+1);\cos ^2(c+d x)\right)}{d (3-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{3}{2}}(c+d x)}","\frac{2 B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-5);\frac{1}{4} (2 n-1);\cos ^2(c+d x)\right)}{d (5-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{5}{2}}(c+d x)}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-3);\frac{1}{4} (2 n+1);\cos ^2(c+d x)\right)}{d (3-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{3}{2}}(c+d x)}",1,"(2*B*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-5 + 2*n)/4, (-1 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(5 - 2*n)*Cos[c + d*x]^(5/2)*Sqrt[Sin[c + d*x]^2]) + (2*C*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-3 + 2*n)/4, (1 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(3 - 2*n)*Cos[c + d*x]^(3/2)*Sqrt[Sin[c + d*x]^2])","A",5,4,40,0.1000,1,"{20, 3010, 2748, 2643}"
232,1,173,0,0.2091679,"\int (a+a \cos (e+f x))^m \left(B \cos (e+f x)+C \cos ^2(e+f x)\right) \, dx","Int[(a + a*Cos[e + f*x])^m*(B*Cos[e + f*x] + C*Cos[e + f*x]^2),x]","\frac{2^{m+\frac{1}{2}} \left(B m (m+2)+C \left(m^2+m+1\right)\right) \sin (e+f x) (\cos (e+f x)+1)^{-m-\frac{1}{2}} (a \cos (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x))\right)}{f (m+1) (m+2)}-\frac{(C-B (m+2)) \sin (e+f x) (a \cos (e+f x)+a)^m}{f (m+1) (m+2)}+\frac{C \sin (e+f x) (a \cos (e+f x)+a)^{m+1}}{a f (m+2)}","\frac{2^{m+\frac{1}{2}} \left(B m (m+2)+C \left(m^2+m+1\right)\right) \sin (e+f x) (\cos (e+f x)+1)^{-m-\frac{1}{2}} (a \cos (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x))\right)}{f (m+1) (m+2)}-\frac{(C-B (m+2)) \sin (e+f x) (a \cos (e+f x)+a)^m}{f (m+1) (m+2)}+\frac{C \sin (e+f x) (a \cos (e+f x)+a)^{m+1}}{a f (m+2)}",1,"-(((C - B*(2 + m))*(a + a*Cos[e + f*x])^m*Sin[e + f*x])/(f*(1 + m)*(2 + m))) + (C*(a + a*Cos[e + f*x])^(1 + m)*Sin[e + f*x])/(a*f*(2 + m)) + (2^(1/2 + m)*(B*m*(2 + m) + C*(1 + m + m^2))*(1 + Cos[e + f*x])^(-1/2 - m)*(a + a*Cos[e + f*x])^m*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (1 - Cos[e + f*x])/2]*Sin[e + f*x])/(f*(1 + m)*(2 + m))","A",4,4,32,0.1250,1,"{3023, 2751, 2652, 2651}"
233,1,295,0,0.3628538,"\int (a+b \cos (e+f x))^m \left(B \cos (e+f x)+C \cos ^2(e+f x)\right) \, dx","Int[(a + b*Cos[e + f*x])^m*(B*Cos[e + f*x] + C*Cos[e + f*x]^2),x]","\frac{\sqrt{2} \sin (e+f x) \left(a^2 C-a b B (m+2)+b^2 C (m+1)\right) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\cos (e+f x)+1}}-\frac{\sqrt{2} (a+b) \sin (e+f x) (a C-b B (m+2)) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m-1;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\cos (e+f x)+1}}+\frac{C \sin (e+f x) (a+b \cos (e+f x))^{m+1}}{b f (m+2)}","\frac{\sqrt{2} \sin (e+f x) \left(a^2 C-a b B (m+2)+b^2 C (m+1)\right) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\cos (e+f x)+1}}-\frac{\sqrt{2} (a+b) \sin (e+f x) (a C-b B (m+2)) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m-1;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\cos (e+f x)+1}}+\frac{C \sin (e+f x) (a+b \cos (e+f x))^{m+1}}{b f (m+2)}",1,"(C*(a + b*Cos[e + f*x])^(1 + m)*Sin[e + f*x])/(b*f*(2 + m)) - (Sqrt[2]*(a + b)*(a*C - b*B*(2 + m))*AppellF1[1/2, 1/2, -1 - m, 3/2, (1 - Cos[e + f*x])/2, (b*(1 - Cos[e + f*x]))/(a + b)]*(a + b*Cos[e + f*x])^m*Sin[e + f*x])/(b^2*f*(2 + m)*Sqrt[1 + Cos[e + f*x]]*((a + b*Cos[e + f*x])/(a + b))^m) + (Sqrt[2]*(a^2*C + b^2*C*(1 + m) - a*b*B*(2 + m))*AppellF1[1/2, 1/2, -m, 3/2, (1 - Cos[e + f*x])/2, (b*(1 - Cos[e + f*x]))/(a + b)]*(a + b*Cos[e + f*x])^m*Sin[e + f*x])/(b^2*f*(2 + m)*Sqrt[1 + Cos[e + f*x]]*((a + b*Cos[e + f*x])/(a + b))^m)","A",8,5,32,0.1562,1,"{3023, 2756, 2665, 139, 138}"
234,1,284,0,0.343938,"\int (a+b \cos (c+d x))^{2/3} \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(a + b*Cos[c + d*x])^(2/3)*(B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{\left(-3 a^2 C+8 a b B-5 b^2 C\right) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{4 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{(a+b) (8 b B-3 a C) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{5}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{4 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{5/3}}{8 b d}","-\frac{\left(-3 a^2 C+8 a b B-5 b^2 C\right) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{4 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{(a+b) (8 b B-3 a C) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{5}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{4 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{5/3}}{8 b d}",1,"(3*C*(a + b*Cos[c + d*x])^(5/3)*Sin[c + d*x])/(8*b*d) + ((a + b)*(8*b*B - 3*a*C)*AppellF1[1/2, 1/2, -5/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(4*Sqrt[2]*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(2/3)) - ((8*a*b*B - 3*a^2*C - 5*b^2*C)*AppellF1[1/2, 1/2, -2/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(4*Sqrt[2]*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(2/3))","A",8,5,34,0.1471,1,"{3023, 2756, 2665, 139, 138}"
235,1,284,0,0.3345455,"\int \sqrt[3]{a+b \cos (c+d x)} \left(B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(a + b*Cos[c + d*x])^(1/3)*(B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{\sqrt{2} \left(-3 a^2 C+7 a b B-4 b^2 C\right) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{7 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{\sqrt{2} (a+b) (7 b B-3 a C) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{7 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{4/3}}{7 b d}","-\frac{\sqrt{2} \left(-3 a^2 C+7 a b B-4 b^2 C\right) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{7 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{\sqrt{2} (a+b) (7 b B-3 a C) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{7 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{4/3}}{7 b d}",1,"(3*C*(a + b*Cos[c + d*x])^(4/3)*Sin[c + d*x])/(7*b*d) + (Sqrt[2]*(a + b)*(7*b*B - 3*a*C)*AppellF1[1/2, 1/2, -4/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(7*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(1/3)) - (Sqrt[2]*(7*a*b*B - 3*a^2*C - 4*b^2*C)*AppellF1[1/2, 1/2, -1/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(7*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(1/3))","A",8,5,34,0.1471,1,"{3023, 2756, 2665, 139, 138}"
236,1,281,0,0.3230615,"\int \frac{B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt[3]{a+b \cos (c+d x)}} \, dx","Int[(B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(a + b*Cos[c + d*x])^(1/3),x]","-\frac{\sqrt{2} \left(-3 a^2 C+5 a b B-2 b^2 C\right) \sin (c+d x) \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{5 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{a+b \cos (c+d x)}}+\frac{\sqrt{2} (5 b B-3 a C) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{5 b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{2/3}}{5 b d}","-\frac{\sqrt{2} \left(-3 a^2 C+5 a b B-2 b^2 C\right) \sin (c+d x) \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{5 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{a+b \cos (c+d x)}}+\frac{\sqrt{2} (5 b B-3 a C) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{5 b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{2/3}}{5 b d}",1,"(3*C*(a + b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*b*d) + (Sqrt[2]*(5*b*B - 3*a*C)*AppellF1[1/2, 1/2, -2/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(2/3)) - (Sqrt[2]*(5*a*b*B - 3*a^2*C - 2*b^2*C)*AppellF1[1/2, 1/2, 1/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*((a + b*Cos[c + d*x])/(a + b))^(1/3)*Sin[c + d*x])/(5*b^2*d*Sqrt[1 + Cos[c + d*x]]*(a + b*Cos[c + d*x])^(1/3))","A",8,5,34,0.1471,1,"{3023, 2756, 2665, 139, 138}"
237,1,281,0,0.3272184,"\int \frac{B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^{2/3}} \, dx","Int[(B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(a + b*Cos[c + d*x])^(2/3),x]","-\frac{\left(-3 a^2 C+4 a b B-b^2 C\right) \sin (c+d x) \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{2 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} (a+b \cos (c+d x))^{2/3}}+\frac{(4 b B-3 a C) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{2 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{3 C \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)}}{4 b d}","-\frac{\left(-3 a^2 C+4 a b B-b^2 C\right) \sin (c+d x) \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{2 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} (a+b \cos (c+d x))^{2/3}}+\frac{(4 b B-3 a C) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{2 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{3 C \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)}}{4 b d}",1,"(3*C*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(4*b*d) + ((4*b*B - 3*a*C)*AppellF1[1/2, 1/2, -1/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(2*Sqrt[2]*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(1/3)) - ((4*a*b*B - 3*a^2*C - b^2*C)*AppellF1[1/2, 1/2, 2/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*((a + b*Cos[c + d*x])/(a + b))^(2/3)*Sin[c + d*x])/(2*Sqrt[2]*b^2*d*Sqrt[1 + Cos[c + d*x]]*(a + b*Cos[c + d*x])^(2/3))","A",8,5,34,0.1471,1,"{3023, 2756, 2665, 139, 138}"
238,1,187,0,0.1614992,"\int (a \cos (e+f x))^m \left(A+B \cos (e+f x)+C \cos ^2(e+f x)\right) \, dx","Int[(a*Cos[e + f*x])^m*(A + B*Cos[e + f*x] + C*Cos[e + f*x]^2),x]","-\frac{B \sin (e+f x) (a \cos (e+f x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};\cos ^2(e+f x)\right)}{a^2 f (m+2) \sqrt{\sin ^2(e+f x)}}-\frac{(A (m+2)+C (m+1)) \sin (e+f x) (a \cos (e+f x))^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{a f (m+1) (m+2) \sqrt{\sin ^2(e+f x)}}+\frac{C \sin (e+f x) (a \cos (e+f x))^{m+1}}{a f (m+2)}","-\frac{B \sin (e+f x) (a \cos (e+f x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};\cos ^2(e+f x)\right)}{a^2 f (m+2) \sqrt{\sin ^2(e+f x)}}-\frac{(A (m+2)+C (m+1)) \sin (e+f x) (a \cos (e+f x))^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{a f (m+1) (m+2) \sqrt{\sin ^2(e+f x)}}+\frac{C \sin (e+f x) (a \cos (e+f x))^{m+1}}{a f (m+2)}",1,"(C*(a*Cos[e + f*x])^(1 + m)*Sin[e + f*x])/(a*f*(2 + m)) - ((C*(1 + m) + A*(2 + m))*(a*Cos[e + f*x])^(1 + m)*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, Cos[e + f*x]^2]*Sin[e + f*x])/(a*f*(1 + m)*(2 + m)*Sqrt[Sin[e + f*x]^2]) - (B*(a*Cos[e + f*x])^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, Cos[e + f*x]^2]*Sin[e + f*x])/(a^2*f*(2 + m)*Sqrt[Sin[e + f*x]^2])","A",4,3,31,0.09677,1,"{3023, 2748, 2643}"
239,1,209,0,0.2420921,"\int \cos ^2(c+d x) \sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^2*Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^2 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^3 d}+\frac{10 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{10 b B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^2 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^3 d}+\frac{10 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{10 b B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}",1,"(2*(9*A + 7*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]) + (10*b*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (10*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*(9*A + 7*C)*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*b*d) + (2*B*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^2*d) + (2*C*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^3*d)","A",10,8,41,0.1951,1,"{16, 3023, 2748, 2635, 2640, 2639, 2642, 2641}"
240,1,180,0,0.2036267,"\int \cos (c+d x) \sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 b (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^2 d}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b d}+\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 b (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^2 d}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b d}+\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"(6*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*(7*A + 5*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*B*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b*d) + (2*C*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^2*d)","A",9,8,39,0.2051,1,"{16, 3023, 2748, 2635, 2642, 2641, 2640, 2639}"
241,1,145,0,0.1521825,"\int \sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}+\frac{2 b B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b d}","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}+\frac{2 b B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b d}",1,"(2*(5*A + 3*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d) + (2*C*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b*d)","A",7,7,33,0.2121,1,"{3023, 2748, 2640, 2639, 2635, 2642, 2641}"
242,1,112,0,0.1538978,"\int \sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","\frac{2 b (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}","\frac{2 b (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}",1,"(2*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*b*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",7,7,39,0.1795,1,"{16, 3023, 2748, 2642, 2641, 2640, 2639}"
243,1,109,0,0.1866308,"\int \sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{2 A b \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}+\frac{2 b B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}","-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{2 A b \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}+\frac{2 b B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}",1,"(-2*(A - C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*b*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(d*Sqrt[b*Cos[c + d*x]]) + (2*A*b*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",7,7,41,0.1707,1,"{16, 3021, 2748, 2642, 2641, 2640, 2639}"
244,1,140,0,0.2146165,"\int \sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{2 A b^2 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b B \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{2 A b^2 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b B \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(-2*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*b*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^2*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2)) + (2*b*B*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",8,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2640, 2639, 2642, 2641}"
245,1,181,0,0.2482126,"\int \sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^4(c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^4,x]","\frac{2 A b^3 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 b (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 b^2 B \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}","\frac{2 A b^3 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 b (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 b^2 B \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}",1,"(-2*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^3*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*b^2*B*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2)) + (2*b*(3*A + 5*C)*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",9,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2642, 2641, 2640, 2639}"
246,1,210,0,0.2691627,"\int \sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^5(c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^5,x]","\frac{2 b^2 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 A b^4 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 b (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 b^3 B \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 b B \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}","\frac{2 b^2 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 A b^4 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 b (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 b^3 B \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 b B \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"(-6*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^4*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (2*b^3*B*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*b^2*(5*A + 7*C)*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2)) + (6*b*B*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",10,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2640, 2639, 2642, 2641}"
247,1,210,0,0.2323376,"\int \cos (c+d x) (b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 d}+\frac{2 b (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{10 b^2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^2 d}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b d}+\frac{10 b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 d}+\frac{2 b (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{10 b^2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^2 d}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b d}+\frac{10 b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}",1,"(2*b*(9*A + 7*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]) + (10*b^2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (10*b*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*(9*A + 7*C)*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*d) + (2*B*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b*d) + (2*C*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^2*d)","A",10,8,39,0.2051,1,"{16, 3023, 2748, 2635, 2640, 2639, 2642, 2641}"
248,1,181,0,0.1828722,"\int (b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","\frac{2 b^2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 b (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}+\frac{6 b B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b d}","\frac{2 b^2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 b (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}+\frac{6 b B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b d}",1,"(6*b*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b^2*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*b*(7*A + 5*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*B*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*d) + (2*C*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b*d)","A",8,7,33,0.2121,1,"{3023, 2748, 2635, 2642, 2641, 2640, 2639}"
249,1,146,0,0.1747405,"\int (b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","\frac{2 b (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 b^2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}","\frac{2 b (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 b^2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}",1,"(2*b*(5*A + 3*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b^2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*b*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d) + (2*C*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*d)","A",8,8,39,0.2051,1,"{16, 3023, 2748, 2640, 2639, 2635, 2642, 2641}"
250,1,116,0,0.1784746,"\int (b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","\frac{2 b^2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{2 b C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}","\frac{2 b^2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{2 b C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}",1,"(2*b*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*b^2*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*b*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",7,7,41,0.1707,1,"{16, 3023, 2748, 2642, 2641, 2640, 2639}"
251,1,114,0,0.1851842,"\int (b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{2 A b^2 \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 b (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{2 b^2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}","\frac{2 A b^2 \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 b (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{2 b^2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}",1,"(-2*b*(A - C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*b^2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^2*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",7,7,41,0.1707,1,"{16, 3021, 2748, 2642, 2641, 2640, 2639}"
