1,1,10,0,0.468598," ","integrate(cos(b*x+a),x, algorithm=""maxima"")","\frac{\sin\left(b x + a\right)}{b}"," ",0,"sin(b*x + a)/b","A",0
2,1,22,0,0.301450," ","integrate(cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)}{4 \, b}"," ",0,"1/4*(2*b*x + 2*a + sin(2*b*x + 2*a))/b","A",0
3,1,22,0,0.298420," ","integrate(cos(b*x+a)^3,x, algorithm=""maxima"")","-\frac{\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)}{3 \, b}"," ",0,"-1/3*(sin(b*x + a)^3 - 3*sin(b*x + a))/b","A",0
4,1,33,0,0.485171," ","integrate(cos(b*x+a)^4,x, algorithm=""maxima"")","\frac{12 \, b x + 12 \, a + \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)}{32 \, b}"," ",0,"1/32*(12*b*x + 12*a + sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))/b","A",0
5,1,34,0,0.308194," ","integrate(cos(b*x+a)^5,x, algorithm=""maxima"")","\frac{3 \, \sin\left(b x + a\right)^{5} - 10 \, \sin\left(b x + a\right)^{3} + 15 \, \sin\left(b x + a\right)}{15 \, b}"," ",0,"1/15*(3*sin(b*x + a)^5 - 10*sin(b*x + a)^3 + 15*sin(b*x + a))/b","A",0
6,1,48,0,0.329672," ","integrate(cos(b*x+a)^6,x, algorithm=""maxima"")","-\frac{4 \, \sin\left(2 \, b x + 2 \, a\right)^{3} - 60 \, b x - 60 \, a - 9 \, \sin\left(4 \, b x + 4 \, a\right) - 48 \, \sin\left(2 \, b x + 2 \, a\right)}{192 \, b}"," ",0,"-1/192*(4*sin(2*b*x + 2*a)^3 - 60*b*x - 60*a - 9*sin(4*b*x + 4*a) - 48*sin(2*b*x + 2*a))/b","A",0
7,1,44,0,0.691096," ","integrate(cos(b*x+a)^7,x, algorithm=""maxima"")","-\frac{5 \, \sin\left(b x + a\right)^{7} - 21 \, \sin\left(b x + a\right)^{5} + 35 \, \sin\left(b x + a\right)^{3} - 35 \, \sin\left(b x + a\right)}{35 \, b}"," ",0,"-1/35*(5*sin(b*x + a)^7 - 21*sin(b*x + a)^5 + 35*sin(b*x + a)^3 - 35*sin(b*x + a))/b","A",0
8,1,59,0,0.315933," ","integrate(cos(b*x+a)^8,x, algorithm=""maxima"")","-\frac{128 \, \sin\left(2 \, b x + 2 \, a\right)^{3} - 840 \, b x - 840 \, a - 3 \, \sin\left(8 \, b x + 8 \, a\right) - 168 \, \sin\left(4 \, b x + 4 \, a\right) - 768 \, \sin\left(2 \, b x + 2 \, a\right)}{3072 \, b}"," ",0,"-1/3072*(128*sin(2*b*x + 2*a)^3 - 840*b*x - 840*a - 3*sin(8*b*x + 8*a) - 168*sin(4*b*x + 4*a) - 768*sin(2*b*x + 2*a))/b","A",0
9,0,0,0,0.000000," ","integrate(cos(b*x+a)^(7/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(7/2), x)","F",0
10,0,0,0,0.000000," ","integrate(cos(b*x+a)^(5/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(5/2), x)","F",0
11,0,0,0,0.000000," ","integrate(cos(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(3/2), x)","F",0
12,0,0,0,0.000000," ","integrate(cos(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\cos\left(b x + a\right)}\,{d x}"," ",0,"integrate(sqrt(cos(b*x + a)), x)","F",0
13,0,0,0,0.000000," ","integrate(1/cos(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\cos\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/sqrt(cos(b*x + a)), x)","F",0
14,0,0,0,0.000000," ","integrate(1/cos(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\cos\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(-3/2), x)","F",0
15,0,0,0,0.000000," ","integrate(1/cos(b*x+a)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\cos\left(b x + a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(-5/2), x)","F",0
16,0,0,0,0.000000," ","integrate(1/cos(b*x+a)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{\cos\left(b x + a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(-7/2), x)","F",0
17,0,0,0,0.000000," ","integrate((c*cos(b*x+a))^(7/2),x, algorithm=""maxima"")","\int \left(c \cos\left(b x + a\right)\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((c*cos(b*x + a))^(7/2), x)","F",0
18,0,0,0,0.000000," ","integrate((c*cos(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \left(c \cos\left(b x + a\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((c*cos(b*x + a))^(5/2), x)","F",0
19,0,0,0,0.000000," ","integrate((c*cos(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \left(c \cos\left(b x + a\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*cos(b*x + a))^(3/2), x)","F",0
20,0,0,0,0.000000," ","integrate((c*cos(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c \cos\left(b x + a\right)}\,{d x}"," ",0,"integrate(sqrt(c*cos(b*x + a)), x)","F",0
21,0,0,0,0.000000," ","integrate(1/(c*cos(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c \cos\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/sqrt(c*cos(b*x + a)), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(c*cos(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \cos\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*cos(b*x + a))^(-3/2), x)","F",0
23,0,0,0,0.000000," ","integrate(1/(c*cos(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \cos\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*cos(b*x + a))^(-5/2), x)","F",0
24,0,0,0,0.000000," ","integrate(1/(c*cos(b*x+a))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \cos\left(b x + a\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*cos(b*x + a))^(-7/2), x)","F",0
25,0,0,0,0.000000," ","integrate(cos(b*x+a)^(4/3),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(4/3), x)","F",0
26,0,0,0,0.000000," ","integrate(cos(b*x+a)^(2/3),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(2/3), x)","F",0
27,0,0,0,0.000000," ","integrate(cos(b*x+a)^(1/3),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(1/3), x)","F",0
28,0,0,0,0.000000," ","integrate(1/cos(b*x+a)^(1/3),x, algorithm=""maxima"")","\int \frac{1}{\cos\left(b x + a\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(-1/3), x)","F",0
29,0,0,0,0.000000," ","integrate(1/cos(b*x+a)^(2/3),x, algorithm=""maxima"")","\int \frac{1}{\cos\left(b x + a\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(-2/3), x)","F",0
30,0,0,0,0.000000," ","integrate(1/cos(b*x+a)^(4/3),x, algorithm=""maxima"")","\int \frac{1}{\cos\left(b x + a\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(-4/3), x)","F",0
31,0,0,0,0.000000," ","integrate((c*cos(b*x+a))^(4/3),x, algorithm=""maxima"")","\int \left(c \cos\left(b x + a\right)\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((c*cos(b*x + a))^(4/3), x)","F",0
32,0,0,0,0.000000," ","integrate((c*cos(b*x+a))^(2/3),x, algorithm=""maxima"")","\int \left(c \cos\left(b x + a\right)\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((c*cos(b*x + a))^(2/3), x)","F",0
33,0,0,0,0.000000," ","integrate((c*cos(b*x+a))^(1/3),x, algorithm=""maxima"")","\int \left(c \cos\left(b x + a\right)\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((c*cos(b*x + a))^(1/3), x)","F",0
34,0,0,0,0.000000," ","integrate(1/(c*cos(b*x+a))^(1/3),x, algorithm=""maxima"")","\int \frac{1}{\left(c \cos\left(b x + a\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((c*cos(b*x + a))^(-1/3), x)","F",0
35,0,0,0,0.000000," ","integrate(1/(c*cos(b*x+a))^(2/3),x, algorithm=""maxima"")","\int \frac{1}{\left(c \cos\left(b x + a\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((c*cos(b*x + a))^(-2/3), x)","F",0
36,0,0,0,0.000000," ","integrate(1/(c*cos(b*x+a))^(4/3),x, algorithm=""maxima"")","\int \frac{1}{\left(c \cos\left(b x + a\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((c*cos(b*x + a))^(-4/3), x)","F",0
37,0,0,0,0.000000," ","integrate(cos(b*x+a)^n,x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{n}\,{d x}"," ",0,"integrate(cos(b*x + a)^n, x)","F",0
38,0,0,0,0.000000," ","integrate((c*cos(b*x+a))^n,x, algorithm=""maxima"")","\int \left(c \cos\left(b x + a\right)\right)^{n}\,{d x}"," ",0,"integrate((c*cos(b*x + a))^n, x)","F",0
39,1,31,0,0.682596," ","integrate((a*cos(x)^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{240} \, {\left(3 \, a^{2} \sin\left(5 \, x\right) + 25 \, a^{2} \sin\left(3 \, x\right) + 150 \, a^{2} \sin\left(x\right)\right)} \sqrt{a}"," ",0,"1/240*(3*a^2*sin(5*x) + 25*a^2*sin(3*x) + 150*a^2*sin(x))*sqrt(a)","A",0
40,1,17,0,0.893311," ","integrate((a*cos(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{12} \, {\left(a \sin\left(3 \, x\right) + 9 \, a \sin\left(x\right)\right)} \sqrt{a}"," ",0,"1/12*(a*sin(3*x) + 9*a*sin(x))*sqrt(a)","A",0
41,1,6,0,0.676111," ","integrate((a*cos(x)^2)^(1/2),x, algorithm=""maxima"")","\sqrt{a} \sin\left(x\right)"," ",0,"sqrt(a)*sin(x)","A",0
42,1,38,0,0.678269," ","integrate(1/(a*cos(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)}{2 \, \sqrt{a}}"," ",0,"1/2*(log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1))/sqrt(a)","B",0
43,1,304,0,0.675602," ","integrate(1/(a*cos(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\sin\left(3 \, x\right) - \sin\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) - 4 \, {\left(\cos\left(3 \, x\right) - \cos\left(x\right)\right)} \sin\left(4 \, x\right) + 4 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(3 \, x\right) - 8 \, \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 8 \, \cos\left(x\right) \sin\left(2 \, x\right) - 8 \, \cos\left(2 \, x\right) \sin\left(x\right) - 4 \, \sin\left(x\right)}{4 \, {\left(a \cos\left(4 \, x\right)^{2} + 4 \, a \cos\left(2 \, x\right)^{2} + a \sin\left(4 \, x\right)^{2} + 4 \, a \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, a \sin\left(2 \, x\right)^{2} + 2 \, {\left(2 \, a \cos\left(2 \, x\right) + a\right)} \cos\left(4 \, x\right) + 4 \, a \cos\left(2 \, x\right) + a\right)} \sqrt{a}}"," ",0,"1/4*(4*(sin(3*x) - sin(x))*cos(4*x) + (2*(2*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 4*cos(2*x)^2 + sin(4*x)^2 + 4*sin(4*x)*sin(2*x) + 4*sin(2*x)^2 + 4*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - (2*(2*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 4*cos(2*x)^2 + sin(4*x)^2 + 4*sin(4*x)*sin(2*x) + 4*sin(2*x)^2 + 4*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) - 4*(cos(3*x) - cos(x))*sin(4*x) + 4*(2*cos(2*x) + 1)*sin(3*x) - 8*cos(3*x)*sin(2*x) + 8*cos(x)*sin(2*x) - 8*cos(2*x)*sin(x) - 4*sin(x))/((a*cos(4*x)^2 + 4*a*cos(2*x)^2 + a*sin(4*x)^2 + 4*a*sin(4*x)*sin(2*x) + 4*a*sin(2*x)^2 + 2*(2*a*cos(2*x) + a)*cos(4*x) + 4*a*cos(2*x) + a)*sqrt(a))","B",0
