1,1,20,0,0.0284205,"\int \sin ^m(e+f x) \left(1+m-(2+m) \sin ^2(e+f x)\right) \, dx","Int[Sin[e + f*x]^m*(1 + m - (2 + m)*Sin[e + f*x]^2),x]","\frac{\cos (e+f x) \sin ^{m+1}(e+f x)}{f}","\frac{\cos (e+f x) \sin ^{m+1}(e+f x)}{f}",1,"(Cos[e + f*x]*Sin[e + f*x]^(1 + m))/f","A",1,1,25,0.04000,1,"{3011}"
2,1,18,0,0.021364,"\int \sin ^5(e+f x) \left(6-7 \sin ^2(e+f x)\right) \, dx","Int[Sin[e + f*x]^5*(6 - 7*Sin[e + f*x]^2),x]","\frac{\sin ^6(e+f x) \cos (e+f x)}{f}","\frac{\sin ^6(e+f x) \cos (e+f x)}{f}",1,"(Cos[e + f*x]*Sin[e + f*x]^6)/f","A",1,1,21,0.04762,1,"{3011}"
3,1,18,0,0.0217338,"\int \sin ^4(e+f x) \left(5-6 \sin ^2(e+f x)\right) \, dx","Int[Sin[e + f*x]^4*(5 - 6*Sin[e + f*x]^2),x]","\frac{\sin ^5(e+f x) \cos (e+f x)}{f}","\frac{\sin ^5(e+f x) \cos (e+f x)}{f}",1,"(Cos[e + f*x]*Sin[e + f*x]^5)/f","A",1,1,21,0.04762,1,"{3011}"
4,1,18,0,0.0212001,"\int \sin ^3(e+f x) \left(4-5 \sin ^2(e+f x)\right) \, dx","Int[Sin[e + f*x]^3*(4 - 5*Sin[e + f*x]^2),x]","\frac{\sin ^4(e+f x) \cos (e+f x)}{f}","\frac{\sin ^4(e+f x) \cos (e+f x)}{f}",1,"(Cos[e + f*x]*Sin[e + f*x]^4)/f","A",1,1,21,0.04762,1,"{3011}"
5,1,18,0,0.0214714,"\int \sin ^2(e+f x) \left(3-4 \sin ^2(e+f x)\right) \, dx","Int[Sin[e + f*x]^2*(3 - 4*Sin[e + f*x]^2),x]","\frac{\sin ^3(e+f x) \cos (e+f x)}{f}","\frac{\sin ^3(e+f x) \cos (e+f x)}{f}",1,"(Cos[e + f*x]*Sin[e + f*x]^3)/f","A",1,1,21,0.04762,1,"{3011}"
6,1,18,0,0.0142884,"\int \sin (e+f x) \left(2-3 \sin ^2(e+f x)\right) \, dx","Int[Sin[e + f*x]*(2 - 3*Sin[e + f*x]^2),x]","\frac{\sin ^2(e+f x) \cos (e+f x)}{f}","\frac{\sin ^2(e+f x) \cos (e+f x)}{f}",1,"(Cos[e + f*x]*Sin[e + f*x]^2)/f","A",1,1,19,0.05263,1,"{3011}"
7,1,16,0,0.0126719,"\int \left(1-2 \sin ^2(e+f x)\right) \, dx","Int[1 - 2*Sin[e + f*x]^2,x]","\frac{\sin (e+f x) \cos (e+f x)}{f}","\frac{\sin (e+f x) \cos (e+f x)}{f}",1,"(Cos[e + f*x]*Sin[e + f*x])/f","A",3,2,12,0.1667,1,"{2635, 8}"
8,1,10,0,0.0038965,"\int -\sin (e+f x) \, dx","Int[-Sin[e + f*x],x]","\frac{\cos (e+f x)}{f}","\frac{\cos (e+f x)}{f}",1,"Cos[e + f*x]/f","A",1,1,8,0.1250,1,"{2638}"
9,1,10,0,0.0088738,"\int -\csc ^2(e+f x) \, dx","Int[-Csc[e + f*x]^2,x]","\frac{\cot (e+f x)}{f}","\frac{\cot (e+f x)}{f}",1,"Cot[e + f*x]/f","A",2,2,10,0.2000,1,"{3767, 8}"
10,1,16,0,0.0216889,"\int \csc ^3(e+f x) \left(-2+\sin ^2(e+f x)\right) \, dx","Int[Csc[e + f*x]^3*(-2 + Sin[e + f*x]^2),x]","\frac{\cot (e+f x) \csc (e+f x)}{f}","\frac{\cot (e+f x) \csc (e+f x)}{f}",1,"(Cot[e + f*x]*Csc[e + f*x])/f","A",1,1,19,0.05263,1,"{3011}"
11,1,18,0,0.0215144,"\int \csc ^4(e+f x) \left(-3+2 \sin ^2(e+f x)\right) \, dx","Int[Csc[e + f*x]^4*(-3 + 2*Sin[e + f*x]^2),x]","\frac{\cot (e+f x) \csc ^2(e+f x)}{f}","\frac{\cot (e+f x) \csc ^2(e+f x)}{f}",1,"(Cot[e + f*x]*Csc[e + f*x]^2)/f","A",1,1,21,0.04762,1,"{3011}"