252,1,145,0,0.2110586,"\int (b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^4(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^4,x]","\frac{2 b^2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^3 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b^2 B \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 b B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{2 b^2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^3 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b^2 B \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 b B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(-2*b*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*b^2*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^3*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2)) + (2*b^2*B*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",8,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2640, 2639, 2642, 2641}"
253,1,186,0,0.2410451,"\int (b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^5(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^5,x]","\frac{2 b^2 (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^4 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}-\frac{2 b (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 b^3 B \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b^2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}","\frac{2 b^2 (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^4 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}-\frac{2 b (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 b^3 B \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b^2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}",1,"(-2*b*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b^2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^4*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*b^3*B*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2)) + (2*b^2*(3*A + 5*C)*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",9,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2642, 2641, 2640, 2639}"
254,1,215,0,0.2693742,"\int (b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^6(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^6,x]","\frac{2 b^3 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 b^2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^5 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 b^4 B \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 b^2 B \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{6 b B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}","\frac{2 b^3 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 b^2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^5 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 b^4 B \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 b^2 B \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{6 b B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"(-6*b*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b^2*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^5*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (2*b^4*B*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*b^3*(5*A + 7*C)*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2)) + (6*b^2*B*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",10,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2640, 2639, 2642, 2641}"
255,1,212,0,0.2013875,"\int (b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","\frac{2 b^2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{2 b (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 d}+\frac{10 b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{10 b^3 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b d}","\frac{2 b^2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{2 b (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 d}+\frac{10 b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{10 b^3 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b d}",1,"(2*b^2*(9*A + 7*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]) + (10*b^3*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (10*b^2*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*b*(9*A + 7*C)*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*d) + (2*B*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*d) + (2*C*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b*d)","A",9,7,33,0.2121,1,"{3023, 2748, 2635, 2640, 2639, 2642, 2641}"
256,1,183,0,0.2098199,"\int (b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","\frac{2 b^2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 b^3 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{6 b^2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 b B \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 d}","\frac{2 b^2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 b^3 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{6 b^2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 b B \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 d}",1,"(6*b^2*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b^3*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*b^2*(7*A + 5*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*b*B*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*d) + (2*C*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*d)","A",9,8,39,0.2051,1,"{16, 3023, 2748, 2635, 2642, 2641, 2640, 2639}"
257,1,151,0,0.192517,"\int (b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","\frac{2 b^2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}+\frac{2 b^3 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}","\frac{2 b^2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}+\frac{2 b^3 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}",1,"(2*b^2*(5*A + 3*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b^3*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*b^2*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d) + (2*b*C*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*d)","A",8,8,41,0.1951,1,"{16, 3023, 2748, 2640, 2639, 2635, 2642, 2641}"
258,1,120,0,0.1702317,"\int (b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{2 b^3 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b^2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{2 b^2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}","\frac{2 b^3 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b^2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{2 b^2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}",1,"(2*b^2*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*b^3*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*b^2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",7,7,41,0.1707,1,"{16, 3023, 2748, 2642, 2641, 2640, 2639}"
259,1,116,0,0.1902062,"\int (b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^4(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^4,x]","-\frac{2 b^2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{2 A b^3 \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}+\frac{2 b^3 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}","-\frac{2 b^2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{2 A b^3 \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}+\frac{2 b^3 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}",1,"(-2*b^2*(A - C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*b^3*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^3*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",7,7,41,0.1707,1,"{16, 3021, 2748, 2642, 2641, 2640, 2639}"
260,1,147,0,0.2233924,"\int (b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^5(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^5,x]","\frac{2 b^3 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^4 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b^3 B \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 b^2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{2 b^3 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^4 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b^3 B \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 b^2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(-2*b^2*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*b^3*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^4*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2)) + (2*b^3*B*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",8,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2640, 2639, 2642, 2641}"
261,1,188,0,0.2498229,"\int (b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^6(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^6,x]","\frac{2 b^3 (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{2 b^2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 A b^5 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 b^4 B \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b^3 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}","\frac{2 b^3 (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{2 b^2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 A b^5 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 b^4 B \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b^3 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}",1,"(-2*b^2*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b^3*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^5*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*b^4*B*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2)) + (2*b^3*(3*A + 5*C)*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",9,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2642, 2641, 2640, 2639}"
262,1,217,0,0.2678986,"\int (b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^7(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^7,x]","\frac{2 b^4 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 b^3 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^6 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 b^5 B \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 b^3 B \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{6 b^2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}","\frac{2 b^4 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 b^3 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 A b^6 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 b^5 B \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 b^3 B \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{6 b^2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"(-6*b^2*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b^3*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^6*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (2*b^5*B*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*b^4*(5*A + 7*C)*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2)) + (6*b^3*B*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",10,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2640, 2639, 2642, 2641}"
263,1,214,0,0.2211361,"\int \frac{\cos ^3(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^3*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Sqrt[b*Cos[c + d*x]],x]","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^2 d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^3 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^4 d}+\frac{10 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b d}+\frac{10 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^2 d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^3 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^4 d}+\frac{10 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b d}+\frac{10 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}",1,"(2*(9*A + 7*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*b*d*Sqrt[Cos[c + d*x]]) + (10*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (10*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*b*d) + (2*(9*A + 7*C)*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*b^2*d) + (2*B*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^3*d) + (2*C*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^4*d)","A",10,8,41,0.1951,1,"{16, 3023, 2748, 2635, 2640, 2639, 2642, 2641}"
264,1,185,0,0.1939741,"\int \frac{\cos ^2(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^2*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Sqrt[b*Cos[c + d*x]],x]","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b d}+\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^2 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^3 d}+\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b d}+\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^2 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^3 d}+\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}",1,"(6*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b*d*Sqrt[Cos[c + d*x]]) + (2*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*(7*A + 5*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*b*d) + (2*B*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b^2*d) + (2*C*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^3*d)","A",9,8,41,0.1951,1,"{16, 3023, 2748, 2635, 2642, 2641, 2640, 2639}"
265,1,150,0,0.1563284,"\int \frac{\cos (c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Sqrt[b*Cos[c + d*x]],x]","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^2 d}+\frac{2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b d}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^2 d}+\frac{2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b d}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}",1,"(2*(5*A + 3*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b*d*Sqrt[Cos[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*b*d) + (2*C*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b^2*d)","A",8,8,39,0.2051,1,"{16, 3023, 2748, 2640, 2639, 2635, 2642, 2641}"
266,1,117,0,0.1242207,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/Sqrt[b*Cos[c + d*x]],x]","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b d}","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b d}",1,"(2*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b*d*Sqrt[Cos[c + d*x]]) + (2*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*b*d)","A",6,6,33,0.1818,1,"{3023, 2748, 2642, 2641, 2640, 2639}"
267,1,110,0,0.1598976,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec (c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x])/Sqrt[b*Cos[c + d*x]],x]","-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}","-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}",1,"(-2*(A - C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b*d*Sqrt[Cos[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(d*Sqrt[b*Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",7,7,39,0.1795,1,"{16, 3021, 2748, 2642, 2641, 2640, 2639}"
268,1,139,0,0.2027119,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^2(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^2)/Sqrt[b*Cos[c + d*x]],x]","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 A b \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 B \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b d \sqrt{\cos (c+d x)}}","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 A b \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 B \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b d \sqrt{\cos (c+d x)}}",1,"(-2*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b*d*Sqrt[Cos[c + d*x]]) + (2*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2)) + (2*B*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",8,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2640, 2639, 2642, 2641}"
269,1,180,0,0.2307858,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^3(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^3)/Sqrt[b*Cos[c + d*x]],x]","\frac{2 A b^2 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}+\frac{2 b B \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}","\frac{2 A b^2 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 (3 A+5 C) \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}+\frac{2 b B \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}",1,"(-2*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b*d*Sqrt[Cos[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^2*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*b*B*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2)) + (2*(3*A + 5*C)*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",9,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2642, 2641, 2640, 2639}"
270,1,209,0,0.2585647,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^4(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^4)/Sqrt[b*Cos[c + d*x]],x]","\frac{2 A b^3 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 b (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 b^2 B \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 B \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}","\frac{2 A b^3 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 b (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 b^2 B \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 B \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}",1,"(-6*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b*d*Sqrt[Cos[c + d*x]]) + (2*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^3*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (2*b^2*B*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*b*(5*A + 7*C)*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2)) + (6*B*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",10,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2640, 2639, 2642, 2641}"
271,1,217,0,0.220706,"\int \frac{\cos ^4(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]^4*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^3 d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^4 d}+\frac{10 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^2 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^5 d}+\frac{10 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b d \sqrt{b \cos (c+d x)}}","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^3 d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^4 d}+\frac{10 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^2 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^5 d}+\frac{10 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b d \sqrt{b \cos (c+d x)}}",1,"(2*(9*A + 7*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*b^2*d*Sqrt[Cos[c + d*x]]) + (10*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b*d*Sqrt[b*Cos[c + d*x]]) + (10*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*b^2*d) + (2*(9*A + 7*C)*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*b^3*d) + (2*B*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^4*d) + (2*C*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^5*d)","A",10,8,41,0.1951,1,"{16, 3023, 2748, 2635, 2640, 2639, 2642, 2641}"
272,1,188,0,0.2013669,"\int \frac{\cos ^3(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]^3*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^2 d}+\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b d \sqrt{b \cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^3 d}+\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^4 d}","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^2 d}+\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b d \sqrt{b \cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^3 d}+\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^4 d}",1,"(6*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^2*d*Sqrt[Cos[c + d*x]]) + (2*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b*d*Sqrt[b*Cos[c + d*x]]) + (2*(7*A + 5*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*b^2*d) + (2*B*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b^3*d) + (2*C*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^4*d)","A",9,8,41,0.1951,1,"{16, 3023, 2748, 2635, 2642, 2641, 2640, 2639}"
273,1,153,0,0.1612918,"\int \frac{\cos ^2(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]^2*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^2 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^3 d}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^2 d}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^3 d}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}",1,"(2*(5*A + 3*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^2*d*Sqrt[Cos[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b*d*Sqrt[b*Cos[c + d*x]]) + (2*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*b^2*d) + (2*C*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b^3*d)","A",8,8,41,0.1951,1,"{16, 3023, 2748, 2640, 2639, 2635, 2642, 2641}"
