1,1,11,0,1.239522," ","integrate(sin(b*x+a),x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)}{b}"," ",0,"-cos(b*x + a)/b","A",0
2,1,23,0,1.490333," ","integrate(sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{b x - \cos\left(b x + a\right) \sin\left(b x + a\right)}{2 \, b}"," ",0,"1/2*(b*x - cos(b*x + a)*sin(b*x + a))/b","A",0
3,1,22,0,1.146652," ","integrate(sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)}{3 \, b}"," ",0,"1/3*(cos(b*x + a)^3 - 3*cos(b*x + a))/b","A",0
4,1,36,0,1.394590," ","integrate(sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{3 \, b x + {\left(2 \, \cos\left(b x + a\right)^{3} - 5 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{8 \, b}"," ",0,"1/8*(3*b*x + (2*cos(b*x + a)^3 - 5*cos(b*x + a))*sin(b*x + a))/b","A",0
5,1,34,0,1.423176," ","integrate(sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + a\right)^{5} - 10 \, \cos\left(b x + a\right)^{3} + 15 \, \cos\left(b x + a\right)}{15 \, b}"," ",0,"-1/15*(3*cos(b*x + a)^5 - 10*cos(b*x + a)^3 + 15*cos(b*x + a))/b","A",0
6,1,47,0,1.447367," ","integrate(sin(b*x+a)^6,x, algorithm=""fricas"")","\frac{15 \, b x - {\left(8 \, \cos\left(b x + a\right)^{5} - 26 \, \cos\left(b x + a\right)^{3} + 33 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{48 \, b}"," ",0,"1/48*(15*b*x - (8*cos(b*x + a)^5 - 26*cos(b*x + a)^3 + 33*cos(b*x + a))*sin(b*x + a))/b","A",0
7,1,44,0,1.356673," ","integrate(sin(b*x+a)^7,x, algorithm=""fricas"")","\frac{5 \, \cos\left(b x + a\right)^{7} - 21 \, \cos\left(b x + a\right)^{5} + 35 \, \cos\left(b x + a\right)^{3} - 35 \, \cos\left(b x + a\right)}{35 \, b}"," ",0,"1/35*(5*cos(b*x + a)^7 - 21*cos(b*x + a)^5 + 35*cos(b*x + a)^3 - 35*cos(b*x + a))/b","A",0
8,1,56,0,1.413539," ","integrate(sin(b*x+a)^8,x, algorithm=""fricas"")","\frac{105 \, b x + {\left(48 \, \cos\left(b x + a\right)^{7} - 200 \, \cos\left(b x + a\right)^{5} + 326 \, \cos\left(b x + a\right)^{3} - 279 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{384 \, b}"," ",0,"1/384*(105*b*x + (48*cos(b*x + a)^7 - 200*cos(b*x + a)^5 + 326*cos(b*x + a)^3 - 279*cos(b*x + a))*sin(b*x + a))/b","A",0
9,0,0,0,1.472331," ","integrate(sin(b*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x\right)^{2} - 1\right)} \sin\left(b x\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(-(cos(b*x)^2 - 1)*sin(b*x)^(3/2), x)","F",0
10,0,0,0,1.346749," ","integrate(sin(b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x\right)^{2} - 1\right)} \sqrt{\sin\left(b x\right)}, x\right)"," ",0,"integral(-(cos(b*x)^2 - 1)*sqrt(sin(b*x)), x)","F",0
11,0,0,0,1.435963," ","integrate(sin(b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(b x\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(sin(b*x)^(3/2), x)","F",0
12,0,0,0,1.342701," ","integrate(sin(b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\sin\left(b x\right)}, x\right)"," ",0,"integral(sqrt(sin(b*x)), x)","F",0
13,0,0,0,1.199834," ","integrate(1/sin(b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{\sin\left(b x\right)}}, x\right)"," ",0,"integral(1/sqrt(sin(b*x)), x)","F",0
14,0,0,0,1.364160," ","integrate(1/sin(b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{\sin\left(b x\right)}}{\cos\left(b x\right)^{2} - 1}, x\right)"," ",0,"integral(-sqrt(sin(b*x))/(cos(b*x)^2 - 1), x)","F",0
15,0,0,0,1.188555," ","integrate(1/sin(b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{{\left(\cos\left(b x\right)^{2} - 1\right)} \sqrt{\sin\left(b x\right)}}, x\right)"," ",0,"integral(-1/((cos(b*x)^2 - 1)*sqrt(sin(b*x))), x)","F",0
16,0,0,0,1.313331," ","integrate(1/sin(b*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sin\left(b x\right)}}{\cos\left(b x\right)^{4} - 2 \, \cos\left(b x\right)^{2} + 1}, x\right)"," ",0,"integral(sqrt(sin(b*x))/(cos(b*x)^4 - 2*cos(b*x)^2 + 1), x)","F",0
17,0,0,0,1.445013," ","integrate(sin(b*x+a)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sin(b*x + a)^(3/2), x)","F",0
18,0,0,0,1.383436," ","integrate(sin(b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{\sin\left(b x + a\right)}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sqrt(sin(b*x + a)), x)","F",0
19,0,0,0,1.159227," ","integrate(sin(b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(b x + a\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(sin(b*x + a)^(3/2), x)","F",0
20,0,0,0,1.157342," ","integrate(sin(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\sin\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(sin(b*x + a)), x)","F",0
21,0,0,0,1.383778," ","integrate(1/sin(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{\sin\left(b x + a\right)}}, x\right)"," ",0,"integral(1/sqrt(sin(b*x + a)), x)","F",0
22,0,0,0,1.335321," ","integrate(1/sin(b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{\sin\left(b x + a\right)}}{\cos\left(b x + a\right)^{2} - 1}, x\right)"," ",0,"integral(-sqrt(sin(b*x + a))/(cos(b*x + a)^2 - 1), x)","F",0
23,0,0,0,1.053174," ","integrate(1/sin(b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{\sin\left(b x + a\right)}}, x\right)"," ",0,"integral(-1/((cos(b*x + a)^2 - 1)*sqrt(sin(b*x + a))), x)","F",0
24,0,0,0,1.202000," ","integrate(1/sin(b*x+a)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sin\left(b x + a\right)}}{\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1}, x\right)"," ",0,"integral(sqrt(sin(b*x + a))/(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1), x)","F",0
25,0,0,0,1.234596," ","integrate((c*sin(b*x+a))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c^{3} \cos\left(b x + a\right)^{2} - c^{3}\right)} \sqrt{c \sin\left(b x + a\right)} \sin\left(b x + a\right), x\right)"," ",0,"integral(-(c^3*cos(b*x + a)^2 - c^3)*sqrt(c*sin(b*x + a))*sin(b*x + a), x)","F",0
26,0,0,0,1.233958," ","integrate((c*sin(b*x+a))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c^{2} \cos\left(b x + a\right)^{2} - c^{2}\right)} \sqrt{c \sin\left(b x + a\right)}, x\right)"," ",0,"integral(-(c^2*cos(b*x + a)^2 - c^2)*sqrt(c*sin(b*x + a)), x)","F",0
27,0,0,0,1.021664," ","integrate((c*sin(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c \sin\left(b x + a\right)} c \sin\left(b x + a\right), x\right)"," ",0,"integral(sqrt(c*sin(b*x + a))*c*sin(b*x + a), x)","F",0
28,0,0,0,1.330434," ","integrate((c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c \sin\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(c*sin(b*x + a)), x)","F",0
29,0,0,0,1.288913," ","integrate(1/(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c \sin\left(b x + a\right)}}{c \sin\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(c*sin(b*x + a))/(c*sin(b*x + a)), x)","F",0
30,0,0,0,1.376295," ","integrate(1/(c*sin(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{c \sin\left(b x + a\right)}}{c^{2} \cos\left(b x + a\right)^{2} - c^{2}}, x\right)"," ",0,"integral(-sqrt(c*sin(b*x + a))/(c^2*cos(b*x + a)^2 - c^2), x)","F",0
31,0,0,0,1.446285," ","integrate(1/(c*sin(b*x+a))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{c \sin\left(b x + a\right)}}{{\left(c^{3} \cos\left(b x + a\right)^{2} - c^{3}\right)} \sin\left(b x + a\right)}, x\right)"," ",0,"integral(-sqrt(c*sin(b*x + a))/((c^3*cos(b*x + a)^2 - c^3)*sin(b*x + a)), x)","F",0
32,0,0,0,1.260541," ","integrate(1/(c*sin(b*x+a))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c \sin\left(b x + a\right)}}{c^{4} \cos\left(b x + a\right)^{4} - 2 \, c^{4} \cos\left(b x + a\right)^{2} + c^{4}}, x\right)"," ",0,"integral(sqrt(c*sin(b*x + a))/(c^4*cos(b*x + a)^4 - 2*c^4*cos(b*x + a)^2 + c^4), x)","F",0
33,0,0,0,1.153340," ","integrate((c*sin(b*x+a))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(c \sin\left(b x + a\right)\right)^{\frac{1}{3}} c \sin\left(b x + a\right), x\right)"," ",0,"integral((c*sin(b*x + a))^(1/3)*c*sin(b*x + a), x)","F",0
34,0,0,0,1.380520," ","integrate((c*sin(b*x+a))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(c \sin\left(b x + a\right)\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((c*sin(b*x + a))^(2/3), x)","F",0
35,0,0,0,1.430322," ","integrate((c*sin(b*x+a))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(c \sin\left(b x + a\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((c*sin(b*x + a))^(1/3), x)","F",0
36,0,0,0,1.418150," ","integrate(1/(c*sin(b*x+a))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c \sin\left(b x + a\right)\right)^{\frac{2}{3}}}{c \sin\left(b x + a\right)}, x\right)"," ",0,"integral((c*sin(b*x + a))^(2/3)/(c*sin(b*x + a)), x)","F",0
37,0,0,0,1.308696," ","integrate(1/(c*sin(b*x+a))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c \sin\left(b x + a\right)\right)^{\frac{1}{3}}}{c \sin\left(b x + a\right)}, x\right)"," ",0,"integral((c*sin(b*x + a))^(1/3)/(c*sin(b*x + a)), x)","F",0
38,0,0,0,1.435852," ","integrate(1/(c*sin(b*x+a))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(c \sin\left(b x + a\right)\right)^{\frac{2}{3}}}{c^{2} \cos\left(b x + a\right)^{2} - c^{2}}, x\right)"," ",0,"integral(-(c*sin(b*x + a))^(2/3)/(c^2*cos(b*x + a)^2 - c^2), x)","F",0
39,0,0,0,1.436033," ","integrate(sin(b*x+a)^n,x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(b x + a\right)^{n}, x\right)"," ",0,"integral(sin(b*x + a)^n, x)","F",0
40,0,0,0,1.284249," ","integrate((c*sin(b*x+a))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(c \sin\left(b x + a\right)\right)^{n}, x\right)"," ",0,"integral((c*sin(b*x + a))^n, x)","F",0
41,0,0,0,1.434067," ","integrate((a*sin(f*x+e))^m*(b*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(a \sin\left(f x + e\right)\right)^{m} \left(b \sin\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*sin(f*x + e))^m*(b*sin(f*x + e))^n, x)","F",0
42,1,13,0,1.386663," ","integrate(cos(b*x+a)^3*sin(b*x+a),x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{4}}{4 \, b}"," ",0,"-1/4*cos(b*x + a)^4/b","A",0
43,1,13,0,1.381642," ","integrate(cos(b*x+a)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{3}}{3 \, b}"," ",0,"-1/3*cos(b*x + a)^3/b","A",0
44,1,13,0,1.265701," ","integrate(cos(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{2}}{2 \, b}"," ",0,"-1/2*cos(b*x + a)^2/b","A",0
45,1,14,0,1.361125," ","integrate(sec(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{\log\left(-\cos\left(b x + a\right)\right)}{b}"," ",0,"-log(-cos(b*x + a))/b","A",0
46,1,12,0,1.278579," ","integrate(sec(b*x+a)^2*sin(b*x+a),x, algorithm=""fricas"")","\frac{1}{b \cos\left(b x + a\right)}"," ",0,"1/(b*cos(b*x + a))","A",0
47,1,13,0,1.001927," ","integrate(sec(b*x+a)^3*sin(b*x+a),x, algorithm=""fricas"")","\frac{1}{2 \, b \cos\left(b x + a\right)^{2}}"," ",0,"1/2/(b*cos(b*x + a)^2)","A",0
48,1,13,0,1.358991," ","integrate(sec(b*x+a)^4*sin(b*x+a),x, algorithm=""fricas"")","\frac{1}{3 \, b \cos\left(b x + a\right)^{3}}"," ",0,"1/3/(b*cos(b*x + a)^3)","A",0
49,1,53,0,1.352579," ","integrate(cos(b*x+a)^7*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{{\left(35 \, \cos\left(b x + a\right)^{8} - 5 \, \cos\left(b x + a\right)^{6} - 6 \, \cos\left(b x + a\right)^{4} - 8 \, \cos\left(b x + a\right)^{2} - 16\right)} \sin\left(b x + a\right)}{315 \, b}"," ",0,"-1/315*(35*cos(b*x + a)^8 - 5*cos(b*x + a)^6 - 6*cos(b*x + a)^4 - 8*cos(b*x + a)^2 - 16)*sin(b*x + a)/b","A",0
50,1,43,0,1.229298," ","integrate(cos(b*x+a)^5*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{{\left(15 \, \cos\left(b x + a\right)^{6} - 3 \, \cos\left(b x + a\right)^{4} - 4 \, \cos\left(b x + a\right)^{2} - 8\right)} \sin\left(b x + a\right)}{105 \, b}"," ",0,"-1/105*(15*cos(b*x + a)^6 - 3*cos(b*x + a)^4 - 4*cos(b*x + a)^2 - 8)*sin(b*x + a)/b","A",0
51,1,33,0,1.424938," ","integrate(cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{{\left(3 \, \cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2} - 2\right)} \sin\left(b x + a\right)}{15 \, b}"," ",0,"-1/15*(3*cos(b*x + a)^4 - cos(b*x + a)^2 - 2)*sin(b*x + a)/b","A",0
52,1,21,0,0.828383," ","integrate(cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}{3 \, b}"," ",0,"-1/3*(cos(b*x + a)^2 - 1)*sin(b*x + a)/b","A",0
53,1,31,0,1.081547," ","integrate(sec(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b x \cos\left(b x + a\right) - \sin\left(b x + a\right)}{b \cos\left(b x + a\right)}"," ",0,"-(b*x*cos(b*x + a) - sin(b*x + a))/(b*cos(b*x + a))","B",0
54,1,29,0,1.396653," ","integrate(sec(b*x+a)^4*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}{3 \, b \cos\left(b x + a\right)^{3}}"," ",0,"-1/3*(cos(b*x + a)^2 - 1)*sin(b*x + a)/(b*cos(b*x + a)^3)","B",0
55,1,39,0,1.384877," ","integrate(sec(b*x+a)^6*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, \cos\left(b x + a\right)^{4} + \cos\left(b x + a\right)^{2} - 3\right)} \sin\left(b x + a\right)}{15 \, b \cos\left(b x + a\right)^{5}}"," ",0,"-1/15*(2*cos(b*x + a)^4 + cos(b*x + a)^2 - 3)*sin(b*x + a)/(b*cos(b*x + a)^5)","A",0
56,1,51,0,1.379124," ","integrate(sec(b*x+a)^8*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{{\left(8 \, \cos\left(b x + a\right)^{6} + 4 \, \cos\left(b x + a\right)^{4} + 3 \, \cos\left(b x + a\right)^{2} - 15\right)} \sin\left(b x + a\right)}{105 \, b \cos\left(b x + a\right)^{7}}"," ",0,"-1/105*(8*cos(b*x + a)^6 + 4*cos(b*x + a)^4 + 3*cos(b*x + a)^2 - 15)*sin(b*x + a)/(b*cos(b*x + a)^7)","A",0
57,1,61,0,1.357096," ","integrate(sec(b*x+a)^10*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{{\left(16 \, \cos\left(b x + a\right)^{8} + 8 \, \cos\left(b x + a\right)^{6} + 6 \, \cos\left(b x + a\right)^{4} + 5 \, \cos\left(b x + a\right)^{2} - 35\right)} \sin\left(b x + a\right)}{315 \, b \cos\left(b x + a\right)^{9}}"," ",0,"-1/315*(16*cos(b*x + a)^8 + 8*cos(b*x + a)^6 + 6*cos(b*x + a)^4 + 5*cos(b*x + a)^2 - 35)*sin(b*x + a)/(b*cos(b*x + a)^9)","A",0
58,1,57,0,1.344205," ","integrate(cos(b*x+a)^6*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{15 \, b x - {\left(48 \, \cos\left(b x + a\right)^{7} - 8 \, \cos\left(b x + a\right)^{5} - 10 \, \cos\left(b x + a\right)^{3} - 15 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{384 \, b}"," ",0,"1/384*(15*b*x - (48*cos(b*x + a)^7 - 8*cos(b*x + a)^5 - 10*cos(b*x + a)^3 - 15*cos(b*x + a))*sin(b*x + a))/b","A",0
59,1,47,0,0.951173," ","integrate(cos(b*x+a)^4*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{3 \, b x - {\left(8 \, \cos\left(b x + a\right)^{5} - 2 \, \cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{48 \, b}"," ",0,"1/48*(3*b*x - (8*cos(b*x + a)^5 - 2*cos(b*x + a)^3 - 3*cos(b*x + a))*sin(b*x + a))/b","A",0
60,1,36,0,1.314143," ","integrate(cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{b x - {\left(2 \, \cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{8 \, b}"," ",0,"1/8*(b*x - (2*cos(b*x + a)^3 - cos(b*x + a))*sin(b*x + a))/b","A",0
61,1,23,0,1.102256," ","integrate(sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{b x - \cos\left(b x + a\right) \sin\left(b x + a\right)}{2 \, b}"," ",0,"1/2*(b*x - cos(b*x + a)*sin(b*x + a))/b","A",0
62,1,36,0,1.402531," ","integrate(sec(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{\log\left(\sin\left(b x + a\right) + 1\right) - \log\left(-\sin\left(b x + a\right) + 1\right) - 2 \, \sin\left(b x + a\right)}{2 \, b}"," ",0,"1/2*(log(sin(b*x + a) + 1) - log(-sin(b*x + a) + 1) - 2*sin(b*x + a))/b","A",0
63,1,61,0,1.463016," ","integrate(sec(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{2} \log\left(\sin\left(b x + a\right) + 1\right) - \cos\left(b x + a\right)^{2} \log\left(-\sin\left(b x + a\right) + 1\right) - 2 \, \sin\left(b x + a\right)}{4 \, b \cos\left(b x + a\right)^{2}}"," ",0,"-1/4*(cos(b*x + a)^2*log(sin(b*x + a) + 1) - cos(b*x + a)^2*log(-sin(b*x + a) + 1) - 2*sin(b*x + a))/(b*cos(b*x + a)^2)","B",0
64,1,71,0,1.364901," ","integrate(sec(b*x+a)^5*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{4} \log\left(\sin\left(b x + a\right) + 1\right) - \cos\left(b x + a\right)^{4} \log\left(-\sin\left(b x + a\right) + 1\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} - 2\right)} \sin\left(b x + a\right)}{16 \, b \cos\left(b x + a\right)^{4}}"," ",0,"-1/16*(cos(b*x + a)^4*log(sin(b*x + a) + 1) - cos(b*x + a)^4*log(-sin(b*x + a) + 1) + 2*(cos(b*x + a)^2 - 2)*sin(b*x + a))/(b*cos(b*x + a)^4)","A",0
65,1,84,0,1.478106," ","integrate(sec(b*x+a)^7*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + a\right)^{6} \log\left(\sin\left(b x + a\right) + 1\right) - 3 \, \cos\left(b x + a\right)^{6} \log\left(-\sin\left(b x + a\right) + 1\right) + 2 \, {\left(3 \, \cos\left(b x + a\right)^{4} + 2 \, \cos\left(b x + a\right)^{2} - 8\right)} \sin\left(b x + a\right)}{96 \, b \cos\left(b x + a\right)^{6}}"," ",0,"-1/96*(3*cos(b*x + a)^6*log(sin(b*x + a) + 1) - 3*cos(b*x + a)^6*log(-sin(b*x + a) + 1) + 2*(3*cos(b*x + a)^4 + 2*cos(b*x + a)^2 - 8)*sin(b*x + a))/(b*cos(b*x + a)^6)","A",0
66,1,26,0,1.314172," ","integrate(cos(b*x+a)^5*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{3 \, \cos\left(b x + a\right)^{8} - 4 \, \cos\left(b x + a\right)^{6}}{24 \, b}"," ",0,"1/24*(3*cos(b*x + a)^8 - 4*cos(b*x + a)^6)/b","A",0
67,1,26,0,1.092724," ","integrate(cos(b*x+a)^4*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{5 \, \cos\left(b x + a\right)^{7} - 7 \, \cos\left(b x + a\right)^{5}}{35 \, b}"," ",0,"1/35*(5*cos(b*x + a)^7 - 7*cos(b*x + a)^5)/b","A",0
68,1,26,0,1.174197," ","integrate(cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, \cos\left(b x + a\right)^{6} - 3 \, \cos\left(b x + a\right)^{4}}{12 \, b}"," ",0,"1/12*(2*cos(b*x + a)^6 - 3*cos(b*x + a)^4)/b","A",0
69,1,26,0,1.187470," ","integrate(cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}}{15 \, b}"," ",0,"1/15*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)/b","A",0
70,1,24,0,1.098665," ","integrate(cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2}}{4 \, b}"," ",0,"1/4*(cos(b*x + a)^4 - 2*cos(b*x + a)^2)/b","A",0
71,1,25,0,1.297640," ","integrate(sec(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{\cos\left(b x + a\right)^{2} - 2 \, \log\left(-\cos\left(b x + a\right)\right)}{2 \, b}"," ",0,"1/2*(cos(b*x + a)^2 - 2*log(-cos(b*x + a)))/b","A",0
72,1,22,0,1.414544," ","integrate(sec(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{\cos\left(b x + a\right)^{2} + 1}{b \cos\left(b x + a\right)}"," ",0,"(cos(b*x + a)^2 + 1)/(b*cos(b*x + a))","A",0
73,1,34,0,1.375542," ","integrate(sec(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right)\right) + 1}{2 \, b \cos\left(b x + a\right)^{2}}"," ",0,"1/2*(2*cos(b*x + a)^2*log(-cos(b*x + a)) + 1)/(b*cos(b*x + a)^2)","A",0
74,1,25,0,1.160379," ","integrate(sec(b*x+a)^4*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + a\right)^{2} - 1}{3 \, b \cos\left(b x + a\right)^{3}}"," ",0,"-1/3*(3*cos(b*x + a)^2 - 1)/(b*cos(b*x + a)^3)","A",0
75,1,25,0,1.114621," ","integrate(sec(b*x+a)^5*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(b x + a\right)^{2} - 1}{4 \, b \cos\left(b x + a\right)^{4}}"," ",0,"-1/4*(2*cos(b*x + a)^2 - 1)/(b*cos(b*x + a)^4)","A",0
76,1,25,0,1.319443," ","integrate(sec(b*x+a)^6*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{5 \, \cos\left(b x + a\right)^{2} - 3}{15 \, b \cos\left(b x + a\right)^{5}}"," ",0,"-1/15*(5*cos(b*x + a)^2 - 3)/(b*cos(b*x + a)^5)","A",0
77,1,25,0,1.358337," ","integrate(sec(b*x+a)^7*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + a\right)^{2} - 2}{12 \, b \cos\left(b x + a\right)^{6}}"," ",0,"-1/12*(3*cos(b*x + a)^2 - 2)/(b*cos(b*x + a)^6)","A",0
78,1,25,0,1.387012," ","integrate(sec(b*x+a)^8*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{7 \, \cos\left(b x + a\right)^{2} - 5}{35 \, b \cos\left(b x + a\right)^{7}}"," ",0,"-1/35*(7*cos(b*x + a)^2 - 5)/(b*cos(b*x + a)^7)","A",0
79,1,25,0,1.466827," ","integrate(sec(b*x+a)^9*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{4 \, \cos\left(b x + a\right)^{2} - 3}{24 \, b \cos\left(b x + a\right)^{8}}"," ",0,"-1/24*(4*cos(b*x + a)^2 - 3)/(b*cos(b*x + a)^8)","A",0
80,1,63,0,1.125502," ","integrate(cos(b*x+a)^7*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{{\left(105 \, \cos\left(b x + a\right)^{10} - 140 \, \cos\left(b x + a\right)^{8} + 5 \, \cos\left(b x + a\right)^{6} + 6 \, \cos\left(b x + a\right)^{4} + 8 \, \cos\left(b x + a\right)^{2} + 16\right)} \sin\left(b x + a\right)}{1155 \, b}"," ",0,"1/1155*(105*cos(b*x + a)^10 - 140*cos(b*x + a)^8 + 5*cos(b*x + a)^6 + 6*cos(b*x + a)^4 + 8*cos(b*x + a)^2 + 16)*sin(b*x + a)/b","A",0
81,1,53,0,1.321093," ","integrate(cos(b*x+a)^5*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{{\left(35 \, \cos\left(b x + a\right)^{8} - 50 \, \cos\left(b x + a\right)^{6} + 3 \, \cos\left(b x + a\right)^{4} + 4 \, \cos\left(b x + a\right)^{2} + 8\right)} \sin\left(b x + a\right)}{315 \, b}"," ",0,"1/315*(35*cos(b*x + a)^8 - 50*cos(b*x + a)^6 + 3*cos(b*x + a)^4 + 4*cos(b*x + a)^2 + 8)*sin(b*x + a)/b","A",0
82,1,41,0,1.263829," ","integrate(cos(b*x+a)^3*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{{\left(5 \, \cos\left(b x + a\right)^{6} - 8 \, \cos\left(b x + a\right)^{4} + \cos\left(b x + a\right)^{2} + 2\right)} \sin\left(b x + a\right)}{35 \, b}"," ",0,"1/35*(5*cos(b*x + a)^6 - 8*cos(b*x + a)^4 + cos(b*x + a)^2 + 2)*sin(b*x + a)/b","A",0
83,1,31,0,1.048747," ","integrate(cos(b*x+a)*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{{\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right)}{5 \, b}"," ",0,"1/5*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*sin(b*x + a)/b","B",0
84,1,42,0,1.150524," ","integrate(sec(b*x+a)^2*sin(b*x+a)^4,x, algorithm=""fricas"")","-\frac{3 \, b x \cos\left(b x + a\right) - {\left(\cos\left(b x + a\right)^{2} + 2\right)} \sin\left(b x + a\right)}{2 \, b \cos\left(b x + a\right)}"," ",0,"-1/2*(3*b*x*cos(b*x + a) - (cos(b*x + a)^2 + 2)*sin(b*x + a))/(b*cos(b*x + a))","A",0
85,1,46,0,1.343769," ","integrate(sec(b*x+a)^4*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{3 \, b x \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}{3 \, b \cos\left(b x + a\right)^{3}}"," ",0,"1/3*(3*b*x*cos(b*x + a)^3 - (4*cos(b*x + a)^2 - 1)*sin(b*x + a))/(b*cos(b*x + a)^3)","A",0
86,1,39,0,1.123501," ","integrate(sec(b*x+a)^6*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{{\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right)}{5 \, b \cos\left(b x + a\right)^{5}}"," ",0,"1/5*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*sin(b*x + a)/(b*cos(b*x + a)^5)","B",0
87,1,49,0,1.292906," ","integrate(sec(b*x+a)^8*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{{\left(2 \, \cos\left(b x + a\right)^{6} + \cos\left(b x + a\right)^{4} - 8 \, \cos\left(b x + a\right)^{2} + 5\right)} \sin\left(b x + a\right)}{35 \, b \cos\left(b x + a\right)^{7}}"," ",0,"1/35*(2*cos(b*x + a)^6 + cos(b*x + a)^4 - 8*cos(b*x + a)^2 + 5)*sin(b*x + a)/(b*cos(b*x + a)^7)","A",0
88,1,61,0,1.364006," ","integrate(sec(b*x+a)^10*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{{\left(8 \, \cos\left(b x + a\right)^{8} + 4 \, \cos\left(b x + a\right)^{6} + 3 \, \cos\left(b x + a\right)^{4} - 50 \, \cos\left(b x + a\right)^{2} + 35\right)} \sin\left(b x + a\right)}{315 \, b \cos\left(b x + a\right)^{9}}"," ",0,"1/315*(8*cos(b*x + a)^8 + 4*cos(b*x + a)^6 + 3*cos(b*x + a)^4 - 50*cos(b*x + a)^2 + 35)*sin(b*x + a)/(b*cos(b*x + a)^9)","A",0
89,1,66,0,1.392744," ","integrate(cos(b*x+a)^6*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{15 \, b x + {\left(128 \, \cos\left(b x + a\right)^{9} - 176 \, \cos\left(b x + a\right)^{7} + 8 \, \cos\left(b x + a\right)^{5} + 10 \, \cos\left(b x + a\right)^{3} + 15 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{1280 \, b}"," ",0,"1/1280*(15*b*x + (128*cos(b*x + a)^9 - 176*cos(b*x + a)^7 + 8*cos(b*x + a)^5 + 10*cos(b*x + a)^3 + 15*cos(b*x + a))*sin(b*x + a))/b","A",0
90,1,56,0,1.325223," ","integrate(cos(b*x+a)^4*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{3 \, b x + {\left(16 \, \cos\left(b x + a\right)^{7} - 24 \, \cos\left(b x + a\right)^{5} + 2 \, \cos\left(b x + a\right)^{3} + 3 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{128 \, b}"," ",0,"1/128*(3*b*x + (16*cos(b*x + a)^7 - 24*cos(b*x + a)^5 + 2*cos(b*x + a)^3 + 3*cos(b*x + a))*sin(b*x + a))/b","A",0
91,1,46,0,1.344155," ","integrate(cos(b*x+a)^2*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{3 \, b x + {\left(8 \, \cos\left(b x + a\right)^{5} - 14 \, \cos\left(b x + a\right)^{3} + 3 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{48 \, b}"," ",0,"1/48*(3*b*x + (8*cos(b*x + a)^5 - 14*cos(b*x + a)^3 + 3*cos(b*x + a))*sin(b*x + a))/b","A",0
92,1,36,0,1.666382," ","integrate(sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{3 \, b x + {\left(2 \, \cos\left(b x + a\right)^{3} - 5 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{8 \, b}"," ",0,"1/8*(3*b*x + (2*cos(b*x + a)^3 - 5*cos(b*x + a))*sin(b*x + a))/b","A",0
93,1,48,0,1.365699," ","integrate(sec(b*x+a)*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(b x + a\right)^{2} - 4\right)} \sin\left(b x + a\right) + 3 \, \log\left(\sin\left(b x + a\right) + 1\right) - 3 \, \log\left(-\sin\left(b x + a\right) + 1\right)}{6 \, b}"," ",0,"1/6*(2*(cos(b*x + a)^2 - 4)*sin(b*x + a) + 3*log(sin(b*x + a) + 1) - 3*log(-sin(b*x + a) + 1))/b","A",0
94,1,74,0,1.162304," ","integrate(sec(b*x+a)^3*sin(b*x+a)^4,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + a\right)^{2} \log\left(\sin\left(b x + a\right) + 1\right) - 3 \, \cos\left(b x + a\right)^{2} \log\left(-\sin\left(b x + a\right) + 1\right) - 2 \, {\left(2 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right)}{4 \, b \cos\left(b x + a\right)^{2}}"," ",0,"-1/4*(3*cos(b*x + a)^2*log(sin(b*x + a) + 1) - 3*cos(b*x + a)^2*log(-sin(b*x + a) + 1) - 2*(2*cos(b*x + a)^2 + 1)*sin(b*x + a))/(b*cos(b*x + a)^2)","A",0
95,1,74,0,1.609190," ","integrate(sec(b*x+a)^5*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{3 \, \cos\left(b x + a\right)^{4} \log\left(\sin\left(b x + a\right) + 1\right) - 3 \, \cos\left(b x + a\right)^{4} \log\left(-\sin\left(b x + a\right) + 1\right) - 2 \, {\left(5 \, \cos\left(b x + a\right)^{2} - 2\right)} \sin\left(b x + a\right)}{16 \, b \cos\left(b x + a\right)^{4}}"," ",0,"1/16*(3*cos(b*x + a)^4*log(sin(b*x + a) + 1) - 3*cos(b*x + a)^4*log(-sin(b*x + a) + 1) - 2*(5*cos(b*x + a)^2 - 2)*sin(b*x + a))/(b*cos(b*x + a)^4)","A",0
96,1,84,0,1.459630," ","integrate(sec(b*x+a)^7*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{3 \, \cos\left(b x + a\right)^{6} \log\left(\sin\left(b x + a\right) + 1\right) - 3 \, \cos\left(b x + a\right)^{6} \log\left(-\sin\left(b x + a\right) + 1\right) + 2 \, {\left(3 \, \cos\left(b x + a\right)^{4} - 14 \, \cos\left(b x + a\right)^{2} + 8\right)} \sin\left(b x + a\right)}{96 \, b \cos\left(b x + a\right)^{6}}"," ",0,"1/96*(3*cos(b*x + a)^6*log(sin(b*x + a) + 1) - 3*cos(b*x + a)^6*log(-sin(b*x + a) + 1) + 2*(3*cos(b*x + a)^4 - 14*cos(b*x + a)^2 + 8)*sin(b*x + a))/(b*cos(b*x + a)^6)","A",0
97,1,94,0,1.324721," ","integrate(sec(b*x+a)^9*sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{3 \, \cos\left(b x + a\right)^{8} \log\left(\sin\left(b x + a\right) + 1\right) - 3 \, \cos\left(b x + a\right)^{8} \log\left(-\sin\left(b x + a\right) + 1\right) + 2 \, {\left(3 \, \cos\left(b x + a\right)^{6} + 2 \, \cos\left(b x + a\right)^{4} - 24 \, \cos\left(b x + a\right)^{2} + 16\right)} \sin\left(b x + a\right)}{256 \, b \cos\left(b x + a\right)^{8}}"," ",0,"1/256*(3*cos(b*x + a)^8*log(sin(b*x + a) + 1) - 3*cos(b*x + a)^8*log(-sin(b*x + a) + 1) + 2*(3*cos(b*x + a)^6 + 2*cos(b*x + a)^4 - 24*cos(b*x + a)^2 + 16)*sin(b*x + a))/(b*cos(b*x + a)^8)","A",0
98,1,36,0,1.349952," ","integrate(cos(b*x+a)^7*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{10 \, \cos\left(b x + a\right)^{12} - 24 \, \cos\left(b x + a\right)^{10} + 15 \, \cos\left(b x + a\right)^{8}}{120 \, b}"," ",0,"-1/120*(10*cos(b*x + a)^12 - 24*cos(b*x + a)^10 + 15*cos(b*x + a)^8)/b","A",0
99,1,36,0,1.581922," ","integrate(cos(b*x+a)^6*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{63 \, \cos\left(b x + a\right)^{11} - 154 \, \cos\left(b x + a\right)^{9} + 99 \, \cos\left(b x + a\right)^{7}}{693 \, b}"," ",0,"-1/693*(63*cos(b*x + a)^11 - 154*cos(b*x + a)^9 + 99*cos(b*x + a)^7)/b","A",0
100,1,36,0,1.332635," ","integrate(cos(b*x+a)^5*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{6 \, \cos\left(b x + a\right)^{10} - 15 \, \cos\left(b x + a\right)^{8} + 10 \, \cos\left(b x + a\right)^{6}}{60 \, b}"," ",0,"-1/60*(6*cos(b*x + a)^10 - 15*cos(b*x + a)^8 + 10*cos(b*x + a)^6)/b","A",0
101,1,36,0,1.337181," ","integrate(cos(b*x+a)^4*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{35 \, \cos\left(b x + a\right)^{9} - 90 \, \cos\left(b x + a\right)^{7} + 63 \, \cos\left(b x + a\right)^{5}}{315 \, b}"," ",0,"-1/315*(35*cos(b*x + a)^9 - 90*cos(b*x + a)^7 + 63*cos(b*x + a)^5)/b","A",0
102,1,36,0,0.909945," ","integrate(cos(b*x+a)^3*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + a\right)^{8} - 8 \, \cos\left(b x + a\right)^{6} + 6 \, \cos\left(b x + a\right)^{4}}{24 \, b}"," ",0,"-1/24*(3*cos(b*x + a)^8 - 8*cos(b*x + a)^6 + 6*cos(b*x + a)^4)/b","A",0
103,1,36,0,1.038030," ","integrate(cos(b*x+a)^2*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{15 \, \cos\left(b x + a\right)^{7} - 42 \, \cos\left(b x + a\right)^{5} + 35 \, \cos\left(b x + a\right)^{3}}{105 \, b}"," ",0,"-1/105*(15*cos(b*x + a)^7 - 42*cos(b*x + a)^5 + 35*cos(b*x + a)^3)/b","A",0
104,1,34,0,1.248970," ","integrate(cos(b*x+a)*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{6} - 3 \, \cos\left(b x + a\right)^{4} + 3 \, \cos\left(b x + a\right)^{2}}{6 \, b}"," ",0,"-1/6*(cos(b*x + a)^6 - 3*cos(b*x + a)^4 + 3*cos(b*x + a)^2)/b","B",0
105,1,35,0,1.387331," ","integrate(sec(b*x+a)*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{4} - 4 \, \cos\left(b x + a\right)^{2} + 4 \, \log\left(-\cos\left(b x + a\right)\right)}{4 \, b}"," ",0,"-1/4*(cos(b*x + a)^4 - 4*cos(b*x + a)^2 + 4*log(-cos(b*x + a)))/b","A",0
106,1,33,0,1.458356," ","integrate(sec(b*x+a)^2*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{4} - 6 \, \cos\left(b x + a\right)^{2} - 3}{3 \, b \cos\left(b x + a\right)}"," ",0,"-1/3*(cos(b*x + a)^4 - 6*cos(b*x + a)^2 - 3)/(b*cos(b*x + a))","A",0
107,1,54,0,0.998581," ","integrate(sec(b*x+a)^3*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(b x + a\right)^{4} - 8 \, \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right)\right) - \cos\left(b x + a\right)^{2} - 2}{4 \, b \cos\left(b x + a\right)^{2}}"," ",0,"-1/4*(2*cos(b*x + a)^4 - 8*cos(b*x + a)^2*log(-cos(b*x + a)) - cos(b*x + a)^2 - 2)/(b*cos(b*x + a)^2)","A",0
108,1,35,0,1.074082," ","integrate(sec(b*x+a)^4*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + a\right)^{4} + 6 \, \cos\left(b x + a\right)^{2} - 1}{3 \, b \cos\left(b x + a\right)^{3}}"," ",0,"-1/3*(3*cos(b*x + a)^4 + 6*cos(b*x + a)^2 - 1)/(b*cos(b*x + a)^3)","A",0
109,1,44,0,0.826257," ","integrate(sec(b*x+a)^5*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{4 \, \cos\left(b x + a\right)^{4} \log\left(-\cos\left(b x + a\right)\right) + 4 \, \cos\left(b x + a\right)^{2} - 1}{4 \, b \cos\left(b x + a\right)^{4}}"," ",0,"-1/4*(4*cos(b*x + a)^4*log(-cos(b*x + a)) + 4*cos(b*x + a)^2 - 1)/(b*cos(b*x + a)^4)","A",0
110,1,35,0,1.396785," ","integrate(sec(b*x+a)^6*sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{15 \, \cos\left(b x + a\right)^{4} - 10 \, \cos\left(b x + a\right)^{2} + 3}{15 \, b \cos\left(b x + a\right)^{5}}"," ",0,"1/15*(15*cos(b*x + a)^4 - 10*cos(b*x + a)^2 + 3)/(b*cos(b*x + a)^5)","A",0
111,1,35,0,1.352185," ","integrate(sec(b*x+a)^7*sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{3 \, \cos\left(b x + a\right)^{4} - 3 \, \cos\left(b x + a\right)^{2} + 1}{6 \, b \cos\left(b x + a\right)^{6}}"," ",0,"1/6*(3*cos(b*x + a)^4 - 3*cos(b*x + a)^2 + 1)/(b*cos(b*x + a)^6)","B",0
112,1,35,0,1.116807," ","integrate(sec(b*x+a)^8*sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{35 \, \cos\left(b x + a\right)^{4} - 42 \, \cos\left(b x + a\right)^{2} + 15}{105 \, b \cos\left(b x + a\right)^{7}}"," ",0,"1/105*(35*cos(b*x + a)^4 - 42*cos(b*x + a)^2 + 15)/(b*cos(b*x + a)^7)","A",0
113,1,35,0,0.807025," ","integrate(sec(b*x+a)^9*sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{6 \, \cos\left(b x + a\right)^{4} - 8 \, \cos\left(b x + a\right)^{2} + 3}{24 \, b \cos\left(b x + a\right)^{8}}"," ",0,"1/24*(6*cos(b*x + a)^4 - 8*cos(b*x + a)^2 + 3)/(b*cos(b*x + a)^8)","A",0
114,1,35,0,1.186366," ","integrate(sec(b*x+a)^10*sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{63 \, \cos\left(b x + a\right)^{4} - 90 \, \cos\left(b x + a\right)^{2} + 35}{315 \, b \cos\left(b x + a\right)^{9}}"," ",0,"1/315*(63*cos(b*x + a)^4 - 90*cos(b*x + a)^2 + 35)/(b*cos(b*x + a)^9)","A",0
115,1,35,0,1.242976," ","integrate(sec(b*x+a)^11*sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{10 \, \cos\left(b x + a\right)^{4} - 15 \, \cos\left(b x + a\right)^{2} + 6}{60 \, b \cos\left(b x + a\right)^{10}}"," ",0,"1/60*(10*cos(b*x + a)^4 - 15*cos(b*x + a)^2 + 6)/(b*cos(b*x + a)^10)","A",0
116,1,35,0,1.357837," ","integrate(sec(b*x+a)^12*sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{99 \, \cos\left(b x + a\right)^{4} - 154 \, \cos\left(b x + a\right)^{2} + 63}{693 \, b \cos\left(b x + a\right)^{11}}"," ",0,"1/693*(99*cos(b*x + a)^4 - 154*cos(b*x + a)^2 + 63)/(b*cos(b*x + a)^11)","A",0
117,1,35,0,1.156537," ","integrate(sec(b*x+a)^13*sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{15 \, \cos\left(b x + a\right)^{4} - 24 \, \cos\left(b x + a\right)^{2} + 10}{120 \, b \cos\left(b x + a\right)^{12}}"," ",0,"1/120*(15*cos(b*x + a)^4 - 24*cos(b*x + a)^2 + 10)/(b*cos(b*x + a)^12)","A",0
118,1,84,0,1.256696," ","integrate(sec(b*x+a)^3*sin(b*x+a)^6,x, algorithm=""fricas"")","-\frac{15 \, \cos\left(b x + a\right)^{2} \log\left(\sin\left(b x + a\right) + 1\right) - 15 \, \cos\left(b x + a\right)^{2} \log\left(-\sin\left(b x + a\right) + 1\right) + 2 \, {\left(2 \, \cos\left(b x + a\right)^{4} - 14 \, \cos\left(b x + a\right)^{2} - 3\right)} \sin\left(b x + a\right)}{12 \, b \cos\left(b x + a\right)^{2}}"," ",0,"-1/12*(15*cos(b*x + a)^2*log(sin(b*x + a) + 1) - 15*cos(b*x + a)^2*log(-sin(b*x + a) + 1) + 2*(2*cos(b*x + a)^4 - 14*cos(b*x + a)^2 - 3)*sin(b*x + a))/(b*cos(b*x + a)^2)","A",0
119,1,45,0,1.082048," ","integrate(sec(b*x+a)^6*sin(b*x+a)^7,x, algorithm=""fricas"")","\frac{5 \, \cos\left(b x + a\right)^{6} + 15 \, \cos\left(b x + a\right)^{4} - 5 \, \cos\left(b x + a\right)^{2} + 1}{5 \, b \cos\left(b x + a\right)^{5}}"," ",0,"1/5*(5*cos(b*x + a)^6 + 15*cos(b*x + a)^4 - 5*cos(b*x + a)^2 + 1)/(b*cos(b*x + a)^5)","A",0
120,1,60,0,0.781255," ","integrate(cos(b*x+a)^6/sin(b*x+a),x, algorithm=""fricas"")","\frac{6 \, \cos\left(b x + a\right)^{5} + 10 \, \cos\left(b x + a\right)^{3} + 30 \, \cos\left(b x + a\right) - 15 \, \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 15 \, \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right)}{30 \, b}"," ",0,"1/30*(6*cos(b*x + a)^5 + 10*cos(b*x + a)^3 + 30*cos(b*x + a) - 15*log(1/2*cos(b*x + a) + 1/2) + 15*log(-1/2*cos(b*x + a) + 1/2))/b","A",0
121,1,35,0,1.104752," ","integrate(cos(b*x+a)^5/sin(b*x+a),x, algorithm=""fricas"")","\frac{\cos\left(b x + a\right)^{4} + 2 \, \cos\left(b x + a\right)^{2} + 4 \, \log\left(\frac{1}{2} \, \sin\left(b x + a\right)\right)}{4 \, b}"," ",0,"1/4*(cos(b*x + a)^4 + 2*cos(b*x + a)^2 + 4*log(1/2*sin(b*x + a)))/b","A",0
122,1,50,0,1.473921," ","integrate(cos(b*x+a)^4/sin(b*x+a),x, algorithm=""fricas"")","\frac{2 \, \cos\left(b x + a\right)^{3} + 6 \, \cos\left(b x + a\right) - 3 \, \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 3 \, \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right)}{6 \, b}"," ",0,"1/6*(2*cos(b*x + a)^3 + 6*cos(b*x + a) - 3*log(1/2*cos(b*x + a) + 1/2) + 3*log(-1/2*cos(b*x + a) + 1/2))/b","A",0
123,1,25,0,1.406438," ","integrate(cos(b*x+a)^3/sin(b*x+a),x, algorithm=""fricas"")","\frac{\cos\left(b x + a\right)^{2} + 2 \, \log\left(\frac{1}{2} \, \sin\left(b x + a\right)\right)}{2 \, b}"," ",0,"1/2*(cos(b*x + a)^2 + 2*log(1/2*sin(b*x + a)))/b","A",0
124,1,38,0,1.418112," ","integrate(cos(b*x+a)^2/sin(b*x+a),x, algorithm=""fricas"")","\frac{2 \, \cos\left(b x + a\right) - \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right)}{2 \, b}"," ",0,"1/2*(2*cos(b*x + a) - log(1/2*cos(b*x + a) + 1/2) + log(-1/2*cos(b*x + a) + 1/2))/b","A",0