44,1,933,0,1.375282," ","integrate(1/(a*cos(x)^2)^(5/2),x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, \sin\left(7 \, x\right) + 11 \, \sin\left(5 \, x\right) - 11 \, \sin\left(3 \, x\right) - 3 \, \sin\left(x\right)\right)} \cos\left(8 \, x\right) - 24 \, {\left(2 \, \sin\left(6 \, x\right) + 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \cos\left(7 \, x\right) + 16 \, {\left(11 \, \sin\left(5 \, x\right) - 11 \, \sin\left(3 \, x\right) - 3 \, \sin\left(x\right)\right)} \cos\left(6 \, x\right) - 88 \, {\left(3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) - 24 \, {\left(11 \, \sin\left(3 \, x\right) + 3 \, \sin\left(x\right)\right)} \cos\left(4 \, x\right) + 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) + 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(8 \, x\right) + \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 36 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) + 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + 16 \, \sin\left(6 \, x\right)^{2} + 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) + 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(8 \, x\right) + \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 36 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) + 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + 16 \, \sin\left(6 \, x\right)^{2} + 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) - 4 \, {\left(3 \, \cos\left(7 \, x\right) + 11 \, \cos\left(5 \, x\right) - 11 \, \cos\left(3 \, x\right) - 3 \, \cos\left(x\right)\right)} \sin\left(8 \, x\right) + 12 \, {\left(4 \, \cos\left(6 \, x\right) + 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(7 \, x\right) - 16 \, {\left(11 \, \cos\left(5 \, x\right) - 11 \, \cos\left(3 \, x\right) - 3 \, \cos\left(x\right)\right)} \sin\left(6 \, x\right) + 44 \, {\left(6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(5 \, x\right) + 24 \, {\left(11 \, \cos\left(3 \, x\right) + 3 \, \cos\left(x\right)\right)} \sin\left(4 \, x\right) - 44 \, {\left(4 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(3 \, x\right) + 176 \, \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 48 \, \cos\left(x\right) \sin\left(2 \, x\right) - 48 \, \cos\left(2 \, x\right) \sin\left(x\right) - 12 \, \sin\left(x\right)}{16 \, {\left(a^{2} \cos\left(8 \, x\right)^{2} + 16 \, a^{2} \cos\left(6 \, x\right)^{2} + 36 \, a^{2} \cos\left(4 \, x\right)^{2} + 16 \, a^{2} \cos\left(2 \, x\right)^{2} + a^{2} \sin\left(8 \, x\right)^{2} + 16 \, a^{2} \sin\left(6 \, x\right)^{2} + 36 \, a^{2} \sin\left(4 \, x\right)^{2} + 48 \, a^{2} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, a^{2} \sin\left(2 \, x\right)^{2} + 8 \, a^{2} \cos\left(2 \, x\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, x\right) + 6 \, a^{2} \cos\left(4 \, x\right) + 4 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)} \cos\left(8 \, x\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, x\right) + 4 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)} \cos\left(6 \, x\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)} \cos\left(4 \, x\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, x\right) + 3 \, a^{2} \sin\left(4 \, x\right) + 2 \, a^{2} \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, x\right) + 2 \, a^{2} \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right)\right)} \sqrt{a}}"," ",0,"1/16*(4*(3*sin(7*x) + 11*sin(5*x) - 11*sin(3*x) - 3*sin(x))*cos(8*x) - 24*(2*sin(6*x) + 3*sin(4*x) + 2*sin(2*x))*cos(7*x) + 16*(11*sin(5*x) - 11*sin(3*x) - 3*sin(x))*cos(6*x) - 88*(3*sin(4*x) + 2*sin(2*x))*cos(5*x) - 24*(11*sin(3*x) + 3*sin(x))*cos(4*x) + 3*(2*(4*cos(6*x) + 6*cos(4*x) + 4*cos(2*x) + 1)*cos(8*x) + cos(8*x)^2 + 8*(6*cos(4*x) + 4*cos(2*x) + 1)*cos(6*x) + 16*cos(6*x)^2 + 12*(4*cos(2*x) + 1)*cos(4*x) + 36*cos(4*x)^2 + 16*cos(2*x)^2 + 4*(2*sin(6*x) + 3*sin(4*x) + 2*sin(2*x))*sin(8*x) + sin(8*x)^2 + 16*(3*sin(4*x) + 2*sin(2*x))*sin(6*x) + 16*sin(6*x)^2 + 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) + 16*sin(2*x)^2 + 8*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - 3*(2*(4*cos(6*x) + 6*cos(4*x) + 4*cos(2*x) + 1)*cos(8*x) + cos(8*x)^2 + 8*(6*cos(4*x) + 4*cos(2*x) + 1)*cos(6*x) + 16*cos(6*x)^2 + 12*(4*cos(2*x) + 1)*cos(4*x) + 36*cos(4*x)^2 + 16*cos(2*x)^2 + 4*(2*sin(6*x) + 3*sin(4*x) + 2*sin(2*x))*sin(8*x) + sin(8*x)^2 + 16*(3*sin(4*x) + 2*sin(2*x))*sin(6*x) + 16*sin(6*x)^2 + 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) + 16*sin(2*x)^2 + 8*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) - 4*(3*cos(7*x) + 11*cos(5*x) - 11*cos(3*x) - 3*cos(x))*sin(8*x) + 12*(4*cos(6*x) + 6*cos(4*x) + 4*cos(2*x) + 1)*sin(7*x) - 16*(11*cos(5*x) - 11*cos(3*x) - 3*cos(x))*sin(6*x) + 44*(6*cos(4*x) + 4*cos(2*x) + 1)*sin(5*x) + 24*(11*cos(3*x) + 3*cos(x))*sin(4*x) - 44*(4*cos(2*x) + 1)*sin(3*x) + 176*cos(3*x)*sin(2*x) + 48*cos(x)*sin(2*x) - 48*cos(2*x)*sin(x) - 12*sin(x))/((a^2*cos(8*x)^2 + 16*a^2*cos(6*x)^2 + 36*a^2*cos(4*x)^2 + 16*a^2*cos(2*x)^2 + a^2*sin(8*x)^2 + 16*a^2*sin(6*x)^2 + 36*a^2*sin(4*x)^2 + 48*a^2*sin(4*x)*sin(2*x) + 16*a^2*sin(2*x)^2 + 8*a^2*cos(2*x) + a^2 + 2*(4*a^2*cos(6*x) + 6*a^2*cos(4*x) + 4*a^2*cos(2*x) + a^2)*cos(8*x) + 8*(6*a^2*cos(4*x) + 4*a^2*cos(2*x) + a^2)*cos(6*x) + 12*(4*a^2*cos(2*x) + a^2)*cos(4*x) + 4*(2*a^2*sin(6*x) + 3*a^2*sin(4*x) + 2*a^2*sin(2*x))*sin(8*x) + 16*(3*a^2*sin(4*x) + 2*a^2*sin(2*x))*sin(6*x))*sqrt(a))","B",0
45,0,0,0,0.000000," ","integrate((a*cos(x)^3)^(5/2),x, algorithm=""maxima"")","\int \left(a \cos\left(x\right)^{3}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*cos(x)^3)^(5/2), x)","F",0
46,0,0,0,0.000000," ","integrate((a*cos(x)^3)^(3/2),x, algorithm=""maxima"")","\int \left(a \cos\left(x\right)^{3}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*cos(x)^3)^(3/2), x)","F",0
47,0,0,0,0.000000," ","integrate((a*cos(x)^3)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \cos\left(x\right)^{3}}\,{d x}"," ",0,"integrate(sqrt(a*cos(x)^3), x)","F",0
48,0,0,0,0.000000," ","integrate(1/(a*cos(x)^3)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \cos\left(x\right)^{3}}}\,{d x}"," ",0,"integrate(1/sqrt(a*cos(x)^3), x)","F",0
49,0,0,0,0.000000," ","integrate(1/(a*cos(x)^3)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(a \cos\left(x\right)^{3}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*cos(x)^3)^(-3/2), x)","F",0
50,0,0,0,0.000000," ","integrate(1/(a*cos(x)^3)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(a \cos\left(x\right)^{3}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*cos(x)^3)^(-5/2), x)","F",0
51,1,85,0,0.903146," ","integrate((a*cos(x)^4)^(5/2),x, algorithm=""maxima"")","\frac{63}{256} \, a^{\frac{5}{2}} x + \frac{315 \, a^{\frac{5}{2}} \tan\left(x\right)^{9} + 1470 \, a^{\frac{5}{2}} \tan\left(x\right)^{7} + 2688 \, a^{\frac{5}{2}} \tan\left(x\right)^{5} + 2370 \, a^{\frac{5}{2}} \tan\left(x\right)^{3} + 965 \, a^{\frac{5}{2}} \tan\left(x\right)}{1280 \, {\left(\tan\left(x\right)^{10} + 5 \, \tan\left(x\right)^{8} + 10 \, \tan\left(x\right)^{6} + 10 \, \tan\left(x\right)^{4} + 5 \, \tan\left(x\right)^{2} + 1\right)}}"," ",0,"63/256*a^(5/2)*x + 1/1280*(315*a^(5/2)*tan(x)^9 + 1470*a^(5/2)*tan(x)^7 + 2688*a^(5/2)*tan(x)^5 + 2370*a^(5/2)*tan(x)^3 + 965*a^(5/2)*tan(x))/(tan(x)^10 + 5*tan(x)^8 + 10*tan(x)^6 + 10*tan(x)^4 + 5*tan(x)^2 + 1)","A",0
52,1,55,0,0.669113," ","integrate((a*cos(x)^4)^(3/2),x, algorithm=""maxima"")","\frac{5}{16} \, a^{\frac{3}{2}} x + \frac{15 \, a^{\frac{3}{2}} \tan\left(x\right)^{5} + 40 \, a^{\frac{3}{2}} \tan\left(x\right)^{3} + 33 \, a^{\frac{3}{2}} \tan\left(x\right)}{48 \, {\left(\tan\left(x\right)^{6} + 3 \, \tan\left(x\right)^{4} + 3 \, \tan\left(x\right)^{2} + 1\right)}}"," ",0,"5/16*a^(3/2)*x + 1/48*(15*a^(3/2)*tan(x)^5 + 40*a^(3/2)*tan(x)^3 + 33*a^(3/2)*tan(x))/(tan(x)^6 + 3*tan(x)^4 + 3*tan(x)^2 + 1)","A",0
53,1,22,0,1.072850," ","integrate((a*cos(x)^4)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{a} x + \frac{\sqrt{a} \tan\left(x\right)}{2 \, {\left(\tan\left(x\right)^{2} + 1\right)}}"," ",0,"1/2*sqrt(a)*x + 1/2*sqrt(a)*tan(x)/(tan(x)^2 + 1)","A",0
54,1,6,0,0.997200," ","integrate(1/(a*cos(x)^4)^(1/2),x, algorithm=""maxima"")","\frac{\tan\left(x\right)}{\sqrt{a}}"," ",0,"tan(x)/sqrt(a)","A",0
55,1,22,0,0.870220," ","integrate(1/(a*cos(x)^4)^(3/2),x, algorithm=""maxima"")","\frac{3 \, \tan\left(x\right)^{5} + 10 \, \tan\left(x\right)^{3} + 15 \, \tan\left(x\right)}{15 \, a^{\frac{3}{2}}}"," ",0,"1/15*(3*tan(x)^5 + 10*tan(x)^3 + 15*tan(x))/a^(3/2)","A",0
56,1,34,0,0.519530," ","integrate(1/(a*cos(x)^4)^(5/2),x, algorithm=""maxima"")","\frac{35 \, \tan\left(x\right)^{9} + 180 \, \tan\left(x\right)^{7} + 378 \, \tan\left(x\right)^{5} + 420 \, \tan\left(x\right)^{3} + 315 \, \tan\left(x\right)}{315 \, a^{\frac{5}{2}}}"," ",0,"1/315*(35*tan(x)^9 + 180*tan(x)^7 + 378*tan(x)^5 + 420*tan(x)^3 + 315*tan(x))/a^(5/2)","A",0