12,1,18,0,0.0220708,"\int \csc ^5(e+f x) \left(-4+3 \sin ^2(e+f x)\right) \, dx","Int[Csc[e + f*x]^5*(-4 + 3*Sin[e + f*x]^2),x]","\frac{\cot (e+f x) \csc ^3(e+f x)}{f}","\frac{\cot (e+f x) \csc ^3(e+f x)}{f}",1,"(Cot[e + f*x]*Csc[e + f*x]^3)/f","A",1,1,21,0.04762,1,"{3011}"
13,1,171,0,0.1925295,"\int (a+a \sin (e+f x))^m \left(A+C \sin ^2(e+f x)\right) \, dx","Int[(a + a*Sin[e + f*x])^m*(A + C*Sin[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) \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{f (m+1) (m+2)}+\frac{C \cos (e+f x) (a \sin (e+f x)+a)^m}{f \left(m^2+3 m+2\right)}-\frac{C \cos (e+f x) (a \sin (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) \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{f (m+1) (m+2)}+\frac{C \cos (e+f x) (a \sin (e+f x)+a)^m}{f \left(m^2+3 m+2\right)}-\frac{C \cos (e+f x) (a \sin (e+f x)+a)^{m+1}}{a f (m+2)}",1,"(C*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(f*(2 + 3*m + m^2)) - (2^(1/2 + m)*(C*(1 + m + m^2) + A*(2 + 3*m + m^2))*Cos[e + f*x]*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (1 - Sin[e + f*x])/2]*(1 + Sin[e + f*x])^(-1/2 - m)*(a + a*Sin[e + f*x])^m)/(f*(1 + m)*(2 + m)) - (C*Cos[e + f*x]*(a + a*Sin[e + f*x])^(1 + m))/(a*f*(2 + m))","A",4,4,25,0.1600,1,"{3024, 2751, 2652, 2651}"
14,1,211,0,0.2272483,"\int (a+b \sin (e+f x))^m \left(A-A \sin ^2(e+f x)\right) \, dx","Int[(a + b*Sin[e + f*x])^m*(A - A*Sin[e + f*x]^2),x]","\frac{4 \sqrt{2} A \cos (e+f x) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{3}{2},-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{f \sqrt{\sin (e+f x)+1}}-\frac{4 \sqrt{2} A \cos (e+f x) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{f \sqrt{\sin (e+f x)+1}}","\frac{4 \sqrt{2} A \cos (e+f x) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{3}{2},-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{f \sqrt{\sin (e+f x)+1}}-\frac{4 \sqrt{2} A \cos (e+f x) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{f \sqrt{\sin (e+f x)+1}}",1,"(4*Sqrt[2]*A*AppellF1[1/2, -3/2, -m, 3/2, (1 - Sin[e + f*x])/2, (b*(1 - Sin[e + f*x]))/(a + b)]*Cos[e + f*x]*(a + b*Sin[e + f*x])^m)/(f*Sqrt[1 + Sin[e + f*x]]*((a + b*Sin[e + f*x])/(a + b))^m) - (4*Sqrt[2]*A*AppellF1[1/2, -1/2, -m, 3/2, (1 - Sin[e + f*x])/2, (b*(1 - Sin[e + f*x]))/(a + b)]*Cos[e + f*x]*(a + b*Sin[e + f*x])^m)/(f*Sqrt[1 + Sin[e + f*x]]*((a + b*Sin[e + f*x])/(a + b))^m)","A",7,5,26,0.1923,1,"{3018, 2755, 139, 138, 2784}"