125,1,13,0,1.407770," ","integrate(cos(b*x+a)/sin(b*x+a),x, algorithm=""fricas"")","\frac{\log\left(\frac{1}{2} \, \sin\left(b x + a\right)\right)}{b}"," ",0,"log(1/2*sin(b*x + a))/b","A",0
126,1,30,0,1.373662," ","integrate(sec(b*x+a)/sin(b*x+a),x, algorithm=""fricas"")","-\frac{\log\left(\cos\left(b x + a\right)^{2}\right) - \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right)}{2 \, b}"," ",0,"-1/2*(log(cos(b*x + a)^2) - log(-1/4*cos(b*x + a)^2 + 1/4))/b","B",0
127,1,52,0,1.312982," ","integrate(sec(b*x+a)^2/sin(b*x+a),x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right) \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 2}{2 \, b \cos\left(b x + a\right)}"," ",0,"-1/2*(cos(b*x + a)*log(1/2*cos(b*x + a) + 1/2) - cos(b*x + a)*log(-1/2*cos(b*x + a) + 1/2) - 2)/(b*cos(b*x + a))","B",0
128,1,56,0,1.480618," ","integrate(sec(b*x+a)^3/sin(b*x+a),x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right)^{2}\right) - \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) - 1}{2 \, b \cos\left(b x + a\right)^{2}}"," ",0,"-1/2*(cos(b*x + a)^2*log(cos(b*x + a)^2) - cos(b*x + a)^2*log(-1/4*cos(b*x + a)^2 + 1/4) - 1)/(b*cos(b*x + a)^2)","B",0
129,1,67,0,1.366949," ","integrate(sec(b*x+a)^4/sin(b*x+a),x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + a\right)^{3} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 3 \, \cos\left(b x + a\right)^{3} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 6 \, \cos\left(b x + a\right)^{2} - 2}{6 \, b \cos\left(b x + a\right)^{3}}"," ",0,"-1/6*(3*cos(b*x + a)^3*log(1/2*cos(b*x + a) + 1/2) - 3*cos(b*x + a)^3*log(-1/2*cos(b*x + a) + 1/2) - 6*cos(b*x + a)^2 - 2)/(b*cos(b*x + a)^3)","A",0
130,1,67,0,1.494192," ","integrate(sec(b*x+a)^5/sin(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, \cos\left(b x + a\right)^{4} \log\left(\cos\left(b x + a\right)^{2}\right) - 2 \, \cos\left(b x + a\right)^{4} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) - 2 \, \cos\left(b x + a\right)^{2} - 1}{4 \, b \cos\left(b x + a\right)^{4}}"," ",0,"-1/4*(2*cos(b*x + a)^4*log(cos(b*x + a)^2) - 2*cos(b*x + a)^4*log(-1/4*cos(b*x + a)^2 + 1/4) - 2*cos(b*x + a)^2 - 1)/(b*cos(b*x + a)^4)","A",0
131,1,77,0,1.434820," ","integrate(sec(b*x+a)^6/sin(b*x+a),x, algorithm=""fricas"")","-\frac{15 \, \cos\left(b x + a\right)^{5} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 15 \, \cos\left(b x + a\right)^{5} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 30 \, \cos\left(b x + a\right)^{4} - 10 \, \cos\left(b x + a\right)^{2} - 6}{30 \, b \cos\left(b x + a\right)^{5}}"," ",0,"-1/30*(15*cos(b*x + a)^5*log(1/2*cos(b*x + a) + 1/2) - 15*cos(b*x + a)^5*log(-1/2*cos(b*x + a) + 1/2) - 30*cos(b*x + a)^4 - 10*cos(b*x + a)^2 - 6)/(b*cos(b*x + a)^5)","A",0
132,1,77,0,1.569731," ","integrate(sec(b*x+a)^7/sin(b*x+a),x, algorithm=""fricas"")","-\frac{6 \, \cos\left(b x + a\right)^{6} \log\left(\cos\left(b x + a\right)^{2}\right) - 6 \, \cos\left(b x + a\right)^{6} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) - 6 \, \cos\left(b x + a\right)^{4} - 3 \, \cos\left(b x + a\right)^{2} - 2}{12 \, b \cos\left(b x + a\right)^{6}}"," ",0,"-1/12*(6*cos(b*x + a)^6*log(cos(b*x + a)^2) - 6*cos(b*x + a)^6*log(-1/4*cos(b*x + a)^2 + 1/4) - 6*cos(b*x + a)^4 - 3*cos(b*x + a)^2 - 2)/(b*cos(b*x + a)^6)","A",0
133,1,43,0,1.265121," ","integrate(cos(b*x+a)^7/sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{\cos\left(b x + a\right)^{6} + 2 \, \cos\left(b x + a\right)^{4} + 8 \, \cos\left(b x + a\right)^{2} - 16}{5 \, b \sin\left(b x + a\right)}"," ",0,"1/5*(cos(b*x + a)^6 + 2*cos(b*x + a)^4 + 8*cos(b*x + a)^2 - 16)/(b*sin(b*x + a))","A",0
134,1,52,0,1.567117," ","integrate(cos(b*x+a)^6/sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, \cos\left(b x + a\right)^{5} + 5 \, \cos\left(b x + a\right)^{3} - 15 \, b x \sin\left(b x + a\right) - 15 \, \cos\left(b x + a\right)}{8 \, b \sin\left(b x + a\right)}"," ",0,"1/8*(2*cos(b*x + a)^5 + 5*cos(b*x + a)^3 - 15*b*x*sin(b*x + a) - 15*cos(b*x + a))/(b*sin(b*x + a))","A",0
135,1,33,0,1.466900," ","integrate(cos(b*x+a)^5/sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{\cos\left(b x + a\right)^{4} + 4 \, \cos\left(b x + a\right)^{2} - 8}{3 \, b \sin\left(b x + a\right)}"," ",0,"1/3*(cos(b*x + a)^4 + 4*cos(b*x + a)^2 - 8)/(b*sin(b*x + a))","A",0
136,1,40,0,1.201428," ","integrate(cos(b*x+a)^4/sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{\cos\left(b x + a\right)^{3} - 3 \, b x \sin\left(b x + a\right) - 3 \, \cos\left(b x + a\right)}{2 \, b \sin\left(b x + a\right)}"," ",0,"1/2*(cos(b*x + a)^3 - 3*b*x*sin(b*x + a) - 3*cos(b*x + a))/(b*sin(b*x + a))","A",0
137,1,22,0,1.244527," ","integrate(cos(b*x+a)^3/sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{\cos\left(b x + a\right)^{2} - 2}{b \sin\left(b x + a\right)}"," ",0,"(cos(b*x + a)^2 - 2)/(b*sin(b*x + a))","A",0
138,1,29,0,1.339937," ","integrate(cos(b*x+a)^2/sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b x \sin\left(b x + a\right) + \cos\left(b x + a\right)}{b \sin\left(b x + a\right)}"," ",0,"-(b*x*sin(b*x + a) + cos(b*x + a))/(b*sin(b*x + a))","A",0
139,1,13,0,1.284084," ","integrate(cos(b*x+a)/sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{1}{b \sin\left(b x + a\right)}"," ",0,"-1/(b*sin(b*x + a))","A",0
140,1,50,0,1.344905," ","integrate(sec(b*x+a)/sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{\log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 2}{2 \, b \sin\left(b x + a\right)}"," ",0,"1/2*(log(sin(b*x + a) + 1)*sin(b*x + a) - log(-sin(b*x + a) + 1)*sin(b*x + a) - 2)/(b*sin(b*x + a))","B",0
141,1,33,0,1.327245," ","integrate(sec(b*x+a)^2/sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(b x + a\right)^{2} - 1}{b \cos\left(b x + a\right) \sin\left(b x + a\right)}"," ",0,"-(2*cos(b*x + a)^2 - 1)/(b*cos(b*x + a)*sin(b*x + a))","A",0
142,1,85,0,1.429843," ","integrate(sec(b*x+a)^3/sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{3 \, \cos\left(b x + a\right)^{2} \log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, \cos\left(b x + a\right)^{2} \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 6 \, \cos\left(b x + a\right)^{2} + 2}{4 \, b \cos\left(b x + a\right)^{2} \sin\left(b x + a\right)}"," ",0,"1/4*(3*cos(b*x + a)^2*log(sin(b*x + a) + 1)*sin(b*x + a) - 3*cos(b*x + a)^2*log(-sin(b*x + a) + 1)*sin(b*x + a) - 6*cos(b*x + a)^2 + 2)/(b*cos(b*x + a)^2*sin(b*x + a))","A",0
143,1,43,0,1.421824," ","integrate(sec(b*x+a)^4/sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{8 \, \cos\left(b x + a\right)^{4} - 4 \, \cos\left(b x + a\right)^{2} - 1}{3 \, b \cos\left(b x + a\right)^{3} \sin\left(b x + a\right)}"," ",0,"-1/3*(8*cos(b*x + a)^4 - 4*cos(b*x + a)^2 - 1)/(b*cos(b*x + a)^3*sin(b*x + a))","A",0
144,1,95,0,1.261893," ","integrate(sec(b*x+a)^5/sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{15 \, \cos\left(b x + a\right)^{4} \log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 15 \, \cos\left(b x + a\right)^{4} \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 30 \, \cos\left(b x + a\right)^{4} + 10 \, \cos\left(b x + a\right)^{2} + 4}{16 \, b \cos\left(b x + a\right)^{4} \sin\left(b x + a\right)}"," ",0,"1/16*(15*cos(b*x + a)^4*log(sin(b*x + a) + 1)*sin(b*x + a) - 15*cos(b*x + a)^4*log(-sin(b*x + a) + 1)*sin(b*x + a) - 30*cos(b*x + a)^4 + 10*cos(b*x + a)^2 + 4)/(b*cos(b*x + a)^4*sin(b*x + a))","A",0
145,1,71,0,1.419034," ","integrate(cos(b*x+a)^7/sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{8 \, \cos\left(b x + a\right)^{6} + 24 \, \cos\left(b x + a\right)^{4} - 51 \, \cos\left(b x + a\right)^{2} + 96 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(b x + a\right)\right) + 3}{32 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"-1/32*(8*cos(b*x + a)^6 + 24*cos(b*x + a)^4 - 51*cos(b*x + a)^2 + 96*(cos(b*x + a)^2 - 1)*log(1/2*sin(b*x + a)) + 3)/(b*cos(b*x + a)^2 - b)","A",0
146,1,93,0,1.407241," ","integrate(cos(b*x+a)^6/sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{4 \, \cos\left(b x + a\right)^{5} + 20 \, \cos\left(b x + a\right)^{3} - 15 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 30 \, \cos\left(b x + a\right)}{12 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"-1/12*(4*cos(b*x + a)^5 + 20*cos(b*x + a)^3 - 15*(cos(b*x + a)^2 - 1)*log(1/2*cos(b*x + a) + 1/2) + 15*(cos(b*x + a)^2 - 1)*log(-1/2*cos(b*x + a) + 1/2) - 30*cos(b*x + a))/(b*cos(b*x + a)^2 - b)","A",0
147,1,61,0,1.354760," ","integrate(cos(b*x+a)^5/sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(b x + a\right)^{4} - 3 \, \cos\left(b x + a\right)^{2} + 8 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(b x + a\right)\right) - 1}{4 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"-1/4*(2*cos(b*x + a)^4 - 3*cos(b*x + a)^2 + 8*(cos(b*x + a)^2 - 1)*log(1/2*sin(b*x + a)) - 1)/(b*cos(b*x + a)^2 - b)","A",0
148,1,83,0,1.028842," ","integrate(cos(b*x+a)^4/sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{4 \, \cos\left(b x + a\right)^{3} - 3 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 6 \, \cos\left(b x + a\right)}{4 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"-1/4*(4*cos(b*x + a)^3 - 3*(cos(b*x + a)^2 - 1)*log(1/2*cos(b*x + a) + 1/2) + 3*(cos(b*x + a)^2 - 1)*log(-1/2*cos(b*x + a) + 1/2) - 6*cos(b*x + a))/(b*cos(b*x + a)^2 - b)","A",0
149,1,41,0,1.445134," ","integrate(cos(b*x+a)^3/sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(b x + a\right)\right) - 1}{2 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"-1/2*(2*(cos(b*x + a)^2 - 1)*log(1/2*sin(b*x + a)) - 1)/(b*cos(b*x + a)^2 - b)","A",0
150,1,72,0,1.691741," ","integrate(cos(b*x+a)^2/sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 2 \, \cos\left(b x + a\right)}{4 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"1/4*((cos(b*x + a)^2 - 1)*log(1/2*cos(b*x + a) + 1/2) - (cos(b*x + a)^2 - 1)*log(-1/2*cos(b*x + a) + 1/2) + 2*cos(b*x + a))/(b*cos(b*x + a)^2 - b)","B",0
151,1,18,0,1.482126," ","integrate(cos(b*x+a)/sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{2 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"1/2/(b*cos(b*x + a)^2 - b)","A",0
152,1,65,0,1.724640," ","integrate(sec(b*x+a)/sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\cos\left(b x + a\right)^{2}\right) - {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) - 1}{2 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"-1/2*((cos(b*x + a)^2 - 1)*log(cos(b*x + a)^2) - (cos(b*x + a)^2 - 1)*log(-1/4*cos(b*x + a)^2 + 1/4) - 1)/(b*cos(b*x + a)^2 - b)","B",0
153,1,96,0,1.429947," ","integrate(sec(b*x+a)^2/sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{6 \, \cos\left(b x + a\right)^{2} - 3 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 4}{4 \, {\left(b \cos\left(b x + a\right)^{3} - b \cos\left(b x + a\right)\right)}}"," ",0,"1/4*(6*cos(b*x + a)^2 - 3*(cos(b*x + a)^3 - cos(b*x + a))*log(1/2*cos(b*x + a) + 1/2) + 3*(cos(b*x + a)^3 - cos(b*x + a))*log(-1/2*cos(b*x + a) + 1/2) - 4)/(b*cos(b*x + a)^3 - b*cos(b*x + a))","B",0
154,1,102,0,1.183131," ","integrate(sec(b*x+a)^3/sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right)^{2}\right) + 2 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) - 1}{2 \, {\left(b \cos\left(b x + a\right)^{4} - b \cos\left(b x + a\right)^{2}\right)}}"," ",0,"1/2*(2*cos(b*x + a)^2 - 2*(cos(b*x + a)^4 - cos(b*x + a)^2)*log(cos(b*x + a)^2) + 2*(cos(b*x + a)^4 - cos(b*x + a)^2)*log(-1/4*cos(b*x + a)^2 + 1/4) - 1)/(b*cos(b*x + a)^4 - b*cos(b*x + a)^2)","B",0
155,1,112,0,1.799663," ","integrate(sec(b*x+a)^4/sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{30 \, \cos\left(b x + a\right)^{4} - 20 \, \cos\left(b x + a\right)^{2} - 15 \, {\left(\cos\left(b x + a\right)^{5} - \cos\left(b x + a\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(b x + a\right)^{5} - \cos\left(b x + a\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 4}{12 \, {\left(b \cos\left(b x + a\right)^{5} - b \cos\left(b x + a\right)^{3}\right)}}"," ",0,"1/12*(30*cos(b*x + a)^4 - 20*cos(b*x + a)^2 - 15*(cos(b*x + a)^5 - cos(b*x + a)^3)*log(1/2*cos(b*x + a) + 1/2) + 15*(cos(b*x + a)^5 - cos(b*x + a)^3)*log(-1/2*cos(b*x + a) + 1/2) - 4)/(b*cos(b*x + a)^5 - b*cos(b*x + a)^3)","A",0
156,1,112,0,1.194704," ","integrate(sec(b*x+a)^5/sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{6 \, \cos\left(b x + a\right)^{4} - 3 \, \cos\left(b x + a\right)^{2} - 6 \, {\left(\cos\left(b x + a\right)^{6} - \cos\left(b x + a\right)^{4}\right)} \log\left(\cos\left(b x + a\right)^{2}\right) + 6 \, {\left(\cos\left(b x + a\right)^{6} - \cos\left(b x + a\right)^{4}\right)} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) - 1}{4 \, {\left(b \cos\left(b x + a\right)^{6} - b \cos\left(b x + a\right)^{4}\right)}}"," ",0,"1/4*(6*cos(b*x + a)^4 - 3*cos(b*x + a)^2 - 6*(cos(b*x + a)^6 - cos(b*x + a)^4)*log(cos(b*x + a)^2) + 6*(cos(b*x + a)^6 - cos(b*x + a)^4)*log(-1/4*cos(b*x + a)^2 + 1/4) - 1)/(b*cos(b*x + a)^6 - b*cos(b*x + a)^4)","B",0
157,1,68,0,1.415942," ","integrate(cos(b*x+a)^9/sin(b*x+a)^4,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + a\right)^{8} + 8 \, \cos\left(b x + a\right)^{6} + 48 \, \cos\left(b x + a\right)^{4} - 192 \, \cos\left(b x + a\right)^{2} + 128}{15 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"-1/15*(3*cos(b*x + a)^8 + 8*cos(b*x + a)^6 + 48*cos(b*x + a)^4 - 192*cos(b*x + a)^2 + 128)/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","A",0
158,1,89,0,1.393834," ","integrate(cos(b*x+a)^8/sin(b*x+a)^4,x, algorithm=""fricas"")","-\frac{6 \, \cos\left(b x + a\right)^{7} + 21 \, \cos\left(b x + a\right)^{5} - 140 \, \cos\left(b x + a\right)^{3} - 105 \, {\left(b x \cos\left(b x + a\right)^{2} - b x\right)} \sin\left(b x + a\right) + 105 \, \cos\left(b x + a\right)}{24 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"-1/24*(6*cos(b*x + a)^7 + 21*cos(b*x + a)^5 - 140*cos(b*x + a)^3 - 105*(b*x*cos(b*x + a)^2 - b*x)*sin(b*x + a) + 105*cos(b*x + a))/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","A",0
159,1,56,0,1.340806," ","integrate(cos(b*x+a)^7/sin(b*x+a)^4,x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{6} + 6 \, \cos\left(b x + a\right)^{4} - 24 \, \cos\left(b x + a\right)^{2} + 16}{3 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"-1/3*(cos(b*x + a)^6 + 6*cos(b*x + a)^4 - 24*cos(b*x + a)^2 + 16)/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","A",0
160,1,79,0,1.264307," ","integrate(cos(b*x+a)^6/sin(b*x+a)^4,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + a\right)^{5} - 20 \, \cos\left(b x + a\right)^{3} - 15 \, {\left(b x \cos\left(b x + a\right)^{2} - b x\right)} \sin\left(b x + a\right) + 15 \, \cos\left(b x + a\right)}{6 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"-1/6*(3*cos(b*x + a)^5 - 20*cos(b*x + a)^3 - 15*(b*x*cos(b*x + a)^2 - b*x)*sin(b*x + a) + 15*cos(b*x + a))/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","A",0
161,1,48,0,1.302083," ","integrate(cos(b*x+a)^5/sin(b*x+a)^4,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + a\right)^{4} - 12 \, \cos\left(b x + a\right)^{2} + 8}{3 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"-1/3*(3*cos(b*x + a)^4 - 12*cos(b*x + a)^2 + 8)/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","A",0
162,1,69,0,1.714371," ","integrate(cos(b*x+a)^4/sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{4 \, \cos\left(b x + a\right)^{3} + 3 \, {\left(b x \cos\left(b x + a\right)^{2} - b x\right)} \sin\left(b x + a\right) - 3 \, \cos\left(b x + a\right)}{3 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"1/3*(4*cos(b*x + a)^3 + 3*(b*x*cos(b*x + a)^2 - b*x)*sin(b*x + a) - 3*cos(b*x + a))/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","B",0
163,1,38,0,1.031664," ","integrate(cos(b*x+a)^3/sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{3 \, \cos\left(b x + a\right)^{2} - 2}{3 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"1/3*(3*cos(b*x + a)^2 - 2)/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","A",0
164,1,34,0,1.353794," ","integrate(cos(b*x+a)^2/sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{\cos\left(b x + a\right)^{3}}{3 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"1/3*cos(b*x + a)^3/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","B",0
165,1,26,0,0.888432," ","integrate(cos(b*x+a)/sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{1}{3 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"1/3/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","A",0
166,1,94,0,1.225539," ","integrate(sec(b*x+a)/sin(b*x+a)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 6 \, \cos\left(b x + a\right)^{2} + 8}{6 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"1/6*(3*(cos(b*x + a)^2 - 1)*log(sin(b*x + a) + 1)*sin(b*x + a) - 3*(cos(b*x + a)^2 - 1)*log(-sin(b*x + a) + 1)*sin(b*x + a) - 6*cos(b*x + a)^2 + 8)/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","B",0
167,1,54,0,1.139845," ","integrate(sec(b*x+a)^2/sin(b*x+a)^4,x, algorithm=""fricas"")","-\frac{8 \, \cos\left(b x + a\right)^{4} - 12 \, \cos\left(b x + a\right)^{2} + 3}{3 \, {\left(b \cos\left(b x + a\right)^{3} - b \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}"," ",0,"-1/3*(8*cos(b*x + a)^4 - 12*cos(b*x + a)^2 + 3)/((b*cos(b*x + a)^3 - b*cos(b*x + a))*sin(b*x + a))","A",0
168,1,130,0,1.458404," ","integrate(sec(b*x+a)^3/sin(b*x+a)^4,x, algorithm=""fricas"")","-\frac{30 \, \cos\left(b x + a\right)^{4} - 15 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 15 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 40 \, \cos\left(b x + a\right)^{2} + 6}{12 \, {\left(b \cos\left(b x + a\right)^{4} - b \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}"," ",0,"-1/12*(30*cos(b*x + a)^4 - 15*(cos(b*x + a)^4 - cos(b*x + a)^2)*log(sin(b*x + a) + 1)*sin(b*x + a) + 15*(cos(b*x + a)^4 - cos(b*x + a)^2)*log(-sin(b*x + a) + 1)*sin(b*x + a) - 40*cos(b*x + a)^2 + 6)/((b*cos(b*x + a)^4 - b*cos(b*x + a)^2)*sin(b*x + a))","B",0
169,1,66,0,1.291261," ","integrate(sec(b*x+a)^4/sin(b*x+a)^4,x, algorithm=""fricas"")","-\frac{16 \, \cos\left(b x + a\right)^{6} - 24 \, \cos\left(b x + a\right)^{4} + 6 \, \cos\left(b x + a\right)^{2} + 1}{3 \, {\left(b \cos\left(b x + a\right)^{5} - b \cos\left(b x + a\right)^{3}\right)} \sin\left(b x + a\right)}"," ",0,"-1/3*(16*cos(b*x + a)^6 - 24*cos(b*x + a)^4 + 6*cos(b*x + a)^2 + 1)/((b*cos(b*x + a)^5 - b*cos(b*x + a)^3)*sin(b*x + a))","A",0
170,1,140,0,0.881860," ","integrate(sec(b*x+a)^5/sin(b*x+a)^4,x, algorithm=""fricas"")","-\frac{210 \, \cos\left(b x + a\right)^{6} - 280 \, \cos\left(b x + a\right)^{4} - 105 \, {\left(\cos\left(b x + a\right)^{6} - \cos\left(b x + a\right)^{4}\right)} \log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 105 \, {\left(\cos\left(b x + a\right)^{6} - \cos\left(b x + a\right)^{4}\right)} \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 42 \, \cos\left(b x + a\right)^{2} + 12}{48 \, {\left(b \cos\left(b x + a\right)^{6} - b \cos\left(b x + a\right)^{4}\right)} \sin\left(b x + a\right)}"," ",0,"-1/48*(210*cos(b*x + a)^6 - 280*cos(b*x + a)^4 - 105*(cos(b*x + a)^6 - cos(b*x + a)^4)*log(sin(b*x + a) + 1)*sin(b*x + a) + 105*(cos(b*x + a)^6 - cos(b*x + a)^4)*log(-sin(b*x + a) + 1)*sin(b*x + a) + 42*cos(b*x + a)^2 + 12)/((b*cos(b*x + a)^6 - b*cos(b*x + a)^4)*sin(b*x + a))","A",0
171,1,100,0,1.073916," ","integrate(cos(b*x+a)^9/sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{8 \, \cos\left(b x + a\right)^{8} + 32 \, \cos\left(b x + a\right)^{6} - 115 \, \cos\left(b x + a\right)^{4} + 38 \, \cos\left(b x + a\right)^{2} + 192 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \sin\left(b x + a\right)\right) + 29}{32 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)}}"," ",0,"1/32*(8*cos(b*x + a)^8 + 32*cos(b*x + a)^6 - 115*cos(b*x + a)^4 + 38*cos(b*x + a)^2 + 192*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(1/2*sin(b*x + a)) + 29)/(b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)","A",0
172,1,132,0,1.318141," ","integrate(cos(b*x+a)^8/sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{16 \, \cos\left(b x + a\right)^{7} + 112 \, \cos\left(b x + a\right)^{5} - 350 \, \cos\left(b x + a\right)^{3} - 105 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 105 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 210 \, \cos\left(b x + a\right)}{48 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)}}"," ",0,"1/48*(16*cos(b*x + a)^7 + 112*cos(b*x + a)^5 - 350*cos(b*x + a)^3 - 105*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(1/2*cos(b*x + a) + 1/2) + 105*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(-1/2*cos(b*x + a) + 1/2) + 210*cos(b*x + a))/(b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)","A",0
173,1,90,0,0.966499," ","integrate(cos(b*x+a)^7/sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{2 \, \cos\left(b x + a\right)^{6} - 5 \, \cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 12 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \sin\left(b x + a\right)\right) + 4}{4 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)}}"," ",0,"1/4*(2*cos(b*x + a)^6 - 5*cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 12*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(1/2*sin(b*x + a)) + 4)/(b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)","A",0
174,1,122,0,1.254898," ","integrate(cos(b*x+a)^6/sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{16 \, \cos\left(b x + a\right)^{5} - 50 \, \cos\left(b x + a\right)^{3} - 15 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 30 \, \cos\left(b x + a\right)}{16 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)}}"," ",0,"1/16*(16*cos(b*x + a)^5 - 50*cos(b*x + a)^3 - 15*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(1/2*cos(b*x + a) + 1/2) + 15*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(-1/2*cos(b*x + a) + 1/2) + 30*cos(b*x + a))/(b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)","A",0
175,1,70,0,1.266706," ","integrate(cos(b*x+a)^5/sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{4 \, \cos\left(b x + a\right)^{2} - 4 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \sin\left(b x + a\right)\right) - 3}{4 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)}}"," ",0,"-1/4*(4*cos(b*x + a)^2 - 4*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(1/2*sin(b*x + a)) - 3)/(b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)","A",0
176,1,112,0,1.275381," ","integrate(cos(b*x+a)^4/sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{10 \, \cos\left(b x + a\right)^{3} + 3 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 3 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 6 \, \cos\left(b x + a\right)}{16 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)}}"," ",0,"-1/16*(10*cos(b*x + a)^3 + 3*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(1/2*cos(b*x + a) + 1/2) - 3*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(-1/2*cos(b*x + a) + 1/2) - 6*cos(b*x + a))/(b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)","B",0
177,1,39,0,1.126123," ","integrate(cos(b*x+a)^3/sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(b x + a\right)^{2} - 1}{4 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)}}"," ",0,"-1/4*(2*cos(b*x + a)^2 - 1)/(b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)","B",0
178,1,111,0,1.351170," ","integrate(cos(b*x+a)^2/sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(b x + a\right)^{3} - {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 2 \, \cos\left(b x + a\right)}{16 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)}}"," ",0,"-1/16*(2*cos(b*x + a)^3 - (cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(1/2*cos(b*x + a) + 1/2) + (cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(-1/2*cos(b*x + a) + 1/2) + 2*cos(b*x + a))/(b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)","B",0
179,1,27,0,1.207223," ","integrate(cos(b*x+a)/sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)}}"," ",0,"-1/4/(b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)","B",0
180,1,105,0,1.199719," ","integrate(sec(b*x+a)/sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{2 \, \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(\cos\left(b x + a\right)^{2}\right) + 2 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) - 3}{4 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)}}"," ",0,"1/4*(2*cos(b*x + a)^2 - 2*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(cos(b*x + a)^2) + 2*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(-1/4*cos(b*x + a)^2 + 1/4) - 3)/(b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)","B",0
181,1,132,0,1.467667," ","integrate(sec(b*x+a)^2/sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{30 \, \cos\left(b x + a\right)^{4} - 50 \, \cos\left(b x + a\right)^{2} - 15 \, {\left(\cos\left(b x + a\right)^{5} - 2 \, \cos\left(b x + a\right)^{3} + \cos\left(b x + a\right)\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(b x + a\right)^{5} - 2 \, \cos\left(b x + a\right)^{3} + \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 16}{16 \, {\left(b \cos\left(b x + a\right)^{5} - 2 \, b \cos\left(b x + a\right)^{3} + b \cos\left(b x + a\right)\right)}}"," ",0,"1/16*(30*cos(b*x + a)^4 - 50*cos(b*x + a)^2 - 15*(cos(b*x + a)^5 - 2*cos(b*x + a)^3 + cos(b*x + a))*log(1/2*cos(b*x + a) + 1/2) + 15*(cos(b*x + a)^5 - 2*cos(b*x + a)^3 + cos(b*x + a))*log(-1/2*cos(b*x + a) + 1/2) + 16)/(b*cos(b*x + a)^5 - 2*b*cos(b*x + a)^3 + b*cos(b*x + a))","B",0
182,1,138,0,1.286291," ","integrate(sec(b*x+a)^3/sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{6 \, \cos\left(b x + a\right)^{4} - 9 \, \cos\left(b x + a\right)^{2} - 6 \, {\left(\cos\left(b x + a\right)^{6} - 2 \, \cos\left(b x + a\right)^{4} + \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right)^{2}\right) + 6 \, {\left(\cos\left(b x + a\right)^{6} - 2 \, \cos\left(b x + a\right)^{4} + \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) + 2}{4 \, {\left(b \cos\left(b x + a\right)^{6} - 2 \, b \cos\left(b x + a\right)^{4} + b \cos\left(b x + a\right)^{2}\right)}}"," ",0,"1/4*(6*cos(b*x + a)^4 - 9*cos(b*x + a)^2 - 6*(cos(b*x + a)^6 - 2*cos(b*x + a)^4 + cos(b*x + a)^2)*log(cos(b*x + a)^2) + 6*(cos(b*x + a)^6 - 2*cos(b*x + a)^4 + cos(b*x + a)^2)*log(-1/4*cos(b*x + a)^2 + 1/4) + 2)/(b*cos(b*x + a)^6 - 2*b*cos(b*x + a)^4 + b*cos(b*x + a)^2)","B",0
183,1,148,0,1.289882," ","integrate(sec(b*x+a)^4/sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{210 \, \cos\left(b x + a\right)^{6} - 350 \, \cos\left(b x + a\right)^{4} + 112 \, \cos\left(b x + a\right)^{2} - 105 \, {\left(\cos\left(b x + a\right)^{7} - 2 \, \cos\left(b x + a\right)^{5} + \cos\left(b x + a\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 105 \, {\left(\cos\left(b x + a\right)^{7} - 2 \, \cos\left(b x + a\right)^{5} + \cos\left(b x + a\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 16}{48 \, {\left(b \cos\left(b x + a\right)^{7} - 2 \, b \cos\left(b x + a\right)^{5} + b \cos\left(b x + a\right)^{3}\right)}}"," ",0,"1/48*(210*cos(b*x + a)^6 - 350*cos(b*x + a)^4 + 112*cos(b*x + a)^2 - 105*(cos(b*x + a)^7 - 2*cos(b*x + a)^5 + cos(b*x + a)^3)*log(1/2*cos(b*x + a) + 1/2) + 105*(cos(b*x + a)^7 - 2*cos(b*x + a)^5 + cos(b*x + a)^3)*log(-1/2*cos(b*x + a) + 1/2) + 16)/(b*cos(b*x + a)^7 - 2*b*cos(b*x + a)^5 + b*cos(b*x + a)^3)","A",0
184,1,148,0,1.191083," ","integrate(sec(b*x+a)^5/sin(b*x+a)^5,x, algorithm=""fricas"")","\frac{12 \, \cos\left(b x + a\right)^{6} - 18 \, \cos\left(b x + a\right)^{4} + 4 \, \cos\left(b x + a\right)^{2} - 12 \, {\left(\cos\left(b x + a\right)^{8} - 2 \, \cos\left(b x + a\right)^{6} + \cos\left(b x + a\right)^{4}\right)} \log\left(\cos\left(b x + a\right)^{2}\right) + 12 \, {\left(\cos\left(b x + a\right)^{8} - 2 \, \cos\left(b x + a\right)^{6} + \cos\left(b x + a\right)^{4}\right)} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) + 1}{4 \, {\left(b \cos\left(b x + a\right)^{8} - 2 \, b \cos\left(b x + a\right)^{6} + b \cos\left(b x + a\right)^{4}\right)}}"," ",0,"1/4*(12*cos(b*x + a)^6 - 18*cos(b*x + a)^4 + 4*cos(b*x + a)^2 - 12*(cos(b*x + a)^8 - 2*cos(b*x + a)^6 + cos(b*x + a)^4)*log(cos(b*x + a)^2) + 12*(cos(b*x + a)^8 - 2*cos(b*x + a)^6 + cos(b*x + a)^4)*log(-1/4*cos(b*x + a)^2 + 1/4) + 1)/(b*cos(b*x + a)^8 - 2*b*cos(b*x + a)^6 + b*cos(b*x + a)^4)","B",0
185,1,33,0,1.151223," ","integrate(cos(x)^2/sin(x)^6,x, algorithm=""fricas"")","\frac{2 \, \cos\left(x\right)^{5} - 5 \, \cos\left(x\right)^{3}}{15 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)}"," ",0,"1/15*(2*cos(x)^5 - 5*cos(x)^3)/((cos(x)^4 - 2*cos(x)^2 + 1)*sin(x))","B",0
186,1,30,0,1.204394," ","integrate(cos(x)^3/sin(x)^7,x, algorithm=""fricas"")","\frac{3 \, \cos\left(x\right)^{2} - 1}{12 \, {\left(\cos\left(x\right)^{6} - 3 \, \cos\left(x\right)^{4} + 3 \, \cos\left(x\right)^{2} - 1\right)}}"," ",0,"1/12*(3*cos(x)^2 - 1)/(cos(x)^6 - 3*cos(x)^4 + 3*cos(x)^2 - 1)","B",0
187,1,24,0,1.216112," ","integrate((d*cos(b*x+a))^(3/2)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{d \cos\left(b x + a\right)} d \cos\left(b x + a\right)^{2}}{5 \, b}"," ",0,"-2/5*sqrt(d*cos(b*x + a))*d*cos(b*x + a)^2/b","A",0
188,1,21,0,0.862830," ","integrate((d*cos(b*x+a))^(1/2)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \cos\left(b x + a\right)}{3 \, b}"," ",0,"-2/3*sqrt(d*cos(b*x + a))*cos(b*x + a)/b","A",0
189,1,18,0,1.838568," ","integrate(sin(b*x+a)/(d*cos(b*x+a))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{d \cos\left(b x + a\right)}}{b d}"," ",0,"-2*sqrt(d*cos(b*x + a))/(b*d)","A",0
190,1,26,0,0.898900," ","integrate(sin(b*x+a)/(d*cos(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{d \cos\left(b x + a\right)}}{b d^{2} \cos\left(b x + a\right)}"," ",0,"2*sqrt(d*cos(b*x + a))/(b*d^2*cos(b*x + a))","A",0
191,1,26,0,1.402915," ","integrate(sin(b*x+a)/(d*cos(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{d \cos\left(b x + a\right)}}{3 \, b d^{3} \cos\left(b x + a\right)^{2}}"," ",0,"2/3*sqrt(d*cos(b*x + a))/(b*d^3*cos(b*x + a)^2)","A",0
192,1,26,0,1.369991," ","integrate(sin(b*x+a)/(d*cos(b*x+a))^(7/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{d \cos\left(b x + a\right)}}{5 \, b d^{4} \cos\left(b x + a\right)^{3}}"," ",0,"2/5*sqrt(d*cos(b*x + a))/(b*d^4*cos(b*x + a)^3)","A",0
193,1,26,0,1.229376," ","integrate(sin(b*x+a)/(d*cos(b*x+a))^(9/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{d \cos\left(b x + a\right)}}{7 \, b d^{5} \cos\left(b x + a\right)^{4}}"," ",0,"2/7*sqrt(d*cos(b*x + a))/(b*d^5*cos(b*x + a)^4)","A",0
194,0,0,0,1.503189," ","integrate((d*cos(b*x+a))^(9/2)*sin(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(d^{4} \cos\left(b x + a\right)^{6} - d^{4} \cos\left(b x + a\right)^{4}\right)} \sqrt{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral(-(d^4*cos(b*x + a)^6 - d^4*cos(b*x + a)^4)*sqrt(d*cos(b*x + a)), x)","F",0
195,0,0,0,1.202289," ","integrate((d*cos(b*x+a))^(7/2)*sin(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(d^{3} \cos\left(b x + a\right)^{5} - d^{3} \cos\left(b x + a\right)^{3}\right)} \sqrt{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral(-(d^3*cos(b*x + a)^5 - d^3*cos(b*x + a)^3)*sqrt(d*cos(b*x + a)), x)","F",0
196,0,0,0,0.785329," ","integrate((d*cos(b*x+a))^(5/2)*sin(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(d^{2} \cos\left(b x + a\right)^{4} - d^{2} \cos\left(b x + a\right)^{2}\right)} \sqrt{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral(-(d^2*cos(b*x + a)^4 - d^2*cos(b*x + a)^2)*sqrt(d*cos(b*x + a)), x)","F",0
197,0,0,0,1.503031," ","integrate((d*cos(b*x+a))^(3/2)*sin(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(d \cos\left(b x + a\right)^{3} - d \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral(-(d*cos(b*x + a)^3 - d*cos(b*x + a))*sqrt(d*cos(b*x + a)), x)","F",0
198,0,0,0,1.257318," ","integrate((d*cos(b*x+a))^(1/2)*sin(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right)^{2} - 1\right)}, x\right)"," ",0,"integral(-sqrt(d*cos(b*x + a))*(cos(b*x + a)^2 - 1), x)","F",0
199,0,0,0,1.263652," ","integrate(sin(b*x+a)^2/(d*cos(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right)^{2} - 1\right)}}{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral(-sqrt(d*cos(b*x + a))*(cos(b*x + a)^2 - 1)/(d*cos(b*x + a)), x)","F",0
200,0,0,0,1.236271," ","integrate(sin(b*x+a)^2/(d*cos(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right)^{2} - 1\right)}}{d^{2} \cos\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(-sqrt(d*cos(b*x + a))*(cos(b*x + a)^2 - 1)/(d^2*cos(b*x + a)^2), x)","F",0
201,0,0,0,1.211203," ","integrate(sin(b*x+a)^2/(d*cos(b*x+a))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right)^{2} - 1\right)}}{d^{3} \cos\left(b x + a\right)^{3}}, x\right)"," ",0,"integral(-sqrt(d*cos(b*x + a))*(cos(b*x + a)^2 - 1)/(d^3*cos(b*x + a)^3), x)","F",0
202,0,0,0,1.072916," ","integrate(sin(b*x+a)^2/(d*cos(b*x+a))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right)^{2} - 1\right)}}{d^{4} \cos\left(b x + a\right)^{4}}, x\right)"," ",0,"integral(-sqrt(d*cos(b*x + a))*(cos(b*x + a)^2 - 1)/(d^4*cos(b*x + a)^4), x)","F",0
203,0,0,0,1.387295," ","integrate(sin(b*x+a)^2/(d*cos(b*x+a))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right)^{2} - 1\right)}}{d^{5} \cos\left(b x + a\right)^{5}}, x\right)"," ",0,"integral(-sqrt(d*cos(b*x + a))*(cos(b*x + a)^2 - 1)/(d^5*cos(b*x + a)^5), x)","F",0
204,1,34,0,1.157143," ","integrate((d*cos(b*x+a))^(1/2)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, \cos\left(b x + a\right)^{3} - 7 \, \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)}}{21 \, b}"," ",0,"2/21*(3*cos(b*x + a)^3 - 7*cos(b*x + a))*sqrt(d*cos(b*x + a))/b","A",0
205,1,28,0,0.988550," ","integrate(sin(b*x+a)^3/(d*cos(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right)^{2} - 5\right)}}{5 \, b d}"," ",0,"2/5*sqrt(d*cos(b*x + a))*(cos(b*x + a)^2 - 5)/(b*d)","A",0
206,1,36,0,1.382820," ","integrate(sin(b*x+a)^3/(d*cos(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right)^{2} + 3\right)}}{3 \, b d^{2} \cos\left(b x + a\right)}"," ",0,"2/3*sqrt(d*cos(b*x + a))*(cos(b*x + a)^2 + 3)/(b*d^2*cos(b*x + a))","A",0
207,1,38,0,1.349988," ","integrate(sin(b*x+a)^3/(d*cos(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{d \cos\left(b x + a\right)} {\left(3 \, \cos\left(b x + a\right)^{2} + 1\right)}}{3 \, b d^{3} \cos\left(b x + a\right)^{2}}"," ",0,"2/3*sqrt(d*cos(b*x + a))*(3*cos(b*x + a)^2 + 1)/(b*d^3*cos(b*x + a)^2)","A",0
208,1,38,0,1.009702," ","integrate(sin(b*x+a)^3/(d*cos(b*x+a))^(7/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{d \cos\left(b x + a\right)} {\left(5 \, \cos\left(b x + a\right)^{2} - 1\right)}}{5 \, b d^{4} \cos\left(b x + a\right)^{3}}"," ",0,"-2/5*sqrt(d*cos(b*x + a))*(5*cos(b*x + a)^2 - 1)/(b*d^4*cos(b*x + a)^3)","A",0
209,1,38,0,1.299100," ","integrate(sin(b*x+a)^3/(d*cos(b*x+a))^(9/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{d \cos\left(b x + a\right)} {\left(7 \, \cos\left(b x + a\right)^{2} - 3\right)}}{21 \, b d^{5} \cos\left(b x + a\right)^{4}}"," ",0,"-2/21*sqrt(d*cos(b*x + a))*(7*cos(b*x + a)^2 - 3)/(b*d^5*cos(b*x + a)^4)","A",0
210,1,38,0,1.437626," ","integrate(sin(b*x+a)^3/(d*cos(b*x+a))^(11/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{d \cos\left(b x + a\right)} {\left(9 \, \cos\left(b x + a\right)^{2} - 5\right)}}{45 \, b d^{6} \cos\left(b x + a\right)^{5}}"," ",0,"-2/45*sqrt(d*cos(b*x + a))*(9*cos(b*x + a)^2 - 5)/(b*d^6*cos(b*x + a)^5)","A",0
211,0,0,0,1.385140," ","integrate((d*cos(b*x+a))^(9/2)*sin(b*x+a)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{4} \cos\left(b x + a\right)^{8} - 2 \, d^{4} \cos\left(b x + a\right)^{6} + d^{4} \cos\left(b x + a\right)^{4}\right)} \sqrt{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral((d^4*cos(b*x + a)^8 - 2*d^4*cos(b*x + a)^6 + d^4*cos(b*x + a)^4)*sqrt(d*cos(b*x + a)), x)","F",0
212,0,0,0,1.102255," ","integrate((d*cos(b*x+a))^(7/2)*sin(b*x+a)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{3} \cos\left(b x + a\right)^{7} - 2 \, d^{3} \cos\left(b x + a\right)^{5} + d^{3} \cos\left(b x + a\right)^{3}\right)} \sqrt{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral((d^3*cos(b*x + a)^7 - 2*d^3*cos(b*x + a)^5 + d^3*cos(b*x + a)^3)*sqrt(d*cos(b*x + a)), x)","F",0