274,1,120,0,0.1412325,"\int \frac{\cos (c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}+\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^2 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^2 d}","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}+\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^2 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^2 d}",1,"(2*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b^2*d*Sqrt[Cos[c + d*x]]) + (2*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b*d*Sqrt[b*Cos[c + d*x]]) + (2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*b^2*d)","A",7,7,39,0.1795,1,"{16, 3023, 2748, 2642, 2641, 2640, 2639}"
275,1,116,0,0.1414645,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(3/2),x]","-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^2 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{b d \sqrt{b \cos (c+d x)}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b d \sqrt{b \cos (c+d x)}}","-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^2 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{b d \sqrt{b \cos (c+d x)}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b d \sqrt{b \cos (c+d x)}}",1,"(-2*(A - C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b^2*d*Sqrt[Cos[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(b*d*Sqrt[b*Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(b*d*Sqrt[b*Cos[c + d*x]])","A",6,6,33,0.1818,1,"{3021, 2748, 2642, 2641, 2640, 2639}"
276,1,144,0,0.1924063,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec (c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x])/(b*Cos[c + d*x])^(3/2),x]","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}-\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^2 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x)}{b d \sqrt{b \cos (c+d x)}}","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}-\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^2 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x)}{b d \sqrt{b \cos (c+d x)}}",1,"(-2*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b^2*d*Sqrt[Cos[c + d*x]]) + (2*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b*d*Sqrt[b*Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2)) + (2*B*Sin[c + d*x])/(b*d*Sqrt[b*Cos[c + d*x]])","A",8,8,39,0.2051,1,"{16, 3021, 2748, 2636, 2640, 2639, 2642, 2641}"
277,1,183,0,0.2414632,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^2(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^2)/(b*Cos[c + d*x])^(3/2),x]","-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 (3 A+5 C) \sin (c+d x)}{5 b d \sqrt{b \cos (c+d x)}}+\frac{2 A b \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 B \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}","-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 (3 A+5 C) \sin (c+d x)}{5 b d \sqrt{b \cos (c+d x)}}+\frac{2 A b \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 B \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}",1,"(-2*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^2*d*Sqrt[Cos[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*B*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2)) + (2*(3*A + 5*C)*Sin[c + d*x])/(5*b*d*Sqrt[b*Cos[c + d*x]])","A",9,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2642, 2641, 2640, 2639}"
278,1,212,0,0.2664254,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^3(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^3)/(b*Cos[c + d*x])^(3/2),x]","\frac{2 A b^2 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b d \sqrt{b \cos (c+d x)}}-\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 b B \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 B \sin (c+d x)}{5 b d \sqrt{b \cos (c+d x)}}","\frac{2 A b^2 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{2 (5 A+7 C) \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b d \sqrt{b \cos (c+d x)}}-\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}+\frac{2 b B \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 B \sin (c+d x)}{5 b d \sqrt{b \cos (c+d x)}}",1,"(-6*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^2*d*Sqrt[Cos[c + d*x]]) + (2*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b^2*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (2*b*B*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*(5*A + 7*C)*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2)) + (6*B*Sin[c + d*x])/(5*b*d*Sqrt[b*Cos[c + d*x]])","A",10,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2640, 2639, 2642, 2641}"
279,1,217,0,0.2252938,"\int \frac{\cos ^5(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^5*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^4 d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^5 d}+\frac{10 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^3 d}+\frac{10 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^6 d}","\frac{2 (9 A+7 C) \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^4 d}+\frac{2 (9 A+7 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^5 d}+\frac{10 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^3 d}+\frac{10 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^6 d}",1,"(2*(9*A + 7*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*b^3*d*Sqrt[Cos[c + d*x]]) + (10*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b^2*d*Sqrt[b*Cos[c + d*x]]) + (10*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*b^3*d) + (2*(9*A + 7*C)*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*b^4*d) + (2*B*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^5*d) + (2*C*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^6*d)","A",10,8,41,0.1951,1,"{16, 3023, 2748, 2635, 2640, 2639, 2642, 2641}"
280,1,188,0,0.1955669,"\int \frac{\cos ^4(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^4*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^3 d}+\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^4 d}+\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^5 d}","\frac{2 (7 A+5 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^3 d}+\frac{2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^4 d}+\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^5 d}",1,"(6*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^3*d*Sqrt[Cos[c + d*x]]) + (2*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*(7*A + 5*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*b^3*d) + (2*B*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b^4*d) + (2*C*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^5*d)","A",9,8,41,0.1951,1,"{16, 3023, 2748, 2635, 2642, 2641, 2640, 2639}"
281,1,153,0,0.1580589,"\int \frac{\cos ^3(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^3*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^3 d}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^4 d}","\frac{2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^3 d}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^4 d}",1,"(2*(5*A + 3*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^3*d*Sqrt[Cos[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*b^3*d) + (2*C*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b^4*d)","A",8,8,41,0.1951,1,"{16, 3023, 2748, 2640, 2639, 2635, 2642, 2641}"
282,1,120,0,0.1428937,"\int \frac{\cos ^2(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^2*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^3 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^3 d}","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^3 d \sqrt{\cos (c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^3 d}",1,"(2*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b^3*d*Sqrt[Cos[c + d*x]]) + (2*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*b^3*d)","A",7,7,41,0.1707,1,"{16, 3023, 2748, 2642, 2641, 2640, 2639}"
283,1,116,0,0.1538235,"\int \frac{\cos (c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^3 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b^2 d \sqrt{b \cos (c+d x)}}","-\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^3 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b^2 d \sqrt{b \cos (c+d x)}}",1,"(-2*(A - C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b^3*d*Sqrt[Cos[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(b^2*d*Sqrt[b*Cos[c + d*x]])","A",7,7,39,0.1795,1,"{16, 3021, 2748, 2642, 2641, 2640, 2639}"
284,1,147,0,0.1627028,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{3 b d (b \cos (c+d x))^{3/2}}+\frac{2 B \sin (c+d x)}{b^2 d \sqrt{b \cos (c+d x)}}-\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^3 d \sqrt{\cos (c+d x)}}","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 A \sin (c+d x)}{3 b d (b \cos (c+d x))^{3/2}}+\frac{2 B \sin (c+d x)}{b^2 d \sqrt{b \cos (c+d x)}}-\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^3 d \sqrt{\cos (c+d x)}}",1,"(-2*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b^3*d*Sqrt[Cos[c + d*x]]) + (2*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(3*b*d*(b*Cos[c + d*x])^(3/2)) + (2*B*Sin[c + d*x])/(b^2*d*Sqrt[b*Cos[c + d*x]])","A",7,7,33,0.2121,1,"{3021, 2748, 2636, 2640, 2639, 2642, 2641}"
285,1,185,0,0.2190044,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec (c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x])/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (3 A+5 C) \sin (c+d x)}{5 b^2 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 B \sin (c+d x)}{3 b d (b \cos (c+d x))^{3/2}}","\frac{2 (3 A+5 C) \sin (c+d x)}{5 b^2 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 B \sin (c+d x)}{3 b d (b \cos (c+d x))^{3/2}}",1,"(-2*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^3*d*Sqrt[Cos[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*B*Sin[c + d*x])/(3*b*d*(b*Cos[c + d*x])^(3/2)) + (2*(3*A + 5*C)*Sin[c + d*x])/(5*b^2*d*Sqrt[b*Cos[c + d*x]])","A",9,8,39,0.2051,1,"{16, 3021, 2748, 2636, 2642, 2641, 2640, 2639}"
286,1,212,0,0.270625,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^2(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^2)/(b*Cos[c + d*x])^(5/2),x]","\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 (5 A+7 C) \sin (c+d x)}{21 b d (b \cos (c+d x))^{3/2}}+\frac{2 A b \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{6 B \sin (c+d x)}{5 b^2 d \sqrt{b \cos (c+d x)}}-\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}","\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 (5 A+7 C) \sin (c+d x)}{21 b d (b \cos (c+d x))^{3/2}}+\frac{2 A b \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{6 B \sin (c+d x)}{5 b^2 d \sqrt{b \cos (c+d x)}}-\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 B \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}",1,"(-6*B*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^3*d*Sqrt[Cos[c + d*x]]) + (2*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*A*b*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (2*B*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (2*(5*A + 7*C)*Sin[c + d*x])/(21*b*d*(b*Cos[c + d*x])^(3/2)) + (6*B*Sin[c + d*x])/(5*b^2*d*Sqrt[b*Cos[c + d*x]])","A",10,8,41,0.1951,1,"{16, 3021, 2748, 2636, 2640, 2639, 2642, 2641}"
287,1,188,0,0.1889848,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(b \cos (c+d x))^{7/2}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(7/2),x]","\frac{2 (3 A+5 C) \sin (c+d x)}{5 b^3 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^4 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{5 b d (b \cos (c+d x))^{5/2}}+\frac{2 B \sin (c+d x)}{3 b^2 d (b \cos (c+d x))^{3/2}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^3 d \sqrt{b \cos (c+d x)}}","\frac{2 (3 A+5 C) \sin (c+d x)}{5 b^3 d \sqrt{b \cos (c+d x)}}-\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^4 d \sqrt{\cos (c+d x)}}+\frac{2 A \sin (c+d x)}{5 b d (b \cos (c+d x))^{5/2}}+\frac{2 B \sin (c+d x)}{3 b^2 d (b \cos (c+d x))^{3/2}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^3 d \sqrt{b \cos (c+d x)}}",1,"(-2*(3*A + 5*C)*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^4*d*Sqrt[Cos[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*b^3*d*Sqrt[b*Cos[c + d*x]]) + (2*A*Sin[c + d*x])/(5*b*d*(b*Cos[c + d*x])^(5/2)) + (2*B*Sin[c + d*x])/(3*b^2*d*(b*Cos[c + d*x])^(3/2)) + (2*(3*A + 5*C)*Sin[c + d*x])/(5*b^3*d*Sqrt[b*Cos[c + d*x]])","A",8,7,33,0.2121,1,"{3021, 2748, 2636, 2642, 2641, 2640, 2639}"
288,1,223,0,0.1253703,"\int \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{(5 A+4 C) \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{(5 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{3 B x \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{B \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}+\frac{3 B \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{5 d}","-\frac{(5 A+4 C) \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{(5 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{3 B x \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{B \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}+\frac{3 B \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{5 d}",1,"(3*B*x*Sqrt[b*Cos[c + d*x]])/(8*Sqrt[Cos[c + d*x]]) + ((5*A + 4*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(5*d*Sqrt[Cos[c + d*x]]) + (3*B*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d) + (B*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d) + (C*Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(5*d) - ((5*A + 4*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(15*d*Sqrt[Cos[c + d*x]])","A",8,6,43,0.1395,1,"{17, 3023, 2748, 2633, 2635, 8}"
289,1,184,0,0.1072167,"\int \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","\frac{x (4 A+3 C) \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}-\frac{B \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}","\frac{x (4 A+3 C) \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}-\frac{B \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}",1,"((4*A + 3*C)*x*Sqrt[b*Cos[c + d*x]])/(8*Sqrt[Cos[c + d*x]]) + (B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) + ((4*A + 3*C)*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d) + (C*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d) - (B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Cos[c + d*x]])","A",7,6,43,0.1395,1,"{17, 3023, 2748, 2635, 8, 2633}"
290,1,143,0,0.0603876,"\int \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","\frac{(3 A+2 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{B x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{3 d}","\frac{(3 A+2 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{B x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{3 d}",1,"(B*x*Sqrt[b*Cos[c + d*x]])/(2*Sqrt[Cos[c + d*x]]) + ((3*A + 2*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Sqrt[Cos[c + d*x]]) + (B*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d) + (C*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",3,3,43,0.06977,1,"{17, 3023, 2734}"
291,1,123,0,0.0382755,"\int \frac{\sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt{\cos (c+d x)}} \, dx","Int[(Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Sqrt[Cos[c + d*x]],x]","\frac{A x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{C x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}","\frac{A x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{C x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}",1,"(A*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (C*x*Sqrt[b*Cos[c + d*x]])/(2*Sqrt[Cos[c + d*x]]) + (B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) + (C*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d)","A",5,4,43,0.09302,1,"{17, 2637, 2635, 8}"
292,1,93,0,0.0568781,"\int \frac{\sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Int[(Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(3/2),x]","\frac{A \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{B x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{A \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{B x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(B*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (A*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(d*Sqrt[Cos[c + d*x]]) + (C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]])","A",4,4,43,0.09302,1,"{17, 3023, 2735, 3770}"
293,1,93,0,0.0658156,"\int \frac{\sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Int[(Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(5/2),x]","\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}+\frac{B \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{C x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}","\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}+\frac{B \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{C x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}",1,"(C*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (B*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(d*Sqrt[Cos[c + d*x]]) + (A*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2))","A",4,4,43,0.09302,1,"{17, 3021, 2735, 3770}"
294,1,111,0,0.1043332,"\int \frac{\sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Int[(Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(7/2),x]","\frac{(A+2 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}+\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}","\frac{(A+2 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}+\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}",1,"((A + 2*C)*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(2*d*Sqrt[Cos[c + d*x]]) + (A*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d*Cos[c + d*x]^(5/2)) + (B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2))","A",6,6,43,0.1395,1,"{17, 3021, 2748, 3767, 8, 3770}"
295,1,152,0,0.1156702,"\int \frac{\sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Int[(Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(9/2),x]","\frac{(2 A+3 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{B \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{B \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}","\frac{(2 A+3 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{B \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{B \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}",1,"(B*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(2*d*Sqrt[Cos[c + d*x]]) + (A*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Cos[c + d*x]^(7/2)) + (B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d*Cos[c + d*x]^(5/2)) + ((2*A + 3*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Cos[c + d*x]^(3/2))","A",7,7,43,0.1628,1,"{17, 3021, 2748, 3768, 3770, 3767, 8}"
296,1,193,0,0.1173912,"\int \frac{\sqrt{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{11}{2}}(c+d x)} \, dx","Int[(Sqrt[b*Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(11/2),x]","\frac{(3 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{(3 A+4 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}+\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}+\frac{B \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}","\frac{(3 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{(3 A+4 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}+\frac{A \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}+\frac{B \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}",1,"((3*A + 4*C)*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(8*d*Sqrt[Cos[c + d*x]]) + (A*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d*Cos[c + d*x]^(9/2)) + ((3*A + 4*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d*Cos[c + d*x]^(5/2)) + (B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2)) + (B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Cos[c + d*x]^(7/2))","A",7,6,43,0.1395,1,"{17, 3021, 2748, 3767, 3768, 3770}"
297,1,229,0,0.1270842,"\int \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{b (5 A+4 C) \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{b (5 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{3 b B x \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b B \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}+\frac{3 b B \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}+\frac{b C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{5 d}","-\frac{b (5 A+4 C) \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{b (5 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{3 b B x \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b B \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}+\frac{3 b B \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}+\frac{b C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{5 d}",1,"(3*b*B*x*Sqrt[b*Cos[c + d*x]])/(8*Sqrt[Cos[c + d*x]]) + (b*(5*A + 4*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(5*d*Sqrt[Cos[c + d*x]]) + (3*b*B*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d) + (b*B*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d) + (b*C*Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(5*d) - (b*(5*A + 4*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(15*d*Sqrt[Cos[c + d*x]])","A",8,6,43,0.1395,1,"{17, 3023, 2748, 2633, 2635, 8}"