57,0,0,0,0.000000," ","integrate((b*cos(d*x+c)^m)^n,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)^{m}\right)^{n}\,{d x}"," ",0,"integrate((b*cos(d*x + c)^m)^n, x)","F",0
58,0,0,0,0.000000," ","integrate((c*cos(b*x+a)^m)^(5/2),x, algorithm=""maxima"")","\int \left(c \cos\left(b x + a\right)^{m}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((c*cos(b*x + a)^m)^(5/2), x)","F",0
59,-2,0,0,0.000000," ","integrate((c*cos(b*x+a)^m)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: BINDING-STACK overflow at size 10240. Stack can probably be resized.Proceed with caution.","F(-2)",0
60,0,0,0,0.000000," ","integrate((c*cos(b*x+a)^m)^(1/2),x, algorithm=""maxima"")","\int \sqrt{c \cos\left(b x + a\right)^{m}}\,{d x}"," ",0,"integrate(sqrt(c*cos(b*x + a)^m), x)","F",0
61,0,0,0,0.000000," ","integrate(1/(c*cos(b*x+a)^m)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c \cos\left(b x + a\right)^{m}}}\,{d x}"," ",0,"integrate(1/sqrt(c*cos(b*x + a)^m), x)","F",0
62,0,0,0,0.000000," ","integrate(1/(c*cos(b*x+a)^m)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \cos\left(b x + a\right)^{m}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*cos(b*x + a)^m)^(-3/2), x)","F",0
63,0,0,0,0.000000," ","integrate(1/(c*cos(b*x+a)^m)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \cos\left(b x + a\right)^{m}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*cos(b*x + a)^m)^(-5/2), x)","F",0
64,0,0,0,0.000000," ","integrate((c*cos(b*x+a)^m)^(1/m),x, algorithm=""maxima"")","\int \left(c \cos\left(b x + a\right)^{m}\right)^{\left(\frac{1}{m}\right)}\,{d x}"," ",0,"integrate((c*cos(b*x + a)^m)^(1/m), x)","F",0
65,0,0,0,0.000000," ","integrate((a*(b*cos(d*x+c))^p)^n,x, algorithm=""maxima"")","\int \left(\left(b \cos\left(d x + c\right)\right)^{p} a\right)^{n}\,{d x}"," ",0,"integrate(((b*cos(d*x + c))^p*a)^n, x)","F",0
66,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right)} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c))*cos(d*x + c)^5, x)","F",0
67,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right)} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c))*cos(d*x + c)^4, x)","F",0
68,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right)} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c))*cos(d*x + c)^3, x)","F",0
69,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right)} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c))*cos(d*x + c)^2, x)","F",0
70,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right)} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c))*cos(d*x + c), x)","F",0
71,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c)), x)","F",0
72,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c))*sec(d*x + c), x)","F",0
73,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c))*sec(d*x + c)^2, x)","F",0
74,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c))*sec(d*x + c)^3, x)","F",0
75,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c))*sec(d*x + c)^4, x)","F",0
76,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c))*sec(d*x + c)^5, x)","F",0
77,0,0,0,0.000000," ","integrate(sec(d*x+c)^6*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c))*sec(d*x + c)^6, x)","F",0
78,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(3/2)*cos(d*x + c)^4, x)","F",0
79,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(3/2)*cos(d*x + c)^3, x)","F",0
80,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(3/2)*cos(d*x + c)^2, x)","F",0
81,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(3/2)*cos(d*x + c), x)","F",0
82,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(3/2), x)","F",0
83,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2)*sec(d*x+c),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(3/2)*sec(d*x + c), x)","F",0
84,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(3/2)*sec(d*x + c)^2, x)","F",0
85,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(3/2)*sec(d*x + c)^3, x)","F",0
86,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(3/2)*sec(d*x + c)^4, x)","F",0
87,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(3/2)*sec(d*x + c)^5, x)","F",0
88,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(3/2)*sec(d*x + c)^6, x)","F",0
89,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2)*sec(d*x+c)^7,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)^{7}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(3/2)*sec(d*x + c)^7, x)","F",0
90,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(5/2)*cos(d*x + c)^3, x)","F",0
91,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(5/2)*cos(d*x + c)^2, x)","F",0
92,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(5/2)*cos(d*x + c), x)","F",0
93,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(5/2), x)","F",0
94,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*sec(d*x+c),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(5/2)*sec(d*x + c), x)","F",0
95,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(5/2)*sec(d*x + c)^2, x)","F",0
96,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(5/2)*sec(d*x + c)^3, x)","F",0
97,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(5/2)*sec(d*x + c)^4, x)","F",0
98,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(5/2)*sec(d*x + c)^5, x)","F",0
99,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(5/2)*sec(d*x + c)^6, x)","F",0
100,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*sec(d*x+c)^7,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)^{7}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(5/2)*sec(d*x + c)^7, x)","F",0
101,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*sec(d*x+c)^8,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)^{8}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(5/2)*sec(d*x + c)^8, x)","F",0
102,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(7/2), x)","F",0
103,0,0,0,0.000000," ","integrate(cos(d*x+c)^6/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{6}}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(cos(d*x + c)^6/sqrt(b*cos(d*x + c)), x)","F",0
104,0,0,0,0.000000," ","integrate(cos(d*x+c)^5/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{5}}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(cos(d*x + c)^5/sqrt(b*cos(d*x + c)), x)","F",0
105,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4}}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/sqrt(b*cos(d*x + c)), x)","F",0
106,0,0,0,0.000000," ","integrate(cos(d*x+c)^3/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3/sqrt(b*cos(d*x + c)), x)","F",0
107,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/sqrt(b*cos(d*x + c)), x)","F",0
108,0,0,0,0.000000," ","integrate(cos(d*x+c)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(cos(d*x + c)/sqrt(b*cos(d*x + c)), x)","F",0
109,0,0,0,0.000000," ","integrate(1/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/sqrt(b*cos(d*x + c)), x)","F",0
110,0,0,0,0.000000," ","integrate(sec(d*x+c)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sec(d*x + c)/sqrt(b*cos(d*x + c)), x)","F",0
111,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/sqrt(b*cos(d*x + c)), x)","F",0
112,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/sqrt(b*cos(d*x + c)), x)","F",0
113,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{4}}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/sqrt(b*cos(d*x + c)), x)","F",0
114,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{5}}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/sqrt(b*cos(d*x + c)), x)","F",0
115,0,0,0,0.000000," ","integrate(cos(d*x+c)^7/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{7}}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^7/(b*cos(d*x + c))^(3/2), x)","F",0
116,0,0,0,0.000000," ","integrate(cos(d*x+c)^6/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{6}}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^6/(b*cos(d*x + c))^(3/2), x)","F",0
117,0,0,0,0.000000," ","integrate(cos(d*x+c)^5/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{5}}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^5/(b*cos(d*x + c))^(3/2), x)","F",0
118,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4}}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/(b*cos(d*x + c))^(3/2), x)","F",0
119,0,0,0,0.000000," ","integrate(cos(d*x+c)^3/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{3}}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3/(b*cos(d*x + c))^(3/2), x)","F",0
120,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*cos(d*x + c))^(3/2), x)","F",0
121,0,0,0,0.000000," ","integrate(cos(d*x+c)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*cos(d*x + c))^(3/2), x)","F",0
122,0,0,0,0.000000," ","integrate(1/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(-3/2), x)","F",0
123,0,0,0,0.000000," ","integrate(sec(d*x+c)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*cos(d*x + c))^(3/2), x)","F",0
124,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*cos(d*x + c))^(3/2), x)","F",0
125,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*cos(d*x + c))^(3/2), x)","F",0
126,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{4}}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(b*cos(d*x + c))^(3/2), x)","F",0
127,0,0,0,0.000000," ","integrate(cos(d*x+c)^8/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{8}}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^8/(b*cos(d*x + c))^(5/2), x)","F",0