213,0,0,0,1.472981," ","integrate((d*cos(b*x+a))^(5/2)*sin(b*x+a)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{2} \cos\left(b x + a\right)^{6} - 2 \, d^{2} \cos\left(b x + a\right)^{4} + d^{2} \cos\left(b x + a\right)^{2}\right)} \sqrt{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral((d^2*cos(b*x + a)^6 - 2*d^2*cos(b*x + a)^4 + d^2*cos(b*x + a)^2)*sqrt(d*cos(b*x + a)), x)","F",0
214,0,0,0,1.498048," ","integrate((d*cos(b*x+a))^(3/2)*sin(b*x+a)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(d \cos\left(b x + a\right)^{5} - 2 \, d \cos\left(b x + a\right)^{3} + d \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral((d*cos(b*x + a)^5 - 2*d*cos(b*x + a)^3 + d*cos(b*x + a))*sqrt(d*cos(b*x + a)), x)","F",0
215,0,0,0,1.375397," ","integrate((d*cos(b*x+a))^(1/2)*sin(b*x+a)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \sqrt{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral((cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*sqrt(d*cos(b*x + a)), x)","F",0
216,0,0,0,1.273894," ","integrate(sin(b*x+a)^4/(d*cos(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \sqrt{d \cos\left(b x + a\right)}}{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral((cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*sqrt(d*cos(b*x + a))/(d*cos(b*x + a)), x)","F",0
217,0,0,0,1.205865," ","integrate(sin(b*x+a)^4/(d*cos(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \sqrt{d \cos\left(b x + a\right)}}{d^{2} \cos\left(b x + a\right)^{2}}, x\right)"," ",0,"integral((cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*sqrt(d*cos(b*x + a))/(d^2*cos(b*x + a)^2), x)","F",0
218,0,0,0,1.253919," ","integrate(sin(b*x+a)^4/(d*cos(b*x+a))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \sqrt{d \cos\left(b x + a\right)}}{d^{3} \cos\left(b x + a\right)^{3}}, x\right)"," ",0,"integral((cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*sqrt(d*cos(b*x + a))/(d^3*cos(b*x + a)^3), x)","F",0
219,0,0,0,1.462637," ","integrate(sin(b*x+a)^4/(d*cos(b*x+a))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \sqrt{d \cos\left(b x + a\right)}}{d^{4} \cos\left(b x + a\right)^{4}}, x\right)"," ",0,"integral((cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*sqrt(d*cos(b*x + a))/(d^4*cos(b*x + a)^4), x)","F",0
220,0,0,0,1.224537," ","integrate(sin(b*x+a)^4/(d*cos(b*x+a))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \sqrt{d \cos\left(b x + a\right)}}{d^{5} \cos\left(b x + a\right)^{5}}, x\right)"," ",0,"integral((cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*sqrt(d*cos(b*x + a))/(d^5*cos(b*x + a)^5), x)","F",0
221,1,44,0,1.233448," ","integrate(cos(b*x+a)^(3/2)*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(45 \, \cos\left(b x + a\right)^{6} - 130 \, \cos\left(b x + a\right)^{4} + 117 \, \cos\left(b x + a\right)^{2}\right)} \sqrt{\cos\left(b x + a\right)}}{585 \, b}"," ",0,"-2/585*(45*cos(b*x + a)^6 - 130*cos(b*x + a)^4 + 117*cos(b*x + a)^2)*sqrt(cos(b*x + a))/b","A",0
222,1,313,0,1.502188," ","integrate((d*cos(b*x+a))^(9/2)*csc(b*x+a),x, algorithm=""fricas"")","\left[\frac{42 \, \sqrt{-d} d^{4} \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d}}{d \cos\left(b x + a\right) + d}\right) + 21 \, \sqrt{-d} d^{4} \log\left(-\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, {\left(3 \, d^{4} \cos\left(b x + a\right)^{3} + 7 \, d^{4} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)}}{84 \, b}, -\frac{42 \, d^{\frac{9}{2}} \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d}}{d \cos\left(b x + a\right) - d}\right) - 21 \, d^{\frac{9}{2}} \log\left(-\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) - 8 \, {\left(3 \, d^{4} \cos\left(b x + a\right)^{3} + 7 \, d^{4} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)}}{84 \, b}\right]"," ",0,"[1/84*(42*sqrt(-d)*d^4*arctan(2*sqrt(d*cos(b*x + a))*sqrt(-d)/(d*cos(b*x + a) + d)) + 21*sqrt(-d)*d^4*log(-(d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*(3*d^4*cos(b*x + a)^3 + 7*d^4*cos(b*x + a))*sqrt(d*cos(b*x + a)))/b, -1/84*(42*d^(9/2)*arctan(2*sqrt(d*cos(b*x + a))*sqrt(d)/(d*cos(b*x + a) - d)) - 21*d^(9/2)*log(-(d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) - 8*(3*d^4*cos(b*x + a)^3 + 7*d^4*cos(b*x + a))*sqrt(d*cos(b*x + a)))/b]","A",0
223,1,299,0,1.928850," ","integrate((d*cos(b*x+a))^(7/2)*csc(b*x+a),x, algorithm=""fricas"")","\left[\frac{10 \, \sqrt{-d} d^{3} \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d}}{d \cos\left(b x + a\right) + d}\right) + 5 \, \sqrt{-d} d^{3} \log\left(-\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, {\left(d^{3} \cos\left(b x + a\right)^{2} + 5 \, d^{3}\right)} \sqrt{d \cos\left(b x + a\right)}}{20 \, b}, \frac{10 \, d^{\frac{7}{2}} \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d}}{d \cos\left(b x + a\right) - d}\right) + 5 \, d^{\frac{7}{2}} \log\left(-\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, {\left(d^{3} \cos\left(b x + a\right)^{2} + 5 \, d^{3}\right)} \sqrt{d \cos\left(b x + a\right)}}{20 \, b}\right]"," ",0,"[1/20*(10*sqrt(-d)*d^3*arctan(2*sqrt(d*cos(b*x + a))*sqrt(-d)/(d*cos(b*x + a) + d)) + 5*sqrt(-d)*d^3*log(-(d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*(d^3*cos(b*x + a)^2 + 5*d^3)*sqrt(d*cos(b*x + a)))/b, 1/20*(10*d^(7/2)*arctan(2*sqrt(d*cos(b*x + a))*sqrt(d)/(d*cos(b*x + a) - d)) + 5*d^(7/2)*log(-(d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) + 8*(d^3*cos(b*x + a)^2 + 5*d^3)*sqrt(d*cos(b*x + a)))/b]","A",0
224,1,281,0,1.746325," ","integrate((d*cos(b*x+a))^(5/2)*csc(b*x+a),x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{-d} d^{2} \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d}}{d \cos\left(b x + a\right) + d}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)} d^{2} \cos\left(b x + a\right) + 3 \, \sqrt{-d} d^{2} \log\left(-\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right)}{12 \, b}, -\frac{6 \, d^{\frac{5}{2}} \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d}}{d \cos\left(b x + a\right) - d}\right) - 8 \, \sqrt{d \cos\left(b x + a\right)} d^{2} \cos\left(b x + a\right) - 3 \, d^{\frac{5}{2}} \log\left(-\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right)}{12 \, b}\right]"," ",0,"[1/12*(6*sqrt(-d)*d^2*arctan(2*sqrt(d*cos(b*x + a))*sqrt(-d)/(d*cos(b*x + a) + d)) + 8*sqrt(d*cos(b*x + a))*d^2*cos(b*x + a) + 3*sqrt(-d)*d^2*log(-(d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)))/b, -1/12*(6*d^(5/2)*arctan(2*sqrt(d*cos(b*x + a))*sqrt(d)/(d*cos(b*x + a) - d)) - 8*sqrt(d*cos(b*x + a))*d^2*cos(b*x + a) - 3*d^(5/2)*log(-(d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)))/b]","B",0
225,1,259,0,1.905644," ","integrate((d*cos(b*x+a))^(3/2)*csc(b*x+a),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-d} d \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d}}{d \cos\left(b x + a\right) + d}\right) + \sqrt{-d} d \log\left(-\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)} d}{4 \, b}, \frac{2 \, d^{\frac{3}{2}} \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d}}{d \cos\left(b x + a\right) - d}\right) + d^{\frac{3}{2}} \log\left(-\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)} d}{4 \, b}\right]"," ",0,"[1/4*(2*sqrt(-d)*d*arctan(2*sqrt(d*cos(b*x + a))*sqrt(-d)/(d*cos(b*x + a) + d)) + sqrt(-d)*d*log(-(d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a))*d)/b, 1/4*(2*d^(3/2)*arctan(2*sqrt(d*cos(b*x + a))*sqrt(d)/(d*cos(b*x + a) - d)) + d^(3/2)*log(-(d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a))*d)/b]","A",0
226,1,238,0,1.557342," ","integrate((d*cos(b*x+a))^(1/2)*csc(b*x+a),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) + 1\right)}}{2 \, d \cos\left(b x + a\right)}\right) + \sqrt{-d} \log\left(\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right)}{4 \, b}, \frac{2 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right) - 1\right)}}{2 \, \sqrt{d} \cos\left(b x + a\right)}\right) + \sqrt{d} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right)}{4 \, b}\right]"," ",0,"[1/4*(2*sqrt(-d)*arctan(1/2*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) + 1)/(d*cos(b*x + a))) + sqrt(-d)*log((d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)))/b, 1/4*(2*sqrt(d)*arctan(1/2*sqrt(d*cos(b*x + a))*(cos(b*x + a) - 1)/(sqrt(d)*cos(b*x + a))) + sqrt(d)*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)))/b]","B",0
227,1,246,0,1.476354," ","integrate(csc(b*x+a)/(d*cos(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) + 1\right)}}{2 \, d \cos\left(b x + a\right)}\right) - \sqrt{-d} \log\left(\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right)}{4 \, b d}, -\frac{2 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right) - 1\right)}}{2 \, \sqrt{d} \cos\left(b x + a\right)}\right) - \sqrt{d} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right)}{4 \, b d}\right]"," ",0,"[1/4*(2*sqrt(-d)*arctan(1/2*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) + 1)/(d*cos(b*x + a))) - sqrt(-d)*log((d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)))/(b*d), -1/4*(2*sqrt(d)*arctan(1/2*sqrt(d*cos(b*x + a))*(cos(b*x + a) - 1)/(sqrt(d)*cos(b*x + a))) - sqrt(d)*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)))/(b*d)]","B",0
228,1,309,0,1.568583," ","integrate(csc(b*x+a)/(d*cos(b*x+a))^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) + 1\right)}}{2 \, d \cos\left(b x + a\right)}\right) \cos\left(b x + a\right) - \sqrt{-d} \cos\left(b x + a\right) \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)}}{4 \, b d^{2} \cos\left(b x + a\right)}, \frac{2 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right) - 1\right)}}{2 \, \sqrt{d} \cos\left(b x + a\right)}\right) \cos\left(b x + a\right) + \sqrt{d} \cos\left(b x + a\right) \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)}}{4 \, b d^{2} \cos\left(b x + a\right)}\right]"," ",0,"[1/4*(2*sqrt(-d)*arctan(1/2*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) + 1)/(d*cos(b*x + a)))*cos(b*x + a) - sqrt(-d)*cos(b*x + a)*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a)))/(b*d^2*cos(b*x + a)), 1/4*(2*sqrt(d)*arctan(1/2*sqrt(d*cos(b*x + a))*(cos(b*x + a) - 1)/(sqrt(d)*cos(b*x + a)))*cos(b*x + a) + sqrt(d)*cos(b*x + a)*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a)))/(b*d^2*cos(b*x + a))]","B",0
229,1,318,0,1.183031," ","integrate(csc(b*x+a)/(d*cos(b*x+a))^(5/2),x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{-d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) + 1\right)}}{2 \, d \cos\left(b x + a\right)}\right) \cos\left(b x + a\right)^{2} - 3 \, \sqrt{-d} \cos\left(b x + a\right)^{2} \log\left(\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)}}{12 \, b d^{3} \cos\left(b x + a\right)^{2}}, -\frac{6 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right) - 1\right)}}{2 \, \sqrt{d} \cos\left(b x + a\right)}\right) \cos\left(b x + a\right)^{2} - 3 \, \sqrt{d} \cos\left(b x + a\right)^{2} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) - 8 \, \sqrt{d \cos\left(b x + a\right)}}{12 \, b d^{3} \cos\left(b x + a\right)^{2}}\right]"," ",0,"[1/12*(6*sqrt(-d)*arctan(1/2*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) + 1)/(d*cos(b*x + a)))*cos(b*x + a)^2 - 3*sqrt(-d)*cos(b*x + a)^2*log((d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a)))/(b*d^3*cos(b*x + a)^2), -1/12*(6*sqrt(d)*arctan(1/2*sqrt(d*cos(b*x + a))*(cos(b*x + a) - 1)/(sqrt(d)*cos(b*x + a)))*cos(b*x + a)^2 - 3*sqrt(d)*cos(b*x + a)^2*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) - 8*sqrt(d*cos(b*x + a)))/(b*d^3*cos(b*x + a)^2)]","B",0
230,1,342,0,1.543170," ","integrate(csc(b*x+a)/(d*cos(b*x+a))^(7/2),x, algorithm=""fricas"")","\left[\frac{10 \, \sqrt{-d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) + 1\right)}}{2 \, d \cos\left(b x + a\right)}\right) \cos\left(b x + a\right)^{3} - 5 \, \sqrt{-d} \cos\left(b x + a\right)^{3} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)} {\left(5 \, \cos\left(b x + a\right)^{2} + 1\right)}}{20 \, b d^{4} \cos\left(b x + a\right)^{3}}, \frac{10 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right) - 1\right)}}{2 \, \sqrt{d} \cos\left(b x + a\right)}\right) \cos\left(b x + a\right)^{3} + 5 \, \sqrt{d} \cos\left(b x + a\right)^{3} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)} {\left(5 \, \cos\left(b x + a\right)^{2} + 1\right)}}{20 \, b d^{4} \cos\left(b x + a\right)^{3}}\right]"," ",0,"[1/20*(10*sqrt(-d)*arctan(1/2*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) + 1)/(d*cos(b*x + a)))*cos(b*x + a)^3 - 5*sqrt(-d)*cos(b*x + a)^3*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a))*(5*cos(b*x + a)^2 + 1))/(b*d^4*cos(b*x + a)^3), 1/20*(10*sqrt(d)*arctan(1/2*sqrt(d*cos(b*x + a))*(cos(b*x + a) - 1)/(sqrt(d)*cos(b*x + a)))*cos(b*x + a)^3 + 5*sqrt(d)*cos(b*x + a)^3*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a))*(5*cos(b*x + a)^2 + 1))/(b*d^4*cos(b*x + a)^3)]","B",0
231,1,342,0,1.782997," ","integrate(csc(b*x+a)/(d*cos(b*x+a))^(9/2),x, algorithm=""fricas"")","\left[\frac{42 \, \sqrt{-d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) + 1\right)}}{2 \, d \cos\left(b x + a\right)}\right) \cos\left(b x + a\right)^{4} - 21 \, \sqrt{-d} \cos\left(b x + a\right)^{4} \log\left(\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)} {\left(7 \, \cos\left(b x + a\right)^{2} + 3\right)}}{84 \, b d^{5} \cos\left(b x + a\right)^{4}}, -\frac{42 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right) - 1\right)}}{2 \, \sqrt{d} \cos\left(b x + a\right)}\right) \cos\left(b x + a\right)^{4} - 21 \, \sqrt{d} \cos\left(b x + a\right)^{4} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) - 8 \, \sqrt{d \cos\left(b x + a\right)} {\left(7 \, \cos\left(b x + a\right)^{2} + 3\right)}}{84 \, b d^{5} \cos\left(b x + a\right)^{4}}\right]"," ",0,"[1/84*(42*sqrt(-d)*arctan(1/2*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) + 1)/(d*cos(b*x + a)))*cos(b*x + a)^4 - 21*sqrt(-d)*cos(b*x + a)^4*log((d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a))*(7*cos(b*x + a)^2 + 3))/(b*d^5*cos(b*x + a)^4), -1/84*(42*sqrt(d)*arctan(1/2*sqrt(d*cos(b*x + a))*(cos(b*x + a) - 1)/(sqrt(d)*cos(b*x + a)))*cos(b*x + a)^4 - 21*sqrt(d)*cos(b*x + a)^4*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) - 8*sqrt(d*cos(b*x + a))*(7*cos(b*x + a)^2 + 3))/(b*d^5*cos(b*x + a)^4)]","A",0
232,0,0,0,0.821108," ","integrate((d*cos(b*x+a))^(11/2)*csc(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \cos\left(b x + a\right)} d^{5} \cos\left(b x + a\right)^{5} \csc\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*d^5*cos(b*x + a)^5*csc(b*x + a)^2, x)","F",0
233,0,0,0,1.337893," ","integrate((d*cos(b*x+a))^(9/2)*csc(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \cos\left(b x + a\right)} d^{4} \cos\left(b x + a\right)^{4} \csc\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*d^4*cos(b*x + a)^4*csc(b*x + a)^2, x)","F",0
234,0,0,0,1.242303," ","integrate((d*cos(b*x+a))^(7/2)*csc(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \cos\left(b x + a\right)} d^{3} \cos\left(b x + a\right)^{3} \csc\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*d^3*cos(b*x + a)^3*csc(b*x + a)^2, x)","F",0
235,0,0,0,1.291495," ","integrate((d*cos(b*x+a))^(5/2)*csc(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \cos\left(b x + a\right)} d^{2} \cos\left(b x + a\right)^{2} \csc\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*d^2*cos(b*x + a)^2*csc(b*x + a)^2, x)","F",0
236,0,0,0,0.850230," ","integrate((d*cos(b*x+a))^(3/2)*csc(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \cos\left(b x + a\right)} d \cos\left(b x + a\right) \csc\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*d*cos(b*x + a)*csc(b*x + a)^2, x)","F",0
237,0,0,0,1.222772," ","integrate((d*cos(b*x+a))^(1/2)*csc(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \cos\left(b x + a\right)} \csc\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*csc(b*x + a)^2, x)","F",0
238,0,0,0,1.394748," ","integrate(csc(b*x+a)^2/(d*cos(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \csc\left(b x + a\right)^{2}}{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*csc(b*x + a)^2/(d*cos(b*x + a)), x)","F",0
239,0,0,0,1.197545," ","integrate(csc(b*x+a)^2/(d*cos(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \csc\left(b x + a\right)^{2}}{d^{2} \cos\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*csc(b*x + a)^2/(d^2*cos(b*x + a)^2), x)","F",0
240,0,0,0,0.970779," ","integrate(csc(b*x+a)^2/(d*cos(b*x+a))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \csc\left(b x + a\right)^{2}}{d^{3} \cos\left(b x + a\right)^{3}}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*csc(b*x + a)^2/(d^3*cos(b*x + a)^3), x)","F",0
241,0,0,0,0.911232," ","integrate(csc(b*x+a)^2/(d*cos(b*x+a))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \csc\left(b x + a\right)^{2}}{d^{4} \cos\left(b x + a\right)^{4}}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*csc(b*x + a)^2/(d^4*cos(b*x + a)^4), x)","F",0
242,1,419,0,2.237830," ","integrate((d*cos(b*x+a))^(11/2)*csc(b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{90 \, {\left(d^{5} \cos\left(b x + a\right)^{2} - d^{5}\right)} \sqrt{-d} \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d}}{d \cos\left(b x + a\right) + d}\right) - 45 \, {\left(d^{5} \cos\left(b x + a\right)^{2} - d^{5}\right)} \sqrt{-d} \log\left(-\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, {\left(4 \, d^{5} \cos\left(b x + a\right)^{4} + 36 \, d^{5} \cos\left(b x + a\right)^{2} - 45 \, d^{5}\right)} \sqrt{d \cos\left(b x + a\right)}}{80 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}, -\frac{90 \, {\left(d^{5} \cos\left(b x + a\right)^{2} - d^{5}\right)} \sqrt{d} \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d}}{d \cos\left(b x + a\right) - d}\right) - 45 \, {\left(d^{5} \cos\left(b x + a\right)^{2} - d^{5}\right)} \sqrt{d} \log\left(-\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, {\left(4 \, d^{5} \cos\left(b x + a\right)^{4} + 36 \, d^{5} \cos\left(b x + a\right)^{2} - 45 \, d^{5}\right)} \sqrt{d \cos\left(b x + a\right)}}{80 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}\right]"," ",0,"[-1/80*(90*(d^5*cos(b*x + a)^2 - d^5)*sqrt(-d)*arctan(2*sqrt(d*cos(b*x + a))*sqrt(-d)/(d*cos(b*x + a) + d)) - 45*(d^5*cos(b*x + a)^2 - d^5)*sqrt(-d)*log(-(d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*(4*d^5*cos(b*x + a)^4 + 36*d^5*cos(b*x + a)^2 - 45*d^5)*sqrt(d*cos(b*x + a)))/(b*cos(b*x + a)^2 - b), -1/80*(90*(d^5*cos(b*x + a)^2 - d^5)*sqrt(d)*arctan(2*sqrt(d*cos(b*x + a))*sqrt(d)/(d*cos(b*x + a) - d)) - 45*(d^5*cos(b*x + a)^2 - d^5)*sqrt(d)*log(-(d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) + 8*(4*d^5*cos(b*x + a)^4 + 36*d^5*cos(b*x + a)^2 - 45*d^5)*sqrt(d*cos(b*x + a)))/(b*cos(b*x + a)^2 - b)]","A",0
243,1,405,0,1.992507," ","integrate((d*cos(b*x+a))^(9/2)*csc(b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{42 \, {\left(d^{4} \cos\left(b x + a\right)^{2} - d^{4}\right)} \sqrt{-d} \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d}}{d \cos\left(b x + a\right) + d}\right) - 21 \, {\left(d^{4} \cos\left(b x + a\right)^{2} - d^{4}\right)} \sqrt{-d} \log\left(-\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, {\left(4 \, d^{4} \cos\left(b x + a\right)^{3} - 7 \, d^{4} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)}}{48 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}, \frac{42 \, {\left(d^{4} \cos\left(b x + a\right)^{2} - d^{4}\right)} \sqrt{d} \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d}}{d \cos\left(b x + a\right) - d}\right) + 21 \, {\left(d^{4} \cos\left(b x + a\right)^{2} - d^{4}\right)} \sqrt{d} \log\left(-\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) - 8 \, {\left(4 \, d^{4} \cos\left(b x + a\right)^{3} - 7 \, d^{4} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)}}{48 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}\right]"," ",0,"[-1/48*(42*(d^4*cos(b*x + a)^2 - d^4)*sqrt(-d)*arctan(2*sqrt(d*cos(b*x + a))*sqrt(-d)/(d*cos(b*x + a) + d)) - 21*(d^4*cos(b*x + a)^2 - d^4)*sqrt(-d)*log(-(d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*(4*d^4*cos(b*x + a)^3 - 7*d^4*cos(b*x + a))*sqrt(d*cos(b*x + a)))/(b*cos(b*x + a)^2 - b), 1/48*(42*(d^4*cos(b*x + a)^2 - d^4)*sqrt(d)*arctan(2*sqrt(d*cos(b*x + a))*sqrt(d)/(d*cos(b*x + a) - d)) + 21*(d^4*cos(b*x + a)^2 - d^4)*sqrt(d)*log(-(d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) - 8*(4*d^4*cos(b*x + a)^3 - 7*d^4*cos(b*x + a))*sqrt(d*cos(b*x + a)))/(b*cos(b*x + a)^2 - b)]","B",0
244,1,393,0,2.184916," ","integrate((d*cos(b*x+a))^(7/2)*csc(b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{10 \, {\left(d^{3} \cos\left(b x + a\right)^{2} - d^{3}\right)} \sqrt{-d} \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d}}{d \cos\left(b x + a\right) + d}\right) - 5 \, {\left(d^{3} \cos\left(b x + a\right)^{2} - d^{3}\right)} \sqrt{-d} \log\left(-\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, {\left(4 \, d^{3} \cos\left(b x + a\right)^{2} - 5 \, d^{3}\right)} \sqrt{d \cos\left(b x + a\right)}}{16 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}, -\frac{10 \, {\left(d^{3} \cos\left(b x + a\right)^{2} - d^{3}\right)} \sqrt{d} \arctan\left(\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d}}{d \cos\left(b x + a\right) - d}\right) - 5 \, {\left(d^{3} \cos\left(b x + a\right)^{2} - d^{3}\right)} \sqrt{d} \log\left(-\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, {\left(4 \, d^{3} \cos\left(b x + a\right)^{2} - 5 \, d^{3}\right)} \sqrt{d \cos\left(b x + a\right)}}{16 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}\right]"," ",0,"[-1/16*(10*(d^3*cos(b*x + a)^2 - d^3)*sqrt(-d)*arctan(2*sqrt(d*cos(b*x + a))*sqrt(-d)/(d*cos(b*x + a) + d)) - 5*(d^3*cos(b*x + a)^2 - d^3)*sqrt(-d)*log(-(d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*(4*d^3*cos(b*x + a)^2 - 5*d^3)*sqrt(d*cos(b*x + a)))/(b*cos(b*x + a)^2 - b), -1/16*(10*(d^3*cos(b*x + a)^2 - d^3)*sqrt(d)*arctan(2*sqrt(d*cos(b*x + a))*sqrt(d)/(d*cos(b*x + a) - d)) - 5*(d^3*cos(b*x + a)^2 - d^3)*sqrt(d)*log(-(d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) + 8*(4*d^3*cos(b*x + a)^2 - 5*d^3)*sqrt(d*cos(b*x + a)))/(b*cos(b*x + a)^2 - b)]","B",0
245,1,380,0,1.796429," ","integrate((d*cos(b*x+a))^(5/2)*csc(b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{8 \, \sqrt{d \cos\left(b x + a\right)} d^{2} \cos\left(b x + a\right) - 6 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) + 1\right)}}{2 \, d \cos\left(b x + a\right)}\right) + 3 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} \sqrt{-d} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right)}{16 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}, \frac{8 \, \sqrt{d \cos\left(b x + a\right)} d^{2} \cos\left(b x + a\right) - 6 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right) - 1\right)}}{2 \, \sqrt{d} \cos\left(b x + a\right)}\right) + 3 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} \sqrt{d} \log\left(\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right)}{16 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}\right]"," ",0,"[1/16*(8*sqrt(d*cos(b*x + a))*d^2*cos(b*x + a) - 6*(d^2*cos(b*x + a)^2 - d^2)*sqrt(-d)*arctan(1/2*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) + 1)/(d*cos(b*x + a))) + 3*(d^2*cos(b*x + a)^2 - d^2)*sqrt(-d)*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)))/(b*cos(b*x + a)^2 - b), 1/16*(8*sqrt(d*cos(b*x + a))*d^2*cos(b*x + a) - 6*(d^2*cos(b*x + a)^2 - d^2)*sqrt(d)*arctan(1/2*sqrt(d*cos(b*x + a))*(cos(b*x + a) - 1)/(sqrt(d)*cos(b*x + a))) + 3*(d^2*cos(b*x + a)^2 - d^2)*sqrt(d)*log((d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)))/(b*cos(b*x + a)^2 - b)]","B",0
246,1,347,0,1.447046," ","integrate((d*cos(b*x+a))^(3/2)*csc(b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(d \cos\left(b x + a\right)^{2} - d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) + 1\right)}}{2 \, d \cos\left(b x + a\right)}\right) - {\left(d \cos\left(b x + a\right)^{2} - d\right)} \sqrt{-d} \log\left(\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) - 8 \, \sqrt{d \cos\left(b x + a\right)} d}{16 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}, \frac{2 \, {\left(d \cos\left(b x + a\right)^{2} - d\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right) - 1\right)}}{2 \, \sqrt{d} \cos\left(b x + a\right)}\right) + {\left(d \cos\left(b x + a\right)^{2} - d\right)} \sqrt{d} \log\left(\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)} d}{16 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}\right]"," ",0,"[-1/16*(2*(d*cos(b*x + a)^2 - d)*sqrt(-d)*arctan(1/2*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) + 1)/(d*cos(b*x + a))) - (d*cos(b*x + a)^2 - d)*sqrt(-d)*log((d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) - 8*sqrt(d*cos(b*x + a))*d)/(b*cos(b*x + a)^2 - b), 1/16*(2*(d*cos(b*x + a)^2 - d)*sqrt(d)*arctan(1/2*sqrt(d*cos(b*x + a))*(cos(b*x + a) - 1)/(sqrt(d)*cos(b*x + a))) + (d*cos(b*x + a)^2 - d)*sqrt(d)*log((d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a))*d)/(b*cos(b*x + a)^2 - b)]","B",0
247,1,340,0,1.254056," ","integrate((d*cos(b*x+a))^(1/2)*csc(b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) + 1\right)}}{2 \, d \cos\left(b x + a\right)}\right) + {\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{-d} \log\left(\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)} \cos\left(b x + a\right)}{16 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}, \frac{2 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right) - 1\right)}}{2 \, \sqrt{d} \cos\left(b x + a\right)}\right) + {\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{d} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)} \cos\left(b x + a\right)}{16 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}\right]"," ",0,"[1/16*(2*(cos(b*x + a)^2 - 1)*sqrt(-d)*arctan(1/2*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) + 1)/(d*cos(b*x + a))) + (cos(b*x + a)^2 - 1)*sqrt(-d)*log((d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a))*cos(b*x + a))/(b*cos(b*x + a)^2 - b), 1/16*(2*(cos(b*x + a)^2 - 1)*sqrt(d)*arctan(1/2*sqrt(d*cos(b*x + a))*(cos(b*x + a) - 1)/(sqrt(d)*cos(b*x + a))) + (cos(b*x + a)^2 - 1)*sqrt(d)*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a))*cos(b*x + a))/(b*cos(b*x + a)^2 - b)]","B",0
248,1,334,0,0.914943," ","integrate(csc(b*x+a)^3/(d*cos(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) + 1\right)}}{2 \, d \cos\left(b x + a\right)}\right) - 3 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{-d} \log\left(\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)}}{16 \, {\left(b d \cos\left(b x + a\right)^{2} - b d\right)}}, -\frac{6 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right) - 1\right)}}{2 \, \sqrt{d} \cos\left(b x + a\right)}\right) - 3 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{d} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) - 8 \, \sqrt{d \cos\left(b x + a\right)}}{16 \, {\left(b d \cos\left(b x + a\right)^{2} - b d\right)}}\right]"," ",0,"[1/16*(6*(cos(b*x + a)^2 - 1)*sqrt(-d)*arctan(1/2*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) + 1)/(d*cos(b*x + a))) - 3*(cos(b*x + a)^2 - 1)*sqrt(-d)*log((d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a)))/(b*d*cos(b*x + a)^2 - b*d), -1/16*(6*(cos(b*x + a)^2 - 1)*sqrt(d)*arctan(1/2*sqrt(d*cos(b*x + a))*(cos(b*x + a) - 1)/(sqrt(d)*cos(b*x + a))) - 3*(cos(b*x + a)^2 - 1)*sqrt(d)*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) - 8*sqrt(d*cos(b*x + a)))/(b*d*cos(b*x + a)^2 - b*d)]","B",0
249,1,406,0,1.531803," ","integrate(csc(b*x+a)^3/(d*cos(b*x+a))^(3/2),x, algorithm=""fricas"")","\left[\frac{10 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) + 1\right)}}{2 \, d \cos\left(b x + a\right)}\right) - 5 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sqrt{-d} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)} {\left(5 \, \cos\left(b x + a\right)^{2} - 4\right)}}{16 \, {\left(b d^{2} \cos\left(b x + a\right)^{3} - b d^{2} \cos\left(b x + a\right)\right)}}, \frac{10 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right) - 1\right)}}{2 \, \sqrt{d} \cos\left(b x + a\right)}\right) + 5 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sqrt{d} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)} {\left(5 \, \cos\left(b x + a\right)^{2} - 4\right)}}{16 \, {\left(b d^{2} \cos\left(b x + a\right)^{3} - b d^{2} \cos\left(b x + a\right)\right)}}\right]"," ",0,"[1/16*(10*(cos(b*x + a)^3 - cos(b*x + a))*sqrt(-d)*arctan(1/2*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) + 1)/(d*cos(b*x + a))) - 5*(cos(b*x + a)^3 - cos(b*x + a))*sqrt(-d)*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a))*(5*cos(b*x + a)^2 - 4))/(b*d^2*cos(b*x + a)^3 - b*d^2*cos(b*x + a)), 1/16*(10*(cos(b*x + a)^3 - cos(b*x + a))*sqrt(d)*arctan(1/2*sqrt(d*cos(b*x + a))*(cos(b*x + a) - 1)/(sqrt(d)*cos(b*x + a))) + 5*(cos(b*x + a)^3 - cos(b*x + a))*sqrt(d)*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a))*(5*cos(b*x + a)^2 - 4))/(b*d^2*cos(b*x + a)^3 - b*d^2*cos(b*x + a))]","B",0
250,1,418,0,1.133991," ","integrate(csc(b*x+a)^3/(d*cos(b*x+a))^(5/2),x, algorithm=""fricas"")","\left[\frac{42 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) + 1\right)}}{2 \, d \cos\left(b x + a\right)}\right) - 21 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \sqrt{-d} \log\left(\frac{d \cos\left(b x + a\right)^{2} + 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, \sqrt{d \cos\left(b x + a\right)} {\left(7 \, \cos\left(b x + a\right)^{2} - 4\right)}}{48 \, {\left(b d^{3} \cos\left(b x + a\right)^{4} - b d^{3} \cos\left(b x + a\right)^{2}\right)}}, -\frac{42 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right) - 1\right)}}{2 \, \sqrt{d} \cos\left(b x + a\right)}\right) - 21 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \sqrt{d} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) - 8 \, \sqrt{d \cos\left(b x + a\right)} {\left(7 \, \cos\left(b x + a\right)^{2} - 4\right)}}{48 \, {\left(b d^{3} \cos\left(b x + a\right)^{4} - b d^{3} \cos\left(b x + a\right)^{2}\right)}}\right]"," ",0,"[1/48*(42*(cos(b*x + a)^4 - cos(b*x + a)^2)*sqrt(-d)*arctan(1/2*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) + 1)/(d*cos(b*x + a))) - 21*(cos(b*x + a)^4 - cos(b*x + a)^2)*sqrt(-d)*log((d*cos(b*x + a)^2 + 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*sqrt(d*cos(b*x + a))*(7*cos(b*x + a)^2 - 4))/(b*d^3*cos(b*x + a)^4 - b*d^3*cos(b*x + a)^2), -1/48*(42*(cos(b*x + a)^4 - cos(b*x + a)^2)*sqrt(d)*arctan(1/2*sqrt(d*cos(b*x + a))*(cos(b*x + a) - 1)/(sqrt(d)*cos(b*x + a))) - 21*(cos(b*x + a)^4 - cos(b*x + a)^2)*sqrt(d)*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) - 8*sqrt(d*cos(b*x + a))*(7*cos(b*x + a)^2 - 4))/(b*d^3*cos(b*x + a)^4 - b*d^3*cos(b*x + a)^2)]","B",0
251,1,438,0,1.244873," ","integrate(csc(b*x+a)^3/(d*cos(b*x+a))^(7/2),x, algorithm=""fricas"")","\left[\frac{90 \, {\left(\cos\left(b x + a\right)^{5} - \cos\left(b x + a\right)^{3}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) + 1\right)}}{2 \, d \cos\left(b x + a\right)}\right) - 45 \, {\left(\cos\left(b x + a\right)^{5} - \cos\left(b x + a\right)^{3}\right)} \sqrt{-d} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{-d} {\left(\cos\left(b x + a\right) - 1\right)} - 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, {\left(45 \, \cos\left(b x + a\right)^{4} - 36 \, \cos\left(b x + a\right)^{2} - 4\right)} \sqrt{d \cos\left(b x + a\right)}}{80 \, {\left(b d^{4} \cos\left(b x + a\right)^{5} - b d^{4} \cos\left(b x + a\right)^{3}\right)}}, \frac{90 \, {\left(\cos\left(b x + a\right)^{5} - \cos\left(b x + a\right)^{3}\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \cos\left(b x + a\right)} {\left(\cos\left(b x + a\right) - 1\right)}}{2 \, \sqrt{d} \cos\left(b x + a\right)}\right) + 45 \, {\left(\cos\left(b x + a\right)^{5} - \cos\left(b x + a\right)^{3}\right)} \sqrt{d} \log\left(\frac{d \cos\left(b x + a\right)^{2} - 4 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{d} {\left(\cos\left(b x + a\right) + 1\right)} + 6 \, d \cos\left(b x + a\right) + d}{\cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1}\right) + 8 \, {\left(45 \, \cos\left(b x + a\right)^{4} - 36 \, \cos\left(b x + a\right)^{2} - 4\right)} \sqrt{d \cos\left(b x + a\right)}}{80 \, {\left(b d^{4} \cos\left(b x + a\right)^{5} - b d^{4} \cos\left(b x + a\right)^{3}\right)}}\right]"," ",0,"[1/80*(90*(cos(b*x + a)^5 - cos(b*x + a)^3)*sqrt(-d)*arctan(1/2*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) + 1)/(d*cos(b*x + a))) - 45*(cos(b*x + a)^5 - cos(b*x + a)^3)*sqrt(-d)*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(-d)*(cos(b*x + a) - 1) - 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 + 2*cos(b*x + a) + 1)) + 8*(45*cos(b*x + a)^4 - 36*cos(b*x + a)^2 - 4)*sqrt(d*cos(b*x + a)))/(b*d^4*cos(b*x + a)^5 - b*d^4*cos(b*x + a)^3), 1/80*(90*(cos(b*x + a)^5 - cos(b*x + a)^3)*sqrt(d)*arctan(1/2*sqrt(d*cos(b*x + a))*(cos(b*x + a) - 1)/(sqrt(d)*cos(b*x + a))) + 45*(cos(b*x + a)^5 - cos(b*x + a)^3)*sqrt(d)*log((d*cos(b*x + a)^2 - 4*sqrt(d*cos(b*x + a))*sqrt(d)*(cos(b*x + a) + 1) + 6*d*cos(b*x + a) + d)/(cos(b*x + a)^2 - 2*cos(b*x + a) + 1)) + 8*(45*cos(b*x + a)^4 - 36*cos(b*x + a)^2 - 4)*sqrt(d*cos(b*x + a)))/(b*d^4*cos(b*x + a)^5 - b*d^4*cos(b*x + a)^3)]","A",0
252,1,21,0,1.539305," ","integrate((d*cos(b*x+a))^(1/5)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{5 \, \left(d \cos\left(b x + a\right)\right)^{\frac{1}{5}} \cos\left(b x + a\right)}{6 \, b}"," ",0,"-5/6*(d*cos(b*x + a))^(1/5)*cos(b*x + a)/b","A",0
253,1,14,0,1.265336," ","integrate(cos(x)^3*sin(x)^(1/2),x, algorithm=""fricas"")","\frac{2}{21} \, {\left(3 \, \cos\left(x\right)^{2} + 4\right)} \sin\left(x\right)^{\frac{3}{2}}"," ",0,"2/21*(3*cos(x)^2 + 4)*sin(x)^(3/2)","A",0
254,1,20,0,1.156561," ","integrate(cos(x)^3*sin(x)^(3/2),x, algorithm=""fricas"")","-\frac{2}{45} \, {\left(5 \, \cos\left(x\right)^{4} - \cos\left(x\right)^{2} - 4\right)} \sqrt{\sin\left(x\right)}"," ",0,"-2/45*(5*cos(x)^4 - cos(x)^2 - 4)*sqrt(sin(x))","A",0
255,1,20,0,0.816750," ","integrate(cos(x)^3*sin(x)^(5/2),x, algorithm=""fricas"")","-\frac{2}{77} \, {\left(7 \, \cos\left(x\right)^{4} - 3 \, \cos\left(x\right)^{2} - 4\right)} \sin\left(x\right)^{\frac{3}{2}}"," ",0,"-2/77*(7*cos(x)^4 - 3*cos(x)^2 - 4)*sin(x)^(3/2)","A",0
256,1,12,0,1.382248," ","integrate(cos(x)^3/sin(x)^(1/2),x, algorithm=""fricas"")","\frac{2}{5} \, {\left(\cos\left(x\right)^{2} + 4\right)} \sqrt{\sin\left(x\right)}"," ",0,"2/5*(cos(x)^2 + 4)*sqrt(sin(x))","A",0
257,0,0,0,1.292429," ","integrate((d*cos(b*x+a))^(9/2)*(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} d^{4} \cos\left(b x + a\right)^{4}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*d^4*cos(b*x + a)^4, x)","F",0
258,0,0,0,1.065482," ","integrate((d*cos(b*x+a))^(5/2)*(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} d^{2} \cos\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*d^2*cos(b*x + a)^2, x)","F",0
259,0,0,0,1.423741," ","integrate((d*cos(b*x+a))^(1/2)*(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)), x)","F",0
260,0,0,0,0.986190," ","integrate((c*sin(b*x+a))^(1/2)/(d*cos(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}}{d^{2} \cos\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))/(d^2*cos(b*x + a)^2), x)","F",0
261,0,0,0,1.506848," ","integrate((c*sin(b*x+a))^(1/2)/(d*cos(b*x+a))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}}{d^{4} \cos\left(b x + a\right)^{4}}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))/(d^4*cos(b*x + a)^4), x)","F",0