298,1,189,0,0.1185216,"\int \sqrt{\cos (c+d x)} (b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","\frac{b x (4 A+3 C) \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b (4 A+3 C) \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}-\frac{b B \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{b C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}","\frac{b x (4 A+3 C) \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b (4 A+3 C) \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}-\frac{b B \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{b C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}",1,"(b*(4*A + 3*C)*x*Sqrt[b*Cos[c + d*x]])/(8*Sqrt[Cos[c + d*x]]) + (b*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) + (b*(4*A + 3*C)*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d) + (b*C*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d) - (b*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Cos[c + d*x]])","A",7,6,43,0.1395,1,"{17, 3023, 2748, 2635, 8, 2633}"
299,1,147,0,0.0590462,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt{\cos (c+d x)}} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Sqrt[Cos[c + d*x]],x]","\frac{b (3 A+2 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{b B x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b B \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}+\frac{b C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{3 d}","\frac{b (3 A+2 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{b B x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b B \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}+\frac{b C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{3 d}",1,"(b*B*x*Sqrt[b*Cos[c + d*x]])/(2*Sqrt[Cos[c + d*x]]) + (b*(3*A + 2*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Sqrt[Cos[c + d*x]]) + (b*B*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d) + (b*C*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",3,3,43,0.06977,1,"{17, 3023, 2734}"
300,1,127,0,0.0381749,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(3/2),x]","\frac{A b x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{b C x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b C \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}","\frac{A b x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{b C x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b C \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}",1,"(A*b*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (b*C*x*Sqrt[b*Cos[c + d*x]])/(2*Sqrt[Cos[c + d*x]]) + (b*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) + (b*C*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d)","A",5,4,43,0.09302,1,"{17, 2637, 2635, 8}"
301,1,96,0,0.0549559,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(5/2),x]","\frac{A b \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{b B x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{b C \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{A b \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{b B x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{b C \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(b*B*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (A*b*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(d*Sqrt[Cos[c + d*x]]) + (b*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]])","A",4,4,43,0.09302,1,"{17, 3023, 2735, 3770}"
302,1,96,0,0.0607124,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(7/2),x]","\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}+\frac{b B \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{b C x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}","\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}+\frac{b B \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{b C x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}",1,"(b*C*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (b*B*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(d*Sqrt[Cos[c + d*x]]) + (A*b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2))","A",4,4,43,0.09302,1,"{17, 3021, 2735, 3770}"
303,1,114,0,0.0871232,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(9/2),x]","\frac{b (A+2 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}+\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}","\frac{b (A+2 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}+\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}",1,"(b*(A + 2*C)*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(2*d*Sqrt[Cos[c + d*x]]) + (A*b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d*Cos[c + d*x]^(5/2)) + (b*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2))","A",6,6,43,0.1395,1,"{17, 3021, 2748, 3767, 8, 3770}"
304,1,156,0,0.1062622,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{11}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(11/2),x]","\frac{b (2 A+3 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b B \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}","\frac{b (2 A+3 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b B \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}",1,"(b*B*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(2*d*Sqrt[Cos[c + d*x]]) + (A*b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Cos[c + d*x]^(7/2)) + (b*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d*Cos[c + d*x]^(5/2)) + (b*(2*A + 3*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Cos[c + d*x]^(3/2))","A",7,7,43,0.1628,1,"{17, 3021, 2748, 3768, 3770, 3767, 8}"
305,1,198,0,0.1242117,"\int \frac{(b \cos (c+d x))^{3/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{13}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(13/2),x]","\frac{b (3 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b (3 A+4 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}+\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}+\frac{b B \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}","\frac{b (3 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b (3 A+4 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}+\frac{A b \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}+\frac{b B \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{b B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}",1,"(b*(3*A + 4*C)*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(8*d*Sqrt[Cos[c + d*x]]) + (A*b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d*Cos[c + d*x]^(9/2)) + (b*(3*A + 4*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d*Cos[c + d*x]^(5/2)) + (b*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2)) + (b*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Cos[c + d*x]^(7/2))","A",7,6,43,0.1395,1,"{17, 3021, 2748, 3767, 3768, 3770}"
306,1,241,0,0.1278507,"\int \sqrt{\cos (c+d x)} (b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{b^2 (5 A+4 C) \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{b^2 (5 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{3 b^2 B x \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b^2 B \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}+\frac{3 b^2 B \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}+\frac{b^2 C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{5 d}","-\frac{b^2 (5 A+4 C) \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{b^2 (5 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{3 b^2 B x \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b^2 B \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}+\frac{3 b^2 B \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}+\frac{b^2 C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{5 d}",1,"(3*b^2*B*x*Sqrt[b*Cos[c + d*x]])/(8*Sqrt[Cos[c + d*x]]) + (b^2*(5*A + 4*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(5*d*Sqrt[Cos[c + d*x]]) + (3*b^2*B*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d) + (b^2*B*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d) + (b^2*C*Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(5*d) - (b^2*(5*A + 4*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(15*d*Sqrt[Cos[c + d*x]])","A",8,6,43,0.1395,1,"{17, 3023, 2748, 2633, 2635, 8}"
307,1,199,0,0.1126835,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt{\cos (c+d x)}} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Sqrt[Cos[c + d*x]],x]","\frac{b^2 x (4 A+3 C) \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b^2 (4 A+3 C) \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}-\frac{b^2 B \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{b^2 C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}","\frac{b^2 x (4 A+3 C) \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b^2 (4 A+3 C) \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}-\frac{b^2 B \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{b^2 C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}",1,"(b^2*(4*A + 3*C)*x*Sqrt[b*Cos[c + d*x]])/(8*Sqrt[Cos[c + d*x]]) + (b^2*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) + (b^2*(4*A + 3*C)*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d) + (b^2*C*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d) - (b^2*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Cos[c + d*x]])","A",7,6,43,0.1395,1,"{17, 3023, 2748, 2635, 8, 2633}"
308,1,155,0,0.0607352,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(3/2),x]","\frac{b^2 (3 A+2 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{b^2 B x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b^2 B \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}+\frac{b^2 C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{3 d}","\frac{b^2 (3 A+2 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{b^2 B x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b^2 B \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}+\frac{b^2 C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{3 d}",1,"(b^2*B*x*Sqrt[b*Cos[c + d*x]])/(2*Sqrt[Cos[c + d*x]]) + (b^2*(3*A + 2*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Sqrt[Cos[c + d*x]]) + (b^2*B*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d) + (b^2*C*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",3,3,43,0.06977,1,"{17, 3023, 2734}"
309,1,135,0,0.0374911,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(5/2),x]","\frac{A b^2 x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{b^2 C x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b^2 C \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}","\frac{A b^2 x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}+\frac{b^2 C x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b^2 C \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}",1,"(A*b^2*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (b^2*C*x*Sqrt[b*Cos[c + d*x]])/(2*Sqrt[Cos[c + d*x]]) + (b^2*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) + (b^2*C*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d)","A",5,4,43,0.09302,1,"{17, 2637, 2635, 8}"
310,1,102,0,0.0608191,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(7/2),x]","\frac{A b^2 \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{b^2 B x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{b^2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{A b^2 \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{b^2 B x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}+\frac{b^2 C \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(b^2*B*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (A*b^2*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(d*Sqrt[Cos[c + d*x]]) + (b^2*C*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]])","A",4,4,43,0.09302,1,"{17, 3023, 2735, 3770}"
311,1,102,0,0.0639631,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(9/2),x]","\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}+\frac{b^2 B \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{b^2 C x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}","\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}+\frac{b^2 B \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}+\frac{b^2 C x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}",1,"(b^2*C*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]] + (b^2*B*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(d*Sqrt[Cos[c + d*x]]) + (A*b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2))","A",4,4,43,0.09302,1,"{17, 3021, 2735, 3770}"
312,1,120,0,0.0969051,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{11}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(11/2),x]","\frac{b^2 (A+2 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}+\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}","\frac{b^2 (A+2 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}+\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}",1,"(b^2*(A + 2*C)*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(2*d*Sqrt[Cos[c + d*x]]) + (A*b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d*Cos[c + d*x]^(5/2)) + (b^2*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2))","A",6,6,43,0.1395,1,"{17, 3021, 2748, 3767, 8, 3770}"
313,1,164,0,0.1100162,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{13}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(13/2),x]","\frac{b^2 (2 A+3 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b^2 B \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}","\frac{b^2 (2 A+3 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b^2 B \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}",1,"(b^2*B*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(2*d*Sqrt[Cos[c + d*x]]) + (A*b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Cos[c + d*x]^(7/2)) + (b^2*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d*Cos[c + d*x]^(5/2)) + (b^2*(2*A + 3*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d*Cos[c + d*x]^(3/2))","A",7,7,43,0.1628,1,"{17, 3021, 2748, 3768, 3770, 3767, 8}"
314,1,208,0,0.1258836,"\int \frac{(b \cos (c+d x))^{5/2} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{15}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(15/2),x]","\frac{b^2 (3 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b^2 (3 A+4 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}+\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}+\frac{b^2 B \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}","\frac{b^2 (3 A+4 C) \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b^2 (3 A+4 C) \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}+\frac{A b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}+\frac{b^2 B \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{b^2 B \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}",1,"(b^2*(3*A + 4*C)*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(8*d*Sqrt[Cos[c + d*x]]) + (A*b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d*Cos[c + d*x]^(9/2)) + (b^2*(3*A + 4*C)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d*Cos[c + d*x]^(5/2)) + (b^2*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2)) + (b^2*B*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Cos[c + d*x]^(7/2))","A",7,6,43,0.1395,1,"{17, 3021, 2748, 3767, 3768, 3770}"
315,1,184,0,0.139417,"\int \frac{\cos ^{\frac{5}{2}}(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Sqrt[b*Cos[c + d*x]],x]","\frac{x (4 A+3 C) \sqrt{\cos (c+d x)}}{8 \sqrt{b \cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 d \sqrt{b \cos (c+d x)}}-\frac{B \sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 d \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 d \sqrt{b \cos (c+d x)}}","\frac{x (4 A+3 C) \sqrt{\cos (c+d x)}}{8 \sqrt{b \cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 d \sqrt{b \cos (c+d x)}}-\frac{B \sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 d \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 d \sqrt{b \cos (c+d x)}}",1,"((4*A + 3*C)*x*Sqrt[Cos[c + d*x]])/(8*Sqrt[b*Cos[c + d*x]]) + (B*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]]) + ((4*A + 3*C)*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(8*d*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(7/2)*Sin[c + d*x])/(4*d*Sqrt[b*Cos[c + d*x]]) - (B*Sqrt[Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[b*Cos[c + d*x]])","A",7,6,43,0.1395,1,"{17, 3023, 2748, 2635, 8, 2633}"
316,1,143,0,0.062233,"\int \frac{\cos ^{\frac{3}{2}}(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Sqrt[b*Cos[c + d*x]],x]","\frac{(3 A+2 C) \sin (c+d x) \sqrt{\cos (c+d x)}}{3 d \sqrt{b \cos (c+d x)}}+\frac{B x \sqrt{\cos (c+d x)}}{2 \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x)}{3 d \sqrt{b \cos (c+d x)}}","\frac{(3 A+2 C) \sin (c+d x) \sqrt{\cos (c+d x)}}{3 d \sqrt{b \cos (c+d x)}}+\frac{B x \sqrt{\cos (c+d x)}}{2 \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x)}{3 d \sqrt{b \cos (c+d x)}}",1,"(B*x*Sqrt[Cos[c + d*x]])/(2*Sqrt[b*Cos[c + d*x]]) + ((3*A + 2*C)*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(3*d*Sqrt[b*Cos[c + d*x]]) + (B*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(2*d*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(5/2)*Sin[c + d*x])/(3*d*Sqrt[b*Cos[c + d*x]])","A",3,3,43,0.06977,1,"{17, 3023, 2734}"
317,1,123,0,0.0330262,"\int \frac{\sqrt{\cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt{b \cos (c+d x)}} \, dx","Int[(Sqrt[Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Sqrt[b*Cos[c + d*x]],x]","\frac{A x \sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{2 \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 d \sqrt{b \cos (c+d x)}}","\frac{A x \sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{2 \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 d \sqrt{b \cos (c+d x)}}",1,"(A*x*Sqrt[Cos[c + d*x]])/Sqrt[b*Cos[c + d*x]] + (C*x*Sqrt[Cos[c + d*x]])/(2*Sqrt[b*Cos[c + d*x]]) + (B*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(2*d*Sqrt[b*Cos[c + d*x]])","A",5,4,43,0.09302,1,"{17, 2637, 2635, 8}"
318,1,93,0,0.0576249,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]),x]","\frac{A \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{b \cos (c+d x)}}+\frac{B x \sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}","\frac{A \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{b \cos (c+d x)}}+\frac{B x \sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}",1,"(B*x*Sqrt[Cos[c + d*x]])/Sqrt[b*Cos[c + d*x]] + (A*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(d*Sqrt[b*Cos[c + d*x]]) + (C*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",4,4,43,0.09302,1,"{18, 3023, 2735, 3770}"
319,1,93,0,0.0732515,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]),x]","\frac{A \sin (c+d x)}{d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{B \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}}","\frac{A \sin (c+d x)}{d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{B \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}}",1,"(C*x*Sqrt[Cos[c + d*x]])/Sqrt[b*Cos[c + d*x]] + (B*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",4,4,43,0.09302,1,"{18, 3021, 2735, 3770}"
320,1,111,0,0.0951999,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]),x]","\frac{(A+2 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}","\frac{(A+2 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}",1,"((A + 2*C)*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(2*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(2*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]) + (B*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",6,6,43,0.1395,1,"{18, 3021, 2748, 3767, 8, 3770}"
321,1,152,0,0.118751,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]),x]","\frac{(2 A+3 C) \sin (c+d x)}{3 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{3 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{b \cos (c+d x)}}","\frac{(2 A+3 C) \sin (c+d x)}{3 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{3 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{b \cos (c+d x)}}",1,"(B*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(2*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(3*d*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]) + (B*Sin[c + d*x])/(2*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]) + ((2*A + 3*C)*Sin[c + d*x])/(3*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",7,7,43,0.1628,1,"{18, 3021, 2748, 3768, 3770, 3767, 8}"