15,1,286,0,0.3205234,"\int (a+b \sin (e+f x))^m \left(A+C \sin ^2(e+f x)\right) \, dx","Int[(a + b*Sin[e + f*x])^m*(A + C*Sin[e + f*x]^2),x]","-\frac{\sqrt{2} \cos (e+f x) \left(a^2 C+b^2 (A (m+2)+C (m+1))\right) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\sin (e+f x)+1}}+\frac{\sqrt{2} a C (a+b) \cos (e+f x) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (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-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\sin (e+f x)+1}}-\frac{C \cos (e+f x) (a+b \sin (e+f x))^{m+1}}{b f (m+2)}","-\frac{\sqrt{2} \cos (e+f x) \left(a^2 C+b^2 (A (m+2)+C (m+1))\right) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\sin (e+f x)+1}}+\frac{\sqrt{2} a C (a+b) \cos (e+f x) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (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-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\sin (e+f x)+1}}-\frac{C \cos (e+f x) (a+b \sin (e+f x))^{m+1}}{b f (m+2)}",1,"-((C*Cos[e + f*x]*(a + b*Sin[e + f*x])^(1 + m))/(b*f*(2 + m))) + (Sqrt[2]*a*(a + b)*C*AppellF1[1/2, 1/2, -1 - m, 3/2, (1 - Sin[e + f*x])/2, (b*(1 - Sin[e + f*x]))/(a + b)]*Cos[e + f*x]*(a + b*Sin[e + f*x])^m)/(b^2*f*(2 + m)*Sqrt[1 + Sin[e + f*x]]*((a + b*Sin[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 - Sin[e + f*x])/2, (b*(1 - Sin[e + f*x]))/(a + b)]*Cos[e + f*x]*(a + b*Sin[e + f*x])^m)/(b^2*f*(2 + m)*Sqrt[1 + Sin[e + f*x]]*((a + b*Sin[e + f*x])/(a + b))^m)","A",8,5,25,0.2000,1,"{3024, 2756, 2665, 139, 138}"
16,1,73,0,0.0575136,"\int \sin ^5(e+f x) \left(A+C \sin ^2(e+f x)\right) \, dx","Int[Sin[e + f*x]^5*(A + C*Sin[e + f*x]^2),x]","-\frac{(A+3 C) \cos ^5(e+f x)}{5 f}+\frac{(2 A+3 C) \cos ^3(e+f x)}{3 f}-\frac{(A+C) \cos (e+f x)}{f}+\frac{C \cos ^7(e+f x)}{7 f}","-\frac{(A+3 C) \cos ^5(e+f x)}{5 f}+\frac{(2 A+3 C) \cos ^3(e+f x)}{3 f}-\frac{(A+C) \cos (e+f x)}{f}+\frac{C \cos ^7(e+f x)}{7 f}",1,"-(((A + C)*Cos[e + f*x])/f) + ((2*A + 3*C)*Cos[e + f*x]^3)/(3*f) - ((A + 3*C)*Cos[e + f*x]^5)/(5*f) + (C*Cos[e + f*x]^7)/(7*f)","A",3,2,21,0.09524,1,"{3013, 373}"
17,1,184,0,0.2313022,"\int (a+a \sin (e+f x))^m \left(A+B \sin (e+f x)+C \sin ^2(e+f x)\right) \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x] + C*Sin[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) \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{f (m+1) (m+2)}+\frac{(C-B (m+2)) \cos (e+f x) (a \sin (e+f x)+a)^m}{f (m+1) (m+2)}-\frac{C \cos (e+f x) (a \sin (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) \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{f (m+1) (m+2)}+\frac{(C-B (m+2)) \cos (e+f x) (a \sin (e+f x)+a)^m}{f (m+1) (m+2)}-\frac{C \cos (e+f x) (a \sin (e+f x)+a)^{m+1}}{a f (m+2)}",1,"((C - B*(2 + m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(f*(1 + m)*(2 + m)) - (2^(1/2 + m)*(B*m*(2 + m) + C*(1 + m + m^2) + A*(2 + 3*m + m^2))*Cos[e + f*x]*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (1 - Sin[e + f*x])/2]*(1 + Sin[e + f*x])^(-1/2 - m)*(a + a*Sin[e + f*x])^m)/(f*(1 + m)*(2 + m)) - (C*Cos[e + f*x]*(a + a*Sin[e + f*x])^(1 + m))/(a*f*(2 + m))","A",4,4,33,0.1212,1,"{3023, 2751, 2652, 2651}"