262,1,2205,0,133.038157," ","integrate((d*cos(b*x+a))^(3/2)*(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{32 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} d \sin\left(b x + a\right) + 4 \, \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(\frac{{\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{2} d^{5} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + \sqrt{4 \, \sqrt{\frac{c^{2} d^{6}}{b^{4}}} b^{2} c^{3} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{4} d^{10} - 2 \, {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{2} d^{5} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(2 \, c^{2} d^{5} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{\frac{c^{2} d^{6}}{b^{4}}} b^{2} c d^{2} + {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c d^{3} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, c^{4} d^{10} \cos\left(b x + a\right)^{2} - c^{4} d^{10}}\right) + 4 \, \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(\frac{{\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{2} d^{5} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - \sqrt{4 \, \sqrt{\frac{c^{2} d^{6}}{b^{4}}} b^{2} c^{3} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{4} d^{10} + 2 \, {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{2} d^{5} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(2 \, c^{2} d^{5} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{\frac{c^{2} d^{6}}{b^{4}}} b^{2} c d^{2} - {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c d^{3} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, c^{4} d^{10} \cos\left(b x + a\right)^{2} - c^{4} d^{10}}\right) + 4 \, \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{2 \, c^{4} d^{10} \cos\left(b x + a\right) \sin\left(b x + a\right) - \sqrt{4 \, \sqrt{\frac{c^{2} d^{6}}{b^{4}}} b^{2} c^{3} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{4} d^{10} + 2 \, {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{2} d^{5} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c d^{3} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d^{8} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{2} d^{5} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c^{3} d^{7} \cos\left(b x + a\right)^{4} - b^{2} c^{3} d^{7} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{c^{2} d^{6}}{b^{4}}}}{2 \, {\left(2 \, c^{4} d^{10} \cos\left(b x + a\right)^{3} - c^{4} d^{10} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) + 4 \, \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(\frac{2 \, c^{4} d^{10} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{4 \, \sqrt{\frac{c^{2} d^{6}}{b^{4}}} b^{2} c^{3} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{4} d^{10} - 2 \, {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{2} d^{5} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c d^{3} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d^{8} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{2} d^{5} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c^{3} d^{7} \cos\left(b x + a\right)^{4} - b^{2} c^{3} d^{7} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{c^{2} d^{6}}{b^{4}}}}{2 \, {\left(2 \, c^{4} d^{10} \cos\left(b x + a\right)^{3} - c^{4} d^{10} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) - \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(4 \, \sqrt{\frac{c^{2} d^{6}}{b^{4}}} b^{2} c^{3} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{4} d^{10} + 2 \, {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{2} d^{5} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(4 \, \sqrt{\frac{c^{2} d^{6}}{b^{4}}} b^{2} c^{3} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{4} d^{10} - 2 \, {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{2} d^{5} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) - \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(\frac{1}{4} \, \sqrt{\frac{c^{2} d^{6}}{b^{4}}} b^{2} c^{3} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + \frac{1}{16} \, c^{4} d^{10} + \frac{1}{8} \, {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{2} d^{5} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(\frac{1}{4} \, \sqrt{\frac{c^{2} d^{6}}{b^{4}}} b^{2} c^{3} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + \frac{1}{16} \, c^{4} d^{10} - \frac{1}{8} \, {\left(\sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{2} d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{2} d^{5} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}{64 \, b}"," ",0,"1/64*(32*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*d*sin(b*x + a) + 4*sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*arctan(((sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c^3*d^8*cos(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*c^2*d^5*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + sqrt(4*sqrt(c^2*d^6/b^4)*b^2*c^3*d^7*cos(b*x + a)*sin(b*x + a) + c^4*d^10 - 2*(sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c^3*d^8*cos(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*c^2*d^5*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(2*c^2*d^5*cos(b*x + a)*sin(b*x + a) + sqrt(c^2*d^6/b^4)*b^2*c*d^2 + (sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c*d^3*sin(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(2*c^4*d^10*cos(b*x + a)^2 - c^4*d^10)) + 4*sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*arctan(((sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c^3*d^8*cos(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*c^2*d^5*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - sqrt(4*sqrt(c^2*d^6/b^4)*b^2*c^3*d^7*cos(b*x + a)*sin(b*x + a) + c^4*d^10 + 2*(sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c^3*d^8*cos(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*c^2*d^5*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(2*c^2*d^5*cos(b*x + a)*sin(b*x + a) + sqrt(c^2*d^6/b^4)*b^2*c*d^2 - (sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c*d^3*sin(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(2*c^4*d^10*cos(b*x + a)^2 - c^4*d^10)) + 4*sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*arctan(-1/2*(2*c^4*d^10*cos(b*x + a)*sin(b*x + a) - sqrt(4*sqrt(c^2*d^6/b^4)*b^2*c^3*d^7*cos(b*x + a)*sin(b*x + a) + c^4*d^10 + 2*(sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c^3*d^8*cos(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*c^2*d^5*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c*d^3*sin(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + (sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c^3*d^8*sin(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*c^2*d^5*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c^3*d^7*cos(b*x + a)^4 - b^2*c^3*d^7*cos(b*x + a)^2)*sqrt(c^2*d^6/b^4))/((2*c^4*d^10*cos(b*x + a)^3 - c^4*d^10*cos(b*x + a))*sin(b*x + a))) + 4*sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*arctan(1/2*(2*c^4*d^10*cos(b*x + a)*sin(b*x + a) + sqrt(4*sqrt(c^2*d^6/b^4)*b^2*c^3*d^7*cos(b*x + a)*sin(b*x + a) + c^4*d^10 - 2*(sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c^3*d^8*cos(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*c^2*d^5*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c*d^3*sin(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - (sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c^3*d^8*sin(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*c^2*d^5*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c^3*d^7*cos(b*x + a)^4 - b^2*c^3*d^7*cos(b*x + a)^2)*sqrt(c^2*d^6/b^4))/((2*c^4*d^10*cos(b*x + a)^3 - c^4*d^10*cos(b*x + a))*sin(b*x + a))) - sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*log(4*sqrt(c^2*d^6/b^4)*b^2*c^3*d^7*cos(b*x + a)*sin(b*x + a) + c^4*d^10 + 2*(sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c^3*d^8*cos(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*c^2*d^5*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) + sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*log(4*sqrt(c^2*d^6/b^4)*b^2*c^3*d^7*cos(b*x + a)*sin(b*x + a) + c^4*d^10 - 2*(sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c^3*d^8*cos(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*c^2*d^5*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) - sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*log(1/4*sqrt(c^2*d^6/b^4)*b^2*c^3*d^7*cos(b*x + a)*sin(b*x + a) + 1/16*c^4*d^10 + 1/8*(sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c^3*d^8*cos(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*c^2*d^5*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) + sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*log(1/4*sqrt(c^2*d^6/b^4)*b^2*c^3*d^7*cos(b*x + a)*sin(b*x + a) + 1/16*c^4*d^10 - 1/8*(sqrt(2)*(c^2*d^6/b^4)^(1/4)*b*c^3*d^8*cos(b*x + a) + sqrt(2)*(c^2*d^6/b^4)^(3/4)*b^3*c^2*d^5*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/b","B",0
263,1,2003,0,129.345000," ","integrate((c*sin(b*x+a))^(1/2)/(d*cos(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} c^{2} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + \sqrt{4 \, b^{2} c^{3} d \sqrt{\frac{c^{2}}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{4} - 2 \, {\left(\sqrt{2} b^{3} c^{2} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(b^{2} c d \sqrt{\frac{c^{2}}{b^{4} d^{2}}} + 2 \, c^{2} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(\sqrt{2} b^{3} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, c^{4} \cos\left(b x + a\right)^{2} - c^{4}}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} c^{2} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - \sqrt{4 \, b^{2} c^{3} d \sqrt{\frac{c^{2}}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{4} + 2 \, {\left(\sqrt{2} b^{3} c^{2} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(b^{2} c d \sqrt{\frac{c^{2}}{b^{4} d^{2}}} + 2 \, c^{2} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left(\sqrt{2} b^{3} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, c^{4} \cos\left(b x + a\right)^{2} - c^{4}}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \arctan\left(-\frac{2 \, c^{4} \cos\left(b x + a\right) \sin\left(b x + a\right) - \sqrt{4 \, b^{2} c^{3} d \sqrt{\frac{c^{2}}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{4} + 2 \, {\left(\sqrt{2} b^{3} c^{2} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} b^{3} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + {\left(\sqrt{2} b^{3} c^{2} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{3} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c^{3} d \cos\left(b x + a\right)^{4} - b^{2} c^{3} d \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{c^{2}}{b^{4} d^{2}}}}{2 \, {\left(2 \, c^{4} \cos\left(b x + a\right)^{3} - c^{4} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{2 \, c^{4} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{4 \, b^{2} c^{3} d \sqrt{\frac{c^{2}}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{4} - 2 \, {\left(\sqrt{2} b^{3} c^{2} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} b^{3} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - {\left(\sqrt{2} b^{3} c^{2} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{3} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c^{3} d \cos\left(b x + a\right)^{4} - b^{2} c^{3} d \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{c^{2}}{b^{4} d^{2}}}}{2 \, {\left(2 \, c^{4} \cos\left(b x + a\right)^{3} - c^{4} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) - \frac{1}{16} \, \sqrt{2} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \log\left(4 \, b^{2} c^{3} d \sqrt{\frac{c^{2}}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{4} + 2 \, {\left(\sqrt{2} b^{3} c^{2} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) + \frac{1}{16} \, \sqrt{2} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \log\left(4 \, b^{2} c^{3} d \sqrt{\frac{c^{2}}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{4} - 2 \, {\left(\sqrt{2} b^{3} c^{2} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) - \frac{1}{16} \, \sqrt{2} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \log\left(\frac{1}{4} \, b^{2} c^{3} d \sqrt{\frac{c^{2}}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + \frac{1}{16} \, c^{4} + \frac{1}{8} \, {\left(\sqrt{2} b^{3} c^{2} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) + \frac{1}{16} \, \sqrt{2} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \log\left(\frac{1}{4} \, b^{2} c^{3} d \sqrt{\frac{c^{2}}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + \frac{1}{16} \, c^{4} - \frac{1}{8} \, {\left(\sqrt{2} b^{3} c^{2} d \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} \left(\frac{c^{2}}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)"," ",0,"1/4*sqrt(2)*(c^2/(b^4*d^2))^(1/4)*arctan(((sqrt(2)*b^3*c^2*d*(c^2/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*(c^2/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + sqrt(4*b^2*c^3*d*sqrt(c^2/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + c^4 - 2*(sqrt(2)*b^3*c^2*d*(c^2/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*(c^2/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(b^2*c*d*sqrt(c^2/(b^4*d^2)) + 2*c^2*cos(b*x + a)*sin(b*x + a) + (sqrt(2)*b^3*d*(c^2/(b^4*d^2))^(3/4)*cos(b*x + a) + sqrt(2)*b*c*(c^2/(b^4*d^2))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(2*c^4*cos(b*x + a)^2 - c^4)) + 1/4*sqrt(2)*(c^2/(b^4*d^2))^(1/4)*arctan(((sqrt(2)*b^3*c^2*d*(c^2/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*(c^2/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - sqrt(4*b^2*c^3*d*sqrt(c^2/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + c^4 + 2*(sqrt(2)*b^3*c^2*d*(c^2/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*(c^2/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(b^2*c*d*sqrt(c^2/(b^4*d^2)) + 2*c^2*cos(b*x + a)*sin(b*x + a) - (sqrt(2)*b^3*d*(c^2/(b^4*d^2))^(3/4)*cos(b*x + a) + sqrt(2)*b*c*(c^2/(b^4*d^2))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(2*c^4*cos(b*x + a)^2 - c^4)) + 1/4*sqrt(2)*(c^2/(b^4*d^2))^(1/4)*arctan(-1/2*(2*c^4*cos(b*x + a)*sin(b*x + a) - sqrt(4*b^2*c^3*d*sqrt(c^2/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + c^4 + 2*(sqrt(2)*b^3*c^2*d*(c^2/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*(c^2/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*b^3*d*(c^2/(b^4*d^2))^(3/4)*cos(b*x + a) + sqrt(2)*b*c*(c^2/(b^4*d^2))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + (sqrt(2)*b^3*c^2*d*(c^2/(b^4*d^2))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^3*(c^2/(b^4*d^2))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c^3*d*cos(b*x + a)^4 - b^2*c^3*d*cos(b*x + a)^2)*sqrt(c^2/(b^4*d^2)))/((2*c^4*cos(b*x + a)^3 - c^4*cos(b*x + a))*sin(b*x + a))) + 1/4*sqrt(2)*(c^2/(b^4*d^2))^(1/4)*arctan(1/2*(2*c^4*cos(b*x + a)*sin(b*x + a) + sqrt(4*b^2*c^3*d*sqrt(c^2/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + c^4 - 2*(sqrt(2)*b^3*c^2*d*(c^2/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*(c^2/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*b^3*d*(c^2/(b^4*d^2))^(3/4)*cos(b*x + a) + sqrt(2)*b*c*(c^2/(b^4*d^2))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - (sqrt(2)*b^3*c^2*d*(c^2/(b^4*d^2))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^3*(c^2/(b^4*d^2))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c^3*d*cos(b*x + a)^4 - b^2*c^3*d*cos(b*x + a)^2)*sqrt(c^2/(b^4*d^2)))/((2*c^4*cos(b*x + a)^3 - c^4*cos(b*x + a))*sin(b*x + a))) - 1/16*sqrt(2)*(c^2/(b^4*d^2))^(1/4)*log(4*b^2*c^3*d*sqrt(c^2/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + c^4 + 2*(sqrt(2)*b^3*c^2*d*(c^2/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*(c^2/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) + 1/16*sqrt(2)*(c^2/(b^4*d^2))^(1/4)*log(4*b^2*c^3*d*sqrt(c^2/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + c^4 - 2*(sqrt(2)*b^3*c^2*d*(c^2/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*(c^2/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) - 1/16*sqrt(2)*(c^2/(b^4*d^2))^(1/4)*log(1/4*b^2*c^3*d*sqrt(c^2/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + 1/16*c^4 + 1/8*(sqrt(2)*b^3*c^2*d*(c^2/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*(c^2/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) + 1/16*sqrt(2)*(c^2/(b^4*d^2))^(1/4)*log(1/4*b^2*c^3*d*sqrt(c^2/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + 1/16*c^4 - 1/8*(sqrt(2)*b^3*c^2*d*(c^2/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*(c^2/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))","B",0
264,1,42,0,1.067452," ","integrate((c*sin(b*x+a))^(1/2)/(d*cos(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} \sin\left(b x + a\right)}{3 \, b d^{3} \cos\left(b x + a\right)^{2}}"," ",0,"2/3*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*sin(b*x + a)/(b*d^3*cos(b*x + a)^2)","A",0
265,1,54,0,1.277003," ","integrate((c*sin(b*x+a))^(1/2)/(d*cos(b*x+a))^(9/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{d \cos\left(b x + a\right)} {\left(4 \, \cos\left(b x + a\right)^{2} + 3\right)} \sqrt{c \sin\left(b x + a\right)} \sin\left(b x + a\right)}{21 \, b d^{5} \cos\left(b x + a\right)^{4}}"," ",0,"2/21*sqrt(d*cos(b*x + a))*(4*cos(b*x + a)^2 + 3)*sqrt(c*sin(b*x + a))*sin(b*x + a)/(b*d^5*cos(b*x + a)^4)","A",0
266,1,64,0,1.332227," ","integrate((c*sin(b*x+a))^(1/2)/(d*cos(b*x+a))^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(32 \, \cos\left(b x + a\right)^{4} + 24 \, \cos\left(b x + a\right)^{2} + 21\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} \sin\left(b x + a\right)}{231 \, b d^{7} \cos\left(b x + a\right)^{6}}"," ",0,"2/231*(32*cos(b*x + a)^4 + 24*cos(b*x + a)^2 + 21)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*sin(b*x + a)/(b*d^7*cos(b*x + a)^6)","A",0
267,0,0,0,1.192345," ","integrate((d*cos(b*x+a))^(3/2)*(c*sin(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} c d \cos\left(b x + a\right) \sin\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*c*d*cos(b*x + a)*sin(b*x + a), x)","F",0
268,0,0,0,1.060517," ","integrate((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} c \sin\left(b x + a\right)}{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*c*sin(b*x + a)/(d*cos(b*x + a)), x)","F",0
269,0,0,0,1.154274," ","integrate((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} c \sin\left(b x + a\right)}{d^{3} \cos\left(b x + a\right)^{3}}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*c*sin(b*x + a)/(d^3*cos(b*x + a)^3), x)","F",0
270,0,0,0,1.105232," ","integrate((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} c \sin\left(b x + a\right)}{d^{5} \cos\left(b x + a\right)^{5}}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*c*sin(b*x + a)/(d^5*cos(b*x + a)^5), x)","F",0
271,1,1868,0,76.438210," ","integrate((d*cos(b*x+a))^(1/2)*(c*sin(b*x+a))^(3/2),x, algorithm=""fricas"")","-\frac{16 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} c \cos\left(b x + a\right) + 2 \, \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(\frac{2 \, c^{10} d^{4} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{4 \, \sqrt{\frac{c^{6} d^{2}}{b^{4}}} b^{2} c^{7} d^{3} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{10} d^{4} + 2 \, {\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{8} d^{3} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{5} d^{2} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + {\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{8} d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{5} d^{2} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c^{7} d^{3} \cos\left(b x + a\right)^{4} - b^{2} c^{7} d^{3} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{c^{6} d^{2}}{b^{4}}}}{2 \, {\left(2 \, c^{10} d^{4} \cos\left(b x + a\right)^{3} - c^{10} d^{4} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) + 2 \, \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{2 \, c^{10} d^{4} \cos\left(b x + a\right) \sin\left(b x + a\right) - \sqrt{4 \, \sqrt{\frac{c^{6} d^{2}}{b^{4}}} b^{2} c^{7} d^{3} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{10} d^{4} - 2 \, {\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{8} d^{3} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{5} d^{2} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - {\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{8} d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{5} d^{2} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c^{7} d^{3} \cos\left(b x + a\right)^{4} - b^{2} c^{7} d^{3} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{c^{6} d^{2}}{b^{4}}}}{2 \, {\left(2 \, c^{10} d^{4} \cos\left(b x + a\right)^{3} - c^{10} d^{4} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) + 2 \, \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(\frac{{\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{8} d^{3} \cos\left(b x + a\right) - \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{5} d^{2} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + \sqrt{4 \, \sqrt{\frac{c^{6} d^{2}}{b^{4}}} b^{2} c^{7} d^{3} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{10} d^{4} - 2 \, {\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{8} d^{3} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{5} d^{2} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(2 \, c^{5} d^{2} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, c^{10} d^{4} \cos\left(b x + a\right) \sin\left(b x + a\right)}\right) + 2 \, \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(\frac{{\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{8} d^{3} \cos\left(b x + a\right) - \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{5} d^{2} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - \sqrt{4 \, \sqrt{\frac{c^{6} d^{2}}{b^{4}}} b^{2} c^{7} d^{3} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{10} d^{4} + 2 \, {\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{8} d^{3} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{5} d^{2} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(2 \, c^{5} d^{2} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{3} d \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, c^{10} d^{4} \cos\left(b x + a\right) \sin\left(b x + a\right)}\right) - \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(4 \, \sqrt{\frac{c^{6} d^{2}}{b^{4}}} b^{2} c^{7} d^{3} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{10} d^{4} + 2 \, {\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{8} d^{3} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{5} d^{2} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) + \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(4 \, \sqrt{\frac{c^{6} d^{2}}{b^{4}}} b^{2} c^{7} d^{3} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{10} d^{4} - 2 \, {\left(\sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{1}{4}} b c^{8} d^{3} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{6} d^{2}}{b^{4}}\right)^{\frac{3}{4}} b^{3} c^{5} d^{2} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}{32 \, b}"," ",0,"-1/32*(16*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*c*cos(b*x + a) + 2*sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*arctan(1/2*(2*c^10*d^4*cos(b*x + a)*sin(b*x + a) + sqrt(4*sqrt(c^6*d^2/b^4)*b^2*c^7*d^3*cos(b*x + a)*sin(b*x + a) + c^10*d^4 + 2*(sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^8*d^3*sin(b*x + a) + sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*c^5*d^2*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^3*d*cos(b*x + a) + sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + (sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^8*d^3*cos(b*x + a) + sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*c^5*d^2*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c^7*d^3*cos(b*x + a)^4 - b^2*c^7*d^3*cos(b*x + a)^2)*sqrt(c^6*d^2/b^4))/((2*c^10*d^4*cos(b*x + a)^3 - c^10*d^4*cos(b*x + a))*sin(b*x + a))) + 2*sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*arctan(-1/2*(2*c^10*d^4*cos(b*x + a)*sin(b*x + a) - sqrt(4*sqrt(c^6*d^2/b^4)*b^2*c^7*d^3*cos(b*x + a)*sin(b*x + a) + c^10*d^4 - 2*(sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^8*d^3*sin(b*x + a) + sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*c^5*d^2*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^3*d*cos(b*x + a) + sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - (sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^8*d^3*cos(b*x + a) + sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*c^5*d^2*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c^7*d^3*cos(b*x + a)^4 - b^2*c^7*d^3*cos(b*x + a)^2)*sqrt(c^6*d^2/b^4))/((2*c^10*d^4*cos(b*x + a)^3 - c^10*d^4*cos(b*x + a))*sin(b*x + a))) + 2*sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*arctan(1/2*((sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^8*d^3*cos(b*x + a) - sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*c^5*d^2*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + sqrt(4*sqrt(c^6*d^2/b^4)*b^2*c^7*d^3*cos(b*x + a)*sin(b*x + a) + c^10*d^4 - 2*(sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^8*d^3*sin(b*x + a) + sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*c^5*d^2*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(2*c^5*d^2*cos(b*x + a)*sin(b*x + a) + (sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^3*d*cos(b*x + a) + sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(c^10*d^4*cos(b*x + a)*sin(b*x + a))) + 2*sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*arctan(1/2*((sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^8*d^3*cos(b*x + a) - sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*c^5*d^2*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - sqrt(4*sqrt(c^6*d^2/b^4)*b^2*c^7*d^3*cos(b*x + a)*sin(b*x + a) + c^10*d^4 + 2*(sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^8*d^3*sin(b*x + a) + sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*c^5*d^2*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(2*c^5*d^2*cos(b*x + a)*sin(b*x + a) - (sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^3*d*cos(b*x + a) + sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(c^10*d^4*cos(b*x + a)*sin(b*x + a))) - sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*log(4*sqrt(c^6*d^2/b^4)*b^2*c^7*d^3*cos(b*x + a)*sin(b*x + a) + c^10*d^4 + 2*(sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^8*d^3*sin(b*x + a) + sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*c^5*d^2*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) + sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*log(4*sqrt(c^6*d^2/b^4)*b^2*c^7*d^3*cos(b*x + a)*sin(b*x + a) + c^10*d^4 - 2*(sqrt(2)*(c^6*d^2/b^4)^(1/4)*b*c^8*d^3*sin(b*x + a) + sqrt(2)*(c^6*d^2/b^4)^(3/4)*b^3*c^5*d^2*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/b","B",0
272,1,1865,0,78.694434," ","integrate((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} b d^{2} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \arctan\left(\frac{2 \, c^{10} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{4 \, b^{2} c^{7} d^{3} \sqrt{\frac{c^{6}}{b^{4} d^{6}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{10} + 2 \, {\left(\sqrt{2} b^{3} c^{5} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{8} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} b^{3} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + {\left(\sqrt{2} b^{3} c^{5} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{8} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c^{7} d^{3} \cos\left(b x + a\right)^{4} - b^{2} c^{7} d^{3} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{c^{6}}{b^{4} d^{6}}}}{2 \, {\left(2 \, c^{10} \cos\left(b x + a\right)^{3} - c^{10} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) \cos\left(b x + a\right) + 2 \, \sqrt{2} b d^{2} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \arctan\left(-\frac{2 \, c^{10} \cos\left(b x + a\right) \sin\left(b x + a\right) - \sqrt{4 \, b^{2} c^{7} d^{3} \sqrt{\frac{c^{6}}{b^{4} d^{6}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{10} - 2 \, {\left(\sqrt{2} b^{3} c^{5} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{8} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} b^{3} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - {\left(\sqrt{2} b^{3} c^{5} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{8} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c^{7} d^{3} \cos\left(b x + a\right)^{4} - b^{2} c^{7} d^{3} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{c^{6}}{b^{4} d^{6}}}}{2 \, {\left(2 \, c^{10} \cos\left(b x + a\right)^{3} - c^{10} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) \cos\left(b x + a\right) - 2 \, \sqrt{2} b d^{2} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} c^{5} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b c^{8} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + \sqrt{4 \, b^{2} c^{7} d^{3} \sqrt{\frac{c^{6}}{b^{4} d^{6}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{10} - 2 \, {\left(\sqrt{2} b^{3} c^{5} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{8} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(2 \, c^{5} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(\sqrt{2} b^{3} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, c^{10} \cos\left(b x + a\right) \sin\left(b x + a\right)}\right) \cos\left(b x + a\right) - 2 \, \sqrt{2} b d^{2} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} c^{5} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b c^{8} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - \sqrt{4 \, b^{2} c^{7} d^{3} \sqrt{\frac{c^{6}}{b^{4} d^{6}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{10} + 2 \, {\left(\sqrt{2} b^{3} c^{5} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{8} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(2 \, c^{5} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left(\sqrt{2} b^{3} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{3} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, c^{10} \cos\left(b x + a\right) \sin\left(b x + a\right)}\right) \cos\left(b x + a\right) - \sqrt{2} b d^{2} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \log\left(4 \, b^{2} c^{7} d^{3} \sqrt{\frac{c^{6}}{b^{4} d^{6}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{10} + 2 \, {\left(\sqrt{2} b^{3} c^{5} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{8} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) + \sqrt{2} b d^{2} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \log\left(4 \, b^{2} c^{7} d^{3} \sqrt{\frac{c^{6}}{b^{4} d^{6}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{10} - 2 \, {\left(\sqrt{2} b^{3} c^{5} d^{4} \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{8} d \left(\frac{c^{6}}{b^{4} d^{6}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) + 16 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} c}{8 \, b d^{2} \cos\left(b x + a\right)}"," ",0,"1/8*(2*sqrt(2)*b*d^2*(c^6/(b^4*d^6))^(1/4)*arctan(1/2*(2*c^10*cos(b*x + a)*sin(b*x + a) + sqrt(4*b^2*c^7*d^3*sqrt(c^6/(b^4*d^6))*cos(b*x + a)*sin(b*x + a) + c^10 + 2*(sqrt(2)*b^3*c^5*d^4*(c^6/(b^4*d^6))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^8*d*(c^6/(b^4*d^6))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*b^3*d^4*(c^6/(b^4*d^6))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*d*(c^6/(b^4*d^6))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + (sqrt(2)*b^3*c^5*d^4*(c^6/(b^4*d^6))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^8*d*(c^6/(b^4*d^6))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c^7*d^3*cos(b*x + a)^4 - b^2*c^7*d^3*cos(b*x + a)^2)*sqrt(c^6/(b^4*d^6)))/((2*c^10*cos(b*x + a)^3 - c^10*cos(b*x + a))*sin(b*x + a)))*cos(b*x + a) + 2*sqrt(2)*b*d^2*(c^6/(b^4*d^6))^(1/4)*arctan(-1/2*(2*c^10*cos(b*x + a)*sin(b*x + a) - sqrt(4*b^2*c^7*d^3*sqrt(c^6/(b^4*d^6))*cos(b*x + a)*sin(b*x + a) + c^10 - 2*(sqrt(2)*b^3*c^5*d^4*(c^6/(b^4*d^6))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^8*d*(c^6/(b^4*d^6))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*b^3*d^4*(c^6/(b^4*d^6))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*d*(c^6/(b^4*d^6))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - (sqrt(2)*b^3*c^5*d^4*(c^6/(b^4*d^6))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^8*d*(c^6/(b^4*d^6))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c^7*d^3*cos(b*x + a)^4 - b^2*c^7*d^3*cos(b*x + a)^2)*sqrt(c^6/(b^4*d^6)))/((2*c^10*cos(b*x + a)^3 - c^10*cos(b*x + a))*sin(b*x + a)))*cos(b*x + a) - 2*sqrt(2)*b*d^2*(c^6/(b^4*d^6))^(1/4)*arctan(1/2*((sqrt(2)*b^3*c^5*d^4*(c^6/(b^4*d^6))^(3/4)*sin(b*x + a) - sqrt(2)*b*c^8*d*(c^6/(b^4*d^6))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + sqrt(4*b^2*c^7*d^3*sqrt(c^6/(b^4*d^6))*cos(b*x + a)*sin(b*x + a) + c^10 - 2*(sqrt(2)*b^3*c^5*d^4*(c^6/(b^4*d^6))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^8*d*(c^6/(b^4*d^6))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(2*c^5*cos(b*x + a)*sin(b*x + a) + (sqrt(2)*b^3*d^4*(c^6/(b^4*d^6))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*d*(c^6/(b^4*d^6))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(c^10*cos(b*x + a)*sin(b*x + a)))*cos(b*x + a) - 2*sqrt(2)*b*d^2*(c^6/(b^4*d^6))^(1/4)*arctan(1/2*((sqrt(2)*b^3*c^5*d^4*(c^6/(b^4*d^6))^(3/4)*sin(b*x + a) - sqrt(2)*b*c^8*d*(c^6/(b^4*d^6))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - sqrt(4*b^2*c^7*d^3*sqrt(c^6/(b^4*d^6))*cos(b*x + a)*sin(b*x + a) + c^10 + 2*(sqrt(2)*b^3*c^5*d^4*(c^6/(b^4*d^6))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^8*d*(c^6/(b^4*d^6))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(2*c^5*cos(b*x + a)*sin(b*x + a) - (sqrt(2)*b^3*d^4*(c^6/(b^4*d^6))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^3*d*(c^6/(b^4*d^6))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(c^10*cos(b*x + a)*sin(b*x + a)))*cos(b*x + a) - sqrt(2)*b*d^2*(c^6/(b^4*d^6))^(1/4)*cos(b*x + a)*log(4*b^2*c^7*d^3*sqrt(c^6/(b^4*d^6))*cos(b*x + a)*sin(b*x + a) + c^10 + 2*(sqrt(2)*b^3*c^5*d^4*(c^6/(b^4*d^6))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^8*d*(c^6/(b^4*d^6))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) + sqrt(2)*b*d^2*(c^6/(b^4*d^6))^(1/4)*cos(b*x + a)*log(4*b^2*c^7*d^3*sqrt(c^6/(b^4*d^6))*cos(b*x + a)*sin(b*x + a) + c^10 - 2*(sqrt(2)*b^3*c^5*d^4*(c^6/(b^4*d^6))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^8*d*(c^6/(b^4*d^6))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) + 16*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*c)/(b*d^2*cos(b*x + a))","B",0
273,1,50,0,0.994154," ","integrate((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(c \cos\left(b x + a\right)^{2} - c\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}}{5 \, b d^{4} \cos\left(b x + a\right)^{3}}"," ",0,"-2/5*(c*cos(b*x + a)^2 - c)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))/(b*d^4*cos(b*x + a)^3)","A",0
274,1,61,0,1.328422," ","integrate((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(11/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, c \cos\left(b x + a\right)^{4} + c \cos\left(b x + a\right)^{2} - 5 \, c\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}}{45 \, b d^{6} \cos\left(b x + a\right)^{5}}"," ",0,"-2/45*(4*c*cos(b*x + a)^4 + c*cos(b*x + a)^2 - 5*c)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))/(b*d^6*cos(b*x + a)^5)","A",0
275,1,73,0,2.496803," ","integrate((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(15/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(32 \, c \cos\left(b x + a\right)^{6} + 8 \, c \cos\left(b x + a\right)^{4} + 5 \, c \cos\left(b x + a\right)^{2} - 45 \, c\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}}{585 \, b d^{8} \cos\left(b x + a\right)^{7}}"," ",0,"-2/585*(32*c*cos(b*x + a)^6 + 8*c*cos(b*x + a)^4 + 5*c*cos(b*x + a)^2 - 45*c)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))/(b*d^8*cos(b*x + a)^7)","A",0
276,0,0,0,1.844870," ","integrate((d*cos(b*x+a))^(9/2)*(c*sin(b*x+a))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c^{2} d^{4} \cos\left(b x + a\right)^{6} - c^{2} d^{4} \cos\left(b x + a\right)^{4}\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}, x\right)"," ",0,"integral(-(c^2*d^4*cos(b*x + a)^6 - c^2*d^4*cos(b*x + a)^4)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)), x)","F",0
277,0,0,0,1.493684," ","integrate((d*cos(b*x+a))^(5/2)*(c*sin(b*x+a))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c^{2} d^{2} \cos\left(b x + a\right)^{4} - c^{2} d^{2} \cos\left(b x + a\right)^{2}\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}, x\right)"," ",0,"integral(-(c^2*d^2*cos(b*x + a)^4 - c^2*d^2*cos(b*x + a)^2)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)), x)","F",0
278,0,0,0,1.726645," ","integrate((d*cos(b*x+a))^(1/2)*(c*sin(b*x+a))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c^{2} \cos\left(b x + a\right)^{2} - c^{2}\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}, x\right)"," ",0,"integral(-(c^2*cos(b*x + a)^2 - c^2)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)), x)","F",0