322,1,193,0,0.117843,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\frac{9}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(9/2)*Sqrt[b*Cos[c + d*x]]),x]","\frac{(3 A+4 C) \sin (c+d x)}{8 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{(3 A+4 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{4 d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin ^3(c+d x)}{3 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}","\frac{(3 A+4 C) \sin (c+d x)}{8 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{(3 A+4 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{4 d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin ^3(c+d x)}{3 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}",1,"((3*A + 4*C)*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(8*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(4*d*Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]) + ((3*A + 4*C)*Sin[c + d*x])/(8*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]) + (B*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]) + (B*Sin[c + d*x]^3)/(3*d*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]])","A",7,6,43,0.1395,1,"{18, 3021, 2748, 3767, 3768, 3770}"
323,1,199,0,0.1093473,"\int \frac{\cos ^{\frac{7}{2}}(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]^(7/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{x (4 A+3 C) \sqrt{\cos (c+d x)}}{8 b \sqrt{b \cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 b d \sqrt{b \cos (c+d x)}}-\frac{B \sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 b d \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 b d \sqrt{b \cos (c+d x)}}","\frac{x (4 A+3 C) \sqrt{\cos (c+d x)}}{8 b \sqrt{b \cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 b d \sqrt{b \cos (c+d x)}}-\frac{B \sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 b d \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 b d \sqrt{b \cos (c+d x)}}",1,"((4*A + 3*C)*x*Sqrt[Cos[c + d*x]])/(8*b*Sqrt[b*Cos[c + d*x]]) + (B*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(b*d*Sqrt[b*Cos[c + d*x]]) + ((4*A + 3*C)*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(8*b*d*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(7/2)*Sin[c + d*x])/(4*b*d*Sqrt[b*Cos[c + d*x]]) - (B*Sqrt[Cos[c + d*x]]*Sin[c + d*x]^3)/(3*b*d*Sqrt[b*Cos[c + d*x]])","A",7,6,43,0.1395,1,"{17, 3023, 2748, 2635, 8, 2633}"
324,1,155,0,0.0600347,"\int \frac{\cos ^{\frac{5}{2}}(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{(3 A+2 C) \sin (c+d x) \sqrt{\cos (c+d x)}}{3 b d \sqrt{b \cos (c+d x)}}+\frac{B x \sqrt{\cos (c+d x)}}{2 b \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x)}{3 b d \sqrt{b \cos (c+d x)}}","\frac{(3 A+2 C) \sin (c+d x) \sqrt{\cos (c+d x)}}{3 b d \sqrt{b \cos (c+d x)}}+\frac{B x \sqrt{\cos (c+d x)}}{2 b \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x)}{3 b d \sqrt{b \cos (c+d x)}}",1,"(B*x*Sqrt[Cos[c + d*x]])/(2*b*Sqrt[b*Cos[c + d*x]]) + ((3*A + 2*C)*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(3*b*d*Sqrt[b*Cos[c + d*x]]) + (B*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(2*b*d*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(5/2)*Sin[c + d*x])/(3*b*d*Sqrt[b*Cos[c + d*x]])","A",3,3,43,0.06977,1,"{17, 3023, 2734}"
325,1,135,0,0.0325222,"\int \frac{\cos ^{\frac{3}{2}}(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Cos[c + d*x]^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{A x \sqrt{\cos (c+d x)}}{b \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{2 b \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b d \sqrt{b \cos (c+d x)}}","\frac{A x \sqrt{\cos (c+d x)}}{b \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{2 b \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b d \sqrt{b \cos (c+d x)}}",1,"(A*x*Sqrt[Cos[c + d*x]])/(b*Sqrt[b*Cos[c + d*x]]) + (C*x*Sqrt[Cos[c + d*x]])/(2*b*Sqrt[b*Cos[c + d*x]]) + (B*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(b*d*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(2*b*d*Sqrt[b*Cos[c + d*x]])","A",5,4,43,0.09302,1,"{17, 2637, 2635, 8}"
326,1,102,0,0.0598896,"\int \frac{\sqrt{\cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{3/2}} \, dx","Int[(Sqrt[Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(3/2),x]","\frac{A \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b d \sqrt{b \cos (c+d x)}}+\frac{B x \sqrt{\cos (c+d x)}}{b \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}","\frac{A \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b d \sqrt{b \cos (c+d x)}}+\frac{B x \sqrt{\cos (c+d x)}}{b \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}",1,"(B*x*Sqrt[Cos[c + d*x]])/(b*Sqrt[b*Cos[c + d*x]]) + (A*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(b*d*Sqrt[b*Cos[c + d*x]]) + (C*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(b*d*Sqrt[b*Cos[c + d*x]])","A",4,4,43,0.09302,1,"{17, 3023, 2735, 3770}"
327,1,102,0,0.0835293,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt{\cos (c+d x)} (b \cos (c+d x))^{3/2}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(3/2)),x]","\frac{A \sin (c+d x)}{b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{B \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b d \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{b \sqrt{b \cos (c+d x)}}","\frac{A \sin (c+d x)}{b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{B \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b d \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{b \sqrt{b \cos (c+d x)}}",1,"(C*x*Sqrt[Cos[c + d*x]])/(b*Sqrt[b*Cos[c + d*x]]) + (B*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(b*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",4,4,43,0.09302,1,"{18, 3021, 2735, 3770}"
328,1,120,0,0.0927031,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(3/2)),x]","\frac{(A+2 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{2 b d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}","\frac{(A+2 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{2 b d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}",1,"((A + 2*C)*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(2*b*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(2*b*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]) + (B*Sin[c + d*x])/(b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",6,6,43,0.1395,1,"{18, 3021, 2748, 3767, 8, 3770}"
329,1,164,0,0.1238275,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^(3/2)),x]","\frac{(2 A+3 C) \sin (c+d x)}{3 b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{3 b d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{2 b d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b d \sqrt{b \cos (c+d x)}}","\frac{(2 A+3 C) \sin (c+d x)}{3 b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{3 b d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{2 b d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b d \sqrt{b \cos (c+d x)}}",1,"(B*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(2*b*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(3*b*d*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]) + (B*Sin[c + d*x])/(2*b*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]) + ((2*A + 3*C)*Sin[c + d*x])/(3*b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",7,7,43,0.1628,1,"{18, 3021, 2748, 3768, 3770, 3767, 8}"
330,1,208,0,0.1279821,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(7/2)*(b*Cos[c + d*x])^(3/2)),x]","\frac{(3 A+4 C) \sin (c+d x)}{8 b d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{(3 A+4 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 b d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{4 b d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin ^3(c+d x)}{3 b d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}","\frac{(3 A+4 C) \sin (c+d x)}{8 b d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{(3 A+4 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 b d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{4 b d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin ^3(c+d x)}{3 b d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}",1,"((3*A + 4*C)*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(8*b*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(4*b*d*Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]) + ((3*A + 4*C)*Sin[c + d*x])/(8*b*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]) + (B*Sin[c + d*x])/(b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]) + (B*Sin[c + d*x]^3)/(3*b*d*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]])","A",7,6,43,0.1395,1,"{18, 3021, 2748, 3767, 3768, 3770}"
331,1,199,0,0.1165695,"\int \frac{\cos ^{\frac{9}{2}}(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^(9/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{x (4 A+3 C) \sqrt{\cos (c+d x)}}{8 b^2 \sqrt{b \cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 b^2 d \sqrt{b \cos (c+d x)}}-\frac{B \sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)}}{b^2 d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 b^2 d \sqrt{b \cos (c+d x)}}","\frac{x (4 A+3 C) \sqrt{\cos (c+d x)}}{8 b^2 \sqrt{b \cos (c+d x)}}+\frac{(4 A+3 C) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 b^2 d \sqrt{b \cos (c+d x)}}-\frac{B \sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)}}{b^2 d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 b^2 d \sqrt{b \cos (c+d x)}}",1,"((4*A + 3*C)*x*Sqrt[Cos[c + d*x]])/(8*b^2*Sqrt[b*Cos[c + d*x]]) + (B*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(b^2*d*Sqrt[b*Cos[c + d*x]]) + ((4*A + 3*C)*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(8*b^2*d*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(7/2)*Sin[c + d*x])/(4*b^2*d*Sqrt[b*Cos[c + d*x]]) - (B*Sqrt[Cos[c + d*x]]*Sin[c + d*x]^3)/(3*b^2*d*Sqrt[b*Cos[c + d*x]])","A",7,6,43,0.1395,1,"{17, 3023, 2748, 2635, 8, 2633}"
332,1,155,0,0.0636998,"\int \frac{\cos ^{\frac{7}{2}}(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^(7/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{(3 A+2 C) \sin (c+d x) \sqrt{\cos (c+d x)}}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{B x \sqrt{\cos (c+d x)}}{2 b^2 \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b^2 d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x)}{3 b^2 d \sqrt{b \cos (c+d x)}}","\frac{(3 A+2 C) \sin (c+d x) \sqrt{\cos (c+d x)}}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{B x \sqrt{\cos (c+d x)}}{2 b^2 \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b^2 d \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x)}{3 b^2 d \sqrt{b \cos (c+d x)}}",1,"(B*x*Sqrt[Cos[c + d*x]])/(2*b^2*Sqrt[b*Cos[c + d*x]]) + ((3*A + 2*C)*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(3*b^2*d*Sqrt[b*Cos[c + d*x]]) + (B*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(2*b^2*d*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(5/2)*Sin[c + d*x])/(3*b^2*d*Sqrt[b*Cos[c + d*x]])","A",3,3,43,0.06977,1,"{17, 3023, 2734}"
333,1,135,0,0.0361816,"\int \frac{\cos ^{\frac{5}{2}}(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^(5/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{A x \sqrt{\cos (c+d x)}}{b^2 \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)}}{b^2 d \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{2 b^2 \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b^2 d \sqrt{b \cos (c+d x)}}","\frac{A x \sqrt{\cos (c+d x)}}{b^2 \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x) \sqrt{\cos (c+d x)}}{b^2 d \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{2 b^2 \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b^2 d \sqrt{b \cos (c+d x)}}",1,"(A*x*Sqrt[Cos[c + d*x]])/(b^2*Sqrt[b*Cos[c + d*x]]) + (C*x*Sqrt[Cos[c + d*x]])/(2*b^2*Sqrt[b*Cos[c + d*x]]) + (B*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(b^2*d*Sqrt[b*Cos[c + d*x]]) + (C*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(2*b^2*d*Sqrt[b*Cos[c + d*x]])","A",5,4,43,0.09302,1,"{17, 2637, 2635, 8}"
334,1,102,0,0.0615652,"\int \frac{\cos ^{\frac{3}{2}}(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Cos[c + d*x]^(3/2)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{A \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b^2 d \sqrt{b \cos (c+d x)}}+\frac{B x \sqrt{\cos (c+d x)}}{b^2 \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)}}{b^2 d \sqrt{b \cos (c+d x)}}","\frac{A \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b^2 d \sqrt{b \cos (c+d x)}}+\frac{B x \sqrt{\cos (c+d x)}}{b^2 \sqrt{b \cos (c+d x)}}+\frac{C \sin (c+d x) \sqrt{\cos (c+d x)}}{b^2 d \sqrt{b \cos (c+d x)}}",1,"(B*x*Sqrt[Cos[c + d*x]])/(b^2*Sqrt[b*Cos[c + d*x]]) + (A*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(b^2*d*Sqrt[b*Cos[c + d*x]]) + (C*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(b^2*d*Sqrt[b*Cos[c + d*x]])","A",4,4,43,0.09302,1,"{17, 3023, 2735, 3770}"
335,1,102,0,0.0621749,"\int \frac{\sqrt{\cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{5/2}} \, dx","Int[(Sqrt[Cos[c + d*x]]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(5/2),x]","\frac{A \sin (c+d x)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{B \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b^2 d \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{b^2 \sqrt{b \cos (c+d x)}}","\frac{A \sin (c+d x)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{B \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b^2 d \sqrt{b \cos (c+d x)}}+\frac{C x \sqrt{\cos (c+d x)}}{b^2 \sqrt{b \cos (c+d x)}}",1,"(C*x*Sqrt[Cos[c + d*x]])/(b^2*Sqrt[b*Cos[c + d*x]]) + (B*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(b^2*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",4,4,43,0.09302,1,"{17, 3021, 2735, 3770}"
336,1,120,0,0.0919308,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt{\cos (c+d x)} (b \cos (c+d x))^{5/2}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(5/2)),x]","\frac{(A+2 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b^2 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{2 b^2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}","\frac{(A+2 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b^2 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{2 b^2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}",1,"((A + 2*C)*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(2*b^2*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(2*b^2*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]) + (B*Sin[c + d*x])/(b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",6,6,43,0.1395,1,"{18, 3021, 2748, 3767, 8, 3770}"
337,1,164,0,0.1103147,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{5/2}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(5/2)),x]","\frac{(2 A+3 C) \sin (c+d x)}{3 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{3 b^2 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{2 b^2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b^2 d \sqrt{b \cos (c+d x)}}","\frac{(2 A+3 C) \sin (c+d x)}{3 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{3 b^2 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{2 b^2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b^2 d \sqrt{b \cos (c+d x)}}",1,"(B*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(2*b^2*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(3*b^2*d*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]) + (B*Sin[c + d*x])/(2*b^2*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]) + ((2*A + 3*C)*Sin[c + d*x])/(3*b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",7,7,43,0.1628,1,"{18, 3021, 2748, 3768, 3770, 3767, 8}"
338,1,208,0,0.1346478,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^{5/2}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^(5/2)),x]","\frac{(3 A+4 C) \sin (c+d x)}{8 b^2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{(3 A+4 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 b^2 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{4 b^2 d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin ^3(c+d x)}{3 b^2 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}","\frac{(3 A+4 C) \sin (c+d x)}{8 b^2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{(3 A+4 C) \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 b^2 d \sqrt{b \cos (c+d x)}}+\frac{A \sin (c+d x)}{4 b^2 d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin ^3(c+d x)}{3 b^2 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{B \sin (c+d x)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}",1,"((3*A + 4*C)*ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(8*b^2*d*Sqrt[b*Cos[c + d*x]]) + (A*Sin[c + d*x])/(4*b^2*d*Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]) + ((3*A + 4*C)*Sin[c + d*x])/(8*b^2*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]) + (B*Sin[c + d*x])/(b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]) + (B*Sin[c + d*x]^3)/(3*b^2*d*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]])","A",7,6,43,0.1395,1,"{18, 3021, 2748, 3767, 3768, 3770}"
339,1,154,0,0.1530963,"\int \cos (c+d x) (b \cos (c+d x))^{2/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^(2/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{3 (11 A+8 C) \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{88 b^2 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{11/3} \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{17}{6};\cos ^2(c+d x)\right)}{11 b^3 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{8/3}}{11 b^2 d}","-\frac{3 (11 A+8 C) \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{88 b^2 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{11/3} \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{17}{6};\cos ^2(c+d x)\right)}{11 b^3 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{8/3}}{11 b^2 d}",1,"(3*C*(b*Cos[c + d*x])^(8/3)*Sin[c + d*x])/(11*b^2*d) - (3*(11*A + 8*C)*(b*Cos[c + d*x])^(8/3)*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[c + d*x]^2]*Sin[c + d*x])/(88*b^2*d*Sqrt[Sin[c + d*x]^2]) - (3*B*(b*Cos[c + d*x])^(11/3)*Hypergeometric2F1[1/2, 11/6, 17/6, Cos[c + d*x]^2]*Sin[c + d*x])/(11*b^3*d*Sqrt[Sin[c + d*x]^2])","A",5,4,39,0.1026,1,"{16, 3023, 2748, 2643}"
340,1,154,0,0.1350873,"\int (b \cos (c+d x))^{2/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^(2/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{3 (8 A+5 C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{40 b d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{8 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{5/3}}{8 b d}","-\frac{3 (8 A+5 C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{40 b d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{8 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{5/3}}{8 b d}",1,"(3*C*(b*Cos[c + d*x])^(5/3)*Sin[c + d*x])/(8*b*d) - (3*(8*A + 5*C)*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(40*b*d*Sqrt[Sin[c + d*x]^2]) - (3*B*(b*Cos[c + d*x])^(8/3)*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*b^2*d*Sqrt[Sin[c + d*x]^2])","A",4,3,33,0.09091,1,"{3023, 2748, 2643}"
341,1,148,0,0.1561366,"\int (b \cos (c+d x))^{2/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^(2/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","-\frac{3 (5 A+2 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{10 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3}}{5 d}","-\frac{3 (5 A+2 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{10 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3}}{5 d}",1,"(3*C*(b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*d) - (3*(5*A + 2*C)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(10*d*Sqrt[Sin[c + d*x]^2]) - (3*B*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*b*d*Sqrt[Sin[c + d*x]^2])","A",5,4,39,0.1026,1,"{16, 3023, 2748, 2643}"
342,1,147,0,0.1857339,"\int (b \cos (c+d x))^{2/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^(2/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","\frac{3 (2 A-C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b d \sqrt{\sin ^2(c+d x)}}+\frac{3 A b \sin (c+d x)}{d \sqrt[3]{b \cos (c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 d \sqrt{\sin ^2(c+d x)}}","\frac{3 (2 A-C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b d \sqrt{\sin ^2(c+d x)}}+\frac{3 A b \sin (c+d x)}{d \sqrt[3]{b \cos (c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 d \sqrt{\sin ^2(c+d x)}}",1,"(3*A*b*Sin[c + d*x])/(d*(b*Cos[c + d*x])^(1/3)) - (3*B*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(2*d*Sqrt[Sin[c + d*x]^2]) + (3*(2*A - C)*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*b*d*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{16, 3021, 2748, 2643}"