18,1,215,0,0.2343216,"\int (a+b \sin (e+f x))^m \left(A+(A+C) \sin (e+f x)+C \sin ^2(e+f x)\right) \, dx","Int[(a + b*Sin[e + f*x])^m*(A + (A + C)*Sin[e + f*x] + C*Sin[e + f*x]^2),x]","-\frac{2 \sqrt{2} (A-C) \cos (e+f x) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{f \sqrt{\sin (e+f x)+1}}-\frac{4 \sqrt{2} C \cos (e+f x) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{3}{2},-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{f \sqrt{\sin (e+f x)+1}}","-\frac{2 \sqrt{2} (A-C) \cos (e+f x) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{f \sqrt{\sin (e+f x)+1}}-\frac{4 \sqrt{2} C \cos (e+f x) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};-\frac{3}{2},-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{f \sqrt{\sin (e+f x)+1}}",1,"(-4*Sqrt[2]*C*AppellF1[1/2, -3/2, -m, 3/2, (1 - Sin[e + f*x])/2, (b*(1 - Sin[e + f*x]))/(a + b)]*Cos[e + f*x]*(a + b*Sin[e + f*x])^m)/(f*Sqrt[1 + Sin[e + f*x]]*((a + b*Sin[e + f*x])/(a + b))^m) - (2*Sqrt[2]*(A - C)*AppellF1[1/2, -1/2, -m, 3/2, (1 - Sin[e + f*x])/2, (b*(1 - Sin[e + f*x]))/(a + b)]*Cos[e + f*x]*(a + b*Sin[e + f*x])^m)/(f*Sqrt[1 + Sin[e + f*x]]*((a + b*Sin[e + f*x])/(a + b))^m)","A",7,5,35,0.1429,1,"{3017, 2755, 139, 138, 2784}"
19,1,304,0,0.3615887,"\int (a+b \sin (e+f x))^m \left(A+B \sin (e+f x)+C \sin ^2(e+f x)\right) \, dx","Int[(a + b*Sin[e + f*x])^m*(A + B*Sin[e + f*x] + C*Sin[e + f*x]^2),x]","-\frac{\sqrt{2} \cos (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 \sin (e+f x))^m \left(\frac{a+b \sin (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\sin (e+f x)+1}}+\frac{\sqrt{2} (a+b) \cos (e+f x) (a C-b B (m+2)) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (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-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\sin (e+f x)+1}}-\frac{C \cos (e+f x) (a+b \sin (e+f x))^{m+1}}{b f (m+2)}","-\frac{\sqrt{2} \cos (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 \sin (e+f x))^m \left(\frac{a+b \sin (e+f x)}{a+b}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\sin (e+f x)+1}}+\frac{\sqrt{2} (a+b) \cos (e+f x) (a C-b B (m+2)) (a+b \sin (e+f x))^m \left(\frac{a+b \sin (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-\sin (e+f x)),\frac{b (1-\sin (e+f x))}{a+b}\right)}{b^2 f (m+2) \sqrt{\sin (e+f x)+1}}-\frac{C \cos (e+f x) (a+b \sin (e+f x))^{m+1}}{b f (m+2)}",1,"-((C*Cos[e + f*x]*(a + b*Sin[e + f*x])^(1 + m))/(b*f*(2 + m))) + (Sqrt[2]*(a + b)*(a*C - b*B*(2 + m))*AppellF1[1/2, 1/2, -1 - m, 3/2, (1 - Sin[e + f*x])/2, (b*(1 - Sin[e + f*x]))/(a + b)]*Cos[e + f*x]*(a + b*Sin[e + f*x])^m)/(b^2*f*(2 + m)*Sqrt[1 + Sin[e + f*x]]*((a + b*Sin[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 - Sin[e + f*x])/2, (b*(1 - Sin[e + f*x]))/(a + b)]*Cos[e + f*x]*(a + b*Sin[e + f*x])^m)/(b^2*f*(2 + m)*Sqrt[1 + Sin[e + f*x]]*((a + b*Sin[e + f*x])/(a + b))^m)","A",8,5,33,0.1515,1,"{3023, 2756, 2665, 139, 138}"