279,0,0,0,1.951821," ","integrate((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{2} \cos\left(b x + a\right)^{2} - c^{2}\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}}{d^{2} \cos\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(-(c^2*cos(b*x + a)^2 - c^2)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))/(d^2*cos(b*x + a)^2), x)","F",0
280,0,0,0,0.730865," ","integrate((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{2} \cos\left(b x + a\right)^{2} - c^{2}\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}}{d^{4} \cos\left(b x + a\right)^{4}}, x\right)"," ",0,"integral(-(c^2*cos(b*x + a)^2 - c^2)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))/(d^4*cos(b*x + a)^4), x)","F",0
281,0,0,0,1.454766," ","integrate((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{2} \cos\left(b x + a\right)^{2} - c^{2}\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}}{d^{6} \cos\left(b x + a\right)^{6}}, x\right)"," ",0,"integral(-(c^2*cos(b*x + a)^2 - c^2)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))/(d^6*cos(b*x + a)^6), x)","F",0
282,1,2074,0,166.918951," ","integrate((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(1/2),x, algorithm=""fricas"")","-\frac{32 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} c^{2} \sin\left(b x + a\right) - 12 \, \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b d \arctan\left(\frac{{\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{13} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} c^{8} d \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + \sqrt{4 \, \sqrt{\frac{c^{10}}{b^{4} d^{2}}} b^{2} c^{11} d \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{16} - 2 \, {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{13} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} c^{8} d \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(2 \, c^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{\frac{c^{10}}{b^{4} d^{2}}} b^{2} c^{3} d + {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{5} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} d \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, c^{16} \cos\left(b x + a\right)^{2} - c^{16}}\right) - 12 \, \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b d \arctan\left(\frac{{\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{13} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} c^{8} d \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - \sqrt{4 \, \sqrt{\frac{c^{10}}{b^{4} d^{2}}} b^{2} c^{11} d \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{16} + 2 \, {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{13} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} c^{8} d \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(2 \, c^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{\frac{c^{10}}{b^{4} d^{2}}} b^{2} c^{3} d - {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{5} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} d \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, c^{16} \cos\left(b x + a\right)^{2} - c^{16}}\right) - 12 \, \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b d \arctan\left(-\frac{2 \, c^{16} \cos\left(b x + a\right) \sin\left(b x + a\right) - \sqrt{4 \, \sqrt{\frac{c^{10}}{b^{4} d^{2}}} b^{2} c^{11} d \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{16} + 2 \, {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{13} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} c^{8} d \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{5} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} d \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{13} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} c^{8} d \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c^{11} d \cos\left(b x + a\right)^{4} - b^{2} c^{11} d \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{c^{10}}{b^{4} d^{2}}}}{2 \, {\left(2 \, c^{16} \cos\left(b x + a\right)^{3} - c^{16} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) - 12 \, \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b d \arctan\left(\frac{2 \, c^{16} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{4 \, \sqrt{\frac{c^{10}}{b^{4} d^{2}}} b^{2} c^{11} d \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{16} - 2 \, {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{13} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} c^{8} d \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{5} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} d \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{13} \sin\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} c^{8} d \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c^{11} d \cos\left(b x + a\right)^{4} - b^{2} c^{11} d \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{c^{10}}{b^{4} d^{2}}}}{2 \, {\left(2 \, c^{16} \cos\left(b x + a\right)^{3} - c^{16} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) + 3 \, \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b d \log\left(2916 \, \sqrt{\frac{c^{10}}{b^{4} d^{2}}} b^{2} c^{11} d \cos\left(b x + a\right) \sin\left(b x + a\right) + 729 \, c^{16} + 1458 \, {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{13} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} c^{8} d \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) - 3 \, \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b d \log\left(2916 \, \sqrt{\frac{c^{10}}{b^{4} d^{2}}} b^{2} c^{11} d \cos\left(b x + a\right) \sin\left(b x + a\right) + 729 \, c^{16} - 1458 \, {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{13} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} c^{8} d \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) + 3 \, \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b d \log\left(\frac{729}{4} \, \sqrt{\frac{c^{10}}{b^{4} d^{2}}} b^{2} c^{11} d \cos\left(b x + a\right) \sin\left(b x + a\right) + \frac{729}{16} \, c^{16} + \frac{729}{8} \, {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{13} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} c^{8} d \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) - 3 \, \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b d \log\left(\frac{729}{4} \, \sqrt{\frac{c^{10}}{b^{4} d^{2}}} b^{2} c^{11} d \cos\left(b x + a\right) \sin\left(b x + a\right) + \frac{729}{16} \, c^{16} - \frac{729}{8} \, {\left(\sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{1}{4}} b c^{13} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{c^{10}}{b^{4} d^{2}}\right)^{\frac{3}{4}} b^{3} c^{8} d \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}{64 \, b d}"," ",0,"-1/64*(32*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*c^2*sin(b*x + a) - 12*sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*d*arctan(((sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^13*cos(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*c^8*d*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + sqrt(4*sqrt(c^10/(b^4*d^2))*b^2*c^11*d*cos(b*x + a)*sin(b*x + a) + c^16 - 2*(sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^13*cos(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*c^8*d*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(2*c^8*cos(b*x + a)*sin(b*x + a) + sqrt(c^10/(b^4*d^2))*b^2*c^3*d + (sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^5*sin(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*d*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(2*c^16*cos(b*x + a)^2 - c^16)) - 12*sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*d*arctan(((sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^13*cos(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*c^8*d*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - sqrt(4*sqrt(c^10/(b^4*d^2))*b^2*c^11*d*cos(b*x + a)*sin(b*x + a) + c^16 + 2*(sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^13*cos(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*c^8*d*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(2*c^8*cos(b*x + a)*sin(b*x + a) + sqrt(c^10/(b^4*d^2))*b^2*c^3*d - (sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^5*sin(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*d*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(2*c^16*cos(b*x + a)^2 - c^16)) - 12*sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*d*arctan(-1/2*(2*c^16*cos(b*x + a)*sin(b*x + a) - sqrt(4*sqrt(c^10/(b^4*d^2))*b^2*c^11*d*cos(b*x + a)*sin(b*x + a) + c^16 + 2*(sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^13*cos(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*c^8*d*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^5*sin(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*d*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + (sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^13*sin(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*c^8*d*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c^11*d*cos(b*x + a)^4 - b^2*c^11*d*cos(b*x + a)^2)*sqrt(c^10/(b^4*d^2)))/((2*c^16*cos(b*x + a)^3 - c^16*cos(b*x + a))*sin(b*x + a))) - 12*sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*d*arctan(1/2*(2*c^16*cos(b*x + a)*sin(b*x + a) + sqrt(4*sqrt(c^10/(b^4*d^2))*b^2*c^11*d*cos(b*x + a)*sin(b*x + a) + c^16 - 2*(sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^13*cos(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*c^8*d*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^5*sin(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*d*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - (sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^13*sin(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*c^8*d*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c^11*d*cos(b*x + a)^4 - b^2*c^11*d*cos(b*x + a)^2)*sqrt(c^10/(b^4*d^2)))/((2*c^16*cos(b*x + a)^3 - c^16*cos(b*x + a))*sin(b*x + a))) + 3*sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*d*log(2916*sqrt(c^10/(b^4*d^2))*b^2*c^11*d*cos(b*x + a)*sin(b*x + a) + 729*c^16 + 1458*(sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^13*cos(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*c^8*d*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) - 3*sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*d*log(2916*sqrt(c^10/(b^4*d^2))*b^2*c^11*d*cos(b*x + a)*sin(b*x + a) + 729*c^16 - 1458*(sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^13*cos(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*c^8*d*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) + 3*sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*d*log(729/4*sqrt(c^10/(b^4*d^2))*b^2*c^11*d*cos(b*x + a)*sin(b*x + a) + 729/16*c^16 + 729/8*(sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^13*cos(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*c^8*d*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) - 3*sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*d*log(729/4*sqrt(c^10/(b^4*d^2))*b^2*c^11*d*cos(b*x + a)*sin(b*x + a) + 729/16*c^16 - 729/8*(sqrt(2)*(c^10/(b^4*d^2))^(1/4)*b*c^13*cos(b*x + a) + sqrt(2)*(c^10/(b^4*d^2))^(3/4)*b^3*c^8*d*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(b*d)","B",0
283,1,2268,0,164.465318," ","integrate((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} b d^{3} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(\sqrt{2} b^{3} c^{8} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{13} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - \sqrt{4 \, b^{2} c^{11} d^{5} \sqrt{\frac{c^{10}}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{16} - 2 \, {\left(\sqrt{2} b^{3} c^{8} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{13} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(b^{2} c^{3} d^{5} \sqrt{\frac{c^{10}}{b^{4} d^{10}}} + 2 \, c^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(\sqrt{2} b^{3} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{5} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, c^{16} \cos\left(b x + a\right)^{2} - c^{16}}\right) \cos\left(b x + a\right)^{2} + 12 \, \sqrt{2} b d^{3} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(\sqrt{2} b^{3} c^{8} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{13} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + \sqrt{4 \, b^{2} c^{11} d^{5} \sqrt{\frac{c^{10}}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{16} + 2 \, {\left(\sqrt{2} b^{3} c^{8} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{13} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(b^{2} c^{3} d^{5} \sqrt{\frac{c^{10}}{b^{4} d^{10}}} + 2 \, c^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left(\sqrt{2} b^{3} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{5} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, c^{16} \cos\left(b x + a\right)^{2} - c^{16}}\right) \cos\left(b x + a\right)^{2} - 12 \, \sqrt{2} b d^{3} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \arctan\left(-\frac{2 \, c^{16} \cos\left(b x + a\right) \sin\left(b x + a\right) - \sqrt{4 \, b^{2} c^{11} d^{5} \sqrt{\frac{c^{10}}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{16} + 2 \, {\left(\sqrt{2} b^{3} c^{8} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{13} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} b^{3} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{5} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + {\left(\sqrt{2} b^{3} c^{8} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{13} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c^{11} d^{5} \cos\left(b x + a\right)^{4} - b^{2} c^{11} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{c^{10}}{b^{4} d^{10}}}}{2 \, {\left(2 \, c^{16} \cos\left(b x + a\right)^{3} - c^{16} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) \cos\left(b x + a\right)^{2} - 12 \, \sqrt{2} b d^{3} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \arctan\left(\frac{2 \, c^{16} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{4 \, b^{2} c^{11} d^{5} \sqrt{\frac{c^{10}}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{16} - 2 \, {\left(\sqrt{2} b^{3} c^{8} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{13} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} b^{3} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{5} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - {\left(\sqrt{2} b^{3} c^{8} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b c^{13} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c^{11} d^{5} \cos\left(b x + a\right)^{4} - b^{2} c^{11} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{c^{10}}{b^{4} d^{10}}}}{2 \, {\left(2 \, c^{16} \cos\left(b x + a\right)^{3} - c^{16} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) \cos\left(b x + a\right)^{2} + 3 \, \sqrt{2} b d^{3} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)^{2} \log\left(4 \, b^{2} c^{11} d^{5} \sqrt{\frac{c^{10}}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{16} + 2 \, {\left(\sqrt{2} b^{3} c^{8} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{13} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) - 3 \, \sqrt{2} b d^{3} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)^{2} \log\left(4 \, b^{2} c^{11} d^{5} \sqrt{\frac{c^{10}}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + c^{16} - 2 \, {\left(\sqrt{2} b^{3} c^{8} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{13} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) + 3 \, \sqrt{2} b d^{3} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)^{2} \log\left(\frac{1}{4} \, b^{2} c^{11} d^{5} \sqrt{\frac{c^{10}}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + \frac{1}{16} \, c^{16} + \frac{1}{8} \, {\left(\sqrt{2} b^{3} c^{8} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{13} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) - 3 \, \sqrt{2} b d^{3} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)^{2} \log\left(\frac{1}{4} \, b^{2} c^{11} d^{5} \sqrt{\frac{c^{10}}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + \frac{1}{16} \, c^{16} - \frac{1}{8} \, {\left(\sqrt{2} b^{3} c^{8} d^{7} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b c^{13} d^{2} \left(\frac{c^{10}}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) + 32 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} c^{2} \sin\left(b x + a\right)}{48 \, b d^{3} \cos\left(b x + a\right)^{2}}"," ",0,"1/48*(12*sqrt(2)*b*d^3*(c^10/(b^4*d^10))^(1/4)*arctan(-((sqrt(2)*b^3*c^8*d^7*(c^10/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^13*d^2*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - sqrt(4*b^2*c^11*d^5*sqrt(c^10/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + c^16 - 2*(sqrt(2)*b^3*c^8*d^7*(c^10/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^13*d^2*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(b^2*c^3*d^5*sqrt(c^10/(b^4*d^10)) + 2*c^8*cos(b*x + a)*sin(b*x + a) + (sqrt(2)*b^3*d^7*(c^10/(b^4*d^10))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^5*d^2*(c^10/(b^4*d^10))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(2*c^16*cos(b*x + a)^2 - c^16))*cos(b*x + a)^2 + 12*sqrt(2)*b*d^3*(c^10/(b^4*d^10))^(1/4)*arctan(-((sqrt(2)*b^3*c^8*d^7*(c^10/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^13*d^2*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + sqrt(4*b^2*c^11*d^5*sqrt(c^10/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + c^16 + 2*(sqrt(2)*b^3*c^8*d^7*(c^10/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^13*d^2*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(b^2*c^3*d^5*sqrt(c^10/(b^4*d^10)) + 2*c^8*cos(b*x + a)*sin(b*x + a) - (sqrt(2)*b^3*d^7*(c^10/(b^4*d^10))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^5*d^2*(c^10/(b^4*d^10))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(2*c^16*cos(b*x + a)^2 - c^16))*cos(b*x + a)^2 - 12*sqrt(2)*b*d^3*(c^10/(b^4*d^10))^(1/4)*arctan(-1/2*(2*c^16*cos(b*x + a)*sin(b*x + a) - sqrt(4*b^2*c^11*d^5*sqrt(c^10/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + c^16 + 2*(sqrt(2)*b^3*c^8*d^7*(c^10/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^13*d^2*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*b^3*d^7*(c^10/(b^4*d^10))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^5*d^2*(c^10/(b^4*d^10))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + (sqrt(2)*b^3*c^8*d^7*(c^10/(b^4*d^10))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^13*d^2*(c^10/(b^4*d^10))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c^11*d^5*cos(b*x + a)^4 - b^2*c^11*d^5*cos(b*x + a)^2)*sqrt(c^10/(b^4*d^10)))/((2*c^16*cos(b*x + a)^3 - c^16*cos(b*x + a))*sin(b*x + a)))*cos(b*x + a)^2 - 12*sqrt(2)*b*d^3*(c^10/(b^4*d^10))^(1/4)*arctan(1/2*(2*c^16*cos(b*x + a)*sin(b*x + a) + sqrt(4*b^2*c^11*d^5*sqrt(c^10/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + c^16 - 2*(sqrt(2)*b^3*c^8*d^7*(c^10/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^13*d^2*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*b^3*d^7*(c^10/(b^4*d^10))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^5*d^2*(c^10/(b^4*d^10))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - (sqrt(2)*b^3*c^8*d^7*(c^10/(b^4*d^10))^(3/4)*cos(b*x + a) + sqrt(2)*b*c^13*d^2*(c^10/(b^4*d^10))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c^11*d^5*cos(b*x + a)^4 - b^2*c^11*d^5*cos(b*x + a)^2)*sqrt(c^10/(b^4*d^10)))/((2*c^16*cos(b*x + a)^3 - c^16*cos(b*x + a))*sin(b*x + a)))*cos(b*x + a)^2 + 3*sqrt(2)*b*d^3*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a)^2*log(4*b^2*c^11*d^5*sqrt(c^10/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + c^16 + 2*(sqrt(2)*b^3*c^8*d^7*(c^10/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^13*d^2*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) - 3*sqrt(2)*b*d^3*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a)^2*log(4*b^2*c^11*d^5*sqrt(c^10/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + c^16 - 2*(sqrt(2)*b^3*c^8*d^7*(c^10/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^13*d^2*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) + 3*sqrt(2)*b*d^3*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a)^2*log(1/4*b^2*c^11*d^5*sqrt(c^10/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + 1/16*c^16 + 1/8*(sqrt(2)*b^3*c^8*d^7*(c^10/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^13*d^2*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) - 3*sqrt(2)*b*d^3*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a)^2*log(1/4*b^2*c^11*d^5*sqrt(c^10/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + 1/16*c^16 - 1/8*(sqrt(2)*b^3*c^8*d^7*(c^10/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*c^13*d^2*(c^10/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) + 32*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*c^2*sin(b*x + a))/(b*d^3*cos(b*x + a)^2)","B",0
284,1,60,0,1.464386," ","integrate((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(c^{2} \cos\left(b x + a\right)^{2} - c^{2}\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} \sin\left(b x + a\right)}{7 \, b d^{5} \cos\left(b x + a\right)^{4}}"," ",0,"-2/7*(c^2*cos(b*x + a)^2 - c^2)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*sin(b*x + a)/(b*d^5*cos(b*x + a)^4)","A",0
285,1,74,0,2.011154," ","integrate((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(13/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, c^{2} \cos\left(b x + a\right)^{4} + 3 \, c^{2} \cos\left(b x + a\right)^{2} - 7 \, c^{2}\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} \sin\left(b x + a\right)}{77 \, b d^{7} \cos\left(b x + a\right)^{6}}"," ",0,"-2/77*(4*c^2*cos(b*x + a)^4 + 3*c^2*cos(b*x + a)^2 - 7*c^2)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*sin(b*x + a)/(b*d^7*cos(b*x + a)^6)","A",0
286,1,87,0,2.459141," ","integrate((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(17/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(32 \, c^{2} \cos\left(b x + a\right)^{6} + 24 \, c^{2} \cos\left(b x + a\right)^{4} + 21 \, c^{2} \cos\left(b x + a\right)^{2} - 77 \, c^{2}\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} \sin\left(b x + a\right)}{1155 \, b d^{9} \cos\left(b x + a\right)^{8}}"," ",0,"-2/1155*(32*c^2*cos(b*x + a)^6 + 24*c^2*cos(b*x + a)^4 + 21*c^2*cos(b*x + a)^2 - 77*c^2)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*sin(b*x + a)/(b*d^9*cos(b*x + a)^8)","A",0
287,1,1282,0,71.622334," ","integrate(sin(b*x+a)^(7/2)/cos(b*x+a)^(7/2),x, algorithm=""fricas"")","-\frac{10 \, \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 4 \, {\left(b^{2} \cos\left(b x + a\right)^{4} - b^{2} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{1}{b^{4}}}}{2 \, {\left(2 \, \cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) \cos\left(b x + a\right)^{3} + 10 \, \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 4 \, {\left(b^{2} \cos\left(b x + a\right)^{4} - b^{2} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{1}{b^{4}}}}{2 \, {\left(2 \, \cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) \cos\left(b x + a\right)^{3} + 10 \, \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(-\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} {\left({\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)\right)}}{2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)}\right) \cos\left(b x + a\right)^{3} + 10 \, \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(-\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} {\left({\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)\right)}}{2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)}\right) \cos\left(b x + a\right)^{3} - 5 \, \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)^{3} \log\left(4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1\right) + 5 \, \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)^{3} \log\left(4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1\right) + 16 \, {\left(6 \, \cos\left(b x + a\right)^{2} - 1\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)}}{40 \, b \cos\left(b x + a\right)^{3}}"," ",0,"-1/40*(10*sqrt(2)*b*(b^(-4))^(1/4)*arctan(1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + (sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 2*cos(b*x + a)*sin(b*x + a) - 4*(b^2*cos(b*x + a)^4 - b^2*cos(b*x + a)^2)*sqrt(b^(-4)))/((2*cos(b*x + a)^3 - cos(b*x + a))*sin(b*x + a)))*cos(b*x + a)^3 + 10*sqrt(2)*b*(b^(-4))^(1/4)*arctan(1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + (sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - 2*cos(b*x + a)*sin(b*x + a) + 4*(b^2*cos(b*x + a)^4 - b^2*cos(b*x + a)^2)*sqrt(b^(-4)))/((2*cos(b*x + a)^3 - cos(b*x + a))*sin(b*x + a)))*cos(b*x + a)^3 + 10*sqrt(2)*b*(b^(-4))^(1/4)*arctan(-1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) - sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 2*cos(b*x + a)*sin(b*x + a)))/(cos(b*x + a)*sin(b*x + a)))*cos(b*x + a)^3 + 10*sqrt(2)*b*(b^(-4))^(1/4)*arctan(-1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) - sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - 2*cos(b*x + a)*sin(b*x + a)))/(cos(b*x + a)*sin(b*x + a)))*cos(b*x + a)^3 - 5*sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a)^3*log(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1) + 5*sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a)^3*log(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1) + 16*(6*cos(b*x + a)^2 - 1)*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)))/(b*cos(b*x + a)^3)","B",0
288,1,16,0,1.038755," ","integrate(sin(x)^(3/2)/cos(x)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(\cos\left(x\right)^{2} - 1\right)} \sqrt{\sin\left(x\right)}}{5 \, \cos\left(x\right)^{\frac{5}{2}}}"," ",0,"-2/5*(cos(x)^2 - 1)*sqrt(sin(x))/cos(x)^(5/2)","A",0
289,1,447,0,1.724922," ","integrate(sin(x)^(1/2)/cos(x)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{2 \, \cos\left(x\right)^{3} - 2 \, \cos\left(x\right)^{2} \sin\left(x\right) + \sqrt{2} \sqrt{2 \, {\left(\sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(x\right)\right)} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + 4 \, \cos\left(x\right) \sin\left(x\right) + 1} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} - \sqrt{2} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} - 2 \, \cos\left(x\right)}{2 \, {\left(\cos\left(x\right)^{3} + \cos\left(x\right)^{2} \sin\left(x\right) - \cos\left(x\right)\right)}}\right) + \frac{1}{4} \, \sqrt{2} \arctan\left(-\frac{2 \, \cos\left(x\right)^{3} - 2 \, \cos\left(x\right)^{2} \sin\left(x\right) - \sqrt{2} \sqrt{-2 \, {\left(\sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(x\right)\right)} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + 4 \, \cos\left(x\right) \sin\left(x\right) + 1} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + \sqrt{2} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} - 2 \, \cos\left(x\right)}{2 \, {\left(\cos\left(x\right)^{3} + \cos\left(x\right)^{2} \sin\left(x\right) - \cos\left(x\right)\right)}}\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(-\frac{\sqrt{-2 \, {\left(\sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(x\right)\right)} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + 4 \, \cos\left(x\right) \sin\left(x\right) + 1} {\left(\sqrt{2} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + \cos\left(x\right) + \sin\left(x\right)\right)} + \sqrt{2} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)}}{\cos\left(x\right) - \sin\left(x\right)}\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(-\frac{\sqrt{2 \, {\left(\sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(x\right)\right)} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + 4 \, \cos\left(x\right) \sin\left(x\right) + 1} {\left(\sqrt{2} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} - \cos\left(x\right) - \sin\left(x\right)\right)} + \sqrt{2} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)}}{\cos\left(x\right) - \sin\left(x\right)}\right) - \frac{1}{8} \, \sqrt{2} \log\left(2 \, {\left(\sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(x\right)\right)} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + 4 \, \cos\left(x\right) \sin\left(x\right) + 1\right) + \frac{1}{8} \, \sqrt{2} \log\left(-2 \, {\left(\sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(x\right)\right)} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + 4 \, \cos\left(x\right) \sin\left(x\right) + 1\right)"," ",0,"1/4*sqrt(2)*arctan(1/2*(2*cos(x)^3 - 2*cos(x)^2*sin(x) + sqrt(2)*sqrt(2*(sqrt(2)*cos(x) + sqrt(2)*sin(x))*sqrt(cos(x))*sqrt(sin(x)) + 4*cos(x)*sin(x) + 1)*sqrt(cos(x))*sqrt(sin(x)) - sqrt(2)*sqrt(cos(x))*sqrt(sin(x)) - 2*cos(x))/(cos(x)^3 + cos(x)^2*sin(x) - cos(x))) + 1/4*sqrt(2)*arctan(-1/2*(2*cos(x)^3 - 2*cos(x)^2*sin(x) - sqrt(2)*sqrt(-2*(sqrt(2)*cos(x) + sqrt(2)*sin(x))*sqrt(cos(x))*sqrt(sin(x)) + 4*cos(x)*sin(x) + 1)*sqrt(cos(x))*sqrt(sin(x)) + sqrt(2)*sqrt(cos(x))*sqrt(sin(x)) - 2*cos(x))/(cos(x)^3 + cos(x)^2*sin(x) - cos(x))) - 1/4*sqrt(2)*arctan(-(sqrt(-2*(sqrt(2)*cos(x) + sqrt(2)*sin(x))*sqrt(cos(x))*sqrt(sin(x)) + 4*cos(x)*sin(x) + 1)*(sqrt(2)*sqrt(cos(x))*sqrt(sin(x)) + cos(x) + sin(x)) + sqrt(2)*sqrt(cos(x))*sqrt(sin(x)))/(cos(x) - sin(x))) - 1/4*sqrt(2)*arctan(-(sqrt(2*(sqrt(2)*cos(x) + sqrt(2)*sin(x))*sqrt(cos(x))*sqrt(sin(x)) + 4*cos(x)*sin(x) + 1)*(sqrt(2)*sqrt(cos(x))*sqrt(sin(x)) - cos(x) - sin(x)) + sqrt(2)*sqrt(cos(x))*sqrt(sin(x)))/(cos(x) - sin(x))) - 1/8*sqrt(2)*log(2*(sqrt(2)*cos(x) + sqrt(2)*sin(x))*sqrt(cos(x))*sqrt(sin(x)) + 4*cos(x)*sin(x) + 1) + 1/8*sqrt(2)*log(-2*(sqrt(2)*cos(x) + sqrt(2)*sin(x))*sqrt(cos(x))*sqrt(sin(x)) + 4*cos(x)*sin(x) + 1)","B",0
290,1,457,0,1.953236," ","integrate(sin(x)^(5/2)/cos(x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{\cos\left(x\right)} \sin\left(x\right)^{\frac{3}{2}} + \frac{3}{16} \, \sqrt{2} \arctan\left(\frac{2 \, \cos\left(x\right)^{3} - 2 \, \cos\left(x\right)^{2} \sin\left(x\right) + \sqrt{2} \sqrt{2 \, {\left(\sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(x\right)\right)} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + 4 \, \cos\left(x\right) \sin\left(x\right) + 1} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} - \sqrt{2} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} - 2 \, \cos\left(x\right)}{2 \, {\left(\cos\left(x\right)^{3} + \cos\left(x\right)^{2} \sin\left(x\right) - \cos\left(x\right)\right)}}\right) + \frac{3}{16} \, \sqrt{2} \arctan\left(-\frac{2 \, \cos\left(x\right)^{3} - 2 \, \cos\left(x\right)^{2} \sin\left(x\right) - \sqrt{2} \sqrt{-2 \, {\left(\sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(x\right)\right)} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + 4 \, \cos\left(x\right) \sin\left(x\right) + 1} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + \sqrt{2} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} - 2 \, \cos\left(x\right)}{2 \, {\left(\cos\left(x\right)^{3} + \cos\left(x\right)^{2} \sin\left(x\right) - \cos\left(x\right)\right)}}\right) - \frac{3}{16} \, \sqrt{2} \arctan\left(-\frac{\sqrt{-2 \, {\left(\sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(x\right)\right)} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + 4 \, \cos\left(x\right) \sin\left(x\right) + 1} {\left(\sqrt{2} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + \cos\left(x\right) + \sin\left(x\right)\right)} + \sqrt{2} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)}}{\cos\left(x\right) - \sin\left(x\right)}\right) - \frac{3}{16} \, \sqrt{2} \arctan\left(-\frac{\sqrt{2 \, {\left(\sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(x\right)\right)} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + 4 \, \cos\left(x\right) \sin\left(x\right) + 1} {\left(\sqrt{2} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} - \cos\left(x\right) - \sin\left(x\right)\right)} + \sqrt{2} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)}}{\cos\left(x\right) - \sin\left(x\right)}\right) - \frac{3}{32} \, \sqrt{2} \log\left(2 \, {\left(\sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(x\right)\right)} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + 4 \, \cos\left(x\right) \sin\left(x\right) + 1\right) + \frac{3}{32} \, \sqrt{2} \log\left(-2 \, {\left(\sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(x\right)\right)} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)} + 4 \, \cos\left(x\right) \sin\left(x\right) + 1\right)"," ",0,"-1/2*sqrt(cos(x))*sin(x)^(3/2) + 3/16*sqrt(2)*arctan(1/2*(2*cos(x)^3 - 2*cos(x)^2*sin(x) + sqrt(2)*sqrt(2*(sqrt(2)*cos(x) + sqrt(2)*sin(x))*sqrt(cos(x))*sqrt(sin(x)) + 4*cos(x)*sin(x) + 1)*sqrt(cos(x))*sqrt(sin(x)) - sqrt(2)*sqrt(cos(x))*sqrt(sin(x)) - 2*cos(x))/(cos(x)^3 + cos(x)^2*sin(x) - cos(x))) + 3/16*sqrt(2)*arctan(-1/2*(2*cos(x)^3 - 2*cos(x)^2*sin(x) - sqrt(2)*sqrt(-2*(sqrt(2)*cos(x) + sqrt(2)*sin(x))*sqrt(cos(x))*sqrt(sin(x)) + 4*cos(x)*sin(x) + 1)*sqrt(cos(x))*sqrt(sin(x)) + sqrt(2)*sqrt(cos(x))*sqrt(sin(x)) - 2*cos(x))/(cos(x)^3 + cos(x)^2*sin(x) - cos(x))) - 3/16*sqrt(2)*arctan(-(sqrt(-2*(sqrt(2)*cos(x) + sqrt(2)*sin(x))*sqrt(cos(x))*sqrt(sin(x)) + 4*cos(x)*sin(x) + 1)*(sqrt(2)*sqrt(cos(x))*sqrt(sin(x)) + cos(x) + sin(x)) + sqrt(2)*sqrt(cos(x))*sqrt(sin(x)))/(cos(x) - sin(x))) - 3/16*sqrt(2)*arctan(-(sqrt(2*(sqrt(2)*cos(x) + sqrt(2)*sin(x))*sqrt(cos(x))*sqrt(sin(x)) + 4*cos(x)*sin(x) + 1)*(sqrt(2)*sqrt(cos(x))*sqrt(sin(x)) - cos(x) - sin(x)) + sqrt(2)*sqrt(cos(x))*sqrt(sin(x)))/(cos(x) - sin(x))) - 3/32*sqrt(2)*log(2*(sqrt(2)*cos(x) + sqrt(2)*sin(x))*sqrt(cos(x))*sqrt(sin(x)) + 4*cos(x)*sin(x) + 1) + 3/32*sqrt(2)*log(-2*(sqrt(2)*cos(x) + sqrt(2)*sin(x))*sqrt(cos(x))*sqrt(sin(x)) + 4*cos(x)*sin(x) + 1)","B",0
291,0,0,0,1.077644," ","integrate((d*cos(b*x+a))^(7/2)/(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} d^{3} \cos\left(b x + a\right)^{3}}{c \sin\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*d^3*cos(b*x + a)^3/(c*sin(b*x + a)), x)","F",0
292,0,0,0,1.170174," ","integrate((d*cos(b*x+a))^(3/2)/(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} d \cos\left(b x + a\right)}{c \sin\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))*d*cos(b*x + a)/(c*sin(b*x + a)), x)","F",0
293,0,0,0,1.229022," ","integrate(1/(d*cos(b*x+a))^(1/2)/(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}}{c d \cos\left(b x + a\right) \sin\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))/(c*d*cos(b*x + a)*sin(b*x + a)), x)","F",0
294,0,0,0,1.145895," ","integrate(1/(d*cos(b*x+a))^(5/2)/(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}}{c d^{3} \cos\left(b x + a\right)^{3} \sin\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))/(c*d^3*cos(b*x + a)^3*sin(b*x + a)), x)","F",0
295,0,0,0,1.091266," ","integrate(1/(d*cos(b*x+a))^(9/2)/(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}}{c d^{5} \cos\left(b x + a\right)^{5} \sin\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))/(c*d^5*cos(b*x + a)^5*sin(b*x + a)), x)","F",0