343,1,145,0,0.1926408,"\int (b \cos (c+d x))^{2/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(2/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{3 A b^2 \sin (c+d x)}{4 d (b \cos (c+d x))^{4/3}}-\frac{3 (A+4 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{8 d \sqrt{\sin ^2(c+d x)}}+\frac{3 b B \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}","\frac{3 A b^2 \sin (c+d x)}{4 d (b \cos (c+d x))^{4/3}}-\frac{3 (A+4 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{8 d \sqrt{\sin ^2(c+d x)}}+\frac{3 b B \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}",1,"(3*A*b^2*Sin[c + d*x])/(4*d*(b*Cos[c + d*x])^(4/3)) + (3*b*B*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2]) - (3*(A + 4*C)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*d*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{16, 3021, 2748, 2643}"
344,1,152,0,0.1931043,"\int (b \cos (c+d x))^{2/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^4(c+d x) \, dx","Int[(b*Cos[c + d*x])^(2/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^4,x]","\frac{3 A b^3 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/3}}+\frac{3 b (4 A+7 C) \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}+\frac{3 b^2 B \sin (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{4/3}}","\frac{3 A b^3 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/3}}+\frac{3 b (4 A+7 C) \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}+\frac{3 b^2 B \sin (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{4/3}}",1,"(3*A*b^3*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/3)) + (3*b^2*B*Hypergeometric2F1[-2/3, 1/2, 1/3, Cos[c + d*x]^2]*Sin[c + d*x])/(4*d*(b*Cos[c + d*x])^(4/3)*Sqrt[Sin[c + d*x]^2]) + (3*b*(4*A + 7*C)*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{16, 3021, 2748, 2643}"
345,1,154,0,0.1503486,"\int \cos (c+d x) (b \cos (c+d x))^{4/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^(4/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{3 (13 A+10 C) \sin (c+d x) (b \cos (c+d x))^{10/3} \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{130 b^2 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{13/3} \, _2F_1\left(\frac{1}{2},\frac{13}{6};\frac{19}{6};\cos ^2(c+d x)\right)}{13 b^3 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{10/3}}{13 b^2 d}","-\frac{3 (13 A+10 C) \sin (c+d x) (b \cos (c+d x))^{10/3} \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{130 b^2 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{13/3} \, _2F_1\left(\frac{1}{2},\frac{13}{6};\frac{19}{6};\cos ^2(c+d x)\right)}{13 b^3 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{10/3}}{13 b^2 d}",1,"(3*C*(b*Cos[c + d*x])^(10/3)*Sin[c + d*x])/(13*b^2*d) - (3*(13*A + 10*C)*(b*Cos[c + d*x])^(10/3)*Hypergeometric2F1[1/2, 5/3, 8/3, Cos[c + d*x]^2]*Sin[c + d*x])/(130*b^2*d*Sqrt[Sin[c + d*x]^2]) - (3*B*(b*Cos[c + d*x])^(13/3)*Hypergeometric2F1[1/2, 13/6, 19/6, Cos[c + d*x]^2]*Sin[c + d*x])/(13*b^3*d*Sqrt[Sin[c + d*x]^2])","A",5,4,39,0.1026,1,"{16, 3023, 2748, 2643}"
346,1,154,0,0.128679,"\int (b \cos (c+d x))^{4/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^(4/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{3 (10 A+7 C) \sin (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{70 b d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{10/3} \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{10 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{7/3}}{10 b d}","-\frac{3 (10 A+7 C) \sin (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{70 b d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{10/3} \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{10 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{7/3}}{10 b d}",1,"(3*C*(b*Cos[c + d*x])^(7/3)*Sin[c + d*x])/(10*b*d) - (3*(10*A + 7*C)*(b*Cos[c + d*x])^(7/3)*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[c + d*x]^2]*Sin[c + d*x])/(70*b*d*Sqrt[Sin[c + d*x]^2]) - (3*B*(b*Cos[c + d*x])^(10/3)*Hypergeometric2F1[1/2, 5/3, 8/3, Cos[c + d*x]^2]*Sin[c + d*x])/(10*b^2*d*Sqrt[Sin[c + d*x]^2])","A",4,3,33,0.09091,1,"{3023, 2748, 2643}"
347,1,148,0,0.1484928,"\int (b \cos (c+d x))^{4/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^(4/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","-\frac{3 (7 A+4 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{28 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 b d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{4/3}}{7 d}","-\frac{3 (7 A+4 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{28 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 b d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{4/3}}{7 d}",1,"(3*C*(b*Cos[c + d*x])^(4/3)*Sin[c + d*x])/(7*d) - (3*(7*A + 4*C)*(b*Cos[c + d*x])^(4/3)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(28*d*Sqrt[Sin[c + d*x]^2]) - (3*B*(b*Cos[c + d*x])^(7/3)*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[c + d*x]^2]*Sin[c + d*x])/(7*b*d*Sqrt[Sin[c + d*x]^2])","A",5,4,39,0.1026,1,"{16, 3023, 2748, 2643}"
348,1,145,0,0.1736937,"\int (b \cos (c+d x))^{4/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^(4/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","-\frac{3 b (4 A+C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)}}+\frac{3 b C \sin (c+d x) \sqrt[3]{b \cos (c+d x)}}{4 d}","-\frac{3 b (4 A+C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)}}+\frac{3 b C \sin (c+d x) \sqrt[3]{b \cos (c+d x)}}{4 d}",1,"(3*b*C*(b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(4*d) - (3*b*(4*A + C)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sin[c + d*x])/(4*d*Sqrt[Sin[c + d*x]^2]) - (3*B*(b*Cos[c + d*x])^(4/3)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(4*d*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{16, 3023, 2748, 2643}"
349,1,145,0,0.1932684,"\int (b \cos (c+d x))^{4/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(4/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{3 A b^2 \sin (c+d x)}{2 d (b \cos (c+d x))^{2/3}}+\frac{3 (A-2 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{8 d \sqrt{\sin ^2(c+d x)}}-\frac{3 b B \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}","\frac{3 A b^2 \sin (c+d x)}{2 d (b \cos (c+d x))^{2/3}}+\frac{3 (A-2 C) \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{8 d \sqrt{\sin ^2(c+d x)}}-\frac{3 b B \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}",1,"(3*A*b^2*Sin[c + d*x])/(2*d*(b*Cos[c + d*x])^(2/3)) - (3*b*B*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2]) + (3*(A - 2*C)*(b*Cos[c + d*x])^(4/3)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*d*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{16, 3021, 2748, 2643}"
350,1,152,0,0.1938704,"\int (b \cos (c+d x))^{4/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^4(c+d x) \, dx","Int[(b*Cos[c + d*x])^(4/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^4,x]","\frac{3 A b^3 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/3}}-\frac{3 b (2 A+5 C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{5 d \sqrt{\sin ^2(c+d x)}}+\frac{3 b^2 B \sin (c+d x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\cos ^2(c+d x)\right)}{2 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}","\frac{3 A b^3 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/3}}-\frac{3 b (2 A+5 C) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{5 d \sqrt{\sin ^2(c+d x)}}+\frac{3 b^2 B \sin (c+d x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\cos ^2(c+d x)\right)}{2 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}",1,"(3*A*b^3*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/3)) + (3*b^2*B*Hypergeometric2F1[-1/3, 1/2, 2/3, Cos[c + d*x]^2]*Sin[c + d*x])/(2*d*(b*Cos[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2]) - (3*b*(2*A + 5*C)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*d*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{16, 3021, 2748, 2643}"
351,1,154,0,0.1456107,"\int \frac{\cos ^2(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^2*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(1/3),x]","-\frac{3 (11 A+8 C) \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{88 b^3 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{11/3} \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{17}{6};\cos ^2(c+d x)\right)}{11 b^4 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{8/3}}{11 b^3 d}","-\frac{3 (11 A+8 C) \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{88 b^3 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{11/3} \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{17}{6};\cos ^2(c+d x)\right)}{11 b^4 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{8/3}}{11 b^3 d}",1,"(3*C*(b*Cos[c + d*x])^(8/3)*Sin[c + d*x])/(11*b^3*d) - (3*(11*A + 8*C)*(b*Cos[c + d*x])^(8/3)*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[c + d*x]^2]*Sin[c + d*x])/(88*b^3*d*Sqrt[Sin[c + d*x]^2]) - (3*B*(b*Cos[c + d*x])^(11/3)*Hypergeometric2F1[1/2, 11/6, 17/6, Cos[c + d*x]^2]*Sin[c + d*x])/(11*b^4*d*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{16, 3023, 2748, 2643}"
352,1,154,0,0.1481162,"\int \frac{\cos (c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(1/3),x]","-\frac{3 (8 A+5 C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{40 b^2 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{8 b^3 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{5/3}}{8 b^2 d}","-\frac{3 (8 A+5 C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{40 b^2 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{8 b^3 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{5/3}}{8 b^2 d}",1,"(3*C*(b*Cos[c + d*x])^(5/3)*Sin[c + d*x])/(8*b^2*d) - (3*(8*A + 5*C)*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(40*b^2*d*Sqrt[Sin[c + d*x]^2]) - (3*B*(b*Cos[c + d*x])^(8/3)*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*b^3*d*Sqrt[Sin[c + d*x]^2])","A",5,4,39,0.1026,1,"{16, 3023, 2748, 2643}"
353,1,154,0,0.1228421,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(1/3),x]","-\frac{3 (5 A+2 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{10 b d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3}}{5 b d}","-\frac{3 (5 A+2 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{10 b d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3}}{5 b d}",1,"(3*C*(b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*b*d) - (3*(5*A + 2*C)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(10*b*d*Sqrt[Sin[c + d*x]^2]) - (3*B*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*b^2*d*Sqrt[Sin[c + d*x]^2])","A",4,3,33,0.09091,1,"{3023, 2748, 2643}"
354,1,149,0,0.1631308,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec (c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x])/(b*Cos[c + d*x])^(1/3),x]","\frac{3 (2 A-C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 A \sin (c+d x)}{d \sqrt[3]{b \cos (c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 b d \sqrt{\sin ^2(c+d x)}}","\frac{3 (2 A-C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 A \sin (c+d x)}{d \sqrt[3]{b \cos (c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*A*Sin[c + d*x])/(d*(b*Cos[c + d*x])^(1/3)) - (3*B*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(2*b*d*Sqrt[Sin[c + d*x]^2]) + (3*(2*A - C)*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*b^2*d*Sqrt[Sin[c + d*x]^2])","A",5,4,39,0.1026,1,"{16, 3021, 2748, 2643}"
355,1,145,0,0.1740715,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^2(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^2)/(b*Cos[c + d*x])^(1/3),x]","-\frac{3 (A+4 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{8 b d \sqrt{\sin ^2(c+d x)}}+\frac{3 A b \sin (c+d x)}{4 d (b \cos (c+d x))^{4/3}}+\frac{3 B \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}","-\frac{3 (A+4 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{8 b d \sqrt{\sin ^2(c+d x)}}+\frac{3 A b \sin (c+d x)}{4 d (b \cos (c+d x))^{4/3}}+\frac{3 B \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}",1,"(3*A*b*Sin[c + d*x])/(4*d*(b*Cos[c + d*x])^(4/3)) + (3*B*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2]) - (3*(A + 4*C)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*b*d*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{16, 3021, 2748, 2643}"
356,1,149,0,0.1786571,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^3(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^3)/(b*Cos[c + d*x])^(1/3),x]","\frac{3 A b^2 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/3}}+\frac{3 (4 A+7 C) \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}+\frac{3 b B \sin (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{4/3}}","\frac{3 A b^2 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/3}}+\frac{3 (4 A+7 C) \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}+\frac{3 b B \sin (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{4/3}}",1,"(3*A*b^2*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/3)) + (3*b*B*Hypergeometric2F1[-2/3, 1/2, 1/3, Cos[c + d*x]^2]*Sin[c + d*x])/(4*d*(b*Cos[c + d*x])^(4/3)*Sqrt[Sin[c + d*x]^2]) + (3*(4*A + 7*C)*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{16, 3021, 2748, 2643}"
357,1,154,0,0.142863,"\int \frac{\cos ^3(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{4/3}} \, dx","Int[(Cos[c + d*x]^3*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(4/3),x]","-\frac{3 (11 A+8 C) \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{88 b^4 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{11/3} \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{17}{6};\cos ^2(c+d x)\right)}{11 b^5 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{8/3}}{11 b^4 d}","-\frac{3 (11 A+8 C) \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{88 b^4 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{11/3} \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{17}{6};\cos ^2(c+d x)\right)}{11 b^5 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{8/3}}{11 b^4 d}",1,"(3*C*(b*Cos[c + d*x])^(8/3)*Sin[c + d*x])/(11*b^4*d) - (3*(11*A + 8*C)*(b*Cos[c + d*x])^(8/3)*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[c + d*x]^2]*Sin[c + d*x])/(88*b^4*d*Sqrt[Sin[c + d*x]^2]) - (3*B*(b*Cos[c + d*x])^(11/3)*Hypergeometric2F1[1/2, 11/6, 17/6, Cos[c + d*x]^2]*Sin[c + d*x])/(11*b^5*d*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{16, 3023, 2748, 2643}"
358,1,154,0,0.1438387,"\int \frac{\cos ^2(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{4/3}} \, dx","Int[(Cos[c + d*x]^2*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(4/3),x]","-\frac{3 (8 A+5 C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{40 b^3 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{8 b^4 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{5/3}}{8 b^3 d}","-\frac{3 (8 A+5 C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{40 b^3 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{8 b^4 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{5/3}}{8 b^3 d}",1,"(3*C*(b*Cos[c + d*x])^(5/3)*Sin[c + d*x])/(8*b^3*d) - (3*(8*A + 5*C)*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(40*b^3*d*Sqrt[Sin[c + d*x]^2]) - (3*B*(b*Cos[c + d*x])^(8/3)*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*b^4*d*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{16, 3023, 2748, 2643}"
359,1,154,0,0.1400527,"\int \frac{\cos (c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{4/3}} \, dx","Int[(Cos[c + d*x]*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(4/3),x]","-\frac{3 (5 A+2 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{10 b^2 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^3 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3}}{5 b^2 d}","-\frac{3 (5 A+2 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{10 b^2 d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^3 d \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3}}{5 b^2 d}",1,"(3*C*(b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*b^2*d) - (3*(5*A + 2*C)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(10*b^2*d*Sqrt[Sin[c + d*x]^2]) - (3*B*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*b^3*d*Sqrt[Sin[c + d*x]^2])","A",5,4,39,0.1026,1,"{16, 3023, 2748, 2643}"
360,1,152,0,0.1392105,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(b*Cos[c + d*x])^(4/3),x]","\frac{3 (2 A-C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^3 d \sqrt{\sin ^2(c+d x)}}+\frac{3 A \sin (c+d x)}{b d \sqrt[3]{b \cos (c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 b^2 d \sqrt{\sin ^2(c+d x)}}","\frac{3 (2 A-C) \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^3 d \sqrt{\sin ^2(c+d x)}}+\frac{3 A \sin (c+d x)}{b d \sqrt[3]{b \cos (c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(3*A*Sin[c + d*x])/(b*d*(b*Cos[c + d*x])^(1/3)) - (3*B*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(2*b^2*d*Sqrt[Sin[c + d*x]^2]) + (3*(2*A - C)*(b*Cos[c + d*x])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*b^3*d*Sqrt[Sin[c + d*x]^2])","A",4,3,33,0.09091,1,"{3021, 2748, 2643}"
361,1,147,0,0.1678299,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec (c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x])/(b*Cos[c + d*x])^(4/3),x]","-\frac{3 (A+4 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{8 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 A \sin (c+d x)}{4 d (b \cos (c+d x))^{4/3}}+\frac{3 B \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{b d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}","-\frac{3 (A+4 C) \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{8 b^2 d \sqrt{\sin ^2(c+d x)}}+\frac{3 A \sin (c+d x)}{4 d (b \cos (c+d x))^{4/3}}+\frac{3 B \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{b d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}",1,"(3*A*Sin[c + d*x])/(4*d*(b*Cos[c + d*x])^(4/3)) + (3*B*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2]) - (3*(A + 4*C)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*b^2*d*Sqrt[Sin[c + d*x]^2])","A",5,4,39,0.1026,1,"{16, 3021, 2748, 2643}"
362,1,149,0,0.1886933,"\int \frac{\left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^2(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Int[((A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^2)/(b*Cos[c + d*x])^(4/3),x]","\frac{3 (4 A+7 C) \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{7 b d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}+\frac{3 A b \sin (c+d x)}{7 d (b \cos (c+d x))^{7/3}}+\frac{3 B \sin (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{4/3}}","\frac{3 (4 A+7 C) \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{7 b d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}+\frac{3 A b \sin (c+d x)}{7 d (b \cos (c+d x))^{7/3}}+\frac{3 B \sin (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{4/3}}",1,"(3*A*b*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/3)) + (3*B*Hypergeometric2F1[-2/3, 1/2, 1/3, Cos[c + d*x]^2]*Sin[c + d*x])/(4*d*(b*Cos[c + d*x])^(4/3)*Sqrt[Sin[c + d*x]^2]) + (3*(4*A + 7*C)*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sin[c + d*x])/(7*b*d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{16, 3021, 2748, 2643}"
363,1,222,0,0.2121607,"\int \cos ^m(c+d x) (b \cos (c+d x))^{4/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^m*(b*Cos[c + d*x])^(4/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{3 b \left(\frac{A}{3 m+7}+\frac{C}{3 m+10}\right) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+7);\frac{1}{6} (3 m+13);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}-\frac{3 b B \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+3}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+10);\frac{1}{6} (3 m+16);\cos ^2(c+d x)\right)}{d (3 m+10) \sqrt{\sin ^2(c+d x)}}+\frac{3 b C \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+2}(c+d x)}{d (3 m+10)}","-\frac{3 b (A (3 m+10)+C (3 m+7)) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+7);\frac{1}{6} (3 m+13);\cos ^2(c+d x)\right)}{d (3 m+7) (3 m+10) \sqrt{\sin ^2(c+d x)}}-\frac{3 b B \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+3}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+10);\frac{1}{6} (3 m+16);\cos ^2(c+d x)\right)}{d (3 m+10) \sqrt{\sin ^2(c+d x)}}+\frac{3 b C \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+2}(c+d x)}{d (3 m+10)}",1,"(3*b*C*Cos[c + d*x]^(2 + m)*(b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(d*(10 + 3*m)) - (3*b*(A/(7 + 3*m) + C/(10 + 3*m))*Cos[c + d*x]^(2 + m)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/2, (7 + 3*m)/6, (13 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2]) - (3*b*B*Cos[c + d*x]^(3 + m)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/2, (10 + 3*m)/6, (16 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(10 + 3*m)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{20, 3023, 2748, 2643}"