128,0,0,0,0.000000," ","integrate(cos(d*x+c)^7/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{7}}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^7/(b*cos(d*x + c))^(5/2), x)","F",0
129,0,0,0,0.000000," ","integrate(cos(d*x+c)^6/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{6}}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^6/(b*cos(d*x + c))^(5/2), x)","F",0
130,0,0,0,0.000000," ","integrate(cos(d*x+c)^5/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{5}}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^5/(b*cos(d*x + c))^(5/2), x)","F",0
131,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4}}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/(b*cos(d*x + c))^(5/2), x)","F",0
132,0,0,0,0.000000," ","integrate(cos(d*x+c)^3/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{3}}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3/(b*cos(d*x + c))^(5/2), x)","F",0
133,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*cos(d*x + c))^(5/2), x)","F",0
134,0,0,0,0.000000," ","integrate(cos(d*x+c)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*cos(d*x + c))^(5/2), x)","F",0
135,0,0,0,0.000000," ","integrate(1/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(-5/2), x)","F",0
136,0,0,0,0.000000," ","integrate(sec(d*x+c)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*cos(d*x + c))^(5/2), x)","F",0
137,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*cos(d*x + c))^(5/2), x)","F",0
138,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*cos(d*x + c))^(5/2), x)","F",0
139,0,0,0,0.000000," ","integrate(1/(b*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{\left(b \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(-7/2), x)","F",0
140,1,49,0,0.771334," ","integrate(cos(d*x+c)^(7/2)*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \sqrt{b}}{32 \, d}"," ",0,"1/32*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sqrt(b)/d","A",0
141,1,42,0,1.118588," ","integrate(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b} {\left(\sin\left(3 \, d x + 3 \, c\right) + 9 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)\right)}}{12 \, d}"," ",0,"1/12*sqrt(b)*(sin(3*d*x + 3*c) + 9*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))/d","A",0
142,1,25,0,1.099279," ","integrate(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} \sqrt{b}}{4 \, d}"," ",0,"1/4*(2*d*x + 2*c + sin(2*d*x + 2*c))*sqrt(b)/d","A",0
143,1,13,0,0.866929," ","integrate(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b} \sin\left(d x + c\right)}{d}"," ",0,"sqrt(b)*sin(d*x + c)/d","A",0
144,1,26,0,0.878725," ","integrate((b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{b} \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{d}"," ",0,"2*sqrt(b)*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/d","A",0
145,1,65,0,1.268396," ","integrate((b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{b} {\left(\log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)}}{2 \, d}"," ",0,"1/2*sqrt(b)*(log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","B",0
146,1,54,0,1.102004," ","integrate((b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{b} \sin\left(2 \, d x + 2 \, c\right)}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"2*sqrt(b)*sin(2*d*x + 2*c)/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*d)","A",0
147,1,661,0,1.128552," ","integrate((b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{{\left(4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{b}}{4 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/4*(4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(b)/((2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*d)","B",0
148,1,294,0,1.126876," ","integrate((b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{4 \, {\left({\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(4 \, d x + 4 \, c\right) - 3 \, \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 9 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)} \sqrt{b}}{3 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"4/3*((3*cos(2*d*x + 2*c) + 1)*sin(6*d*x + 6*c) + 3*(3*cos(2*d*x + 2*c) + 1)*sin(4*d*x + 4*c) - 3*cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 9*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))*sqrt(b)/((2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*d)","B",0
149,1,1656,0,1.230041," ","integrate((b*cos(d*x+c))^(1/2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","-\frac{{\left(12 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 12 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{b}}{16 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/16*(12*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 3*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 12*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(b)/((2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*d)","B",0
150,1,53,0,1.047178," ","integrate(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{{\left(12 \, {\left(d x + c\right)} b + b \sin\left(4 \, d x + 4 \, c\right) + 8 \, b \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \sqrt{b}}{32 \, d}"," ",0,"1/32*(12*(d*x + c)*b + b*sin(4*d*x + 4*c) + 8*b*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sqrt(b)/d","A",0
151,1,45,0,1.247934," ","integrate(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{{\left(b \sin\left(3 \, d x + 3 \, c\right) + 9 \, b \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)\right)} \sqrt{b}}{12 \, d}"," ",0,"1/12*(b*sin(3*d*x + 3*c) + 9*b*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))*sqrt(b)/d","A",0
152,1,28,0,1.544494," ","integrate(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{{\left(2 \, {\left(d x + c\right)} b + b \sin\left(2 \, d x + 2 \, c\right)\right)} \sqrt{b}}{4 \, d}"," ",0,"1/4*(2*(d*x + c)*b + b*sin(2*d*x + 2*c))*sqrt(b)/d","A",0
153,1,13,0,1.094069," ","integrate((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{b^{\frac{3}{2}} \sin\left(d x + c\right)}{d}"," ",0,"b^(3/2)*sin(d*x + c)/d","A",0
154,1,26,0,0.828194," ","integrate((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{2 \, b^{\frac{3}{2}} \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{d}"," ",0,"2*b^(3/2)*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/d","A",0
155,1,68,0,1.106453," ","integrate((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{{\left(b \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - b \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)} \sqrt{b}}{2 \, d}"," ",0,"1/2*(b*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - b*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))*sqrt(b)/d","B",0
156,1,54,0,0.830514," ","integrate((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{2 \, b^{\frac{3}{2}} \sin\left(2 \, d x + 2 \, c\right)}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"2*b^(3/2)*sin(2*d*x + 2*c)/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*d)","A",0
157,1,691,0,1.205241," ","integrate((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","-\frac{{\left(4 \, {\left(b \sin\left(4 \, d x + 4 \, c\right) + 2 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(b \sin\left(4 \, d x + 4 \, c\right) + 2 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(b \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(b \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(b \cos\left(4 \, d x + 4 \, c\right) + 2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(b \cos\left(4 \, d x + 4 \, c\right) + 2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{b}}{4 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/4*(4*(b*sin(4*d*x + 4*c) + 2*b*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(b*sin(4*d*x + 4*c) + 2*b*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (b*cos(4*d*x + 4*c)^2 + 4*b*cos(2*d*x + 2*c)^2 + b*sin(4*d*x + 4*c)^2 + 4*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b*sin(2*d*x + 2*c)^2 + 2*(2*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (b*cos(4*d*x + 4*c)^2 + 4*b*cos(2*d*x + 2*c)^2 + b*sin(4*d*x + 4*c)^2 + 4*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b*sin(2*d*x + 2*c)^2 + 2*(2*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(b*cos(4*d*x + 4*c) + 2*b*cos(2*d*x + 2*c) + b)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(b*cos(4*d*x + 4*c) + 2*b*cos(2*d*x + 2*c) + b)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(b)/((2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*d)","B",0
158,1,299,0,1.697221," ","integrate((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(3 \, b \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, b \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(3 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(6 \, d x + 6 \, c\right) - 3 \, {\left(3 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sqrt{b}}{3 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-4/3*(3*b*cos(6*d*x + 6*c)*sin(2*d*x + 2*c) + 9*b*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) - (3*b*cos(2*d*x + 2*c) + b)*sin(6*d*x + 6*c) - 3*(3*b*cos(2*d*x + 2*c) + b)*sin(4*d*x + 4*c))*sqrt(b)/((2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*d)","B",0