296,1,1697,0,71.971043," ","integrate((d*cos(b*x+a))^(1/2)/(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{2 \, d^{4} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{4 \, b^{2} c d^{3} \sqrt{\frac{d^{2}}{b^{4} c^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{4} + 2 \, {\left(\sqrt{2} b^{3} c d^{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b d^{3} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} b^{3} c \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + {\left(\sqrt{2} b^{3} c d^{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{3} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c d^{3} \cos\left(b x + a\right)^{4} - b^{2} c d^{3} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d^{2}}{b^{4} c^{2}}}}{2 \, {\left(2 \, d^{4} \cos\left(b x + a\right)^{3} - d^{4} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \arctan\left(-\frac{2 \, d^{4} \cos\left(b x + a\right) \sin\left(b x + a\right) - \sqrt{4 \, b^{2} c d^{3} \sqrt{\frac{d^{2}}{b^{4} c^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{4} - 2 \, {\left(\sqrt{2} b^{3} c d^{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b d^{3} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(\sqrt{2} b^{3} c \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - {\left(\sqrt{2} b^{3} c d^{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{3} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - 4 \, {\left(b^{2} c d^{3} \cos\left(b x + a\right)^{4} - b^{2} c d^{3} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d^{2}}{b^{4} c^{2}}}}{2 \, {\left(2 \, d^{4} \cos\left(b x + a\right)^{3} - d^{4} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(\sqrt{2} b^{3} c d^{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b d^{3} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} - \sqrt{4 \, b^{2} c d^{3} \sqrt{\frac{d^{2}}{b^{4} c^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{4} - 2 \, {\left(\sqrt{2} b^{3} c d^{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b d^{3} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(2 \, d^{2} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(\sqrt{2} b^{3} c \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, d^{4} \cos\left(b x + a\right) \sin\left(b x + a\right)}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(\sqrt{2} b^{3} c d^{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b d^{3} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)} + \sqrt{4 \, b^{2} c d^{3} \sqrt{\frac{d^{2}}{b^{4} c^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{4} + 2 \, {\left(\sqrt{2} b^{3} c d^{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b d^{3} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}} {\left(2 \, d^{2} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left(\sqrt{2} b^{3} c \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)}}{2 \, d^{4} \cos\left(b x + a\right) \sin\left(b x + a\right)}\right) + \frac{1}{8} \, \sqrt{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \log\left(4 \, b^{2} c d^{3} \sqrt{\frac{d^{2}}{b^{4} c^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{4} + 2 \, {\left(\sqrt{2} b^{3} c d^{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b d^{3} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right) - \frac{1}{8} \, \sqrt{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \log\left(4 \, b^{2} c d^{3} \sqrt{\frac{d^{2}}{b^{4} c^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{4} - 2 \, {\left(\sqrt{2} b^{3} c d^{2} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b d^{3} \left(\frac{d^{2}}{b^{4} c^{2}}\right)^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}\right)"," ",0,"-1/4*sqrt(2)*(d^2/(b^4*c^2))^(1/4)*arctan(1/2*(2*d^4*cos(b*x + a)*sin(b*x + a) + sqrt(4*b^2*c*d^3*sqrt(d^2/(b^4*c^2))*cos(b*x + a)*sin(b*x + a) + d^4 + 2*(sqrt(2)*b^3*c*d^2*(d^2/(b^4*c^2))^(3/4)*cos(b*x + a) + sqrt(2)*b*d^3*(d^2/(b^4*c^2))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*b^3*c*(d^2/(b^4*c^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*d*(d^2/(b^4*c^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + (sqrt(2)*b^3*c*d^2*(d^2/(b^4*c^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^3*(d^2/(b^4*c^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c*d^3*cos(b*x + a)^4 - b^2*c*d^3*cos(b*x + a)^2)*sqrt(d^2/(b^4*c^2)))/((2*d^4*cos(b*x + a)^3 - d^4*cos(b*x + a))*sin(b*x + a))) - 1/4*sqrt(2)*(d^2/(b^4*c^2))^(1/4)*arctan(-1/2*(2*d^4*cos(b*x + a)*sin(b*x + a) - sqrt(4*b^2*c*d^3*sqrt(d^2/(b^4*c^2))*cos(b*x + a)*sin(b*x + a) + d^4 - 2*(sqrt(2)*b^3*c*d^2*(d^2/(b^4*c^2))^(3/4)*cos(b*x + a) + sqrt(2)*b*d^3*(d^2/(b^4*c^2))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(sqrt(2)*b^3*c*(d^2/(b^4*c^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*d*(d^2/(b^4*c^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - (sqrt(2)*b^3*c*d^2*(d^2/(b^4*c^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^3*(d^2/(b^4*c^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - 4*(b^2*c*d^3*cos(b*x + a)^4 - b^2*c*d^3*cos(b*x + a)^2)*sqrt(d^2/(b^4*c^2)))/((2*d^4*cos(b*x + a)^3 - d^4*cos(b*x + a))*sin(b*x + a))) - 1/4*sqrt(2)*(d^2/(b^4*c^2))^(1/4)*arctan(-1/2*((sqrt(2)*b^3*c*d^2*(d^2/(b^4*c^2))^(3/4)*sin(b*x + a) - sqrt(2)*b*d^3*(d^2/(b^4*c^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) - sqrt(4*b^2*c*d^3*sqrt(d^2/(b^4*c^2))*cos(b*x + a)*sin(b*x + a) + d^4 - 2*(sqrt(2)*b^3*c*d^2*(d^2/(b^4*c^2))^(3/4)*cos(b*x + a) + sqrt(2)*b*d^3*(d^2/(b^4*c^2))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(2*d^2*cos(b*x + a)*sin(b*x + a) + (sqrt(2)*b^3*c*(d^2/(b^4*c^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*d*(d^2/(b^4*c^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(d^4*cos(b*x + a)*sin(b*x + a))) - 1/4*sqrt(2)*(d^2/(b^4*c^2))^(1/4)*arctan(-1/2*((sqrt(2)*b^3*c*d^2*(d^2/(b^4*c^2))^(3/4)*sin(b*x + a) - sqrt(2)*b*d^3*(d^2/(b^4*c^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)) + sqrt(4*b^2*c*d^3*sqrt(d^2/(b^4*c^2))*cos(b*x + a)*sin(b*x + a) + d^4 + 2*(sqrt(2)*b^3*c*d^2*(d^2/(b^4*c^2))^(3/4)*cos(b*x + a) + sqrt(2)*b*d^3*(d^2/(b^4*c^2))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))*(2*d^2*cos(b*x + a)*sin(b*x + a) - (sqrt(2)*b^3*c*(d^2/(b^4*c^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*d*(d^2/(b^4*c^2))^(1/4)*cos(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))))/(d^4*cos(b*x + a)*sin(b*x + a))) + 1/8*sqrt(2)*(d^2/(b^4*c^2))^(1/4)*log(4*b^2*c*d^3*sqrt(d^2/(b^4*c^2))*cos(b*x + a)*sin(b*x + a) + d^4 + 2*(sqrt(2)*b^3*c*d^2*(d^2/(b^4*c^2))^(3/4)*cos(b*x + a) + sqrt(2)*b*d^3*(d^2/(b^4*c^2))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))) - 1/8*sqrt(2)*(d^2/(b^4*c^2))^(1/4)*log(4*b^2*c*d^3*sqrt(d^2/(b^4*c^2))*cos(b*x + a)*sin(b*x + a) + d^4 - 2*(sqrt(2)*b^3*c*d^2*(d^2/(b^4*c^2))^(3/4)*cos(b*x + a) + sqrt(2)*b*d^3*(d^2/(b^4*c^2))^(1/4)*sin(b*x + a))*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a)))","B",0
297,1,39,0,1.125072," ","integrate(1/(d*cos(b*x+a))^(3/2)/(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}}{b c d^{2} \cos\left(b x + a\right)}"," ",0,"2*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))/(b*c*d^2*cos(b*x + a))","A",0
298,1,51,0,1.183852," ","integrate(1/(d*cos(b*x+a))^(7/2)/(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{d \cos\left(b x + a\right)} {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sqrt{c \sin\left(b x + a\right)}}{5 \, b c d^{4} \cos\left(b x + a\right)^{3}}"," ",0,"2/5*sqrt(d*cos(b*x + a))*(4*cos(b*x + a)^2 + 1)*sqrt(c*sin(b*x + a))/(b*c*d^4*cos(b*x + a)^3)","A",0
299,1,61,0,1.310376," ","integrate(1/(d*cos(b*x+a))^(11/2)/(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(32 \, \cos\left(b x + a\right)^{4} + 8 \, \cos\left(b x + a\right)^{2} + 5\right)} \sqrt{d \cos\left(b x + a\right)} \sqrt{c \sin\left(b x + a\right)}}{45 \, b c d^{6} \cos\left(b x + a\right)^{5}}"," ",0,"2/45*(32*cos(b*x + a)^4 + 8*cos(b*x + a)^2 + 5)*sqrt(d*cos(b*x + a))*sqrt(c*sin(b*x + a))/(b*c*d^6*cos(b*x + a)^5)","A",0
300,1,1185,0,71.469106," ","integrate(cos(b*x+a)^(1/2)/sin(b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 4 \, {\left(b^{2} \cos\left(b x + a\right)^{4} - b^{2} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{1}{b^{4}}}}{2 \, {\left(2 \, \cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) - \frac{1}{4} \, \sqrt{2} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 4 \, {\left(b^{2} \cos\left(b x + a\right)^{4} - b^{2} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{1}{b^{4}}}}{2 \, {\left(2 \, \cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) - \frac{1}{4} \, \sqrt{2} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(-\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} {\left({\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)\right)}}{2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)}\right) - \frac{1}{4} \, \sqrt{2} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(-\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} {\left({\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)\right)}}{2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)}\right) + \frac{1}{8} \, \sqrt{2} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1\right) - \frac{1}{8} \, \sqrt{2} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1\right)"," ",0,"-1/4*sqrt(2)*(b^(-4))^(1/4)*arctan(1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + (sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 2*cos(b*x + a)*sin(b*x + a) - 4*(b^2*cos(b*x + a)^4 - b^2*cos(b*x + a)^2)*sqrt(b^(-4)))/((2*cos(b*x + a)^3 - cos(b*x + a))*sin(b*x + a))) - 1/4*sqrt(2)*(b^(-4))^(1/4)*arctan(1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + (sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - 2*cos(b*x + a)*sin(b*x + a) + 4*(b^2*cos(b*x + a)^4 - b^2*cos(b*x + a)^2)*sqrt(b^(-4)))/((2*cos(b*x + a)^3 - cos(b*x + a))*sin(b*x + a))) - 1/4*sqrt(2)*(b^(-4))^(1/4)*arctan(-1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) - sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 2*cos(b*x + a)*sin(b*x + a)))/(cos(b*x + a)*sin(b*x + a))) - 1/4*sqrt(2)*(b^(-4))^(1/4)*arctan(-1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) - sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - 2*cos(b*x + a)*sin(b*x + a)))/(cos(b*x + a)*sin(b*x + a))) + 1/8*sqrt(2)*(b^(-4))^(1/4)*log(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1) - 1/8*sqrt(2)*(b^(-4))^(1/4)*log(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)","B",0
301,1,1545,0,151.728233," ","integrate(cos(b*x+a)^(3/2)/sin(b*x+a)^(3/2),x, algorithm=""fricas"")","\frac{4 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(-\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} {\left(b^{2} \sqrt{\frac{1}{b^{4}}} + {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)\right)}}{2 \, \cos\left(b x + a\right)^{2} - 1}\right) + 4 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(-\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} {\left(b^{2} \sqrt{\frac{1}{b^{4}}} - {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)\right)}}{2 \, \cos\left(b x + a\right)^{2} - 1}\right) - 4 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 4 \, {\left(b^{2} \cos\left(b x + a\right)^{4} - b^{2} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{1}{b^{4}}}}{2 \, {\left(2 \, \cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) - 4 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 4 \, {\left(b^{2} \cos\left(b x + a\right)^{4} - b^{2} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{1}{b^{4}}}}{2 \, {\left(2 \, \cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) + {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1\right) - {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1\right) + {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(\frac{1}{4} \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + \frac{1}{8} \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + \frac{1}{16}\right) - {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(\frac{1}{4} \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - \frac{1}{8} \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + \frac{1}{16}\right) + 32 \, \sqrt{\cos\left(b x + a\right)} \sin\left(b x + a\right)^{\frac{3}{2}}}{16 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"1/16*(4*(sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*arctan(-((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*(b^2*sqrt(b^(-4)) + (sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 2*cos(b*x + a)*sin(b*x + a)))/(2*cos(b*x + a)^2 - 1)) + 4*(sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*arctan(-((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*(b^2*sqrt(b^(-4)) - (sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 2*cos(b*x + a)*sin(b*x + a)))/(2*cos(b*x + a)^2 - 1)) - 4*(sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*arctan(1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - (sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - 2*cos(b*x + a)*sin(b*x + a) + 4*(b^2*cos(b*x + a)^4 - b^2*cos(b*x + a)^2)*sqrt(b^(-4)))/((2*cos(b*x + a)^3 - cos(b*x + a))*sin(b*x + a))) - 4*(sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*arctan(1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - (sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 2*cos(b*x + a)*sin(b*x + a) - 4*(b^2*cos(b*x + a)^4 - b^2*cos(b*x + a)^2)*sqrt(b^(-4)))/((2*cos(b*x + a)^3 - cos(b*x + a))*sin(b*x + a))) + (sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*log(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1) - (sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*log(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1) + (sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*log(1/4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 1/8*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1/16) - (sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*log(1/4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 1/8*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1/16) + 32*sqrt(cos(b*x + a))*sin(b*x + a)^(3/2))/(b*cos(b*x + a)^2 - b)","B",0
302,1,1321,0,64.418275," ","integrate(cos(b*x+a)^(5/2)/sin(b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{6 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 4 \, {\left(b^{2} \cos\left(b x + a\right)^{4} - b^{2} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{1}{b^{4}}}}{2 \, {\left(2 \, \cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) + 6 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 4 \, {\left(b^{2} \cos\left(b x + a\right)^{4} - b^{2} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{1}{b^{4}}}}{2 \, {\left(2 \, \cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) - 6 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} {\left({\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)\right)}}{2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)}\right) - 6 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} {\left({\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)\right)}}{2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)}\right) - 3 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1\right) + 3 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{2} - \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1\right) + 16 \, \cos\left(b x + a\right)^{\frac{3}{2}} \sqrt{\sin\left(b x + a\right)}}{24 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"1/24*(6*(sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*arctan(1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + (sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 2*cos(b*x + a)*sin(b*x + a) - 4*(b^2*cos(b*x + a)^4 - b^2*cos(b*x + a)^2)*sqrt(b^(-4)))/((2*cos(b*x + a)^3 - cos(b*x + a))*sin(b*x + a))) + 6*(sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*arctan(1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + (sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - 2*cos(b*x + a)*sin(b*x + a) + 4*(b^2*cos(b*x + a)^4 - b^2*cos(b*x + a)^2)*sqrt(b^(-4)))/((2*cos(b*x + a)^3 - cos(b*x + a))*sin(b*x + a))) - 6*(sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*arctan(1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) - sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 2*cos(b*x + a)*sin(b*x + a)))/(cos(b*x + a)*sin(b*x + a))) - 6*(sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*arctan(1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) - sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - 2*cos(b*x + a)*sin(b*x + a)))/(cos(b*x + a)*sin(b*x + a))) - 3*(sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*log(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1) + 3*(sqrt(2)*b*cos(b*x + a)^2 - sqrt(2)*b)*(b^(-4))^(1/4)*log(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1) + 16*cos(b*x + a)^(3/2)*sqrt(sin(b*x + a)))/(b*cos(b*x + a)^2 - b)","B",0
303,1,1670,0,125.690711," ","integrate(cos(b*x+a)^(7/2)/sin(b*x+a)^(7/2),x, algorithm=""fricas"")","-\frac{32 \, {\left(6 \, \cos\left(b x + a\right)^{2} - 5\right)} \sqrt{\cos\left(b x + a\right)} \sin\left(b x + a\right)^{\frac{3}{2}} - 20 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{4} - 2 \, \sqrt{2} b \cos\left(b x + a\right)^{2} + \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} {\left(b^{2} \sqrt{\frac{1}{b^{4}}} + {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)\right)}}{2 \, \cos\left(b x + a\right)^{2} - 1}\right) - 20 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{4} - 2 \, \sqrt{2} b \cos\left(b x + a\right)^{2} + \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} {\left(b^{2} \sqrt{\frac{1}{b^{4}}} - {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)\right)}}{2 \, \cos\left(b x + a\right)^{2} - 1}\right) - 20 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{4} - 2 \, \sqrt{2} b \cos\left(b x + a\right)^{2} + \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 4 \, {\left(b^{2} \cos\left(b x + a\right)^{4} - b^{2} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{1}{b^{4}}}}{2 \, {\left(2 \, \cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) - 20 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{4} - 2 \, \sqrt{2} b \cos\left(b x + a\right)^{2} + \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} - {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \cos\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \sin\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 4 \, {\left(b^{2} \cos\left(b x + a\right)^{4} - b^{2} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{1}{b^{4}}}}{2 \, {\left(2 \, \cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}\right) + 5 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{4} - 2 \, \sqrt{2} b \cos\left(b x + a\right)^{2} + \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1\right) - 5 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{4} - 2 \, \sqrt{2} b \cos\left(b x + a\right)^{2} + \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(4 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + 1\right) + 5 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{4} - 2 \, \sqrt{2} b \cos\left(b x + a\right)^{2} + \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(\frac{1}{4} \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + \frac{1}{8} \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + \frac{1}{16}\right) - 5 \, {\left(\sqrt{2} b \cos\left(b x + a\right)^{4} - 2 \, \sqrt{2} b \cos\left(b x + a\right)^{2} + \sqrt{2} b\right)} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(\frac{1}{4} \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - \frac{1}{8} \, {\left(\sqrt{2} b^{3} \frac{1}{b^{4}}^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \frac{1}{b^{4}}^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right)} \sqrt{\sin\left(b x + a\right)} + \frac{1}{16}\right)}{80 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)}}"," ",0,"-1/80*(32*(6*cos(b*x + a)^2 - 5)*sqrt(cos(b*x + a))*sin(b*x + a)^(3/2) - 20*(sqrt(2)*b*cos(b*x + a)^4 - 2*sqrt(2)*b*cos(b*x + a)^2 + sqrt(2)*b)*(b^(-4))^(1/4)*arctan(((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*(b^2*sqrt(b^(-4)) + (sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 2*cos(b*x + a)*sin(b*x + a)))/(2*cos(b*x + a)^2 - 1)) - 20*(sqrt(2)*b*cos(b*x + a)^4 - 2*sqrt(2)*b*cos(b*x + a)^2 + sqrt(2)*b)*(b^(-4))^(1/4)*arctan(((sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*(b^2*sqrt(b^(-4)) - (sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 2*cos(b*x + a)*sin(b*x + a)))/(2*cos(b*x + a)^2 - 1)) - 20*(sqrt(2)*b*cos(b*x + a)^4 - 2*sqrt(2)*b*cos(b*x + a)^2 + sqrt(2)*b)*(b^(-4))^(1/4)*arctan(1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - (sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - 2*cos(b*x + a)*sin(b*x + a) + 4*(b^2*cos(b*x + a)^4 - b^2*cos(b*x + a)^2)*sqrt(b^(-4)))/((2*cos(b*x + a)^3 - cos(b*x + a))*sin(b*x + a))) - 20*(sqrt(2)*b*cos(b*x + a)^4 - 2*sqrt(2)*b*cos(b*x + a)^2 + sqrt(2)*b)*(b^(-4))^(1/4)*arctan(1/2*((sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1)*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) - (sqrt(2)*b^3*(b^(-4))^(3/4)*cos(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*sin(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 2*cos(b*x + a)*sin(b*x + a) - 4*(b^2*cos(b*x + a)^4 - b^2*cos(b*x + a)^2)*sqrt(b^(-4)))/((2*cos(b*x + a)^3 - cos(b*x + a))*sin(b*x + a))) + 5*(sqrt(2)*b*cos(b*x + a)^4 - 2*sqrt(2)*b*cos(b*x + a)^2 + sqrt(2)*b)*(b^(-4))^(1/4)*log(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1) - 5*(sqrt(2)*b*cos(b*x + a)^4 - 2*sqrt(2)*b*cos(b*x + a)^2 + sqrt(2)*b)*(b^(-4))^(1/4)*log(4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1) + 5*(sqrt(2)*b*cos(b*x + a)^4 - 2*sqrt(2)*b*cos(b*x + a)^2 + sqrt(2)*b)*(b^(-4))^(1/4)*log(1/4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) + 1/8*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1/16) - 5*(sqrt(2)*b*cos(b*x + a)^4 - 2*sqrt(2)*b*cos(b*x + a)^2 + sqrt(2)*b)*(b^(-4))^(1/4)*log(1/4*b^2*sqrt(b^(-4))*cos(b*x + a)*sin(b*x + a) - 1/8*(sqrt(2)*b^3*(b^(-4))^(3/4)*sin(b*x + a) + sqrt(2)*b*(b^(-4))^(1/4)*cos(b*x + a))*sqrt(cos(b*x + a))*sqrt(sin(b*x + a)) + 1/16))/(b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)","B",0
304,0,0,0,0.989838," ","integrate(cos(f*x+e)^4*(b*sin(f*x+e))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}} \cos\left(f x + e\right)^{4}, x\right)"," ",0,"integral((b*sin(f*x + e))^(1/3)*cos(f*x + e)^4, x)","F",0
305,0,0,0,0.988391," ","integrate(cos(f*x+e)^2*(b*sin(f*x+e))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}} \cos\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*sin(f*x + e))^(1/3)*cos(f*x + e)^2, x)","F",0
306,0,0,0,1.208542," ","integrate((b*sin(f*x+e))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((b*sin(f*x + e))^(1/3), x)","F",0
307,0,0,0,1.182360," ","integrate(sec(f*x+e)^2*(b*sin(f*x+e))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}} \sec\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*sin(f*x + e))^(1/3)*sec(f*x + e)^2, x)","F",0
308,0,0,0,1.087291," ","integrate(sec(f*x+e)^4*(b*sin(f*x+e))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}} \sec\left(f x + e\right)^{4}, x\right)"," ",0,"integral((b*sin(f*x + e))^(1/3)*sec(f*x + e)^4, x)","F",0
309,0,0,0,0.961070," ","integrate(cos(f*x+e)^4*(b*sin(f*x+e))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}} b \cos\left(f x + e\right)^{4} \sin\left(f x + e\right), x\right)"," ",0,"integral((b*sin(f*x + e))^(2/3)*b*cos(f*x + e)^4*sin(f*x + e), x)","F",0
310,0,0,0,0.976700," ","integrate(cos(f*x+e)^2*(b*sin(f*x+e))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}} b \cos\left(f x + e\right)^{2} \sin\left(f x + e\right), x\right)"," ",0,"integral((b*sin(f*x + e))^(2/3)*b*cos(f*x + e)^2*sin(f*x + e), x)","F",0
311,0,0,0,1.095041," ","integrate((b*sin(f*x+e))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}} b \sin\left(f x + e\right), x\right)"," ",0,"integral((b*sin(f*x + e))^(2/3)*b*sin(f*x + e), x)","F",0
312,0,0,0,1.080812," ","integrate(sec(f*x+e)^2*(b*sin(f*x+e))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}} b \sec\left(f x + e\right)^{2} \sin\left(f x + e\right), x\right)"," ",0,"integral((b*sin(f*x + e))^(2/3)*b*sec(f*x + e)^2*sin(f*x + e), x)","F",0
313,0,0,0,1.044087," ","integrate(sec(f*x+e)^4*(b*sin(f*x+e))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}} b \sec\left(f x + e\right)^{4} \sin\left(f x + e\right), x\right)"," ",0,"integral((b*sin(f*x + e))^(2/3)*b*sec(f*x + e)^4*sin(f*x + e), x)","F",0
314,0,0,0,1.301411," ","integrate(cos(f*x+e)^4/(b*sin(f*x+e))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}} \cos\left(f x + e\right)^{4}}{b \sin\left(f x + e\right)}, x\right)"," ",0,"integral((b*sin(f*x + e))^(2/3)*cos(f*x + e)^4/(b*sin(f*x + e)), x)","F",0
315,0,0,0,0.887307," ","integrate(cos(f*x+e)^2/(b*sin(f*x+e))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}} \cos\left(f x + e\right)^{2}}{b \sin\left(f x + e\right)}, x\right)"," ",0,"integral((b*sin(f*x + e))^(2/3)*cos(f*x + e)^2/(b*sin(f*x + e)), x)","F",0
316,0,0,0,1.804764," ","integrate(1/(b*sin(f*x+e))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}}}{b \sin\left(f x + e\right)}, x\right)"," ",0,"integral((b*sin(f*x + e))^(2/3)/(b*sin(f*x + e)), x)","F",0
317,0,0,0,1.135185," ","integrate(sec(f*x+e)^2/(b*sin(f*x+e))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}} \sec\left(f x + e\right)^{2}}{b \sin\left(f x + e\right)}, x\right)"," ",0,"integral((b*sin(f*x + e))^(2/3)*sec(f*x + e)^2/(b*sin(f*x + e)), x)","F",0
318,0,0,0,0.998360," ","integrate(sec(f*x+e)^4/(b*sin(f*x+e))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}} \sec\left(f x + e\right)^{4}}{b \sin\left(f x + e\right)}, x\right)"," ",0,"integral((b*sin(f*x + e))^(2/3)*sec(f*x + e)^4/(b*sin(f*x + e)), x)","F",0
319,0,0,0,1.062191," ","integrate(cos(f*x+e)^4/(b*sin(f*x+e))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}} \cos\left(f x + e\right)^{4}}{b^{2} \cos\left(f x + e\right)^{2} - b^{2}}, x\right)"," ",0,"integral(-(b*sin(f*x + e))^(1/3)*cos(f*x + e)^4/(b^2*cos(f*x + e)^2 - b^2), x)","F",0
320,0,0,0,1.073582," ","integrate(cos(f*x+e)^2/(b*sin(f*x+e))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}} \cos\left(f x + e\right)^{2}}{b^{2} \cos\left(f x + e\right)^{2} - b^{2}}, x\right)"," ",0,"integral(-(b*sin(f*x + e))^(1/3)*cos(f*x + e)^2/(b^2*cos(f*x + e)^2 - b^2), x)","F",0
321,0,0,0,1.136266," ","integrate(1/(b*sin(f*x+e))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}}}{b^{2} \cos\left(f x + e\right)^{2} - b^{2}}, x\right)"," ",0,"integral(-(b*sin(f*x + e))^(1/3)/(b^2*cos(f*x + e)^2 - b^2), x)","F",0
322,0,0,0,0.977565," ","integrate(sec(f*x+e)^2/(b*sin(f*x+e))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}} \sec\left(f x + e\right)^{2}}{b^{2} \cos\left(f x + e\right)^{2} - b^{2}}, x\right)"," ",0,"integral(-(b*sin(f*x + e))^(1/3)*sec(f*x + e)^2/(b^2*cos(f*x + e)^2 - b^2), x)","F",0
323,0,0,0,1.263438," ","integrate(sec(f*x+e)^4/(b*sin(f*x+e))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}} \sec\left(f x + e\right)^{4}}{b^{2} \cos\left(f x + e\right)^{2} - b^{2}}, x\right)"," ",0,"integral(-(b*sin(f*x + e))^(1/3)*sec(f*x + e)^4/(b^2*cos(f*x + e)^2 - b^2), x)","F",0
324,1,144,0,0.902722," ","integrate(sin(b*x+a)^(1/3)/cos(b*x+a)^(1/3),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} \cos\left(b x + a\right) - 2 \, \sqrt{3} \cos\left(b x + a\right)^{\frac{1}{3}} \sin\left(b x + a\right)^{\frac{2}{3}}}{3 \, \cos\left(b x + a\right)}\right) - 2 \, \log\left(\frac{\cos\left(b x + a\right)^{\frac{1}{3}} \sin\left(b x + a\right)^{\frac{2}{3}} + \cos\left(b x + a\right)}{\cos\left(b x + a\right)}\right) + \log\left(\frac{\cos\left(b x + a\right)^{2} - \cos\left(b x + a\right)^{\frac{4}{3}} \sin\left(b x + a\right)^{\frac{2}{3}} + \cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{4}{3}}}{\cos\left(b x + a\right)^{2}}\right)}{4 \, b}"," ",0,"1/4*(2*sqrt(3)*arctan(-1/3*(sqrt(3)*cos(b*x + a) - 2*sqrt(3)*cos(b*x + a)^(1/3)*sin(b*x + a)^(2/3))/cos(b*x + a)) - 2*log((cos(b*x + a)^(1/3)*sin(b*x + a)^(2/3) + cos(b*x + a))/cos(b*x + a)) + log((cos(b*x + a)^2 - cos(b*x + a)^(4/3)*sin(b*x + a)^(2/3) + cos(b*x + a)^(2/3)*sin(b*x + a)^(4/3))/cos(b*x + a)^2))/b","A",0
325,-1,0,0,0.000000," ","integrate(sin(b*x+a)^(2/3)/cos(b*x+a)^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate(sin(b*x+a)^(4/3)/cos(b*x+a)^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,1,197,0,1.745814," ","integrate(sin(b*x+a)^(5/3)/cos(b*x+a)^(5/3),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} \arctan\left(\frac{2 \, \sqrt{3} \cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{1}{3}} - \sqrt{3} \sin\left(b x + a\right)}{3 \, \sin\left(b x + a\right)}\right) \cos\left(b x + a\right) + \cos\left(b x + a\right) \log\left(\frac{4 \, {\left(\cos\left(b x + a\right)^{2} - \cos\left(b x + a\right)^{\frac{4}{3}} \sin\left(b x + a\right)^{\frac{2}{3}} + \cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{4}{3}} - 1\right)}}{\cos\left(b x + a\right)^{2} - 1}\right) - 2 \, \cos\left(b x + a\right) \log\left(-\frac{2 \, {\left(\cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{1}{3}} + \sin\left(b x + a\right)\right)}}{\sin\left(b x + a\right)}\right) + 6 \, \cos\left(b x + a\right)^{\frac{1}{3}} \sin\left(b x + a\right)^{\frac{2}{3}}}{4 \, b \cos\left(b x + a\right)}"," ",0,"1/4*(2*sqrt(3)*arctan(1/3*(2*sqrt(3)*cos(b*x + a)^(2/3)*sin(b*x + a)^(1/3) - sqrt(3)*sin(b*x + a))/sin(b*x + a))*cos(b*x + a) + cos(b*x + a)*log(4*(cos(b*x + a)^2 - cos(b*x + a)^(4/3)*sin(b*x + a)^(2/3) + cos(b*x + a)^(2/3)*sin(b*x + a)^(4/3) - 1)/(cos(b*x + a)^2 - 1)) - 2*cos(b*x + a)*log(-2*(cos(b*x + a)^(2/3)*sin(b*x + a)^(1/3) + sin(b*x + a))/sin(b*x + a)) + 6*cos(b*x + a)^(1/3)*sin(b*x + a)^(2/3))/(b*cos(b*x + a))","A",0
328,1,195,0,1.788449," ","integrate(sin(b*x+a)^(7/3)/cos(b*x+a)^(7/3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} \cos\left(b x + a\right) - 2 \, \sqrt{3} \cos\left(b x + a\right)^{\frac{1}{3}} \sin\left(b x + a\right)^{\frac{2}{3}}}{3 \, \cos\left(b x + a\right)}\right) \cos\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right)^{2} \log\left(\frac{\cos\left(b x + a\right)^{\frac{1}{3}} \sin\left(b x + a\right)^{\frac{2}{3}} + \cos\left(b x + a\right)}{\cos\left(b x + a\right)}\right) + \cos\left(b x + a\right)^{2} \log\left(\frac{\cos\left(b x + a\right)^{2} - \cos\left(b x + a\right)^{\frac{4}{3}} \sin\left(b x + a\right)^{\frac{2}{3}} + \cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{4}{3}}}{\cos\left(b x + a\right)^{2}}\right) - 3 \, \cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{4}{3}}}{4 \, b \cos\left(b x + a\right)^{2}}"," ",0,"-1/4*(2*sqrt(3)*arctan(-1/3*(sqrt(3)*cos(b*x + a) - 2*sqrt(3)*cos(b*x + a)^(1/3)*sin(b*x + a)^(2/3))/cos(b*x + a))*cos(b*x + a)^2 - 2*cos(b*x + a)^2*log((cos(b*x + a)^(1/3)*sin(b*x + a)^(2/3) + cos(b*x + a))/cos(b*x + a)) + cos(b*x + a)^2*log((cos(b*x + a)^2 - cos(b*x + a)^(4/3)*sin(b*x + a)^(2/3) + cos(b*x + a)^(2/3)*sin(b*x + a)^(4/3))/cos(b*x + a)^2) - 3*cos(b*x + a)^(2/3)*sin(b*x + a)^(4/3))/(b*cos(b*x + a)^2)","A",0
329,1,152,0,1.308527," ","integrate(cos(b*x+a)^(1/3)/sin(b*x+a)^(1/3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \arctan\left(\frac{2 \, \sqrt{3} \cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{1}{3}} - \sqrt{3} \sin\left(b x + a\right)}{3 \, \sin\left(b x + a\right)}\right) + \log\left(\frac{4 \, {\left(\cos\left(b x + a\right)^{2} - \cos\left(b x + a\right)^{\frac{4}{3}} \sin\left(b x + a\right)^{\frac{2}{3}} + \cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{4}{3}} - 1\right)}}{\cos\left(b x + a\right)^{2} - 1}\right) - 2 \, \log\left(-\frac{2 \, {\left(\cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{1}{3}} + \sin\left(b x + a\right)\right)}}{\sin\left(b x + a\right)}\right)}{4 \, b}"," ",0,"-1/4*(2*sqrt(3)*arctan(1/3*(2*sqrt(3)*cos(b*x + a)^(2/3)*sin(b*x + a)^(1/3) - sqrt(3)*sin(b*x + a))/sin(b*x + a)) + log(4*(cos(b*x + a)^2 - cos(b*x + a)^(4/3)*sin(b*x + a)^(2/3) + cos(b*x + a)^(2/3)*sin(b*x + a)^(4/3) - 1)/(cos(b*x + a)^2 - 1)) - 2*log(-2*(cos(b*x + a)^(2/3)*sin(b*x + a)^(1/3) + sin(b*x + a))/sin(b*x + a)))/b","A",0
330,-1,0,0,0.000000," ","integrate(cos(b*x+a)^(2/3)/sin(b*x+a)^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,-1,0,0,0.000000," ","integrate(cos(b*x+a)^(4/3)/sin(b*x+a)^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,1,189,0,1.039815," ","integrate(cos(b*x+a)^(5/3)/sin(b*x+a)^(5/3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} \cos\left(b x + a\right) - 2 \, \sqrt{3} \cos\left(b x + a\right)^{\frac{1}{3}} \sin\left(b x + a\right)^{\frac{2}{3}}}{3 \, \cos\left(b x + a\right)}\right) \sin\left(b x + a\right) - 2 \, \log\left(\frac{\cos\left(b x + a\right)^{\frac{1}{3}} \sin\left(b x + a\right)^{\frac{2}{3}} + \cos\left(b x + a\right)}{\cos\left(b x + a\right)}\right) \sin\left(b x + a\right) + \log\left(\frac{\cos\left(b x + a\right)^{2} - \cos\left(b x + a\right)^{\frac{4}{3}} \sin\left(b x + a\right)^{\frac{2}{3}} + \cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{4}{3}}}{\cos\left(b x + a\right)^{2}}\right) \sin\left(b x + a\right) + 6 \, \cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{1}{3}}}{4 \, b \sin\left(b x + a\right)}"," ",0,"-1/4*(2*sqrt(3)*arctan(-1/3*(sqrt(3)*cos(b*x + a) - 2*sqrt(3)*cos(b*x + a)^(1/3)*sin(b*x + a)^(2/3))/cos(b*x + a))*sin(b*x + a) - 2*log((cos(b*x + a)^(1/3)*sin(b*x + a)^(2/3) + cos(b*x + a))/cos(b*x + a))*sin(b*x + a) + log((cos(b*x + a)^2 - cos(b*x + a)^(4/3)*sin(b*x + a)^(2/3) + cos(b*x + a)^(2/3)*sin(b*x + a)^(4/3))/cos(b*x + a)^2)*sin(b*x + a) + 6*cos(b*x + a)^(2/3)*sin(b*x + a)^(1/3))/(b*sin(b*x + a))","A",0
333,1,219,0,1.020911," ","integrate(cos(b*x+a)^(7/3)/sin(b*x+a)^(7/3),x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{3} \cos\left(b x + a\right)^{2} - \sqrt{3}\right)} \arctan\left(\frac{2 \, \sqrt{3} \cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{1}{3}} - \sqrt{3} \sin\left(b x + a\right)}{3 \, \sin\left(b x + a\right)}\right) + {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\frac{4 \, {\left(\cos\left(b x + a\right)^{2} - \cos\left(b x + a\right)^{\frac{4}{3}} \sin\left(b x + a\right)^{\frac{2}{3}} + \cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{4}{3}} - 1\right)}}{\cos\left(b x + a\right)^{2} - 1}\right) - 2 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(-\frac{2 \, {\left(\cos\left(b x + a\right)^{\frac{2}{3}} \sin\left(b x + a\right)^{\frac{1}{3}} + \sin\left(b x + a\right)\right)}}{\sin\left(b x + a\right)}\right) + 3 \, \cos\left(b x + a\right)^{\frac{4}{3}} \sin\left(b x + a\right)^{\frac{2}{3}}}{4 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"1/4*(2*(sqrt(3)*cos(b*x + a)^2 - sqrt(3))*arctan(1/3*(2*sqrt(3)*cos(b*x + a)^(2/3)*sin(b*x + a)^(1/3) - sqrt(3)*sin(b*x + a))/sin(b*x + a)) + (cos(b*x + a)^2 - 1)*log(4*(cos(b*x + a)^2 - cos(b*x + a)^(4/3)*sin(b*x + a)^(2/3) + cos(b*x + a)^(2/3)*sin(b*x + a)^(4/3) - 1)/(cos(b*x + a)^2 - 1)) - 2*(cos(b*x + a)^2 - 1)*log(-2*(cos(b*x + a)^(2/3)*sin(b*x + a)^(1/3) + sin(b*x + a))/sin(b*x + a)) + 3*cos(b*x + a)^(4/3)*sin(b*x + a)^(2/3))/(b*cos(b*x + a)^2 - b)","A",0
334,1,18,0,1.165857," ","integrate(cos(x)^(2/3)/sin(x)^(8/3),x, algorithm=""fricas"")","\frac{3 \, \cos\left(x\right)^{\frac{5}{3}} \sin\left(x\right)^{\frac{1}{3}}}{5 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"3/5*cos(x)^(5/3)*sin(x)^(1/3)/(cos(x)^2 - 1)","A",0
335,1,10,0,0.996721," ","integrate(sin(x)^(2/3)/cos(x)^(8/3),x, algorithm=""fricas"")","\frac{3 \, \sin\left(x\right)^{\frac{5}{3}}}{5 \, \cos\left(x\right)^{\frac{5}{3}}}"," ",0,"3/5*sin(x)^(5/3)/cos(x)^(5/3)","A",0
336,0,0,0,1.253504," ","integrate(cos(f*x+e)^n*sin(f*x+e)^m,x, algorithm=""fricas"")","{\rm integral}\left(\cos\left(f x + e\right)^{n} \sin\left(f x + e\right)^{m}, x\right)"," ",0,"integral(cos(f*x + e)^n*sin(f*x + e)^m, x)","F",0
337,0,0,0,0.948877," ","integrate((d*cos(f*x+e))^n*sin(f*x+e)^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(d \cos\left(f x + e\right)\right)^{n} \sin\left(f x + e\right)^{m}, x\right)"," ",0,"integral((d*cos(f*x + e))^n*sin(f*x + e)^m, x)","F",0
338,0,0,0,1.017115," ","integrate(cos(f*x+e)^n*(b*sin(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{m} \cos\left(f x + e\right)^{n}, x\right)"," ",0,"integral((b*sin(f*x + e))^m*cos(f*x + e)^n, x)","F",0
339,0,0,0,1.164973," ","integrate((d*cos(f*x+e))^n*(b*sin(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(d \cos\left(f x + e\right)\right)^{n} \left(b \sin\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((d*cos(f*x + e))^n*(b*sin(f*x + e))^m, x)","F",0
340,1,70,0,0.742671," ","integrate(cos(b*x+a)^5*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","\frac{{\left({\left(m^{2} + 4 \, m + 3\right)} \cos\left(b x + a\right)^{4} + 4 \, {\left(m + 1\right)} \cos\left(b x + a\right)^{2} + 8\right)} \left(c \sin\left(b x + a\right)\right)^{m} \sin\left(b x + a\right)}{b m^{3} + 9 \, b m^{2} + 23 \, b m + 15 \, b}"," ",0,"((m^2 + 4*m + 3)*cos(b*x + a)^4 + 4*(m + 1)*cos(b*x + a)^2 + 8)*(c*sin(b*x + a))^m*sin(b*x + a)/(b*m^3 + 9*b*m^2 + 23*b*m + 15*b)","A",0
341,1,46,0,0.953985," ","integrate(cos(b*x+a)^3*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","\frac{{\left({\left(m + 1\right)} \cos\left(b x + a\right)^{2} + 2\right)} \left(c \sin\left(b x + a\right)\right)^{m} \sin\left(b x + a\right)}{b m^{2} + 4 \, b m + 3 \, b}"," ",0,"((m + 1)*cos(b*x + a)^2 + 2)*(c*sin(b*x + a))^m*sin(b*x + a)/(b*m^2 + 4*b*m + 3*b)","A",0