364,1,219,0,0.2125131,"\int \cos ^m(c+d x) (b \cos (c+d x))^{2/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^m*(b*Cos[c + d*x])^(2/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{3 \left(\frac{A}{3 m+5}+\frac{C}{3 m+8}\right) \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+5);\frac{1}{6} (3 m+11);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+8);\frac{1}{6} (3 m+14);\cos ^2(c+d x)\right)}{d (3 m+8) \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+1}(c+d x)}{d (3 m+8)}","-\frac{3 (A (3 m+8)+C (3 m+5)) \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+5);\frac{1}{6} (3 m+11);\cos ^2(c+d x)\right)}{d (3 m+5) (3 m+8) \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+8);\frac{1}{6} (3 m+14);\cos ^2(c+d x)\right)}{d (3 m+8) \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+1}(c+d x)}{d (3 m+8)}",1,"(3*C*Cos[c + d*x]^(1 + m)*(b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(d*(8 + 3*m)) - (3*(A/(5 + 3*m) + C/(8 + 3*m))*Cos[c + d*x]^(1 + m)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/2, (5 + 3*m)/6, (11 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2]) - (3*B*Cos[c + d*x]^(2 + m)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/2, (8 + 3*m)/6, (14 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(8 + 3*m)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{20, 3023, 2748, 2643}"
365,1,219,0,0.201424,"\int \cos ^m(c+d x) \sqrt[3]{b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^m*(b*Cos[c + d*x])^(1/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{3 \left(\frac{A}{3 m+4}+\frac{C}{3 m+7}\right) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+4);\frac{1}{6} (3 m+10);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+7);\frac{1}{6} (3 m+13);\cos ^2(c+d x)\right)}{d (3 m+7) \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+1}(c+d x)}{d (3 m+7)}","-\frac{3 (A (3 m+7)+C (3 m+4)) \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+4);\frac{1}{6} (3 m+10);\cos ^2(c+d x)\right)}{d (3 m+4) (3 m+7) \sqrt{\sin ^2(c+d x)}}-\frac{3 B \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+7);\frac{1}{6} (3 m+13);\cos ^2(c+d x)\right)}{d (3 m+7) \sqrt{\sin ^2(c+d x)}}+\frac{3 C \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+1}(c+d x)}{d (3 m+7)}",1,"(3*C*Cos[c + d*x]^(1 + m)*(b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(d*(7 + 3*m)) - (3*(A/(4 + 3*m) + C/(7 + 3*m))*Cos[c + d*x]^(1 + m)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/2, (4 + 3*m)/6, (10 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2]) - (3*B*Cos[c + d*x]^(2 + m)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/2, (7 + 3*m)/6, (13 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(7 + 3*m)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{20, 3023, 2748, 2643}"
366,1,219,0,0.201154,"\int \frac{\cos ^m(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[(Cos[c + d*x]^m*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(1/3),x]","-\frac{3 \left(\frac{A}{3 m+2}+\frac{C}{3 m+5}\right) \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+2);\frac{1}{6} (3 m+8);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}-\frac{3 B \sin (c+d x) \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+5);\frac{1}{6} (3 m+11);\cos ^2(c+d x)\right)}{d (3 m+5) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}+\frac{3 C \sin (c+d x) \cos ^{m+1}(c+d x)}{d (3 m+5) \sqrt[3]{b \cos (c+d x)}}","-\frac{3 (A (3 m+5)+C (3 m+2)) \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+2);\frac{1}{6} (3 m+8);\cos ^2(c+d x)\right)}{d (3 m+2) (3 m+5) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}-\frac{3 B \sin (c+d x) \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+5);\frac{1}{6} (3 m+11);\cos ^2(c+d x)\right)}{d (3 m+5) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}+\frac{3 C \sin (c+d x) \cos ^{m+1}(c+d x)}{d (3 m+5) \sqrt[3]{b \cos (c+d x)}}",1,"(3*C*Cos[c + d*x]^(1 + m)*Sin[c + d*x])/(d*(5 + 3*m)*(b*Cos[c + d*x])^(1/3)) - (3*(A/(2 + 3*m) + C/(5 + 3*m))*Cos[c + d*x]^(1 + m)*Hypergeometric2F1[1/2, (2 + 3*m)/6, (8 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2]) - (3*B*Cos[c + d*x]^(2 + m)*Hypergeometric2F1[1/2, (5 + 3*m)/6, (11 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(5 + 3*m)*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{20, 3023, 2748, 2643}"
367,1,227,0,0.2330935,"\int \frac{\cos ^m(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{2/3}} \, dx","Int[(Cos[c + d*x]^m*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(2/3),x]","-\frac{3 (A (3 m+4)+3 C m+C) \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+1);\frac{1}{6} (3 m+7);\cos ^2(c+d x)\right)}{d (3 m+1) (3 m+4) \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}-\frac{3 B \sin (c+d x) \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+4);\frac{1}{6} (3 m+10);\cos ^2(c+d x)\right)}{d (3 m+4) \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}+\frac{3 C \sin (c+d x) \cos ^{m+1}(c+d x)}{d (3 m+4) (b \cos (c+d x))^{2/3}}","-\frac{3 (A (3 m+4)+3 C m+C) \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+1);\frac{1}{6} (3 m+7);\cos ^2(c+d x)\right)}{d (3 m+1) (3 m+4) \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}-\frac{3 B \sin (c+d x) \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+4);\frac{1}{6} (3 m+10);\cos ^2(c+d x)\right)}{d (3 m+4) \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}+\frac{3 C \sin (c+d x) \cos ^{m+1}(c+d x)}{d (3 m+4) (b \cos (c+d x))^{2/3}}",1,"(3*C*Cos[c + d*x]^(1 + m)*Sin[c + d*x])/(d*(4 + 3*m)*(b*Cos[c + d*x])^(2/3)) - (3*(C + 3*C*m + A*(4 + 3*m))*Cos[c + d*x]^(1 + m)*Hypergeometric2F1[1/2, (1 + 3*m)/6, (7 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 + 3*m)*(4 + 3*m)*(b*Cos[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2]) - (3*B*Cos[c + d*x]^(2 + m)*Hypergeometric2F1[1/2, (4 + 3*m)/6, (10 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(4 + 3*m)*(b*Cos[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{20, 3023, 2748, 2643}"
368,1,225,0,0.2324118,"\int \frac{\cos ^m(c+d x) \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{(b \cos (c+d x))^{4/3}} \, dx","Int[(Cos[c + d*x]^m*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/(b*Cos[c + d*x])^(4/3),x]","\frac{3 \left(\frac{A}{1-3 m}-\frac{C}{3 m+2}\right) \sin (c+d x) \cos ^m(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m-1);\frac{1}{6} (3 m+5);\cos ^2(c+d x)\right)}{b d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}-\frac{3 B \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+2);\frac{1}{6} (3 m+8);\cos ^2(c+d x)\right)}{b d (3 m+2) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}+\frac{3 C \sin (c+d x) \cos ^m(c+d x)}{b d (3 m+2) \sqrt[3]{b \cos (c+d x)}}","-\frac{3 (C (1-3 m)-A (3 m+2)) \sin (c+d x) \cos ^m(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m-1);\frac{1}{6} (3 m+5);\cos ^2(c+d x)\right)}{b d (1-3 m) (3 m+2) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}-\frac{3 B \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+2);\frac{1}{6} (3 m+8);\cos ^2(c+d x)\right)}{b d (3 m+2) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}+\frac{3 C \sin (c+d x) \cos ^m(c+d x)}{b d (3 m+2) \sqrt[3]{b \cos (c+d x)}}",1,"(3*C*Cos[c + d*x]^m*Sin[c + d*x])/(b*d*(2 + 3*m)*(b*Cos[c + d*x])^(1/3)) + (3*(A/(1 - 3*m) - C/(2 + 3*m))*Cos[c + d*x]^m*Hypergeometric2F1[1/2, (-1 + 3*m)/6, (5 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2]) - (3*B*Cos[c + d*x]^(1 + m)*Hypergeometric2F1[1/2, (2 + 3*m)/6, (8 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(2 + 3*m)*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{20, 3023, 2748, 2643}"
369,1,227,0,0.2322635,"\int (a \cos (c+d x))^m (b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(a*Cos[c + d*x])^m*(b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{B \sin (c+d x) (a \cos (c+d x))^{m+2} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+2);\frac{1}{2} (m+n+4);\cos ^2(c+d x)\right)}{a^2 d (m+n+2) \sqrt{\sin ^2(c+d x)}}-\frac{(A (m+n+2)+C (m+n+1)) \sin (c+d x) (a \cos (c+d x))^{m+1} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);\cos ^2(c+d x)\right)}{a d (m+n+1) (m+n+2) \sqrt{\sin ^2(c+d x)}}+\frac{C \sin (c+d x) (a \cos (c+d x))^{m+1} (b \cos (c+d x))^n}{a d (m+n+2)}","-\frac{B \sin (c+d x) (a \cos (c+d x))^{m+2} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+2);\frac{1}{2} (m+n+4);\cos ^2(c+d x)\right)}{a^2 d (m+n+2) \sqrt{\sin ^2(c+d x)}}-\frac{(A (m+n+2)+C (m+n+1)) \sin (c+d x) (a \cos (c+d x))^{m+1} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);\cos ^2(c+d x)\right)}{a d (m+n+1) (m+n+2) \sqrt{\sin ^2(c+d x)}}+\frac{C \sin (c+d x) (a \cos (c+d x))^{m+1} (b \cos (c+d x))^n}{a d (m+n+2)}",1,"(C*(a*Cos[c + d*x])^(1 + m)*(b*Cos[c + d*x])^n*Sin[c + d*x])/(a*d*(2 + m + n)) - ((C*(1 + m + n) + A*(2 + m + n))*(a*Cos[c + d*x])^(1 + m)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (1 + m + n)/2, (3 + m + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(a*d*(1 + m + n)*(2 + m + n)*Sqrt[Sin[c + d*x]^2]) - (B*(a*Cos[c + d*x])^(2 + m)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (2 + m + n)/2, (4 + m + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(a^2*d*(2 + m + n)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{20, 3023, 2748, 2643}"
370,1,187,0,0.2186375,"\int \cos ^2(c+d x) (b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^2*(b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{(A (n+4)+C (n+3)) \sin (c+d x) (b \cos (c+d x))^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{n+5}{2};\cos ^2(c+d x)\right)}{b^3 d (n+3) (n+4) \sqrt{\sin ^2(c+d x)}}-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+4} \, _2F_1\left(\frac{1}{2},\frac{n+4}{2};\frac{n+6}{2};\cos ^2(c+d x)\right)}{b^4 d (n+4) \sqrt{\sin ^2(c+d x)}}+\frac{C \sin (c+d x) (b \cos (c+d x))^{n+3}}{b^3 d (n+4)}","-\frac{(A (n+4)+C (n+3)) \sin (c+d x) (b \cos (c+d x))^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{n+5}{2};\cos ^2(c+d x)\right)}{b^3 d (n+3) (n+4) \sqrt{\sin ^2(c+d x)}}-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+4} \, _2F_1\left(\frac{1}{2},\frac{n+4}{2};\frac{n+6}{2};\cos ^2(c+d x)\right)}{b^4 d (n+4) \sqrt{\sin ^2(c+d x)}}+\frac{C \sin (c+d x) (b \cos (c+d x))^{n+3}}{b^3 d (n+4)}",1,"(C*(b*Cos[c + d*x])^(3 + n)*Sin[c + d*x])/(b^3*d*(4 + n)) - ((C*(3 + n) + A*(4 + n))*(b*Cos[c + d*x])^(3 + n)*Hypergeometric2F1[1/2, (3 + n)/2, (5 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^3*d*(3 + n)*(4 + n)*Sqrt[Sin[c + d*x]^2]) - (B*(b*Cos[c + d*x])^(4 + n)*Hypergeometric2F1[1/2, (4 + n)/2, (6 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^4*d*(4 + n)*Sqrt[Sin[c + d*x]^2])","A",5,4,39,0.1026,1,"{16, 3023, 2748, 2643}"
371,1,187,0,0.2133009,"\int \cos (c+d x) (b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{(A (n+3)+C (n+2)) \sin (c+d x) (b \cos (c+d x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\cos ^2(c+d x)\right)}{b^2 d (n+2) (n+3) \sqrt{\sin ^2(c+d x)}}-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{n+5}{2};\cos ^2(c+d x)\right)}{b^3 d (n+3) \sqrt{\sin ^2(c+d x)}}+\frac{C \sin (c+d x) (b \cos (c+d x))^{n+2}}{b^2 d (n+3)}","-\frac{(A (n+3)+C (n+2)) \sin (c+d x) (b \cos (c+d x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\cos ^2(c+d x)\right)}{b^2 d (n+2) (n+3) \sqrt{\sin ^2(c+d x)}}-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{n+5}{2};\cos ^2(c+d x)\right)}{b^3 d (n+3) \sqrt{\sin ^2(c+d x)}}+\frac{C \sin (c+d x) (b \cos (c+d x))^{n+2}}{b^2 d (n+3)}",1,"(C*(b*Cos[c + d*x])^(2 + n)*Sin[c + d*x])/(b^2*d*(3 + n)) - ((C*(2 + n) + A*(3 + n))*(b*Cos[c + d*x])^(2 + n)*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^2*d*(2 + n)*(3 + n)*Sqrt[Sin[c + d*x]^2]) - (B*(b*Cos[c + d*x])^(3 + n)*Hypergeometric2F1[1/2, (3 + n)/2, (5 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^3*d*(3 + n)*Sqrt[Sin[c + d*x]^2])","A",5,4,37,0.1081,1,"{16, 3023, 2748, 2643}"
372,1,187,0,0.1679091,"\int (b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{(A (n+2)+C (n+1)) \sin (c+d x) (b \cos (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(c+d x)\right)}{b d (n+1) (n+2) \sqrt{\sin ^2(c+d x)}}-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\cos ^2(c+d x)\right)}{b^2 d (n+2) \sqrt{\sin ^2(c+d x)}}+\frac{C \sin (c+d x) (b \cos (c+d x))^{n+1}}{b d (n+2)}","-\frac{(A (n+2)+C (n+1)) \sin (c+d x) (b \cos (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(c+d x)\right)}{b d (n+1) (n+2) \sqrt{\sin ^2(c+d x)}}-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\cos ^2(c+d x)\right)}{b^2 d (n+2) \sqrt{\sin ^2(c+d x)}}+\frac{C \sin (c+d x) (b \cos (c+d x))^{n+1}}{b d (n+2)}",1,"(C*(b*Cos[c + d*x])^(1 + n)*Sin[c + d*x])/(b*d*(2 + n)) - ((C*(1 + n) + A*(2 + n))*(b*Cos[c + d*x])^(1 + n)*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(1 + n)*(2 + n)*Sqrt[Sin[c + d*x]^2]) - (B*(b*Cos[c + d*x])^(2 + n)*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^2*d*(2 + n)*Sqrt[Sin[c + d*x]^2])","A",4,3,31,0.09677,1,"{3023, 2748, 2643}"
373,1,170,0,0.1911906,"\int (b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x],x]","-\frac{(A n+A+C n) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\cos ^2(c+d x)\right)}{d n (n+1) \sqrt{\sin ^2(c+d x)}}-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(c+d x)\right)}{b d (n+1) \sqrt{\sin ^2(c+d x)}}+\frac{C \sin (c+d x) (b \cos (c+d x))^n}{d (n+1)}","-\frac{(A n+A+C n) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\cos ^2(c+d x)\right)}{d n (n+1) \sqrt{\sin ^2(c+d x)}}-\frac{B \sin (c+d x) (b \cos (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(c+d x)\right)}{b d (n+1) \sqrt{\sin ^2(c+d x)}}+\frac{C \sin (c+d x) (b \cos (c+d x))^n}{d (n+1)}",1,"(C*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(1 + n)) - ((A + A*n + C*n)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, n/2, (2 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*n*(1 + n)*Sqrt[Sin[c + d*x]^2]) - (B*(b*Cos[c + d*x])^(1 + n)*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(1 + n)*Sqrt[Sin[c + d*x]^2])","A",5,4,37,0.1081,1,"{16, 3023, 2748, 2643}"
374,1,173,0,0.230114,"\int (b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^2,x]","-\frac{b (C (1-n)-A n) \sin (c+d x) (b \cos (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n-1}{2};\frac{n+1}{2};\cos ^2(c+d x)\right)}{d (1-n) n \sqrt{\sin ^2(c+d x)}}-\frac{B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\cos ^2(c+d x)\right)}{d n \sqrt{\sin ^2(c+d x)}}+\frac{b C \sin (c+d x) (b \cos (c+d x))^{n-1}}{d n}","-\frac{b (C (1-n)-A n) \sin (c+d x) (b \cos (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n-1}{2};\frac{n+1}{2};\cos ^2(c+d x)\right)}{d (1-n) n \sqrt{\sin ^2(c+d x)}}-\frac{B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\cos ^2(c+d x)\right)}{d n \sqrt{\sin ^2(c+d x)}}+\frac{b C \sin (c+d x) (b \cos (c+d x))^{n-1}}{d n}",1,"(b*C*(b*Cos[c + d*x])^(-1 + n)*Sin[c + d*x])/(d*n) - (b*(C*(1 - n) - A*n)*(b*Cos[c + d*x])^(-1 + n)*Hypergeometric2F1[1/2, (-1 + n)/2, (1 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - n)*n*Sqrt[Sin[c + d*x]^2]) - (B*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, n/2, (2 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*n*Sqrt[Sin[c + d*x]^2])","A",5,4,39,0.1026,1,"{16, 3023, 2748, 2643}"
375,1,194,0,0.2559244,"\int (b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^3,x]","\frac{b^2 (A (1-n)+C (2-n)) \sin (c+d x) (b \cos (c+d x))^{n-2} \, _2F_1\left(\frac{1}{2},\frac{n-2}{2};\frac{n}{2};\cos ^2(c+d x)\right)}{d (1-n) (2-n) \sqrt{\sin ^2(c+d x)}}-\frac{b^2 C \sin (c+d x) (b \cos (c+d x))^{n-2}}{d (1-n)}+\frac{b B \sin (c+d x) (b \cos (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n-1}{2};\frac{n+1}{2};\cos ^2(c+d x)\right)}{d (1-n) \sqrt{\sin ^2(c+d x)}}","\frac{b^2 (A (1-n)+C (2-n)) \sin (c+d x) (b \cos (c+d x))^{n-2} \, _2F_1\left(\frac{1}{2},\frac{n-2}{2};\frac{n}{2};\cos ^2(c+d x)\right)}{d (1-n) (2-n) \sqrt{\sin ^2(c+d x)}}-\frac{b^2 C \sin (c+d x) (b \cos (c+d x))^{n-2}}{d (1-n)}+\frac{b B \sin (c+d x) (b \cos (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n-1}{2};\frac{n+1}{2};\cos ^2(c+d x)\right)}{d (1-n) \sqrt{\sin ^2(c+d x)}}",1,"-((b^2*C*(b*Cos[c + d*x])^(-2 + n)*Sin[c + d*x])/(d*(1 - n))) + (b^2*(A*(1 - n) + C*(2 - n))*(b*Cos[c + d*x])^(-2 + n)*Hypergeometric2F1[1/2, (-2 + n)/2, n/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - n)*(2 - n)*Sqrt[Sin[c + d*x]^2]) + (b*B*(b*Cos[c + d*x])^(-1 + n)*Hypergeometric2F1[1/2, (-1 + n)/2, (1 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - n)*Sqrt[Sin[c + d*x]^2])","A",5,4,39,0.1026,1,"{16, 3023, 2748, 2643}"
376,1,196,0,0.2615609,"\int (b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \sec ^4(c+d x) \, dx","Int[(b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)*Sec[c + d*x]^4,x]","\frac{b^3 (A (2-n)+C (3-n)) \sin (c+d x) (b \cos (c+d x))^{n-3} \, _2F_1\left(\frac{1}{2},\frac{n-3}{2};\frac{n-1}{2};\cos ^2(c+d x)\right)}{d (2-n) (3-n) \sqrt{\sin ^2(c+d x)}}+\frac{b^2 B \sin (c+d x) (b \cos (c+d x))^{n-2} \, _2F_1\left(\frac{1}{2},\frac{n-2}{2};\frac{n}{2};\cos ^2(c+d x)\right)}{d (2-n) \sqrt{\sin ^2(c+d x)}}-\frac{b^3 C \sin (c+d x) (b \cos (c+d x))^{n-3}}{d (2-n)}","\frac{b^3 (A (2-n)+C (3-n)) \sin (c+d x) (b \cos (c+d x))^{n-3} \, _2F_1\left(\frac{1}{2},\frac{n-3}{2};\frac{n-1}{2};\cos ^2(c+d x)\right)}{d (2-n) (3-n) \sqrt{\sin ^2(c+d x)}}+\frac{b^2 B \sin (c+d x) (b \cos (c+d x))^{n-2} \, _2F_1\left(\frac{1}{2},\frac{n-2}{2};\frac{n}{2};\cos ^2(c+d x)\right)}{d (2-n) \sqrt{\sin ^2(c+d x)}}-\frac{b^3 C \sin (c+d x) (b \cos (c+d x))^{n-3}}{d (2-n)}",1,"-((b^3*C*(b*Cos[c + d*x])^(-3 + n)*Sin[c + d*x])/(d*(2 - n))) + (b^3*(A*(2 - n) + C*(3 - n))*(b*Cos[c + d*x])^(-3 + n)*Hypergeometric2F1[1/2, (-3 + n)/2, (-1 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(2 - n)*(3 - n)*Sqrt[Sin[c + d*x]^2]) + (b^2*B*(b*Cos[c + d*x])^(-2 + n)*Hypergeometric2F1[1/2, (-2 + n)/2, n/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(2 - n)*Sqrt[Sin[c + d*x]^2])","A",5,4,39,0.1026,1,"{16, 3023, 2748, 2643}"
377,1,213,0,0.2374121,"\int \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{2 \left(\frac{A}{2 n+5}+\frac{C}{2 n+7}\right) \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+5);\frac{1}{4} (2 n+9);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}-\frac{2 B \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+7);\frac{1}{4} (2 n+11);\cos ^2(c+d x)\right)}{d (2 n+7) \sqrt{\sin ^2(c+d x)}}+\frac{2 C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n}{d (2 n+7)}","-\frac{2 (A (2 n+7)+C (2 n+5)) \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+5);\frac{1}{4} (2 n+9);\cos ^2(c+d x)\right)}{d (2 n+5) (2 n+7) \sqrt{\sin ^2(c+d x)}}-\frac{2 B \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+7);\frac{1}{4} (2 n+11);\cos ^2(c+d x)\right)}{d (2 n+7) \sqrt{\sin ^2(c+d x)}}+\frac{2 C \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n}{d (2 n+7)}",1,"(2*C*Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(7 + 2*n)) - (2*(A/(5 + 2*n) + C/(7 + 2*n))*Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (5 + 2*n)/4, (9 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2]) - (2*B*Cos[c + d*x]^(7/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (7 + 2*n)/4, (11 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(7 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{20, 3023, 2748, 2643}"
378,1,213,0,0.2159993,"\int \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","-\frac{2 \left(\frac{A}{2 n+3}+\frac{C}{2 n+5}\right) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}-\frac{2 B \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+5);\frac{1}{4} (2 n+9);\cos ^2(c+d x)\right)}{d (2 n+5) \sqrt{\sin ^2(c+d x)}}+\frac{2 C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n}{d (2 n+5)}","-\frac{2 (A (2 n+5)+C (2 n+3)) \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\cos ^2(c+d x)\right)}{d (2 n+3) (2 n+5) \sqrt{\sin ^2(c+d x)}}-\frac{2 B \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+5);\frac{1}{4} (2 n+9);\cos ^2(c+d x)\right)}{d (2 n+5) \sqrt{\sin ^2(c+d x)}}+\frac{2 C \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n}{d (2 n+5)}",1,"(2*C*Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(5 + 2*n)) - (2*(A/(3 + 2*n) + C/(5 + 2*n))*Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (3 + 2*n)/4, (7 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2]) - (2*B*Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (5 + 2*n)/4, (9 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(5 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{20, 3023, 2748, 2643}"