159,1,1742,0,1.232347," ","integrate((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","-\frac{{\left(12 \, {\left(b \sin\left(8 \, d x + 8 \, c\right) + 4 \, b \sin\left(6 \, d x + 6 \, c\right) + 6 \, b \sin\left(4 \, d x + 4 \, c\right) + 4 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(b \sin\left(8 \, d x + 8 \, c\right) + 4 \, b \sin\left(6 \, d x + 6 \, c\right) + 6 \, b \sin\left(4 \, d x + 4 \, c\right) + 4 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(b \sin\left(8 \, d x + 8 \, c\right) + 4 \, b \sin\left(6 \, d x + 6 \, c\right) + 6 \, b \sin\left(4 \, d x + 4 \, c\right) + 4 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12 \, {\left(b \sin\left(8 \, d x + 8 \, c\right) + 4 \, b \sin\left(6 \, d x + 6 \, c\right) + 6 \, b \sin\left(4 \, d x + 4 \, c\right) + 4 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, {\left(b \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, b \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, b \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, b \cos\left(6 \, d x + 6 \, c\right) + 6 \, b \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, b \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, b \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, b \sin\left(6 \, d x + 6 \, c\right) + 3 \, b \sin\left(4 \, d x + 4 \, c\right) + 2 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, b \sin\left(4 \, d x + 4 \, c\right) + 2 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + b\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 3 \, {\left(b \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, b \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, b \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, b \cos\left(6 \, d x + 6 \, c\right) + 6 \, b \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, b \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, b \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, b \sin\left(6 \, d x + 6 \, c\right) + 3 \, b \sin\left(4 \, d x + 4 \, c\right) + 2 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, b \sin\left(4 \, d x + 4 \, c\right) + 2 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + b\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 12 \, {\left(b \cos\left(8 \, d x + 8 \, c\right) + 4 \, b \cos\left(6 \, d x + 6 \, c\right) + 6 \, b \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(b \cos\left(8 \, d x + 8 \, c\right) + 4 \, b \cos\left(6 \, d x + 6 \, c\right) + 6 \, b \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(b \cos\left(8 \, d x + 8 \, c\right) + 4 \, b \cos\left(6 \, d x + 6 \, c\right) + 6 \, b \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, {\left(b \cos\left(8 \, d x + 8 \, c\right) + 4 \, b \cos\left(6 \, d x + 6 \, c\right) + 6 \, b \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{b}}{16 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/16*(12*(b*sin(8*d*x + 8*c) + 4*b*sin(6*d*x + 6*c) + 6*b*sin(4*d*x + 4*c) + 4*b*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(b*sin(8*d*x + 8*c) + 4*b*sin(6*d*x + 6*c) + 6*b*sin(4*d*x + 4*c) + 4*b*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(b*sin(8*d*x + 8*c) + 4*b*sin(6*d*x + 6*c) + 6*b*sin(4*d*x + 4*c) + 4*b*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12*(b*sin(8*d*x + 8*c) + 4*b*sin(6*d*x + 6*c) + 6*b*sin(4*d*x + 4*c) + 4*b*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*(b*cos(8*d*x + 8*c)^2 + 16*b*cos(6*d*x + 6*c)^2 + 36*b*cos(4*d*x + 4*c)^2 + 16*b*cos(2*d*x + 2*c)^2 + b*sin(8*d*x + 8*c)^2 + 16*b*sin(6*d*x + 6*c)^2 + 36*b*sin(4*d*x + 4*c)^2 + 48*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*b*sin(2*d*x + 2*c)^2 + 2*(4*b*cos(6*d*x + 6*c) + 6*b*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*cos(8*d*x + 8*c) + 8*(6*b*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*cos(6*d*x + 6*c) + 12*(4*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 8*b*cos(2*d*x + 2*c) + 4*(2*b*sin(6*d*x + 6*c) + 3*b*sin(4*d*x + 4*c) + 2*b*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*b*sin(4*d*x + 4*c) + 2*b*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + b)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 3*(b*cos(8*d*x + 8*c)^2 + 16*b*cos(6*d*x + 6*c)^2 + 36*b*cos(4*d*x + 4*c)^2 + 16*b*cos(2*d*x + 2*c)^2 + b*sin(8*d*x + 8*c)^2 + 16*b*sin(6*d*x + 6*c)^2 + 36*b*sin(4*d*x + 4*c)^2 + 48*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*b*sin(2*d*x + 2*c)^2 + 2*(4*b*cos(6*d*x + 6*c) + 6*b*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*cos(8*d*x + 8*c) + 8*(6*b*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*cos(6*d*x + 6*c) + 12*(4*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 8*b*cos(2*d*x + 2*c) + 4*(2*b*sin(6*d*x + 6*c) + 3*b*sin(4*d*x + 4*c) + 2*b*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*b*sin(4*d*x + 4*c) + 2*b*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + b)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 12*(b*cos(8*d*x + 8*c) + 4*b*cos(6*d*x + 6*c) + 6*b*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(b*cos(8*d*x + 8*c) + 4*b*cos(6*d*x + 6*c) + 6*b*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(b*cos(8*d*x + 8*c) + 4*b*cos(6*d*x + 6*c) + 6*b*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*(b*cos(8*d*x + 8*c) + 4*b*cos(6*d*x + 6*c) + 6*b*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(b)/((2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*d)","B",0
160,1,77,0,1.015022," ","integrate(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\left(3 \, b^{2} \sin\left(5 \, d x + 5 \, c\right) + 25 \, b^{2} \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 150 \, b^{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)\right)} \sqrt{b}}{240 \, d}"," ",0,"1/240*(3*b^2*sin(5*d*x + 5*c) + 25*b^2*sin(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 150*b^2*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))))*sqrt(b)/d","A",0
161,1,59,0,1.099388," ","integrate(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\left(12 \, {\left(d x + c\right)} b^{2} + b^{2} \sin\left(4 \, d x + 4 \, c\right) + 8 \, b^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \sqrt{b}}{32 \, d}"," ",0,"1/32*(12*(d*x + c)*b^2 + b^2*sin(4*d*x + 4*c) + 8*b^2*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sqrt(b)/d","A",0
162,1,49,0,1.226371," ","integrate(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\left(b^{2} \sin\left(3 \, d x + 3 \, c\right) + 9 \, b^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)\right)} \sqrt{b}}{12 \, d}"," ",0,"1/12*(b^2*sin(3*d*x + 3*c) + 9*b^2*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))*sqrt(b)/d","A",0
163,1,32,0,1.089261," ","integrate((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{{\left(2 \, {\left(d x + c\right)} b^{2} + b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sqrt{b}}{4 \, d}"," ",0,"1/4*(2*(d*x + c)*b^2 + b^2*sin(2*d*x + 2*c))*sqrt(b)/d","A",0
164,1,13,0,1.481737," ","integrate((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{b^{\frac{5}{2}} \sin\left(d x + c\right)}{d}"," ",0,"b^(5/2)*sin(d*x + c)/d","A",0
165,1,26,0,1.204117," ","integrate((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{2 \, b^{\frac{5}{2}} \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{d}"," ",0,"2*b^(5/2)*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/d","A",0
166,1,72,0,1.356836," ","integrate((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{{\left(b^{2} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - b^{2} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)} \sqrt{b}}{2 \, d}"," ",0,"1/2*(b^2*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - b^2*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))*sqrt(b)/d","B",0
167,1,54,0,1.119963," ","integrate((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{2 \, b^{\frac{5}{2}} \sin\left(2 \, d x + 2 \, c\right)}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"2*b^(5/2)*sin(2*d*x + 2*c)/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*d)","A",0
168,1,747,0,1.830548," ","integrate((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","-\frac{{\left(4 \, {\left(b^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(b^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(b^{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(b^{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{b}}{4 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/4*(4*(b^2*sin(4*d*x + 4*c) + 2*b^2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(b^2*sin(4*d*x + 4*c) + 2*b^2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (b^2*cos(4*d*x + 4*c)^2 + 4*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(4*d*x + 4*c)^2 + 4*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b^2*sin(2*d*x + 2*c)^2 + 4*b^2*cos(2*d*x + 2*c) + b^2 + 2*(2*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c))*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (b^2*cos(4*d*x + 4*c)^2 + 4*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(4*d*x + 4*c)^2 + 4*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b^2*sin(2*d*x + 2*c)^2 + 4*b^2*cos(2*d*x + 2*c) + b^2 + 2*(2*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c))*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(b^2*cos(4*d*x + 4*c) + 2*b^2*cos(2*d*x + 2*c) + b^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(b^2*cos(4*d*x + 4*c) + 2*b^2*cos(2*d*x + 2*c) + b^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(b)/((2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*d)","B",0