342,1,24,0,0.665264," ","integrate(cos(b*x+a)*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","\frac{\left(c \sin\left(b x + a\right)\right)^{m} \sin\left(b x + a\right)}{b m + b}"," ",0,"(c*sin(b*x + a))^m*sin(b*x + a)/(b*m + b)","A",0
343,0,0,0,0.830198," ","integrate(sec(b*x+a)*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(c \sin\left(b x + a\right)\right)^{m} \sec\left(b x + a\right), x\right)"," ",0,"integral((c*sin(b*x + a))^m*sec(b*x + a), x)","F",0
344,0,0,0,1.124894," ","integrate(sec(b*x+a)^3*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(c \sin\left(b x + a\right)\right)^{m} \sec\left(b x + a\right)^{3}, x\right)"," ",0,"integral((c*sin(b*x + a))^m*sec(b*x + a)^3, x)","F",0
345,0,0,0,0.978602," ","integrate(cos(b*x+a)^4*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(c \sin\left(b x + a\right)\right)^{m} \cos\left(b x + a\right)^{4}, x\right)"," ",0,"integral((c*sin(b*x + a))^m*cos(b*x + a)^4, x)","F",0
346,0,0,0,0.801008," ","integrate(cos(b*x+a)^2*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(c \sin\left(b x + a\right)\right)^{m} \cos\left(b x + a\right)^{2}, x\right)"," ",0,"integral((c*sin(b*x + a))^m*cos(b*x + a)^2, x)","F",0
347,0,0,0,0.955457," ","integrate((c*sin(b*x+a))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(c \sin\left(b x + a\right)\right)^{m}, x\right)"," ",0,"integral((c*sin(b*x + a))^m, x)","F",0
348,0,0,0,1.015476," ","integrate(sec(b*x+a)^2*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(c \sin\left(b x + a\right)\right)^{m} \sec\left(b x + a\right)^{2}, x\right)"," ",0,"integral((c*sin(b*x + a))^m*sec(b*x + a)^2, x)","F",0
349,0,0,0,0.971912," ","integrate(sec(b*x+a)^4*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(c \sin\left(b x + a\right)\right)^{m} \sec\left(b x + a\right)^{4}, x\right)"," ",0,"integral((c*sin(b*x + a))^m*sec(b*x + a)^4, x)","F",0
350,0,0,0,1.000264," ","integrate((d*cos(b*x+a))^(3/2)*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \cos\left(b x + a\right)} \left(c \sin\left(b x + a\right)\right)^{m} d \cos\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*(c*sin(b*x + a))^m*d*cos(b*x + a), x)","F",0
351,0,0,0,0.930682," ","integrate((d*cos(b*x+a))^(1/2)*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \cos\left(b x + a\right)} \left(c \sin\left(b x + a\right)\right)^{m}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*(c*sin(b*x + a))^m, x)","F",0
352,0,0,0,0.765248," ","integrate((c*sin(b*x+a))^m/(d*cos(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \left(c \sin\left(b x + a\right)\right)^{m}}{d \cos\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*(c*sin(b*x + a))^m/(d*cos(b*x + a)), x)","F",0
353,0,0,0,0.632515," ","integrate((c*sin(b*x+a))^m/(d*cos(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \left(c \sin\left(b x + a\right)\right)^{m}}{d^{2} \cos\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*(c*sin(b*x + a))^m/(d^2*cos(b*x + a)^2), x)","F",0
354,0,0,0,1.023484," ","integrate((c*sin(b*x+a))^m/(d*cos(b*x+a))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \cos\left(b x + a\right)} \left(c \sin\left(b x + a\right)\right)^{m}}{d^{3} \cos\left(b x + a\right)^{3}}, x\right)"," ",0,"integral(sqrt(d*cos(b*x + a))*(c*sin(b*x + a))^m/(d^3*cos(b*x + a)^3), x)","F",0
355,1,84,0,0.950634," ","integrate((d*cos(b*x+a))^n*sin(b*x+a)^5,x, algorithm=""fricas"")","-\frac{{\left({\left(n^{2} + 4 \, n + 3\right)} \cos\left(b x + a\right)^{5} - 2 \, {\left(n^{2} + 6 \, n + 5\right)} \cos\left(b x + a\right)^{3} + {\left(n^{2} + 8 \, n + 15\right)} \cos\left(b x + a\right)\right)} \left(d \cos\left(b x + a\right)\right)^{n}}{b n^{3} + 9 \, b n^{2} + 23 \, b n + 15 \, b}"," ",0,"-((n^2 + 4*n + 3)*cos(b*x + a)^5 - 2*(n^2 + 6*n + 5)*cos(b*x + a)^3 + (n^2 + 8*n + 15)*cos(b*x + a))*(d*cos(b*x + a))^n/(b*n^3 + 9*b*n^2 + 23*b*n + 15*b)","A",0
356,1,50,0,0.772162," ","integrate((d*cos(b*x+a))^n*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{{\left({\left(n + 1\right)} \cos\left(b x + a\right)^{3} - {\left(n + 3\right)} \cos\left(b x + a\right)\right)} \left(d \cos\left(b x + a\right)\right)^{n}}{b n^{2} + 4 \, b n + 3 \, b}"," ",0,"((n + 1)*cos(b*x + a)^3 - (n + 3)*cos(b*x + a))*(d*cos(b*x + a))^n/(b*n^2 + 4*b*n + 3*b)","A",0
357,1,25,0,0.755728," ","integrate((d*cos(b*x+a))^n*sin(b*x+a),x, algorithm=""fricas"")","-\frac{\left(d \cos\left(b x + a\right)\right)^{n} \cos\left(b x + a\right)}{b n + b}"," ",0,"-(d*cos(b*x + a))^n*cos(b*x + a)/(b*n + b)","A",0
358,0,0,0,0.809202," ","integrate((d*cos(b*x+a))^n*csc(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\left(d \cos\left(b x + a\right)\right)^{n} \csc\left(b x + a\right), x\right)"," ",0,"integral((d*cos(b*x + a))^n*csc(b*x + a), x)","F",0
359,0,0,0,0.722463," ","integrate((d*cos(b*x+a))^n*csc(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\left(d \cos\left(b x + a\right)\right)^{n} \csc\left(b x + a\right)^{3}, x\right)"," ",0,"integral((d*cos(b*x + a))^n*csc(b*x + a)^3, x)","F",0
360,0,0,0,0.714925," ","integrate((d*cos(b*x+a))^n*csc(b*x+a)^5,x, algorithm=""fricas"")","{\rm integral}\left(\left(d \cos\left(b x + a\right)\right)^{n} \csc\left(b x + a\right)^{5}, x\right)"," ",0,"integral((d*cos(b*x + a))^n*csc(b*x + a)^5, x)","F",0
361,0,0,0,1.032959," ","integrate((d*cos(b*x+a))^n*sin(b*x+a)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \left(d \cos\left(b x + a\right)\right)^{n}, x\right)"," ",0,"integral((cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*(d*cos(b*x + a))^n, x)","F",0
362,0,0,0,0.871805," ","integrate((d*cos(b*x+a))^n*sin(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} \left(d \cos\left(b x + a\right)\right)^{n}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*(d*cos(b*x + a))^n, x)","F",0
363,0,0,0,1.224368," ","integrate((d*cos(b*x+a))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(d \cos\left(b x + a\right)\right)^{n}, x\right)"," ",0,"integral((d*cos(b*x + a))^n, x)","F",0
364,0,0,0,0.731501," ","integrate((d*cos(b*x+a))^n*csc(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\left(d \cos\left(b x + a\right)\right)^{n} \csc\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*cos(b*x + a))^n*csc(b*x + a)^2, x)","F",0
365,0,0,0,1.271902," ","integrate((d*cos(b*x+a))^n*csc(b*x+a)^4,x, algorithm=""fricas"")","{\rm integral}\left(\left(d \cos\left(b x + a\right)\right)^{n} \csc\left(b x + a\right)^{4}, x\right)"," ",0,"integral((d*cos(b*x + a))^n*csc(b*x + a)^4, x)","F",0
366,0,0,0,1.208367," ","integrate((d*cos(b*x+a))^n*(c*sin(b*x+a))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c^{2} \cos\left(b x + a\right)^{2} - c^{2}\right)} \sqrt{c \sin\left(b x + a\right)} \left(d \cos\left(b x + a\right)\right)^{n}, x\right)"," ",0,"integral(-(c^2*cos(b*x + a)^2 - c^2)*sqrt(c*sin(b*x + a))*(d*cos(b*x + a))^n, x)","F",0
367,0,0,0,1.002767," ","integrate((d*cos(b*x+a))^n*(c*sin(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c \sin\left(b x + a\right)} \left(d \cos\left(b x + a\right)\right)^{n} c \sin\left(b x + a\right), x\right)"," ",0,"integral(sqrt(c*sin(b*x + a))*(d*cos(b*x + a))^n*c*sin(b*x + a), x)","F",0
368,0,0,0,0.745997," ","integrate((d*cos(b*x+a))^n*(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c \sin\left(b x + a\right)} \left(d \cos\left(b x + a\right)\right)^{n}, x\right)"," ",0,"integral(sqrt(c*sin(b*x + a))*(d*cos(b*x + a))^n, x)","F",0
369,0,0,0,0.813778," ","integrate((d*cos(b*x+a))^n/(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c \sin\left(b x + a\right)} \left(d \cos\left(b x + a\right)\right)^{n}}{c \sin\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(c*sin(b*x + a))*(d*cos(b*x + a))^n/(c*sin(b*x + a)), x)","F",0
370,0,0,0,0.921321," ","integrate((d*cos(b*x+a))^n/(c*sin(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{c \sin\left(b x + a\right)} \left(d \cos\left(b x + a\right)\right)^{n}}{c^{2} \cos\left(b x + a\right)^{2} - c^{2}}, x\right)"," ",0,"integral(-sqrt(c*sin(b*x + a))*(d*cos(b*x + a))^n/(c^2*cos(b*x + a)^2 - c^2), x)","F",0
371,1,56,0,0.932955," ","integrate(sin(f*x+e)^7*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, \cos\left(f x + e\right)^{7} - 65 \, \cos\left(f x + e\right)^{5} + 117 \, \cos\left(f x + e\right)^{3} - 195 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{195 \, f}"," ",0,"2/195*(15*cos(f*x + e)^7 - 65*cos(f*x + e)^5 + 117*cos(f*x + e)^3 - 195*cos(f*x + e))*sqrt(b/cos(f*x + e))/f","A",0
372,1,46,0,0.923336," ","integrate(sin(f*x+e)^5*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, \cos\left(f x + e\right)^{5} - 18 \, \cos\left(f x + e\right)^{3} + 45 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{45 \, f}"," ",0,"-2/45*(5*cos(f*x + e)^5 - 18*cos(f*x + e)^3 + 45*cos(f*x + e))*sqrt(b/cos(f*x + e))/f","A",0
373,1,34,0,0.883884," ","integrate(sin(f*x+e)^3*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{5 \, f}"," ",0,"2/5*(cos(f*x + e)^3 - 5*cos(f*x + e))*sqrt(b/cos(f*x + e))/f","A",0
374,1,23,0,0.867812," ","integrate(sin(f*x+e)*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{f}"," ",0,"-2*sqrt(b/cos(f*x + e))*cos(f*x + e)/f","A",0
375,1,247,0,1.133500," ","integrate(csc(f*x+e)*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) + \sqrt{-b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right)}{4 \, f}, -\frac{2 \, \sqrt{b} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) - \sqrt{b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right)}{4 \, f}\right]"," ",0,"[1/4*(2*sqrt(-b)*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) + sqrt(-b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)))/f, -1/4*(2*sqrt(b)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) - sqrt(b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)))/f]","B",0
376,1,354,0,0.964223," ","integrate(csc(f*x+e)^3*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) + 3 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{16 \, {\left(f \cos\left(f x + e\right)^{2} - f\right)}}, -\frac{6 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) - 3 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right) - 8 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{16 \, {\left(f \cos\left(f x + e\right)^{2} - f\right)}}\right]"," ",0,"[1/16*(6*(cos(f*x + e)^2 - 1)*sqrt(-b)*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) + 3*(cos(f*x + e)^2 - 1)*sqrt(-b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*sqrt(b/cos(f*x + e))*cos(f*x + e))/(f*cos(f*x + e)^2 - f), -1/16*(6*(cos(f*x + e)^2 - 1)*sqrt(b)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) - 3*(cos(f*x + e)^2 - 1)*sqrt(b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)) - 8*sqrt(b/cos(f*x + e))*cos(f*x + e))/(f*cos(f*x + e)^2 - f)]","B",0
377,1,438,0,1.275551," ","integrate(csc(f*x+e)^5*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{42 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) + 21 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} - 11 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{128 \, {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} + f\right)}}, -\frac{42 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) - 21 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right) - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} - 11 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{128 \, {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} + f\right)}}\right]"," ",0,"[1/128*(42*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(-b)*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) + 21*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(-b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*(7*cos(f*x + e)^3 - 11*cos(f*x + e))*sqrt(b/cos(f*x + e)))/(f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 + f), -1/128*(42*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(b)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) - 21*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)) - 8*(7*cos(f*x + e)^3 - 11*cos(f*x + e))*sqrt(b/cos(f*x + e)))/(f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 + f)]","B",0
378,0,0,0,0.960548," ","integrate(sin(f*x+e)^6*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(f x + e\right)^{6} - 3 \, \cos\left(f x + e\right)^{4} + 3 \, \cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral(-(cos(f*x + e)^6 - 3*cos(f*x + e)^4 + 3*cos(f*x + e)^2 - 1)*sqrt(b*sec(f*x + e)), x)","F",0
379,0,0,0,0.863470," ","integrate(sin(f*x+e)^4*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral((cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(b*sec(f*x + e)), x)","F",0
380,0,0,0,1.106312," ","integrate(sin(f*x+e)^2*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*sqrt(b*sec(f*x + e)), x)","F",0
381,0,0,0,0.782006," ","integrate((b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e)), x)","F",0
382,0,0,0,1.013726," ","integrate(csc(f*x+e)^2*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} \csc\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*csc(f*x + e)^2, x)","F",0
383,0,0,0,0.734597," ","integrate(csc(f*x+e)^4*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} \csc\left(f x + e\right)^{4}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*csc(f*x + e)^4, x)","F",0
384,0,0,0,0.641505," ","integrate(csc(f*x+e)^6*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} \csc\left(f x + e\right)^{6}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*csc(f*x + e)^6, x)","F",0
385,1,54,0,0.984383," ","integrate((b*sec(f*x+e))^(3/2)*sin(f*x+e)^7,x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, b \cos\left(f x + e\right)^{6} - 33 \, b \cos\left(f x + e\right)^{4} + 77 \, b \cos\left(f x + e\right)^{2} + 77 \, b\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{77 \, f}"," ",0,"2/77*(7*b*cos(f*x + e)^6 - 33*b*cos(f*x + e)^4 + 77*b*cos(f*x + e)^2 + 77*b)*sqrt(b/cos(f*x + e))/f","A",0
386,1,43,0,0.878398," ","integrate((b*sec(f*x+e))^(3/2)*sin(f*x+e)^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b \cos\left(f x + e\right)^{4} - 14 \, b \cos\left(f x + e\right)^{2} - 21 \, b\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{21 \, f}"," ",0,"-2/21*(3*b*cos(f*x + e)^4 - 14*b*cos(f*x + e)^2 - 21*b)*sqrt(b/cos(f*x + e))/f","A",0
387,1,31,0,0.985497," ","integrate((b*sec(f*x+e))^(3/2)*sin(f*x+e)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(b \cos\left(f x + e\right)^{2} + 3 \, b\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{3 \, f}"," ",0,"2/3*(b*cos(f*x + e)^2 + 3*b)*sqrt(b/cos(f*x + e))/f","A",0
388,1,18,0,1.086168," ","integrate((b*sec(f*x+e))^(3/2)*sin(f*x+e),x, algorithm=""fricas"")","\frac{2 \, b \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{f}"," ",0,"2*b*sqrt(b/cos(f*x + e))/f","A",0
389,1,278,0,1.098727," ","integrate(csc(f*x+e)*(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-b} b \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) + \sqrt{-b} b \log\left(\frac{b \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, b \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{4 \, f}, \frac{2 \, b^{\frac{3}{2}} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) + b^{\frac{3}{2}} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, b \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{4 \, f}\right]"," ",0,"[1/4*(2*sqrt(-b)*b*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) + sqrt(-b)*b*log((b*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*b*sqrt(b/cos(f*x + e)))/f, 1/4*(2*b^(3/2)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) + b^(3/2)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)) + 8*b*sqrt(b/cos(f*x + e)))/f]","B",0
390,1,388,0,0.957146," ","integrate(csc(f*x+e)^3*(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{10 \, {\left(b \cos\left(f x + e\right)^{2} - b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) + 5 \, {\left(b \cos\left(f x + e\right)^{2} - b\right)} \sqrt{-b} \log\left(\frac{b \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(5 \, b \cos\left(f x + e\right)^{2} - 4 \, b\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{16 \, {\left(f \cos\left(f x + e\right)^{2} - f\right)}}, \frac{10 \, {\left(b \cos\left(f x + e\right)^{2} - b\right)} \sqrt{b} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) + 5 \, {\left(b \cos\left(f x + e\right)^{2} - b\right)} \sqrt{b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(5 \, b \cos\left(f x + e\right)^{2} - 4 \, b\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{16 \, {\left(f \cos\left(f x + e\right)^{2} - f\right)}}\right]"," ",0,"[1/16*(10*(b*cos(f*x + e)^2 - b)*sqrt(-b)*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) + 5*(b*cos(f*x + e)^2 - b)*sqrt(-b)*log((b*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*(5*b*cos(f*x + e)^2 - 4*b)*sqrt(b/cos(f*x + e)))/(f*cos(f*x + e)^2 - f), 1/16*(10*(b*cos(f*x + e)^2 - b)*sqrt(b)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) + 5*(b*cos(f*x + e)^2 - b)*sqrt(b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)) + 8*(5*b*cos(f*x + e)^2 - 4*b)*sqrt(b/cos(f*x + e)))/(f*cos(f*x + e)^2 - f)]","B",0
391,0,0,0,0.833160," ","integrate((b*sec(f*x+e))^(3/2)*sin(f*x+e)^6,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b \cos\left(f x + e\right)^{6} - 3 \, b \cos\left(f x + e\right)^{4} + 3 \, b \cos\left(f x + e\right)^{2} - b\right)} \sqrt{b \sec\left(f x + e\right)} \sec\left(f x + e\right), x\right)"," ",0,"integral(-(b*cos(f*x + e)^6 - 3*b*cos(f*x + e)^4 + 3*b*cos(f*x + e)^2 - b)*sqrt(b*sec(f*x + e))*sec(f*x + e), x)","F",0
392,0,0,0,1.135085," ","integrate((b*sec(f*x+e))^(3/2)*sin(f*x+e)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(f x + e\right)^{4} - 2 \, b \cos\left(f x + e\right)^{2} + b\right)} \sqrt{b \sec\left(f x + e\right)} \sec\left(f x + e\right), x\right)"," ",0,"integral((b*cos(f*x + e)^4 - 2*b*cos(f*x + e)^2 + b)*sqrt(b*sec(f*x + e))*sec(f*x + e), x)","F",0
393,0,0,0,0.935200," ","integrate((b*sec(f*x+e))^(3/2)*sin(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b \cos\left(f x + e\right)^{2} - b\right)} \sqrt{b \sec\left(f x + e\right)} \sec\left(f x + e\right), x\right)"," ",0,"integral(-(b*cos(f*x + e)^2 - b)*sqrt(b*sec(f*x + e))*sec(f*x + e), x)","F",0
394,0,0,0,0.794135," ","integrate((b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} b \sec\left(f x + e\right), x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*b*sec(f*x + e), x)","F",0
395,0,0,0,0.877213," ","integrate(csc(f*x+e)^2*(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} b \csc\left(f x + e\right)^{2} \sec\left(f x + e\right), x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*b*csc(f*x + e)^2*sec(f*x + e), x)","F",0
396,0,0,0,1.028726," ","integrate(csc(f*x+e)^4*(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} b \csc\left(f x + e\right)^{4} \sec\left(f x + e\right), x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*b*csc(f*x + e)^4*sec(f*x + e), x)","F",0
397,1,70,0,0.878964," ","integrate((b*sec(f*x+e))^(5/2)*sin(f*x+e)^7,x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{2} \cos\left(f x + e\right)^{6} - 27 \, b^{2} \cos\left(f x + e\right)^{4} + 135 \, b^{2} \cos\left(f x + e\right)^{2} + 15 \, b^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{45 \, f \cos\left(f x + e\right)}"," ",0,"2/45*(5*b^2*cos(f*x + e)^6 - 27*b^2*cos(f*x + e)^4 + 135*b^2*cos(f*x + e)^2 + 15*b^2)*sqrt(b/cos(f*x + e))/(f*cos(f*x + e))","A",0
398,1,57,0,0.825959," ","integrate((b*sec(f*x+e))^(5/2)*sin(f*x+e)^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b^{2} \cos\left(f x + e\right)^{4} - 30 \, b^{2} \cos\left(f x + e\right)^{2} - 5 \, b^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{15 \, f \cos\left(f x + e\right)}"," ",0,"-2/15*(3*b^2*cos(f*x + e)^4 - 30*b^2*cos(f*x + e)^2 - 5*b^2)*sqrt(b/cos(f*x + e))/(f*cos(f*x + e))","A",0
399,1,42,0,0.932839," ","integrate((b*sec(f*x+e))^(5/2)*sin(f*x+e)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} \cos\left(f x + e\right)^{2} + b^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{3 \, f \cos\left(f x + e\right)}"," ",0,"2/3*(3*b^2*cos(f*x + e)^2 + b^2)*sqrt(b/cos(f*x + e))/(f*cos(f*x + e))","A",0
400,1,28,0,0.916059," ","integrate((b*sec(f*x+e))^(5/2)*sin(f*x+e),x, algorithm=""fricas"")","\frac{2 \, b^{2} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{3 \, f \cos\left(f x + e\right)}"," ",0,"2/3*b^2*sqrt(b/cos(f*x + e))/(f*cos(f*x + e))","A",0
401,1,328,0,1.057928," ","integrate(csc(f*x+e)*(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{-b} b^{2} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) \cos\left(f x + e\right) + 3 \, \sqrt{-b} b^{2} \cos\left(f x + e\right) \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, b^{2} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{12 \, f \cos\left(f x + e\right)}, -\frac{6 \, b^{\frac{5}{2}} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) \cos\left(f x + e\right) - 3 \, b^{\frac{5}{2}} \cos\left(f x + e\right) \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right) - 8 \, b^{2} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{12 \, f \cos\left(f x + e\right)}\right]"," ",0,"[1/12*(6*sqrt(-b)*b^2*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b)*cos(f*x + e) + 3*sqrt(-b)*b^2*cos(f*x + e)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*b^2*sqrt(b/cos(f*x + e)))/(f*cos(f*x + e)), -1/12*(6*b^(5/2)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b))*cos(f*x + e) - 3*b^(5/2)*cos(f*x + e)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)) - 8*b^2*sqrt(b/cos(f*x + e)))/(f*cos(f*x + e))]","B",0
402,1,448,0,0.995590," ","integrate(csc(f*x+e)^3*(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{42 \, {\left(b^{2} \cos\left(f x + e\right)^{3} - b^{2} \cos\left(f x + e\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) + 21 \, {\left(b^{2} \cos\left(f x + e\right)^{3} - b^{2} \cos\left(f x + e\right)\right)} \sqrt{-b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(7 \, b^{2} \cos\left(f x + e\right)^{2} - 4 \, b^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{48 \, {\left(f \cos\left(f x + e\right)^{3} - f \cos\left(f x + e\right)\right)}}, -\frac{42 \, {\left(b^{2} \cos\left(f x + e\right)^{3} - b^{2} \cos\left(f x + e\right)\right)} \sqrt{b} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) - 21 \, {\left(b^{2} \cos\left(f x + e\right)^{3} - b^{2} \cos\left(f x + e\right)\right)} \sqrt{b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right) - 8 \, {\left(7 \, b^{2} \cos\left(f x + e\right)^{2} - 4 \, b^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{48 \, {\left(f \cos\left(f x + e\right)^{3} - f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/48*(42*(b^2*cos(f*x + e)^3 - b^2*cos(f*x + e))*sqrt(-b)*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) + 21*(b^2*cos(f*x + e)^3 - b^2*cos(f*x + e))*sqrt(-b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*(7*b^2*cos(f*x + e)^2 - 4*b^2)*sqrt(b/cos(f*x + e)))/(f*cos(f*x + e)^3 - f*cos(f*x + e)), -1/48*(42*(b^2*cos(f*x + e)^3 - b^2*cos(f*x + e))*sqrt(b)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) - 21*(b^2*cos(f*x + e)^3 - b^2*cos(f*x + e))*sqrt(b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)) - 8*(7*b^2*cos(f*x + e)^2 - 4*b^2)*sqrt(b/cos(f*x + e)))/(f*cos(f*x + e)^3 - f*cos(f*x + e))]","B",0
403,1,542,0,1.136159," ","integrate(csc(f*x+e)^5*(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{462 \, {\left(b^{2} \cos\left(f x + e\right)^{5} - 2 \, b^{2} \cos\left(f x + e\right)^{3} + b^{2} \cos\left(f x + e\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) + 231 \, {\left(b^{2} \cos\left(f x + e\right)^{5} - 2 \, b^{2} \cos\left(f x + e\right)^{3} + b^{2} \cos\left(f x + e\right)\right)} \sqrt{-b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(77 \, b^{2} \cos\left(f x + e\right)^{4} - 121 \, b^{2} \cos\left(f x + e\right)^{2} + 32 \, b^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{384 \, {\left(f \cos\left(f x + e\right)^{5} - 2 \, f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)\right)}}, -\frac{462 \, {\left(b^{2} \cos\left(f x + e\right)^{5} - 2 \, b^{2} \cos\left(f x + e\right)^{3} + b^{2} \cos\left(f x + e\right)\right)} \sqrt{b} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) - 231 \, {\left(b^{2} \cos\left(f x + e\right)^{5} - 2 \, b^{2} \cos\left(f x + e\right)^{3} + b^{2} \cos\left(f x + e\right)\right)} \sqrt{b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right) - 8 \, {\left(77 \, b^{2} \cos\left(f x + e\right)^{4} - 121 \, b^{2} \cos\left(f x + e\right)^{2} + 32 \, b^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{384 \, {\left(f \cos\left(f x + e\right)^{5} - 2 \, f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/384*(462*(b^2*cos(f*x + e)^5 - 2*b^2*cos(f*x + e)^3 + b^2*cos(f*x + e))*sqrt(-b)*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) + 231*(b^2*cos(f*x + e)^5 - 2*b^2*cos(f*x + e)^3 + b^2*cos(f*x + e))*sqrt(-b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*(77*b^2*cos(f*x + e)^4 - 121*b^2*cos(f*x + e)^2 + 32*b^2)*sqrt(b/cos(f*x + e)))/(f*cos(f*x + e)^5 - 2*f*cos(f*x + e)^3 + f*cos(f*x + e)), -1/384*(462*(b^2*cos(f*x + e)^5 - 2*b^2*cos(f*x + e)^3 + b^2*cos(f*x + e))*sqrt(b)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) - 231*(b^2*cos(f*x + e)^5 - 2*b^2*cos(f*x + e)^3 + b^2*cos(f*x + e))*sqrt(b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)) - 8*(77*b^2*cos(f*x + e)^4 - 121*b^2*cos(f*x + e)^2 + 32*b^2)*sqrt(b/cos(f*x + e)))/(f*cos(f*x + e)^5 - 2*f*cos(f*x + e)^3 + f*cos(f*x + e))]","B",0
404,0,0,0,0.859270," ","integrate((b*sec(f*x+e))^(5/2)*sin(f*x+e)^6,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} \cos\left(f x + e\right)^{6} - 3 \, b^{2} \cos\left(f x + e\right)^{4} + 3 \, b^{2} \cos\left(f x + e\right)^{2} - b^{2}\right)} \sqrt{b \sec\left(f x + e\right)} \sec\left(f x + e\right)^{2}, x\right)"," ",0,"integral(-(b^2*cos(f*x + e)^6 - 3*b^2*cos(f*x + e)^4 + 3*b^2*cos(f*x + e)^2 - b^2)*sqrt(b*sec(f*x + e))*sec(f*x + e)^2, x)","F",0
405,0,0,0,0.966456," ","integrate((b*sec(f*x+e))^(5/2)*sin(f*x+e)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(f x + e\right)^{4} - 2 \, b^{2} \cos\left(f x + e\right)^{2} + b^{2}\right)} \sqrt{b \sec\left(f x + e\right)} \sec\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b^2*cos(f*x + e)^4 - 2*b^2*cos(f*x + e)^2 + b^2)*sqrt(b*sec(f*x + e))*sec(f*x + e)^2, x)","F",0
406,0,0,0,0.998327," ","integrate((b*sec(f*x+e))^(5/2)*sin(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} \cos\left(f x + e\right)^{2} - b^{2}\right)} \sqrt{b \sec\left(f x + e\right)} \sec\left(f x + e\right)^{2}, x\right)"," ",0,"integral(-(b^2*cos(f*x + e)^2 - b^2)*sqrt(b*sec(f*x + e))*sec(f*x + e)^2, x)","F",0
407,0,0,0,0.953404," ","integrate((b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} b^{2} \sec\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*b^2*sec(f*x + e)^2, x)","F",0
408,0,0,0,0.955246," ","integrate(csc(f*x+e)^2*(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} b^{2} \csc\left(f x + e\right)^{2} \sec\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*b^2*csc(f*x + e)^2*sec(f*x + e)^2, x)","F",0
409,0,0,0,0.964905," ","integrate(csc(f*x+e)^4*(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} b^{2} \csc\left(f x + e\right)^{4} \sec\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*b^2*csc(f*x + e)^4*sec(f*x + e)^2, x)","F",0
410,1,61,0,1.042469," ","integrate(sin(f*x+e)^7/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(77 \, \cos\left(f x + e\right)^{8} - 315 \, \cos\left(f x + e\right)^{6} + 495 \, \cos\left(f x + e\right)^{4} - 385 \, \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{1155 \, b f}"," ",0,"2/1155*(77*cos(f*x + e)^8 - 315*cos(f*x + e)^6 + 495*cos(f*x + e)^4 - 385*cos(f*x + e)^2)*sqrt(b/cos(f*x + e))/(b*f)","A",0
411,1,51,0,0.770462," ","integrate(sin(f*x+e)^5/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(21 \, \cos\left(f x + e\right)^{6} - 66 \, \cos\left(f x + e\right)^{4} + 77 \, \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{231 \, b f}"," ",0,"-2/231*(21*cos(f*x + e)^6 - 66*cos(f*x + e)^4 + 77*cos(f*x + e)^2)*sqrt(b/cos(f*x + e))/(b*f)","A",0
412,1,41,0,0.928193," ","integrate(sin(f*x+e)^3/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, \cos\left(f x + e\right)^{4} - 7 \, \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{21 \, b f}"," ",0,"2/21*(3*cos(f*x + e)^4 - 7*cos(f*x + e)^2)*sqrt(b/cos(f*x + e))/(b*f)","A",0
413,1,28,0,0.899896," ","integrate(sin(f*x+e)/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2}}{3 \, b f}"," ",0,"-2/3*sqrt(b/cos(f*x + e))*cos(f*x + e)^2/(b*f)","A",0
414,1,253,0,1.027958," ","integrate(csc(f*x+e)/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) - \sqrt{-b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right)}{4 \, b f}, \frac{2 \, \sqrt{b} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) + \sqrt{b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right)}{4 \, b f}\right]"," ",0,"[1/4*(2*sqrt(-b)*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) - sqrt(-b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)))/(b*f), 1/4*(2*sqrt(b)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) + sqrt(b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)))/(b*f)]","B",0
415,1,361,0,1.153010," ","integrate(csc(f*x+e)^3/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) + 8 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right)}{16 \, {\left(b f \cos\left(f x + e\right)^{2} - b f\right)}}, \frac{2 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) + 8 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right)}{16 \, {\left(b f \cos\left(f x + e\right)^{2} - b f\right)}}\right]"," ",0,"[1/16*(2*(cos(f*x + e)^2 - 1)*sqrt(-b)*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) + 8*sqrt(b/cos(f*x + e))*cos(f*x + e)^2 - (cos(f*x + e)^2 - 1)*sqrt(-b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)))/(b*f*cos(f*x + e)^2 - b*f), 1/16*(2*(cos(f*x + e)^2 - 1)*sqrt(b)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) + 8*sqrt(b/cos(f*x + e))*cos(f*x + e)^2 + (cos(f*x + e)^2 - 1)*sqrt(b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)))/(b*f*cos(f*x + e)^2 - b*f)]","B",0
416,1,450,0,1.107842," ","integrate(csc(f*x+e)^5/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{10 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) - 5 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(5 \, \cos\left(f x + e\right)^{4} - 9 \, \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{128 \, {\left(b f \cos\left(f x + e\right)^{4} - 2 \, b f \cos\left(f x + e\right)^{2} + b f\right)}}, \frac{10 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) + 5 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(5 \, \cos\left(f x + e\right)^{4} - 9 \, \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{128 \, {\left(b f \cos\left(f x + e\right)^{4} - 2 \, b f \cos\left(f x + e\right)^{2} + b f\right)}}\right]"," ",0,"[1/128*(10*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(-b)*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) - 5*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(-b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*(5*cos(f*x + e)^4 - 9*cos(f*x + e)^2)*sqrt(b/cos(f*x + e)))/(b*f*cos(f*x + e)^4 - 2*b*f*cos(f*x + e)^2 + b*f), 1/128*(10*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(b)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) + 5*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)) + 8*(5*cos(f*x + e)^4 - 9*cos(f*x + e)^2)*sqrt(b/cos(f*x + e)))/(b*f*cos(f*x + e)^4 - 2*b*f*cos(f*x + e)^2 + b*f)]","B",0
417,0,0,0,1.021231," ","integrate(sin(f*x+e)^6/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(f x + e\right)^{6} - 3 \, \cos\left(f x + e\right)^{4} + 3 \, \cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b \sec\left(f x + e\right)}}{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral(-(cos(f*x + e)^6 - 3*cos(f*x + e)^4 + 3*cos(f*x + e)^2 - 1)*sqrt(b*sec(f*x + e))/(b*sec(f*x + e)), x)","F",0
418,0,0,0,0.648986," ","integrate(sin(f*x+e)^4/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{b \sec\left(f x + e\right)}}{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral((cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(b*sec(f*x + e))/(b*sec(f*x + e)), x)","F",0
419,0,0,0,0.690049," ","integrate(sin(f*x+e)^2/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b \sec\left(f x + e\right)}}{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*sqrt(b*sec(f*x + e))/(b*sec(f*x + e)), x)","F",0
420,0,0,0,0.858351," ","integrate(1/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)}}{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))/(b*sec(f*x + e)), x)","F",0
421,0,0,0,0.847914," ","integrate(csc(f*x+e)^2/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \csc\left(f x + e\right)^{2}}{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*csc(f*x + e)^2/(b*sec(f*x + e)), x)","F",0
422,0,0,0,0.945641," ","integrate(csc(f*x+e)^4/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \csc\left(f x + e\right)^{4}}{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*csc(f*x + e)^4/(b*sec(f*x + e)), x)","F",0
423,0,0,0,0.748543," ","integrate(csc(f*x+e)^6/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \csc\left(f x + e\right)^{6}}{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*csc(f*x + e)^6/(b*sec(f*x + e)), x)","F",0
424,1,61,0,1.016960," ","integrate(sin(f*x+e)^7/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(195 \, \cos\left(f x + e\right)^{9} - 765 \, \cos\left(f x + e\right)^{7} + 1105 \, \cos\left(f x + e\right)^{5} - 663 \, \cos\left(f x + e\right)^{3}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{3315 \, b^{2} f}"," ",0,"2/3315*(195*cos(f*x + e)^9 - 765*cos(f*x + e)^7 + 1105*cos(f*x + e)^5 - 663*cos(f*x + e)^3)*sqrt(b/cos(f*x + e))/(b^2*f)","A",0
425,1,51,0,1.060399," ","integrate(sin(f*x+e)^5/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(45 \, \cos\left(f x + e\right)^{7} - 130 \, \cos\left(f x + e\right)^{5} + 117 \, \cos\left(f x + e\right)^{3}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{585 \, b^{2} f}"," ",0,"-2/585*(45*cos(f*x + e)^7 - 130*cos(f*x + e)^5 + 117*cos(f*x + e)^3)*sqrt(b/cos(f*x + e))/(b^2*f)","A",0
426,1,41,0,1.072412," ","integrate(sin(f*x+e)^3/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, \cos\left(f x + e\right)^{5} - 9 \, \cos\left(f x + e\right)^{3}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{45 \, b^{2} f}"," ",0,"2/45*(5*cos(f*x + e)^5 - 9*cos(f*x + e)^3)*sqrt(b/cos(f*x + e))/(b^2*f)","A",0
427,1,28,0,0.977637," ","integrate(sin(f*x+e)/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{3}}{5 \, b^{2} f}"," ",0,"-2/5*sqrt(b/cos(f*x + e))*cos(f*x + e)^3/(b^2*f)","A",0
428,1,314,0,1.133496," ","integrate(csc(f*x+e)/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-b} \arctan\left(\frac{2 \, \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{b \cos\left(f x + e\right) + b}\right) + 8 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) - \sqrt{-b} \log\left(-\frac{b \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right)}{4 \, b^{2} f}, \frac{2 \, \sqrt{b} \arctan\left(\frac{2 \, \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{b \cos\left(f x + e\right) - b}\right) + 8 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + \sqrt{b} \log\left(-\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right)}{4 \, b^{2} f}\right]"," ",0,"[1/4*(2*sqrt(-b)*arctan(2*sqrt(-b)*sqrt(b/cos(f*x + e))*cos(f*x + e)/(b*cos(f*x + e) + b)) + 8*sqrt(b/cos(f*x + e))*cos(f*x + e) - sqrt(-b)*log(-(b*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)))/(b^2*f), 1/4*(2*sqrt(b)*arctan(2*sqrt(b)*sqrt(b/cos(f*x + e))*cos(f*x + e)/(b*cos(f*x + e) - b)) + 8*sqrt(b/cos(f*x + e))*cos(f*x + e) + sqrt(b)*log(-(b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)))/(b^2*f)]","B",0