379,1,221,0,0.196848,"\int \frac{(b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\sqrt{\cos (c+d x)}} \, dx","Int[((b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Sqrt[Cos[c + d*x]],x]","-\frac{2 (A (2 n+3)+2 C n+C) \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\cos ^2(c+d x)\right)}{d (2 n+1) (2 n+3) \sqrt{\sin ^2(c+d x)}}-\frac{2 B \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\cos ^2(c+d x)\right)}{d (2 n+3) \sqrt{\sin ^2(c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n}{d (2 n+3)}","-\frac{2 (A (2 n+3)+2 C n+C) \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\cos ^2(c+d x)\right)}{d (2 n+1) (2 n+3) \sqrt{\sin ^2(c+d x)}}-\frac{2 B \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\cos ^2(c+d x)\right)}{d (2 n+3) \sqrt{\sin ^2(c+d x)}}+\frac{2 C \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n}{d (2 n+3)}",1,"(2*C*Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(3 + 2*n)) - (2*(C + 2*C*n + A*(3 + 2*n))*Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (1 + 2*n)/4, (5 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 + 2*n)*(3 + 2*n)*Sqrt[Sin[c + d*x]^2]) - (2*B*Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (3 + 2*n)/4, (7 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(3 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{20, 3023, 2748, 2643}"
380,1,217,0,0.2015448,"\int \frac{(b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(3/2),x]","\frac{2 (2 A n+A-C (1-2 n)) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-1);\frac{1}{4} (2 n+3);\cos ^2(c+d x)\right)}{d \left(1-4 n^2\right) \sqrt{\sin ^2(c+d x)} \sqrt{\cos (c+d x)}}-\frac{2 B \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\cos ^2(c+d x)\right)}{d (2 n+1) \sqrt{\sin ^2(c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (2 n+1) \sqrt{\cos (c+d x)}}","\frac{2 (2 A n+A-C (1-2 n)) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-1);\frac{1}{4} (2 n+3);\cos ^2(c+d x)\right)}{d \left(1-4 n^2\right) \sqrt{\sin ^2(c+d x)} \sqrt{\cos (c+d x)}}-\frac{2 B \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\cos ^2(c+d x)\right)}{d (2 n+1) \sqrt{\sin ^2(c+d x)}}+\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (2 n+1) \sqrt{\cos (c+d x)}}",1,"(2*C*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(1 + 2*n)*Sqrt[Cos[c + d*x]]) + (2*(A - C*(1 - 2*n) + 2*A*n)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-1 + 2*n)/4, (3 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - 4*n^2)*Sqrt[Cos[c + d*x]]*Sqrt[Sin[c + d*x]^2]) - (2*B*Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (1 + 2*n)/4, (5 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{20, 3023, 2748, 2643}"
381,1,221,0,0.2167547,"\int \frac{(b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(5/2),x]","\frac{2 (-2 A n+A+C (3-2 n)) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-3);\frac{1}{4} (2 n+1);\cos ^2(c+d x)\right)}{d (1-2 n) (3-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{3}{2}}(c+d x)}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-1);\frac{1}{4} (2 n+3);\cos ^2(c+d x)\right)}{d (1-2 n) \sqrt{\sin ^2(c+d x)} \sqrt{\cos (c+d x)}}-\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (1-2 n) \cos ^{\frac{3}{2}}(c+d x)}","\frac{2 (-2 A n+A+C (3-2 n)) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-3);\frac{1}{4} (2 n+1);\cos ^2(c+d x)\right)}{d (1-2 n) (3-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{3}{2}}(c+d x)}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-1);\frac{1}{4} (2 n+3);\cos ^2(c+d x)\right)}{d (1-2 n) \sqrt{\sin ^2(c+d x)} \sqrt{\cos (c+d x)}}-\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (1-2 n) \cos ^{\frac{3}{2}}(c+d x)}",1,"(-2*C*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(1 - 2*n)*Cos[c + d*x]^(3/2)) + (2*(A + C*(3 - 2*n) - 2*A*n)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-3 + 2*n)/4, (1 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - 2*n)*(3 - 2*n)*Cos[c + d*x]^(3/2)*Sqrt[Sin[c + d*x]^2]) + (2*B*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-1 + 2*n)/4, (3 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - 2*n)*Sqrt[Cos[c + d*x]]*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{20, 3023, 2748, 2643}"
382,1,213,0,0.2120402,"\int \frac{(b \cos (c+d x))^n \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right)}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Int[((b*Cos[c + d*x])^n*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2))/Cos[c + d*x]^(7/2),x]","\frac{2 \left(\frac{A}{5-2 n}+\frac{C}{3-2 n}\right) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-5);\frac{1}{4} (2 n-1);\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \cos ^{\frac{5}{2}}(c+d x)}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-3);\frac{1}{4} (2 n+1);\cos ^2(c+d x)\right)}{d (3-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{3}{2}}(c+d x)}-\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (3-2 n) \cos ^{\frac{5}{2}}(c+d x)}","\frac{2 (A (3-2 n)+C (5-2 n)) \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-5);\frac{1}{4} (2 n-1);\cos ^2(c+d x)\right)}{d (3-2 n) (5-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{5}{2}}(c+d x)}+\frac{2 B \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-3);\frac{1}{4} (2 n+1);\cos ^2(c+d x)\right)}{d (3-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{3}{2}}(c+d x)}-\frac{2 C \sin (c+d x) (b \cos (c+d x))^n}{d (3-2 n) \cos ^{\frac{5}{2}}(c+d x)}",1,"(-2*C*(b*Cos[c + d*x])^n*Sin[c + d*x])/(d*(3 - 2*n)*Cos[c + d*x]^(5/2)) + (2*(C/(3 - 2*n) + A/(5 - 2*n))*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-5 + 2*n)/4, (-1 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Cos[c + d*x]^(5/2)*Sqrt[Sin[c + d*x]^2]) + (2*B*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-3 + 2*n)/4, (1 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(3 - 2*n)*Cos[c + d*x]^(3/2)*Sqrt[Sin[c + d*x]^2])","A",5,4,41,0.09756,1,"{20, 3023, 2748, 2643}"
383,1,183,0,0.2476945,"\int (a+a \cos (e+f x))^m \left(A+B \cos (e+f x)+C \cos ^2(e+f x)\right) \, dx","Int[(a + a*Cos[e + f*x])^m*(A + B*Cos[e + f*x] + C*Cos[e + f*x]^2),x]","\frac{2^{m+\frac{1}{2}} \left(A \left(m^2+3 m+2\right)+B m (m+2)+C \left(m^2+m+1\right)\right) \sin (e+f x) (\cos (e+f x)+1)^{-m-\frac{1}{2}} (a \cos (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x))\right)}{f (m+1) (m+2)}-\frac{(C-B (m+2)) \sin (e+f x) (a \cos (e+f x)+a)^m}{f (m+1) (m+2)}+\frac{C \sin (e+f x) (a \cos (e+f x)+a)^{m+1}}{a f (m+2)}","\frac{2^{m+\frac{1}{2}} \left(A \left(m^2+3 m+2\right)+B m (m+2)+C \left(m^2+m+1\right)\right) \sin (e+f x) (\cos (e+f x)+1)^{-m-\frac{1}{2}} (a \cos (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x))\right)}{f (m+1) (m+2)}-\frac{(C-B (m+2)) \sin (e+f x) (a \cos (e+f x)+a)^m}{f (m+1) (m+2)}+\frac{C \sin (e+f x) (a \cos (e+f x)+a)^{m+1}}{a f (m+2)}",1,"-(((C - B*(2 + m))*(a + a*Cos[e + f*x])^m*Sin[e + f*x])/(f*(1 + m)*(2 + m))) + (C*(a + a*Cos[e + f*x])^(1 + m)*Sin[e + f*x])/(a*f*(2 + m)) + (2^(1/2 + m)*(B*m*(2 + m) + C*(1 + m + m^2) + A*(2 + 3*m + m^2))*(1 + Cos[e + f*x])^(-1/2 - m)*(a + a*Cos[e + f*x])^m*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (1 - Cos[e + f*x])/2]*Sin[e + f*x])/(f*(1 + m)*(2 + m))","A",4,4,33,0.1212,1,"{3023, 2751, 2652, 2651}"
384,1,144,0,0.1887197,"\int (a+a \cos (c+d x))^{2/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(a + a*Cos[c + d*x])^(2/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","\frac{(40 A+16 B+19 C) \sin (c+d x) (a \cos (c+d x)+a)^{2/3} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{10\ 2^{5/6} d (\cos (c+d x)+1)^{7/6}}+\frac{3 (8 B-3 C) \sin (c+d x) (a \cos (c+d x)+a)^{2/3}}{40 d}+\frac{3 C \sin (c+d x) (a \cos (c+d x)+a)^{5/3}}{8 a d}","\frac{(40 A+16 B+19 C) \sin (c+d x) (a \cos (c+d x)+a)^{2/3} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{10\ 2^{5/6} d (\cos (c+d x)+1)^{7/6}}+\frac{3 (8 B-3 C) \sin (c+d x) (a \cos (c+d x)+a)^{2/3}}{40 d}+\frac{3 C \sin (c+d x) (a \cos (c+d x)+a)^{5/3}}{8 a d}",1,"(3*(8*B - 3*C)*(a + a*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(40*d) + (3*C*(a + a*Cos[c + d*x])^(5/3)*Sin[c + d*x])/(8*a*d) + ((40*A + 16*B + 19*C)*(a + a*Cos[c + d*x])^(2/3)*Hypergeometric2F1[-1/6, 1/2, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(10*2^(5/6)*d*(1 + Cos[c + d*x])^(7/6))","A",4,4,35,0.1143,1,"{3023, 2751, 2652, 2651}"
385,1,144,0,0.1784635,"\int \sqrt[3]{a+a \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(a + a*Cos[c + d*x])^(1/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","\frac{(28 A+7 B+13 C) \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{14 \sqrt[6]{2} d (\cos (c+d x)+1)^{5/6}}+\frac{3 (7 B-3 C) \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a}}{28 d}+\frac{3 C \sin (c+d x) (a \cos (c+d x)+a)^{4/3}}{7 a d}","\frac{(28 A+7 B+13 C) \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{14 \sqrt[6]{2} d (\cos (c+d x)+1)^{5/6}}+\frac{3 (7 B-3 C) \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a}}{28 d}+\frac{3 C \sin (c+d x) (a \cos (c+d x)+a)^{4/3}}{7 a d}",1,"(3*(7*B - 3*C)*(a + a*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(28*d) + (3*C*(a + a*Cos[c + d*x])^(4/3)*Sin[c + d*x])/(7*a*d) + ((28*A + 7*B + 13*C)*(a + a*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(14*2^(1/6)*d*(1 + Cos[c + d*x])^(5/6))","A",4,4,35,0.1143,1,"{3023, 2751, 2652, 2651}"
386,1,144,0,0.1755082,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt[3]{a+a \cos (c+d x)}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(a + a*Cos[c + d*x])^(1/3),x]","\frac{(10 A-5 B+7 C) \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{5\ 2^{5/6} d \sqrt[6]{\cos (c+d x)+1} \sqrt[3]{a \cos (c+d x)+a}}+\frac{3 (5 B-3 C) \sin (c+d x)}{10 d \sqrt[3]{a \cos (c+d x)+a}}+\frac{3 C \sin (c+d x) (a \cos (c+d x)+a)^{2/3}}{5 a d}","\frac{(10 A-5 B+7 C) \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{5\ 2^{5/6} d \sqrt[6]{\cos (c+d x)+1} \sqrt[3]{a \cos (c+d x)+a}}+\frac{3 (5 B-3 C) \sin (c+d x)}{10 d \sqrt[3]{a \cos (c+d x)+a}}+\frac{3 C \sin (c+d x) (a \cos (c+d x)+a)^{2/3}}{5 a d}",1,"(3*(5*B - 3*C)*Sin[c + d*x])/(10*d*(a + a*Cos[c + d*x])^(1/3)) + (3*C*(a + a*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*a*d) + ((10*A - 5*B + 7*C)*Hypergeometric2F1[1/2, 5/6, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(5*2^(5/6)*d*(1 + Cos[c + d*x])^(1/6)*(a + a*Cos[c + d*x])^(1/3))","A",4,4,35,0.1143,1,"{3023, 2751, 2652, 2651}"
387,1,144,0,0.196683,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+a \cos (c+d x))^{2/3}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(a + a*Cos[c + d*x])^(2/3),x]","-\frac{(4 A-8 B+7 C) \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{2 \sqrt[6]{2} a d (\cos (c+d x)+1)^{5/6}}+\frac{3 (A-B+C) \sin (c+d x)}{d (a \cos (c+d x)+a)^{2/3}}+\frac{3 C \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a}}{4 a d}","-\frac{(4 A-8 B+7 C) \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{2 \sqrt[6]{2} a d (\cos (c+d x)+1)^{5/6}}+\frac{3 (A-B+C) \sin (c+d x)}{d (a \cos (c+d x)+a)^{2/3}}+\frac{3 C \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a}}{4 a d}",1,"(3*(A - B + C)*Sin[c + d*x])/(d*(a + a*Cos[c + d*x])^(2/3)) + (3*C*(a + a*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(4*a*d) - ((4*A - 8*B + 7*C)*(a + a*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(2*2^(1/6)*a*d*(1 + Cos[c + d*x])^(5/6))","A",4,4,35,0.1143,1,"{3023, 2750, 2652, 2651}"
388,1,290,0,0.3682627,"\int (a+b \cos (c+d x))^{2/3} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(a + b*Cos[c + d*x])^(2/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","\frac{\sin (c+d x) \left(3 a^2 C-8 a b B+8 A b^2+5 b^2 C\right) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{4 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{(a+b) (8 b B-3 a C) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{5}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{4 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{5/3}}{8 b d}","\frac{\sin (c+d x) \left(3 a^2 C-8 a b B+8 A b^2+5 b^2 C\right) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{4 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{(a+b) (8 b B-3 a C) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{5}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{4 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{5/3}}{8 b d}",1,"(3*C*(a + b*Cos[c + d*x])^(5/3)*Sin[c + d*x])/(8*b*d) + ((a + b)*(8*b*B - 3*a*C)*AppellF1[1/2, 1/2, -5/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(4*Sqrt[2]*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(2/3)) + ((8*A*b^2 - 8*a*b*B + 3*a^2*C + 5*b^2*C)*AppellF1[1/2, 1/2, -2/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(4*Sqrt[2]*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(2/3))","A",8,5,35,0.1429,1,"{3023, 2756, 2665, 139, 138}"
389,1,290,0,0.3372346,"\int \sqrt[3]{a+b \cos (c+d x)} \left(A+B \cos (c+d x)+C \cos ^2(c+d x)\right) \, dx","Int[(a + b*Cos[c + d*x])^(1/3)*(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2),x]","\frac{\sqrt{2} \sin (c+d x) \left(3 a^2 C-7 a b B+7 A b^2+4 b^2 C\right) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{7 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{\sqrt{2} (a+b) (7 b B-3 a C) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{7 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{4/3}}{7 b d}","\frac{\sqrt{2} \sin (c+d x) \left(3 a^2 C-7 a b B+7 A b^2+4 b^2 C\right) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{7 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{\sqrt{2} (a+b) (7 b B-3 a C) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{7 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{4/3}}{7 b d}",1,"(3*C*(a + b*Cos[c + d*x])^(4/3)*Sin[c + d*x])/(7*b*d) + (Sqrt[2]*(a + b)*(7*b*B - 3*a*C)*AppellF1[1/2, 1/2, -4/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(7*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(1/3)) + (Sqrt[2]*(7*A*b^2 - 7*a*b*B + 3*a^2*C + 4*b^2*C)*AppellF1[1/2, 1/2, -1/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(7*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(1/3))","A",8,5,35,0.1429,1,"{3023, 2756, 2665, 139, 138}"
390,1,287,0,0.3259531,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt[3]{a+b \cos (c+d x)}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(a + b*Cos[c + d*x])^(1/3),x]","\frac{\sqrt{2} \sin (c+d x) \left(3 a^2 C-5 a b B+5 A b^2+2 b^2 C\right) \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{5 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{a+b \cos (c+d x)}}+\frac{\sqrt{2} (5 b B-3 a C) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{5 b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{2/3}}{5 b d}","\frac{\sqrt{2} \sin (c+d x) \left(3 a^2 C-5 a b B+5 A b^2+2 b^2 C\right) \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{5 b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{a+b \cos (c+d x)}}+\frac{\sqrt{2} (5 b B-3 a C) \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{5 b^2 d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}+\frac{3 C \sin (c+d x) (a+b \cos (c+d x))^{2/3}}{5 b d}",1,"(3*C*(a + b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*b*d) + (Sqrt[2]*(5*b*B - 3*a*C)*AppellF1[1/2, 1/2, -2/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(5*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(2/3)) + (Sqrt[2]*(5*A*b^2 - 5*a*b*B + 3*a^2*C + 2*b^2*C)*AppellF1[1/2, 1/2, 1/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*((a + b*Cos[c + d*x])/(a + b))^(1/3)*Sin[c + d*x])/(5*b^2*d*Sqrt[1 + Cos[c + d*x]]*(a + b*Cos[c + d*x])^(1/3))","A",8,5,35,0.1429,1,"{3023, 2756, 2665, 139, 138}"
391,1,286,0,0.3237893,"\int \frac{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^{2/3}} \, dx","Int[(A + B*Cos[c + d*x] + C*Cos[c + d*x]^2)/(a + b*Cos[c + d*x])^(2/3),x]","\frac{\sin (c+d x) \left(3 a^2 C-4 a b B+4 A b^2+b^2 C\right) \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{2 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} (a+b \cos (c+d x))^{2/3}}+\frac{(4 b B-3 a C) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{2 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{3 C \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)}}{4 b d}","\frac{\sin (c+d x) \left(3 a^2 C-4 a b B+4 A b^2+b^2 C\right) \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{2 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} (a+b \cos (c+d x))^{2/3}}+\frac{(4 b B-3 a C) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{2 \sqrt{2} b^2 d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{3 C \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)}}{4 b d}",1,"(3*C*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(4*b*d) + ((4*b*B - 3*a*C)*AppellF1[1/2, 1/2, -1/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(2*Sqrt[2]*b^2*d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(1/3)) + ((4*A*b^2 - 4*a*b*B + 3*a^2*C + b^2*C)*AppellF1[1/2, 1/2, 2/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*((a + b*Cos[c + d*x])/(a + b))^(2/3)*Sin[c + d*x])/(2*Sqrt[2]*b^2*d*Sqrt[1 + Cos[c + d*x]]*(a + b*Cos[c + d*x])^(2/3))","A",8,5,35,0.1429,1,"{3023, 2756, 2665, 139, 138}"
392,1,215,0,0.2529919,"\int (a+b \cos (e+f x))^m \left(A+(A+C) \cos (e+f x)+C \cos ^2(e+f x)\right) \, dx","Int[(a + b*Cos[e + f*x])^m*(A + (A + C)*Cos[e + f*x] + C*Cos[e + f*x]^2),x]","\frac{2 \sqrt{2} (A-C) \sin (e+f x) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{f \sqrt{\cos (e+f x)+1}}+\frac{4 \sqrt{2} C \sin (e+f x) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{3}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{f \sqrt{\cos (e+f x)+1}}","\frac{2 \sqrt{2} (A-C) \sin (e+f x) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{f \sqrt{\cos (e+f x)+1}}+\frac{4 \sqrt{2} C \sin (e+f x) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{3}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{f \sqrt{\cos (e+f x)+1}}",1,"(4*Sqrt[2]*C*AppellF1[1/2, -3/2, -m, 3/2, (1 - Cos[e + f*x])/2, (b*(1 - Cos[e + f*x]))/(a + b)]*(a + b*Cos[e + f*x])^m*Sin[e + f*x])/(f*Sqrt[1 + Cos[e + f*x]]*((a + b*Cos[e + f*x])/(a + b))^m) + (2*Sqrt[2]*(A - C)*AppellF1[1/2, -1/2, -m, 3/2, (1 - Cos[e + f*x])/2, (b*(1 - Cos[e + f*x]))/(a + b)]*(a + b*Cos[e + f*x])^m*Sin[e + f*x])/(f*Sqrt[1 + Cos[e + f*x]]*((a + b*Cos[e + f*x])/(a + b))^m)","A",7,5,35,0.1429,1,"{3017, 2755, 139, 138, 2784}"
393,1,303,0,0.375155,"\int (a+b \cos (e+f x))^m \left(A+B \cos (e+f x)+C \cos ^2(e+f x)\right) \, dx","Int[(a + b*Cos[e + f*x])^m*(A + B*Cos[e + f*x] + C*Cos[e + f*x]^2),x]","\frac{\sqrt{2} \sin (e+f x) \left(a^2 C-a b B (m+2)+A b^2 (m+2)+b^2 C (m+1)\right) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\cos (e+f x)+1}}-\frac{\sqrt{2} (a+b) \sin (e+f x) (a C-b B (m+2)) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m-1;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\cos (e+f x)+1}}+\frac{C \sin (e+f x) (a+b \cos (e+f x))^{m+1}}{b f (m+2)}","\frac{\sqrt{2} \sin (e+f x) \left(a^2 C-a b B (m+2)+A b^2 (m+2)+b^2 C (m+1)\right) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\cos (e+f x)+1}}-\frac{\sqrt{2} (a+b) \sin (e+f x) (a C-b B (m+2)) (a+b \cos (e+f x))^m \left(\frac{a+b \cos (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m-1;\frac{3}{2};\frac{1}{2} (1-\cos (e+f x)),\frac{b (1-\cos (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\cos (e+f x)+1}}+\frac{C \sin (e+f x) (a+b \cos (e+f x))^{m+1}}{b f (m+2)}",1,"(C*(a + b*Cos[e + f*x])^(1 + m)*Sin[e + f*x])/(b*f*(2 + m)) - (Sqrt[2]*(a + b)*(a*C - b*B*(2 + m))*AppellF1[1/2, 1/2, -1 - m, 3/2, (1 - Cos[e + f*x])/2, (b*(1 - Cos[e + f*x]))/(a + b)]*(a + b*Cos[e + f*x])^m*Sin[e + f*x])/(b^2*f*(2 + m)*Sqrt[1 + Cos[e + f*x]]*((a + b*Cos[e + f*x])/(a + b))^m) + (Sqrt[2]*(a^2*C + b^2*C*(1 + m) + A*b^2*(2 + m) - a*b*B*(2 + m))*AppellF1[1/2, 1/2, -m, 3/2, (1 - Cos[e + f*x])/2, (b*(1 - Cos[e + f*x]))/(a + b)]*(a + b*Cos[e + f*x])^m*Sin[e + f*x])/(b^2*f*(2 + m)*Sqrt[1 + Cos[e + f*x]]*((a + b*Cos[e + f*x])/(a + b))^m)","A",8,5,33,0.1515,1,"{3023, 2756, 2665, 139, 138}"