169,1,311,0,1.264549," ","integrate((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(3 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(3 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right) - 3 \, {\left(3 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sqrt{b}}{3 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-4/3*(3*b^2*cos(6*d*x + 6*c)*sin(2*d*x + 2*c) + 9*b^2*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) - (3*b^2*cos(2*d*x + 2*c) + b^2)*sin(6*d*x + 6*c) - 3*(3*b^2*cos(2*d*x + 2*c) + b^2)*sin(4*d*x + 4*c))*sqrt(b)/((2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*d)","B",0
170,1,1914,0,1.584342," ","integrate((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(15/2),x, algorithm=""maxima"")","-\frac{{\left(12 \, {\left(b^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, b^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(b^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, b^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(b^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, b^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12 \, {\left(b^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, b^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, {\left(b^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, b^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 3 \, {\left(b^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, b^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 12 \, {\left(b^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(b^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(b^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, {\left(b^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{b}}{16 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/16*(12*(b^2*sin(8*d*x + 8*c) + 4*b^2*sin(6*d*x + 6*c) + 6*b^2*sin(4*d*x + 4*c) + 4*b^2*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(b^2*sin(8*d*x + 8*c) + 4*b^2*sin(6*d*x + 6*c) + 6*b^2*sin(4*d*x + 4*c) + 4*b^2*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(b^2*sin(8*d*x + 8*c) + 4*b^2*sin(6*d*x + 6*c) + 6*b^2*sin(4*d*x + 4*c) + 4*b^2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12*(b^2*sin(8*d*x + 8*c) + 4*b^2*sin(6*d*x + 6*c) + 6*b^2*sin(4*d*x + 4*c) + 4*b^2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*(b^2*cos(8*d*x + 8*c)^2 + 16*b^2*cos(6*d*x + 6*c)^2 + 36*b^2*cos(4*d*x + 4*c)^2 + 16*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(8*d*x + 8*c)^2 + 16*b^2*sin(6*d*x + 6*c)^2 + 36*b^2*sin(4*d*x + 4*c)^2 + 48*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*b^2*sin(2*d*x + 2*c)^2 + 8*b^2*cos(2*d*x + 2*c) + b^2 + 2*(4*b^2*cos(6*d*x + 6*c) + 6*b^2*cos(4*d*x + 4*c) + 4*b^2*cos(2*d*x + 2*c) + b^2)*cos(8*d*x + 8*c) + 8*(6*b^2*cos(4*d*x + 4*c) + 4*b^2*cos(2*d*x + 2*c) + b^2)*cos(6*d*x + 6*c) + 12*(4*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c) + 4*(2*b^2*sin(6*d*x + 6*c) + 3*b^2*sin(4*d*x + 4*c) + 2*b^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*b^2*sin(4*d*x + 4*c) + 2*b^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 3*(b^2*cos(8*d*x + 8*c)^2 + 16*b^2*cos(6*d*x + 6*c)^2 + 36*b^2*cos(4*d*x + 4*c)^2 + 16*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(8*d*x + 8*c)^2 + 16*b^2*sin(6*d*x + 6*c)^2 + 36*b^2*sin(4*d*x + 4*c)^2 + 48*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*b^2*sin(2*d*x + 2*c)^2 + 8*b^2*cos(2*d*x + 2*c) + b^2 + 2*(4*b^2*cos(6*d*x + 6*c) + 6*b^2*cos(4*d*x + 4*c) + 4*b^2*cos(2*d*x + 2*c) + b^2)*cos(8*d*x + 8*c) + 8*(6*b^2*cos(4*d*x + 4*c) + 4*b^2*cos(2*d*x + 2*c) + b^2)*cos(6*d*x + 6*c) + 12*(4*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c) + 4*(2*b^2*sin(6*d*x + 6*c) + 3*b^2*sin(4*d*x + 4*c) + 2*b^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*b^2*sin(4*d*x + 4*c) + 2*b^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 12*(b^2*cos(8*d*x + 8*c) + 4*b^2*cos(6*d*x + 6*c) + 6*b^2*cos(4*d*x + 4*c) + 4*b^2*cos(2*d*x + 2*c) + b^2)*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(b^2*cos(8*d*x + 8*c) + 4*b^2*cos(6*d*x + 6*c) + 6*b^2*cos(4*d*x + 4*c) + 4*b^2*cos(2*d*x + 2*c) + b^2)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(b^2*cos(8*d*x + 8*c) + 4*b^2*cos(6*d*x + 6*c) + 6*b^2*cos(4*d*x + 4*c) + 4*b^2*cos(2*d*x + 2*c) + b^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*(b^2*cos(8*d*x + 8*c) + 4*b^2*cos(6*d*x + 6*c) + 6*b^2*cos(4*d*x + 4*c) + 4*b^2*cos(2*d*x + 2*c) + b^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(b)/((2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*d)","B",0
171,1,68,0,1.426651," ","integrate(cos(d*x+c)^(11/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{3 \, \sin\left(5 \, d x + 5 \, c\right) + 25 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 150 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)}{240 \, \sqrt{b} d}"," ",0,"1/240*(3*sin(5*d*x + 5*c) + 25*sin(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 150*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))))/(sqrt(b)*d)","A",0
172,1,49,0,1.341973," ","integrate(cos(d*x+c)^(9/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)}{32 \, \sqrt{b} d}"," ",0,"1/32*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))/(sqrt(b)*d)","A",0
173,1,42,0,0.955777," ","integrate(cos(d*x+c)^(7/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sin\left(3 \, d x + 3 \, c\right) + 9 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)}{12 \, \sqrt{b} d}"," ",0,"1/12*(sin(3*d*x + 3*c) + 9*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))/(sqrt(b)*d)","A",0
174,1,25,0,1.256620," ","integrate(cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)}{4 \, \sqrt{b} d}"," ",0,"1/4*(2*d*x + 2*c + sin(2*d*x + 2*c))/(sqrt(b)*d)","A",0
175,1,13,0,1.256869," ","integrate(cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sin\left(d x + c\right)}{\sqrt{b} d}"," ",0,"sin(d*x + c)/(sqrt(b)*d)","A",0
176,1,26,0,0.936645," ","integrate(cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{\sqrt{b} d}"," ",0,"2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(sqrt(b)*d)","A",0
177,1,65,0,1.574118," ","integrate(1/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)}{2 \, \sqrt{b} d}"," ",0,"1/2*(log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/(sqrt(b)*d)","B",0
178,1,59,0,1.591552," ","integrate(1/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{b} \sin\left(2 \, d x + 2 \, c\right)}{{\left(b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} d}"," ",0,"2*sqrt(b)*sin(2*d*x + 2*c)/((b*cos(2*d*x + 2*c)^2 + b*sin(2*d*x + 2*c)^2 + 2*b*cos(2*d*x + 2*c) + b)*d)","B",0
179,1,661,0,1.247161," ","integrate(1/cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)}{4 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{b} d}"," ",0,"-1/4*(4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))/((2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*sqrt(b)*d)","B",0
180,1,294,0,1.599624," ","integrate(1/cos(d*x+c)^(7/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{4 \, {\left({\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(4 \, d x + 4 \, c\right) - 3 \, \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 9 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)}}{3 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{b} d}"," ",0,"4/3*((3*cos(2*d*x + 2*c) + 1)*sin(6*d*x + 6*c) + 3*(3*cos(2*d*x + 2*c) + 1)*sin(4*d*x + 4*c) - 3*cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 9*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))/((2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*sqrt(b)*d)","B",0
181,1,1656,0,1.301392," ","integrate(1/cos(d*x+c)^(9/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{12 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 12 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)}{16 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{b} d}"," ",0,"-1/16*(12*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 3*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 12*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))/((2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*sqrt(b)*d)","B",0
182,1,49,0,1.252175," ","integrate(cos(d*x+c)^(11/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)}{32 \, b^{\frac{3}{2}} d}"," ",0,"1/32*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))/(b^(3/2)*d)","A",0
183,1,42,0,1.002032," ","integrate(cos(d*x+c)^(9/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\sin\left(3 \, d x + 3 \, c\right) + 9 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)}{12 \, b^{\frac{3}{2}} d}"," ",0,"1/12*(sin(3*d*x + 3*c) + 9*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))/(b^(3/2)*d)","A",0
184,1,25,0,1.500417," ","integrate(cos(d*x+c)^(7/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)}{4 \, b^{\frac{3}{2}} d}"," ",0,"1/4*(2*d*x + 2*c + sin(2*d*x + 2*c))/(b^(3/2)*d)","A",0
185,1,13,0,1.479891," ","integrate(cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\sin\left(d x + c\right)}{b^{\frac{3}{2}} d}"," ",0,"sin(d*x + c)/(b^(3/2)*d)","A",0
186,1,26,0,1.046923," ","integrate(cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{b^{\frac{3}{2}} d}"," ",0,"2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(b^(3/2)*d)","A",0