429,1,364,0,1.088935," ","integrate(csc(f*x+e)^3/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) + {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 8 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{16 \, {\left(b^{2} f \cos\left(f x + e\right)^{2} - b^{2} f\right)}}, \frac{2 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) + {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \log\left(\frac{b \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{16 \, {\left(b^{2} f \cos\left(f x + e\right)^{2} - b^{2} f\right)}}\right]"," ",0,"[-1/16*(2*(cos(f*x + e)^2 - 1)*sqrt(-b)*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) + (cos(f*x + e)^2 - 1)*sqrt(-b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 8*sqrt(b/cos(f*x + e))*cos(f*x + e))/(b^2*f*cos(f*x + e)^2 - b^2*f), 1/16*(2*(cos(f*x + e)^2 - 1)*sqrt(b)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) + (cos(f*x + e)^2 - 1)*sqrt(b)*log((b*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)) + 8*sqrt(b/cos(f*x + e))*cos(f*x + e))/(b^2*f*cos(f*x + e)^2 - b^2*f)]","B",0
430,1,454,0,1.090683," ","integrate(csc(f*x+e)^5/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) + 3 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \log\left(\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{128 \, {\left(b^{2} f \cos\left(f x + e\right)^{4} - 2 \, b^{2} f \cos\left(f x + e\right)^{2} + b^{2} f\right)}}, \frac{6 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) + 3 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \log\left(\frac{b \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right) - 8 \, {\left(\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{128 \, {\left(b^{2} f \cos\left(f x + e\right)^{4} - 2 \, b^{2} f \cos\left(f x + e\right)^{2} + b^{2} f\right)}}\right]"," ",0,"[-1/128*(6*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(-b)*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) + 3*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(-b)*log((b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*(cos(f*x + e)^3 + 3*cos(f*x + e))*sqrt(b/cos(f*x + e)))/(b^2*f*cos(f*x + e)^4 - 2*b^2*f*cos(f*x + e)^2 + b^2*f), 1/128*(6*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(b)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) + 3*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(b)*log((b*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)) - 8*(cos(f*x + e)^3 + 3*cos(f*x + e))*sqrt(b/cos(f*x + e)))/(b^2*f*cos(f*x + e)^4 - 2*b^2*f*cos(f*x + e)^2 + b^2*f)]","B",0
431,0,0,0,0.998985," ","integrate(sin(f*x+e)^4/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{b \sec\left(f x + e\right)}}{b^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral((cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(b*sec(f*x + e))/(b^2*sec(f*x + e)^2), x)","F",0
432,0,0,0,0.709728," ","integrate(sin(f*x+e)^2/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b \sec\left(f x + e\right)}}{b^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*sqrt(b*sec(f*x + e))/(b^2*sec(f*x + e)^2), x)","F",0
433,0,0,0,0.831412," ","integrate(1/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)}}{b^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))/(b^2*sec(f*x + e)^2), x)","F",0
434,0,0,0,0.909023," ","integrate(csc(f*x+e)^2/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \csc\left(f x + e\right)^{2}}{b^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*csc(f*x + e)^2/(b^2*sec(f*x + e)^2), x)","F",0
435,0,0,0,0.922369," ","integrate(csc(f*x+e)^4/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \csc\left(f x + e\right)^{4}}{b^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*csc(f*x + e)^4/(b^2*sec(f*x + e)^2), x)","F",0
436,0,0,0,0.690386," ","integrate(csc(f*x+e)^6/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \csc\left(f x + e\right)^{6}}{b^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*csc(f*x + e)^6/(b^2*sec(f*x + e)^2), x)","F",0
437,1,61,0,0.846021," ","integrate(sin(f*x+e)^7/(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(385 \, \cos\left(f x + e\right)^{10} - 1463 \, \cos\left(f x + e\right)^{8} + 1995 \, \cos\left(f x + e\right)^{6} - 1045 \, \cos\left(f x + e\right)^{4}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{7315 \, b^{3} f}"," ",0,"2/7315*(385*cos(f*x + e)^10 - 1463*cos(f*x + e)^8 + 1995*cos(f*x + e)^6 - 1045*cos(f*x + e)^4)*sqrt(b/cos(f*x + e))/(b^3*f)","A",0
438,1,51,0,0.880880," ","integrate(sin(f*x+e)^5/(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(77 \, \cos\left(f x + e\right)^{8} - 210 \, \cos\left(f x + e\right)^{6} + 165 \, \cos\left(f x + e\right)^{4}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{1155 \, b^{3} f}"," ",0,"-2/1155*(77*cos(f*x + e)^8 - 210*cos(f*x + e)^6 + 165*cos(f*x + e)^4)*sqrt(b/cos(f*x + e))/(b^3*f)","A",0
439,1,41,0,0.827441," ","integrate(sin(f*x+e)^3/(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, \cos\left(f x + e\right)^{6} - 11 \, \cos\left(f x + e\right)^{4}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{77 \, b^{3} f}"," ",0,"2/77*(7*cos(f*x + e)^6 - 11*cos(f*x + e)^4)*sqrt(b/cos(f*x + e))/(b^3*f)","A",0
440,1,28,0,0.937234," ","integrate(sin(f*x+e)/(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{4}}{7 \, b^{3} f}"," ",0,"-2/7*sqrt(b/cos(f*x + e))*cos(f*x + e)^4/(b^3*f)","A",0
441,1,319,0,1.545561," ","integrate(csc(f*x+e)/(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{8 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + 6 \, \sqrt{-b} \arctan\left(\frac{2 \, \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{b \cos\left(f x + e\right) + b}\right) - 3 \, \sqrt{-b} \log\left(-\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right)}{12 \, b^{3} f}, \frac{8 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} - 6 \, \sqrt{b} \arctan\left(\frac{2 \, \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{b \cos\left(f x + e\right) - b}\right) + 3 \, \sqrt{b} \log\left(-\frac{b \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right)}{12 \, b^{3} f}\right]"," ",0,"[1/12*(8*sqrt(b/cos(f*x + e))*cos(f*x + e)^2 + 6*sqrt(-b)*arctan(2*sqrt(-b)*sqrt(b/cos(f*x + e))*cos(f*x + e)/(b*cos(f*x + e) + b)) - 3*sqrt(-b)*log(-(b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)))/(b^3*f), 1/12*(8*sqrt(b/cos(f*x + e))*cos(f*x + e)^2 - 6*sqrt(b)*arctan(2*sqrt(b)*sqrt(b/cos(f*x + e))*cos(f*x + e)/(b*cos(f*x + e) - b)) + 3*sqrt(b)*log(-(b*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)))/(b^3*f)]","B",0
442,1,370,0,1.315771," ","integrate(csc(f*x+e)^3/(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) - 8 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + 3 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \log\left(\frac{b \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right)}{16 \, {\left(b^{3} f \cos\left(f x + e\right)^{2} - b^{3} f\right)}}, -\frac{6 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) - 8 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} - 3 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \log\left(\frac{b \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right)}{16 \, {\left(b^{3} f \cos\left(f x + e\right)^{2} - b^{3} f\right)}}\right]"," ",0,"[-1/16*(6*(cos(f*x + e)^2 - 1)*sqrt(-b)*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) - 8*sqrt(b/cos(f*x + e))*cos(f*x + e)^2 + 3*(cos(f*x + e)^2 - 1)*sqrt(-b)*log((b*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)))/(b^3*f*cos(f*x + e)^2 - b^3*f), -1/16*(6*(cos(f*x + e)^2 - 1)*sqrt(b)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) - 8*sqrt(b/cos(f*x + e))*cos(f*x + e)^2 - 3*(cos(f*x + e)^2 - 1)*sqrt(b)*log((b*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)))/(b^3*f*cos(f*x + e)^2 - b^3*f)]","B",0
443,1,458,0,1.188612," ","integrate(csc(f*x+e)^5/(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{2 \, b}\right) + 3 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \log\left(\frac{b \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} - 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(3 \, \cos\left(f x + e\right)^{4} + \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{128 \, {\left(b^{3} f \cos\left(f x + e\right)^{4} - 2 \, b^{3} f \cos\left(f x + e\right)^{2} + b^{3} f\right)}}, -\frac{6 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \arctan\left(\frac{\sqrt{\frac{b}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) - 1\right)}}{2 \, \sqrt{b}}\right) - 3 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \log\left(\frac{b \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b}{\cos\left(f x + e\right)}} + 6 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(3 \, \cos\left(f x + e\right)^{4} + \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{128 \, {\left(b^{3} f \cos\left(f x + e\right)^{4} - 2 \, b^{3} f \cos\left(f x + e\right)^{2} + b^{3} f\right)}}\right]"," ",0,"[-1/128*(6*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(-b)*arctan(1/2*sqrt(-b)*sqrt(b/cos(f*x + e))*(cos(f*x + e) + 1)/b) + 3*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(-b)*log((b*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - cos(f*x + e))*sqrt(-b)*sqrt(b/cos(f*x + e)) - 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*(3*cos(f*x + e)^4 + cos(f*x + e)^2)*sqrt(b/cos(f*x + e)))/(b^3*f*cos(f*x + e)^4 - 2*b^3*f*cos(f*x + e)^2 + b^3*f), -1/128*(6*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(b)*arctan(1/2*sqrt(b/cos(f*x + e))*(cos(f*x + e) - 1)/sqrt(b)) - 3*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(b)*log((b*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(b)*sqrt(b/cos(f*x + e)) + 6*b*cos(f*x + e) + b)/(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)) + 8*(3*cos(f*x + e)^4 + cos(f*x + e)^2)*sqrt(b/cos(f*x + e)))/(b^3*f*cos(f*x + e)^4 - 2*b^3*f*cos(f*x + e)^2 + b^3*f)]","B",0
444,0,0,0,0.745704," ","integrate(sin(f*x+e)^4/(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{b \sec\left(f x + e\right)}}{b^{3} \sec\left(f x + e\right)^{3}}, x\right)"," ",0,"integral((cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(b*sec(f*x + e))/(b^3*sec(f*x + e)^3), x)","F",0
445,0,0,0,0.976337," ","integrate(sin(f*x+e)^2/(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b \sec\left(f x + e\right)}}{b^{3} \sec\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*sqrt(b*sec(f*x + e))/(b^3*sec(f*x + e)^3), x)","F",0
446,0,0,0,0.796846," ","integrate(1/(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)}}{b^{3} \sec\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))/(b^3*sec(f*x + e)^3), x)","F",0
447,0,0,0,1.096589," ","integrate(csc(f*x+e)^2/(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \csc\left(f x + e\right)^{2}}{b^{3} \sec\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*csc(f*x + e)^2/(b^3*sec(f*x + e)^3), x)","F",0
448,0,0,0,1.002785," ","integrate(csc(f*x+e)^4/(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \csc\left(f x + e\right)^{4}}{b^{3} \sec\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*csc(f*x + e)^4/(b^3*sec(f*x + e)^3), x)","F",0
449,0,0,0,0.916677," ","integrate(csc(f*x+e)^6/(b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \csc\left(f x + e\right)^{6}}{b^{3} \sec\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*csc(f*x + e)^6/(b^3*sec(f*x + e)^3), x)","F",0
450,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))^(9/2)*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))^(5/2)*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
452,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))^(1/2)*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
453,1,44,0,1.727102," ","integrate((b*sec(f*x+e))^(1/2)/(a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a^{2} f \sin\left(f x + e\right)}"," ",0,"-2*sqrt(a*sin(f*x + e))*sqrt(b/cos(f*x + e))*cos(f*x + e)/(a^2*f*sin(f*x + e))","A",0
454,1,73,0,1.873349," ","integrate((b*sec(f*x+e))^(1/2)/(a*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, \cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{5 \, {\left(a^{4} f \cos\left(f x + e\right)^{2} - a^{4} f\right)} \sin\left(f x + e\right)}"," ",0,"-2/5*(4*cos(f*x + e)^3 - 5*cos(f*x + e))*sqrt(a*sin(f*x + e))*sqrt(b/cos(f*x + e))/((a^4*f*cos(f*x + e)^2 - a^4*f)*sin(f*x + e))","A",0
455,1,96,0,1.803222," ","integrate((b*sec(f*x+e))^(1/2)/(a*sin(f*x+e))^(11/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(32 \, \cos\left(f x + e\right)^{5} - 72 \, \cos\left(f x + e\right)^{3} + 45 \, \cos\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}}}{45 \, {\left(a^{6} f \cos\left(f x + e\right)^{4} - 2 \, a^{6} f \cos\left(f x + e\right)^{2} + a^{6} f\right)} \sin\left(f x + e\right)}"," ",0,"-2/45*(32*cos(f*x + e)^5 - 72*cos(f*x + e)^3 + 45*cos(f*x + e))*sqrt(a*sin(f*x + e))*sqrt(b/cos(f*x + e))/((a^6*f*cos(f*x + e)^4 - 2*a^6*f*cos(f*x + e)^2 + a^6*f)*sin(f*x + e))","A",0
456,0,0,0,1.615948," ","integrate((a*sin(f*x+e))^(7/2)*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{3} \cos\left(f x + e\right)^{2} - a^{3}\right)} \sqrt{b \sec\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right)} \sin\left(f x + e\right), x\right)"," ",0,"integral(-(a^3*cos(f*x + e)^2 - a^3)*sqrt(b*sec(f*x + e))*sqrt(a*sin(f*x + e))*sin(f*x + e), x)","F",0
457,0,0,0,1.294921," ","integrate((a*sin(f*x+e))^(3/2)*(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right)} a \sin\left(f x + e\right), x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*sqrt(a*sin(f*x + e))*a*sin(f*x + e), x)","F",0
458,0,0,0,1.273411," ","integrate((b*sec(f*x+e))^(1/2)/(a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right)}}{a \sin\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*sqrt(a*sin(f*x + e))/(a*sin(f*x + e)), x)","F",0
459,0,0,0,1.521004," ","integrate((b*sec(f*x+e))^(1/2)/(a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sec\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right)}}{{\left(a^{3} \cos\left(f x + e\right)^{2} - a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(b*sec(f*x + e))*sqrt(a*sin(f*x + e))/((a^3*cos(f*x + e)^2 - a^3)*sin(f*x + e)), x)","F",0
460,0,0,0,1.019405," ","integrate((b*sec(f*x+e))^(1/2)/(a*sin(f*x+e))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right)}}{{\left(a^{5} \cos\left(f x + e\right)^{4} - 2 \, a^{5} \cos\left(f x + e\right)^{2} + a^{5}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*sqrt(a*sin(f*x + e))/((a^5*cos(f*x + e)^4 - 2*a^5*cos(f*x + e)^2 + a^5)*sin(f*x + e)), x)","F",0
461,0,0,0,1.412687," ","integrate(sin(f*x+e)^(9/2)/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{b \sec\left(f x + e\right)} \sqrt{\sin\left(f x + e\right)}}{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral((cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(b*sec(f*x + e))*sqrt(sin(f*x + e))/(b*sec(f*x + e)), x)","F",0
462,0,0,0,1.894331," ","integrate(sin(f*x+e)^(5/2)/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{b \sec\left(f x + e\right)} \sqrt{\sin\left(f x + e\right)}}{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*sqrt(b*sec(f*x + e))*sqrt(sin(f*x + e))/(b*sec(f*x + e)), x)","F",0
463,0,0,0,0.967798," ","integrate(sin(f*x+e)^(1/2)/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \sqrt{\sin\left(f x + e\right)}}{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*sqrt(sin(f*x + e))/(b*sec(f*x + e)), x)","F",0
464,0,0,0,1.126451," ","integrate(1/sin(f*x+e)^(3/2)/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sec\left(f x + e\right)} \sqrt{\sin\left(f x + e\right)}}{{\left(b \cos\left(f x + e\right)^{2} - b\right)} \sec\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(b*sec(f*x + e))*sqrt(sin(f*x + e))/((b*cos(f*x + e)^2 - b)*sec(f*x + e)), x)","F",0
465,0,0,0,1.437496," ","integrate(1/sin(f*x+e)^(7/2)/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \sqrt{\sin\left(f x + e\right)}}{{\left(b \cos\left(f x + e\right)^{4} - 2 \, b \cos\left(f x + e\right)^{2} + b\right)} \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*sqrt(sin(f*x + e))/((b*cos(f*x + e)^4 - 2*b*cos(f*x + e)^2 + b)*sec(f*x + e)), x)","F",0
466,-1,0,0,0.000000," ","integrate(sin(f*x+e)^(3/2)/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
467,-1,0,0,0.000000," ","integrate(1/sin(f*x+e)^(1/2)/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,1,48,0,2.152983," ","integrate(1/sin(f*x+e)^(5/2)/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} \sqrt{\sin\left(f x + e\right)}}{3 \, {\left(b f \cos\left(f x + e\right)^{2} - b f\right)}}"," ",0,"2/3*sqrt(b/cos(f*x + e))*cos(f*x + e)^2*sqrt(sin(f*x + e))/(b*f*cos(f*x + e)^2 - b*f)","A",0
469,1,72,0,2.353644," ","integrate(1/sin(f*x+e)^(9/2)/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, \cos\left(f x + e\right)^{4} - 7 \, \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}} \sqrt{\sin\left(f x + e\right)}}{21 \, {\left(b f \cos\left(f x + e\right)^{4} - 2 \, b f \cos\left(f x + e\right)^{2} + b f\right)}}"," ",0,"2/21*(4*cos(f*x + e)^4 - 7*cos(f*x + e)^2)*sqrt(b/cos(f*x + e))*sqrt(sin(f*x + e))/(b*f*cos(f*x + e)^4 - 2*b*f*cos(f*x + e)^2 + b*f)","A",0
470,1,95,0,1.886900," ","integrate(1/sin(f*x+e)^(13/2)/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(32 \, \cos\left(f x + e\right)^{6} - 88 \, \cos\left(f x + e\right)^{4} + 77 \, \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}} \sqrt{\sin\left(f x + e\right)}}{231 \, {\left(b f \cos\left(f x + e\right)^{6} - 3 \, b f \cos\left(f x + e\right)^{4} + 3 \, b f \cos\left(f x + e\right)^{2} - b f\right)}}"," ",0,"2/231*(32*cos(f*x + e)^6 - 88*cos(f*x + e)^4 + 77*cos(f*x + e)^2)*sqrt(b/cos(f*x + e))*sqrt(sin(f*x + e))/(b*f*cos(f*x + e)^6 - 3*b*f*cos(f*x + e)^4 + 3*b*f*cos(f*x + e)^2 - b*f)","A",0
471,1,116,0,1.713244," ","integrate(1/sin(f*x+e)^(17/2)/(b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(128 \, \cos\left(f x + e\right)^{8} - 480 \, \cos\left(f x + e\right)^{6} + 660 \, \cos\left(f x + e\right)^{4} - 385 \, \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}} \sqrt{\sin\left(f x + e\right)}}{1155 \, {\left(b f \cos\left(f x + e\right)^{8} - 4 \, b f \cos\left(f x + e\right)^{6} + 6 \, b f \cos\left(f x + e\right)^{4} - 4 \, b f \cos\left(f x + e\right)^{2} + b f\right)}}"," ",0,"2/1155*(128*cos(f*x + e)^8 - 480*cos(f*x + e)^6 + 660*cos(f*x + e)^4 - 385*cos(f*x + e)^2)*sqrt(b/cos(f*x + e))*sqrt(sin(f*x + e))/(b*f*cos(f*x + e)^8 - 4*b*f*cos(f*x + e)^6 + 6*b*f*cos(f*x + e)^4 - 4*b*f*cos(f*x + e)^2 + b*f)","A",0
472,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))^(9/2)/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
473,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))^(5/2)/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))^(1/2)/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
475,-1,0,0,0.000000," ","integrate(1/(b*sec(f*x+e))^(3/2)/(a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
476,1,68,0,1.901684," ","integrate(1/(b*sec(f*x+e))^(3/2)/(a*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{3}}{5 \, {\left(a^{4} b^{2} f \cos\left(f x + e\right)^{2} - a^{4} b^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"2/5*sqrt(a*sin(f*x + e))*sqrt(b/cos(f*x + e))*cos(f*x + e)^3/((a^4*b^2*f*cos(f*x + e)^2 - a^4*b^2*f)*sin(f*x + e))","B",0
477,0,0,0,1.599886," ","integrate((a*sin(f*x+e))^(7/2)/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{3} \cos\left(f x + e\right)^{2} - a^{3}\right)} \sqrt{b \sec\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right)} \sin\left(f x + e\right)}{b^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(-(a^3*cos(f*x + e)^2 - a^3)*sqrt(b*sec(f*x + e))*sqrt(a*sin(f*x + e))*sin(f*x + e)/(b^2*sec(f*x + e)^2), x)","F",0
478,0,0,0,1.338836," ","integrate((a*sin(f*x+e))^(3/2)/(b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right)} a \sin\left(f x + e\right)}{b^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*sqrt(a*sin(f*x + e))*a*sin(f*x + e)/(b^2*sec(f*x + e)^2), x)","F",0
479,0,0,0,1.317652," ","integrate(1/(b*sec(f*x+e))^(3/2)/(a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right)}}{a b^{2} \sec\left(f x + e\right)^{2} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*sqrt(a*sin(f*x + e))/(a*b^2*sec(f*x + e)^2*sin(f*x + e)), x)","F",0
480,0,0,0,1.352696," ","integrate(1/(b*sec(f*x+e))^(3/2)/(a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sec\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right)}}{{\left(a^{3} b^{2} \cos\left(f x + e\right)^{2} - a^{3} b^{2}\right)} \sec\left(f x + e\right)^{2} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(b*sec(f*x + e))*sqrt(a*sin(f*x + e))/((a^3*b^2*cos(f*x + e)^2 - a^3*b^2)*sec(f*x + e)^2*sin(f*x + e)), x)","F",0
481,0,0,0,1.448849," ","integrate(1/(b*sec(f*x+e))^(3/2)/(a*sin(f*x+e))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right)}}{{\left(a^{5} b^{2} \cos\left(f x + e\right)^{4} - 2 \, a^{5} b^{2} \cos\left(f x + e\right)^{2} + a^{5} b^{2}\right)} \sec\left(f x + e\right)^{2} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*sqrt(a*sin(f*x + e))/((a^5*b^2*cos(f*x + e)^4 - 2*a^5*b^2*cos(f*x + e)^2 + a^5*b^2)*sec(f*x + e)^2*sin(f*x + e)), x)","F",0
482,0,0,0,0.782762," ","integrate(1/(b*sec(f*x+e))^(3/2)/(a*sin(f*x+e))^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sec\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right)}}{{\left(a^{7} b^{2} \cos\left(f x + e\right)^{6} - 3 \, a^{7} b^{2} \cos\left(f x + e\right)^{4} + 3 \, a^{7} b^{2} \cos\left(f x + e\right)^{2} - a^{7} b^{2}\right)} \sec\left(f x + e\right)^{2} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(b*sec(f*x + e))*sqrt(a*sin(f*x + e))/((a^7*b^2*cos(f*x + e)^6 - 3*a^7*b^2*cos(f*x + e)^4 + 3*a^7*b^2*cos(f*x + e)^2 - a^7*b^2)*sec(f*x + e)^2*sin(f*x + e)), x)","F",0
483,0,0,0,1.404324," ","integrate((d*sec(b*x+a))^(5/2)*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \sec\left(b x + a\right)} \left(c \sin\left(b x + a\right)\right)^{m} d^{2} \sec\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(d*sec(b*x + a))*(c*sin(b*x + a))^m*d^2*sec(b*x + a)^2, x)","F",0
484,0,0,0,1.358820," ","integrate((d*sec(b*x+a))^(3/2)*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \sec\left(b x + a\right)} \left(c \sin\left(b x + a\right)\right)^{m} d \sec\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*sec(b*x + a))*(c*sin(b*x + a))^m*d*sec(b*x + a), x)","F",0
485,0,0,0,0.932863," ","integrate((d*sec(b*x+a))^(1/2)*(c*sin(b*x+a))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \sec\left(b x + a\right)} \left(c \sin\left(b x + a\right)\right)^{m}, x\right)"," ",0,"integral(sqrt(d*sec(b*x + a))*(c*sin(b*x + a))^m, x)","F",0
486,0,0,0,1.158696," ","integrate((c*sin(b*x+a))^m/(d*sec(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \sec\left(b x + a\right)} \left(c \sin\left(b x + a\right)\right)^{m}}{d \sec\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(d*sec(b*x + a))*(c*sin(b*x + a))^m/(d*sec(b*x + a)), x)","F",0
487,0,0,0,1.341190," ","integrate((c*sin(b*x+a))^m/(d*sec(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \sec\left(b x + a\right)} \left(c \sin\left(b x + a\right)\right)^{m}}{d^{2} \sec\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*sec(b*x + a))*(c*sin(b*x + a))^m/(d^2*sec(b*x + a)^2), x)","F",0
488,0,0,0,1.451816," ","integrate(sec(f*x+e)^n*sin(f*x+e)^m,x, algorithm=""fricas"")","{\rm integral}\left(\sec\left(f x + e\right)^{n} \sin\left(f x + e\right)^{m}, x\right)"," ",0,"integral(sec(f*x + e)^n*sin(f*x + e)^m, x)","F",0
489,0,0,0,1.324118," ","integrate(sec(f*x+e)^n*(a*sin(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(a \sin\left(f x + e\right)\right)^{m} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral((a*sin(f*x + e))^m*sec(f*x + e)^n, x)","F",0
490,0,0,0,1.366198," ","integrate((b*sec(f*x+e))^n*sin(f*x+e)^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{n} \sin\left(f x + e\right)^{m}, x\right)"," ",0,"integral((b*sec(f*x + e))^n*sin(f*x + e)^m, x)","F",0
491,0,0,0,1.324758," ","integrate((b*sec(f*x+e))^n*(a*sin(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{n} \left(a \sin\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b*sec(f*x + e))^n*(a*sin(f*x + e))^m, x)","F",0
492,1,85,0,1.528897," ","integrate((b*sec(f*x+e))^n*sin(f*x+e)^5,x, algorithm=""fricas"")","\frac{{\left({\left(n^{2} - 4 \, n + 3\right)} \cos\left(f x + e\right)^{5} - 2 \, {\left(n^{2} - 6 \, n + 5\right)} \cos\left(f x + e\right)^{3} + {\left(n^{2} - 8 \, n + 15\right)} \cos\left(f x + e\right)\right)} \left(\frac{b}{\cos\left(f x + e\right)}\right)^{n}}{f n^{3} - 9 \, f n^{2} + 23 \, f n - 15 \, f}"," ",0,"((n^2 - 4*n + 3)*cos(f*x + e)^5 - 2*(n^2 - 6*n + 5)*cos(f*x + e)^3 + (n^2 - 8*n + 15)*cos(f*x + e))*(b/cos(f*x + e))^n/(f*n^3 - 9*f*n^2 + 23*f*n - 15*f)","A",0
493,1,53,0,1.288657," ","integrate((b*sec(f*x+e))^n*sin(f*x+e)^3,x, algorithm=""fricas"")","-\frac{{\left({\left(n - 1\right)} \cos\left(f x + e\right)^{3} - {\left(n - 3\right)} \cos\left(f x + e\right)\right)} \left(\frac{b}{\cos\left(f x + e\right)}\right)^{n}}{f n^{2} - 4 \, f n + 3 \, f}"," ",0,"-((n - 1)*cos(f*x + e)^3 - (n - 3)*cos(f*x + e))*(b/cos(f*x + e))^n/(f*n^2 - 4*f*n + 3*f)","A",0
494,1,28,0,1.173622," ","integrate((b*sec(f*x+e))^n*sin(f*x+e),x, algorithm=""fricas"")","\frac{\left(\frac{b}{\cos\left(f x + e\right)}\right)^{n} \cos\left(f x + e\right)}{f n - f}"," ",0,"(b/cos(f*x + e))^n*cos(f*x + e)/(f*n - f)","A",0
495,0,0,0,1.161084," ","integrate(csc(f*x+e)*(b*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{n} \csc\left(f x + e\right), x\right)"," ",0,"integral((b*sec(f*x + e))^n*csc(f*x + e), x)","F",0
496,0,0,0,0.690081," ","integrate(csc(f*x+e)^3*(b*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{n} \csc\left(f x + e\right)^{3}, x\right)"," ",0,"integral((b*sec(f*x + e))^n*csc(f*x + e)^3, x)","F",0
497,0,0,0,0.986849," ","integrate((b*sec(f*x+e))^n*sin(f*x+e)^6,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(f x + e\right)^{6} - 3 \, \cos\left(f x + e\right)^{4} + 3 \, \cos\left(f x + e\right)^{2} - 1\right)} \left(b \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(-(cos(f*x + e)^6 - 3*cos(f*x + e)^4 + 3*cos(f*x + e)^2 - 1)*(b*sec(f*x + e))^n, x)","F",0
498,0,0,0,1.142390," ","integrate((b*sec(f*x+e))^n*sin(f*x+e)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \left(b \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*(b*sec(f*x + e))^n, x)","F",0
499,0,0,0,1.473019," ","integrate((b*sec(f*x+e))^n*sin(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(f x + e\right)^{2} - 1\right)} \left(b \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*(b*sec(f*x + e))^n, x)","F",0
500,0,0,0,0.754046," ","integrate((b*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b*sec(f*x + e))^n, x)","F",0
501,0,0,0,1.211095," ","integrate(csc(f*x+e)^2*(b*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{n} \csc\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*sec(f*x + e))^n*csc(f*x + e)^2, x)","F",0
502,0,0,0,1.178322," ","integrate(csc(f*x+e)^4*(b*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{n} \csc\left(f x + e\right)^{4}, x\right)"," ",0,"integral((b*sec(f*x + e))^n*csc(f*x + e)^4, x)","F",0
503,0,0,0,1.347301," ","integrate((b*sec(b*x+a))^n*(c*sin(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c \sin\left(b x + a\right)} \left(b \sec\left(b x + a\right)\right)^{n} c \sin\left(b x + a\right), x\right)"," ",0,"integral(sqrt(c*sin(b*x + a))*(b*sec(b*x + a))^n*c*sin(b*x + a), x)","F",0
504,0,0,0,1.041315," ","integrate((b*sec(b*x+a))^n*(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c \sin\left(b x + a\right)} \left(b \sec\left(b x + a\right)\right)^{n}, x\right)"," ",0,"integral(sqrt(c*sin(b*x + a))*(b*sec(b*x + a))^n, x)","F",0
505,0,0,0,1.224455," ","integrate((b*sec(b*x+a))^n/(c*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c \sin\left(b x + a\right)} \left(b \sec\left(b x + a\right)\right)^{n}}{c \sin\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(c*sin(b*x + a))*(b*sec(b*x + a))^n/(c*sin(b*x + a)), x)","F",0
506,0,0,0,0.850122," ","integrate((b*sec(b*x+a))^n/(c*sin(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{c \sin\left(b x + a\right)} \left(b \sec\left(b x + a\right)\right)^{n}}{c^{2} \cos\left(b x + a\right)^{2} - c^{2}}, x\right)"," ",0,"integral(-sqrt(c*sin(b*x + a))*(b*sec(b*x + a))^n/(c^2*cos(b*x + a)^2 - c^2), x)","F",0
507,0,0,0,1.082976," ","integrate(sin(f*x+e)^4*(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{d \csc\left(f x + e\right)}, x\right)"," ",0,"integral((cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(d*csc(f*x + e)), x)","F",0
508,0,0,0,1.008763," ","integrate(sin(f*x+e)^3*(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{d \csc\left(f x + e\right)} \sin\left(f x + e\right), x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*sqrt(d*csc(f*x + e))*sin(f*x + e), x)","F",0
509,0,0,0,1.062258," ","integrate(sin(f*x+e)^2*(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{d \csc\left(f x + e\right)}, x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*sqrt(d*csc(f*x + e)), x)","F",0
510,0,0,0,1.340515," ","integrate(sin(f*x+e)*(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \csc\left(f x + e\right)} \sin\left(f x + e\right), x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*sin(f*x + e), x)","F",0
511,0,0,0,1.124128," ","integrate((d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \csc\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e)), x)","F",0
512,0,0,0,1.468072," ","integrate(csc(f*x+e)*(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \csc\left(f x + e\right)} \csc\left(f x + e\right), x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*csc(f*x + e), x)","F",0
513,0,0,0,0.984439," ","integrate(csc(f*x+e)^2*(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \csc\left(f x + e\right)} \csc\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*csc(f*x + e)^2, x)","F",0
514,0,0,0,1.043341," ","integrate(csc(f*x+e)^3*(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \csc\left(f x + e\right)} \csc\left(f x + e\right)^{3}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*csc(f*x + e)^3, x)","F",0
515,0,0,0,1.232490," ","integrate((d*csc(f*x+e))^(3/2)*sin(f*x+e)^5,x, algorithm=""fricas"")","{\rm integral}\left({\left(d \cos\left(f x + e\right)^{4} - 2 \, d \cos\left(f x + e\right)^{2} + d\right)} \sqrt{d \csc\left(f x + e\right)} \csc\left(f x + e\right) \sin\left(f x + e\right), x\right)"," ",0,"integral((d*cos(f*x + e)^4 - 2*d*cos(f*x + e)^2 + d)*sqrt(d*csc(f*x + e))*csc(f*x + e)*sin(f*x + e), x)","F",0
516,0,0,0,1.147637," ","integrate((d*csc(f*x+e))^(3/2)*sin(f*x+e)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(d \cos\left(f x + e\right)^{4} - 2 \, d \cos\left(f x + e\right)^{2} + d\right)} \sqrt{d \csc\left(f x + e\right)} \csc\left(f x + e\right), x\right)"," ",0,"integral((d*cos(f*x + e)^4 - 2*d*cos(f*x + e)^2 + d)*sqrt(d*csc(f*x + e))*csc(f*x + e), x)","F",0
517,0,0,0,0.685725," ","integrate((d*csc(f*x+e))^(3/2)*sin(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(d \cos\left(f x + e\right)^{2} - d\right)} \sqrt{d \csc\left(f x + e\right)} \csc\left(f x + e\right) \sin\left(f x + e\right), x\right)"," ",0,"integral(-(d*cos(f*x + e)^2 - d)*sqrt(d*csc(f*x + e))*csc(f*x + e)*sin(f*x + e), x)","F",0
518,0,0,0,0.676930," ","integrate((d*csc(f*x+e))^(3/2)*sin(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(d \cos\left(f x + e\right)^{2} - d\right)} \sqrt{d \csc\left(f x + e\right)} \csc\left(f x + e\right), x\right)"," ",0,"integral(-(d*cos(f*x + e)^2 - d)*sqrt(d*csc(f*x + e))*csc(f*x + e), x)","F",0
519,0,0,0,1.248790," ","integrate((d*csc(f*x+e))^(3/2)*sin(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \csc\left(f x + e\right)} d \csc\left(f x + e\right) \sin\left(f x + e\right), x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*d*csc(f*x + e)*sin(f*x + e), x)","F",0
520,0,0,0,1.079879," ","integrate((d*csc(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \csc\left(f x + e\right)} d \csc\left(f x + e\right), x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*d*csc(f*x + e), x)","F",0
521,0,0,0,1.072933," ","integrate(csc(f*x+e)*(d*csc(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \csc\left(f x + e\right)} d \csc\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*d*csc(f*x + e)^2, x)","F",0
522,0,0,0,0.850891," ","integrate(csc(f*x+e)^2*(d*csc(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \csc\left(f x + e\right)} d \csc\left(f x + e\right)^{3}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*d*csc(f*x + e)^3, x)","F",0
523,0,0,0,1.265631," ","integrate(sin(f*x+e)^3/(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{d \csc\left(f x + e\right)} \sin\left(f x + e\right)}{d \csc\left(f x + e\right)}, x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*sqrt(d*csc(f*x + e))*sin(f*x + e)/(d*csc(f*x + e)), x)","F",0
524,0,0,0,1.203050," ","integrate(sin(f*x+e)^2/(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{d \csc\left(f x + e\right)}}{d \csc\left(f x + e\right)}, x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*sqrt(d*csc(f*x + e))/(d*csc(f*x + e)), x)","F",0
525,0,0,0,0.829530," ","integrate(sin(f*x+e)/(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \csc\left(f x + e\right)} \sin\left(f x + e\right)}{d \csc\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*sin(f*x + e)/(d*csc(f*x + e)), x)","F",0
526,0,0,0,1.274743," ","integrate(1/(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \csc\left(f x + e\right)}}{d \csc\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))/(d*csc(f*x + e)), x)","F",0
527,0,0,0,1.162047," ","integrate(csc(f*x+e)/(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \csc\left(f x + e\right)}}{d}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))/d, x)","F",0
528,0,0,0,0.906122," ","integrate(csc(f*x+e)^2/(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \csc\left(f x + e\right)} \csc\left(f x + e\right)}{d}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*csc(f*x + e)/d, x)","F",0
529,0,0,0,0.738628," ","integrate(csc(f*x+e)^3/(d*csc(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \csc\left(f x + e\right)} \csc\left(f x + e\right)^{2}}{d}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*csc(f*x + e)^2/d, x)","F",0
530,0,0,0,0.995625," ","integrate(sin(f*x+e)^2/(d*csc(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{d \csc\left(f x + e\right)}}{d^{2} \csc\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*sqrt(d*csc(f*x + e))/(d^2*csc(f*x + e)^2), x)","F",0
531,0,0,0,1.507269," ","integrate(sin(f*x+e)/(d*csc(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \csc\left(f x + e\right)} \sin\left(f x + e\right)}{d^{2} \csc\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*sin(f*x + e)/(d^2*csc(f*x + e)^2), x)","F",0
532,0,0,0,1.188941," ","integrate(1/(d*csc(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \csc\left(f x + e\right)}}{d^{2} \csc\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))/(d^2*csc(f*x + e)^2), x)","F",0
533,0,0,0,1.436634," ","integrate(csc(f*x+e)/(d*csc(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \csc\left(f x + e\right)}}{d^{2} \csc\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))/(d^2*csc(f*x + e)), x)","F",0
534,0,0,0,1.258971," ","integrate(csc(f*x+e)^2/(d*csc(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \csc\left(f x + e\right)}}{d^{2}}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))/d^2, x)","F",0
535,0,0,0,1.387511," ","integrate(csc(f*x+e)^3/(d*csc(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \csc\left(f x + e\right)} \csc\left(f x + e\right)}{d^{2}}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*csc(f*x + e)/d^2, x)","F",0
536,0,0,0,1.005381," ","integrate(csc(f*x+e)^4/(d*csc(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \csc\left(f x + e\right)} \csc\left(f x + e\right)^{2}}{d^{2}}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*csc(f*x + e)^2/d^2, x)","F",0
537,0,0,0,1.304738," ","integrate(csc(f*x+e)^5/(d*csc(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \csc\left(f x + e\right)} \csc\left(f x + e\right)^{3}}{d^{2}}, x\right)"," ",0,"integral(sqrt(d*csc(f*x + e))*csc(f*x + e)^3/d^2, x)","F",0
538,0,0,0,0.852355," ","integrate((b*csc(f*x+e))^n*(a*sin(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \csc\left(f x + e\right)\right)^{n} \left(a \sin\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b*csc(f*x + e))^n*(a*sin(f*x + e))^m, x)","F",0