187,1,65,0,1.158988," ","integrate(cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)}{2 \, b^{\frac{3}{2}} d}"," ",0,"1/2*(log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/(b^(3/2)*d)","B",0
188,1,67,0,0.999050," ","integrate(1/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{b} \sin\left(2 \, d x + 2 \, c\right)}{{\left(b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} d}"," ",0,"2*sqrt(b)*sin(2*d*x + 2*c)/((b^2*cos(2*d*x + 2*c)^2 + b^2*sin(2*d*x + 2*c)^2 + 2*b^2*cos(2*d*x + 2*c) + b^2)*d)","B",0
189,1,670,0,1.572101," ","integrate(1/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)}{4 \, {\left(b \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sqrt{b} d}"," ",0,"-1/4*(4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))/((b*cos(4*d*x + 4*c)^2 + 4*b*cos(2*d*x + 2*c)^2 + b*sin(4*d*x + 4*c)^2 + 4*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b*sin(2*d*x + 2*c)^2 + 2*(2*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*sqrt(b)*d)","B",0
190,1,311,0,1.768204," ","integrate(1/cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{4 \, {\left({\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(4 \, d x + 4 \, c\right) - 3 \, \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 9 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)}}{3 \, {\left(b \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, b \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, b \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, b \cos\left(4 \, d x + 4 \, c\right) + 3 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, b \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(b \sin\left(4 \, d x + 4 \, c\right) + b \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + b\right)} \sqrt{b} d}"," ",0,"4/3*((3*cos(2*d*x + 2*c) + 1)*sin(6*d*x + 6*c) + 3*(3*cos(2*d*x + 2*c) + 1)*sin(4*d*x + 4*c) - 3*cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 9*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))/((b*cos(6*d*x + 6*c)^2 + 9*b*cos(4*d*x + 4*c)^2 + 9*b*cos(2*d*x + 2*c)^2 + b*sin(6*d*x + 6*c)^2 + 9*b*sin(4*d*x + 4*c)^2 + 18*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*b*sin(2*d*x + 2*c)^2 + 2*(3*b*cos(4*d*x + 4*c) + 3*b*cos(2*d*x + 2*c) + b)*cos(6*d*x + 6*c) + 6*(3*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 6*b*cos(2*d*x + 2*c) + 6*(b*sin(4*d*x + 4*c) + b*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + b)*sqrt(b)*d)","B",0
191,1,1679,0,2.001153," ","integrate(1/cos(d*x+c)^(7/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{12 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 12 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)}{16 \, {\left(b \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, b \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, b \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, b \cos\left(6 \, d x + 6 \, c\right) + 6 \, b \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, b \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, b \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, b \sin\left(6 \, d x + 6 \, c\right) + 3 \, b \sin\left(4 \, d x + 4 \, c\right) + 2 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, b \sin\left(4 \, d x + 4 \, c\right) + 2 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + b\right)} \sqrt{b} d}"," ",0,"-1/16*(12*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 3*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 12*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))/((b*cos(8*d*x + 8*c)^2 + 16*b*cos(6*d*x + 6*c)^2 + 36*b*cos(4*d*x + 4*c)^2 + 16*b*cos(2*d*x + 2*c)^2 + b*sin(8*d*x + 8*c)^2 + 16*b*sin(6*d*x + 6*c)^2 + 36*b*sin(4*d*x + 4*c)^2 + 48*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*b*sin(2*d*x + 2*c)^2 + 2*(4*b*cos(6*d*x + 6*c) + 6*b*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*cos(8*d*x + 8*c) + 8*(6*b*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*cos(6*d*x + 6*c) + 12*(4*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 8*b*cos(2*d*x + 2*c) + 4*(2*b*sin(6*d*x + 6*c) + 3*b*sin(4*d*x + 4*c) + 2*b*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*b*sin(4*d*x + 4*c) + 2*b*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + b)*sqrt(b)*d)","B",0
192,1,49,0,1.187124," ","integrate(cos(d*x+c)^(13/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)}{32 \, b^{\frac{5}{2}} d}"," ",0,"1/32*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))/(b^(5/2)*d)","A",0
193,1,42,0,1.578730," ","integrate(cos(d*x+c)^(11/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\sin\left(3 \, d x + 3 \, c\right) + 9 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)}{12 \, b^{\frac{5}{2}} d}"," ",0,"1/12*(sin(3*d*x + 3*c) + 9*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))/(b^(5/2)*d)","A",0
194,1,25,0,1.436905," ","integrate(cos(d*x+c)^(9/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)}{4 \, b^{\frac{5}{2}} d}"," ",0,"1/4*(2*d*x + 2*c + sin(2*d*x + 2*c))/(b^(5/2)*d)","A",0
195,1,13,0,1.627727," ","integrate(cos(d*x+c)^(7/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\sin\left(d x + c\right)}{b^{\frac{5}{2}} d}"," ",0,"sin(d*x + c)/(b^(5/2)*d)","A",0
196,1,26,0,1.270870," ","integrate(cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{b^{\frac{5}{2}} d}"," ",0,"2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(b^(5/2)*d)","A",0
197,1,65,0,1.430704," ","integrate(cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)}{2 \, b^{\frac{5}{2}} d}"," ",0,"1/2*(log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/(b^(5/2)*d)","B",0
198,1,67,0,1.346963," ","integrate(cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{b} \sin\left(2 \, d x + 2 \, c\right)}{{\left(b^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) + b^{3}\right)} d}"," ",0,"2*sqrt(b)*sin(2*d*x + 2*c)/((b^3*cos(2*d*x + 2*c)^2 + b^3*sin(2*d*x + 2*c)^2 + 2*b^3*cos(2*d*x + 2*c) + b^3)*d)","B",0
199,1,688,0,1.562562," ","integrate(1/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)}{4 \, {\left(b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sqrt{b} d}"," ",0,"-1/4*(4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))/((b^2*cos(4*d*x + 4*c)^2 + 4*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(4*d*x + 4*c)^2 + 4*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b^2*sin(2*d*x + 2*c)^2 + 4*b^2*cos(2*d*x + 2*c) + b^2 + 2*(2*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c))*sqrt(b)*d)","B",0
200,1,343,0,1.508122," ","integrate(1/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{4 \, {\left({\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(4 \, d x + 4 \, c\right) - 3 \, \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 9 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)}}{3 \, {\left(b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(3 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(b^{2} \sin\left(4 \, d x + 4 \, c\right) + b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \sqrt{b} d}"," ",0,"4/3*((3*cos(2*d*x + 2*c) + 1)*sin(6*d*x + 6*c) + 3*(3*cos(2*d*x + 2*c) + 1)*sin(4*d*x + 4*c) - 3*cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 9*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))/((b^2*cos(6*d*x + 6*c)^2 + 9*b^2*cos(4*d*x + 4*c)^2 + 9*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(6*d*x + 6*c)^2 + 9*b^2*sin(4*d*x + 4*c)^2 + 18*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*b^2*sin(2*d*x + 2*c)^2 + 6*b^2*cos(2*d*x + 2*c) + b^2 + 2*(3*b^2*cos(4*d*x + 4*c) + 3*b^2*cos(2*d*x + 2*c) + b^2)*cos(6*d*x + 6*c) + 6*(3*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c) + 6*(b^2*sin(4*d*x + 4*c) + b^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*sqrt(b)*d)","B",0
201,1,1729,0,1.944702," ","integrate(1/cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{12 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 4 \, \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 12 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, {\left(\cos\left(8 \, d x + 8 \, c\right) + 4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)}{16 \, {\left(b^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, b^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \sqrt{b} d}"," ",0,"-1/16*(12*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12*(sin(8*d*x + 8*c) + 4*sin(6*d*x + 6*c) + 6*sin(4*d*x + 4*c) + 4*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 3*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 12*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*(cos(8*d*x + 8*c) + 4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))/((b^2*cos(8*d*x + 8*c)^2 + 16*b^2*cos(6*d*x + 6*c)^2 + 36*b^2*cos(4*d*x + 4*c)^2 + 16*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(8*d*x + 8*c)^2 + 16*b^2*sin(6*d*x + 6*c)^2 + 36*b^2*sin(4*d*x + 4*c)^2 + 48*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*b^2*sin(2*d*x + 2*c)^2 + 8*b^2*cos(2*d*x + 2*c) + b^2 + 2*(4*b^2*cos(6*d*x + 6*c) + 6*b^2*cos(4*d*x + 4*c) + 4*b^2*cos(2*d*x + 2*c) + b^2)*cos(8*d*x + 8*c) + 8*(6*b^2*cos(4*d*x + 4*c) + 4*b^2*cos(2*d*x + 2*c) + b^2)*cos(6*d*x + 6*c) + 12*(4*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c) + 4*(2*b^2*sin(6*d*x + 6*c) + 3*b^2*sin(4*d*x + 4*c) + 2*b^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*b^2*sin(4*d*x + 4*c) + 2*b^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*sqrt(b)*d)","B",0
202,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(b*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(1/3)*cos(d*x + c)^m, x)","F",0
203,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(1/3)*cos(d*x + c)^2, x)","F",0
204,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(1/3)*cos(d*x + c), x)","F",0
205,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(1/3), x)","F",0
206,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/3)*sec(d*x+c),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(1/3)*sec(d*x + c), x)","F",0
207,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/3)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(1/3)*sec(d*x + c)^2, x)","F",0
208,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/3)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(1/3)*sec(d*x + c)^3, x)","F",0
209,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(2/3)*cos(d*x + c)^m, x)","F",0
210,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(2/3)*cos(d*x + c)^2, x)","F",0
211,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(2/3)*cos(d*x + c), x)","F",0
212,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(2/3), x)","F",0
213,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(2/3)*sec(d*x+c),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(2/3)*sec(d*x + c), x)","F",0
214,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(2/3)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(2/3)*sec(d*x + c)^2, x)","F",0
215,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(2/3)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(2/3)*sec(d*x + c)^3, x)","F",0
216,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(4/3)*cos(d*x + c)^m, x)","F",0
217,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(4/3)*cos(d*x + c)^2, x)","F",0
218,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(4/3)*cos(d*x + c), x)","F",0
219,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(4/3), x)","F",0
220,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(4/3)*sec(d*x+c),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(4/3)*sec(d*x + c), x)","F",0
221,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(4/3)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(4/3)*sec(d*x + c)^2, x)","F",0
222,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(4/3)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(4/3)*sec(d*x + c)^3, x)","F",0
223,0,0,0,0.000000," ","integrate(cos(d*x+c)^m/(b*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{m}}{\left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^m/(b*cos(d*x + c))^(1/3), x)","F",0
224,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(b*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*cos(d*x + c))^(1/3), x)","F",0
225,0,0,0,0.000000," ","integrate(cos(d*x+c)/(b*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*cos(d*x + c))^(1/3), x)","F",0
226,0,0,0,0.000000," ","integrate(1/(b*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{1}{\left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(-1/3), x)","F",0
227,0,0,0,0.000000," ","integrate(sec(d*x+c)/(b*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*cos(d*x + c))^(1/3), x)","F",0
228,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(b*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*cos(d*x + c))^(1/3), x)","F",0
229,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(b*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*cos(d*x + c))^(1/3), x)","F",0
230,0,0,0,0.000000," ","integrate(cos(d*x+c)^m/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{m}}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^m/(b*cos(d*x + c))^(2/3), x)","F",0
231,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*cos(d*x + c))^(2/3), x)","F",0
232,0,0,0,0.000000," ","integrate(cos(d*x+c)/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*cos(d*x + c))^(2/3), x)","F",0
233,0,0,0,0.000000," ","integrate(1/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{1}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(-2/3), x)","F",0
234,0,0,0,0.000000," ","integrate(sec(d*x+c)/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*cos(d*x + c))^(2/3), x)","F",0
235,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*cos(d*x + c))^(2/3), x)","F",0
236,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*cos(d*x + c))^(2/3), x)","F",0
237,0,0,0,0.000000," ","integrate(cos(d*x+c)^m/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{m}}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^m/(b*cos(d*x + c))^(4/3), x)","F",0
238,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*cos(d*x + c))^(4/3), x)","F",0
239,0,0,0,0.000000," ","integrate(cos(d*x+c)/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*cos(d*x + c))^(4/3), x)","F",0
240,0,0,0,0.000000," ","integrate(1/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{1}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^(-4/3), x)","F",0
241,0,0,0,0.000000," ","integrate(sec(d*x+c)/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*cos(d*x + c))^(4/3), x)","F",0
242,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*cos(d*x + c))^(4/3), x)","F",0
243,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*cos(d*x + c))^(4/3), x)","F",0
244,0,0,0,0.000000," ","integrate((a*cos(f*x+e))^m*(b*cos(f*x+e))^n,x, algorithm=""maxima"")","\int \left(a \cos\left(f x + e\right)\right)^{m} \left(b \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*cos(f*x + e))^m*(b*cos(f*x + e))^n, x)","F",0
245,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n*cos(d*x + c)^2, x)","F",0
246,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n*cos(d*x + c), x)","F",0
247,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{n}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n, x)","F",0
248,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*sec(d*x+c),x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n*sec(d*x + c), x)","F",0
249,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*sec(d*x+c)^2,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n*sec(d*x + c)^2, x)","F",0
250,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*sec(d*x+c)^3,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n*sec(d*x + c)^3, x)","F",0
251,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*sec(d*x+c)^4,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n*sec(d*x + c)^4, x)","F",0
252,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n*cos(d*x + c)^(5/2), x)","F",0
253,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n*cos(d*x + c)^(3/2), x)","F",0
254,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \cos\left(d x + c\right)\right)^{n} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n*sqrt(cos(d*x + c)), x)","F",0
255,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(b \cos\left(d x + c\right)\right)^{n}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n/sqrt(cos(d*x + c)), x)","F",0
256,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(b \cos\left(d x + c\right)\right)^{n}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n/cos(d*x + c)^(3/2), x)","F",0
257,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\left(b \cos\left(d x + c\right)\right)^{n}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n/cos(d*x + c)^(5/2), x)","F",0
258,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\left(b \cos\left(d x + c\right)\right)^{n}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n/cos(d*x + c)^(7/2), x)","F",0
259,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{\left(b \cos\left(d x + c\right)\right)^{n}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c))^n/cos(d*x + c)^(9/2), x)","F",0
260,0,0,0,0.000000," ","integrate((a*cos(f*x+e))^m*(b*sec(f*x+e))^n,x, algorithm=""maxima"")","\int \left(a \cos\left(f x + e\right)\right)^{m} \left(b \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*cos(f*x + e))^m*(b*sec(f*x + e))^n, x)","F",0
261,1,13,0,0.639161," ","integrate(cos(b*x+a)*csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{\sin\left(b x + a\right)}}{b}"," ",0,"2*sqrt(sin(b*x + a))/b","A",0
262,1,13,0,0.839431," ","integrate(cos(b*x+a)/csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sin\left(b x + a\right)^{\frac{3}{2}}}{3 \, b}"," ",0,"2/3*sin(b*x + a)^(3/2)/b","A",0
263,0,0,0,0.000000," ","integrate(cos(b*x+a)^2*csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{2} \sqrt{\csc\left(b x + a\right)}\,{d x}"," ",0,"integrate(cos(b*x + a)^2*sqrt(csc(b*x + a)), x)","F",0
264,0,0,0,0.000000," ","integrate(cos(b*x+a)^2/csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{2}}{\sqrt{\csc\left(b x + a\right)}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2/sqrt(csc(b*x + a)), x)","F",0
265,1,13,0,0.601307," ","integrate(cos(x)^3*csc(x)^(9/2),x, algorithm=""maxima"")","\frac{2}{3 \, \sin\left(x\right)^{\frac{3}{2}}} - \frac{2}{7 \, \sin\left(x\right)^{\frac{7}{2}}}"," ",0,"2/3/sin(x)^(3/2) - 2/7/sin(x)^(7/2)","A",0
266,1,25,0,0.697010," ","integrate(cos(b*x+a)^3*csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{5}{\sin\left(b x + a\right)^{2}} - 1\right)} \sin\left(b x + a\right)^{\frac{5}{2}}}{5 \, b}"," ",0,"2/5*(5/sin(b*x + a)^2 - 1)*sin(b*x + a)^(5/2)/b","A",0
267,1,25,0,0.516996," ","integrate(cos(b*x+a)^3/csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{7}{\sin\left(b x + a\right)^{2}} - 3\right)} \sin\left(b x + a\right)^{\frac{7}{2}}}{21 \, b}"," ",0,"2/21*(7/sin(b*x + a)^2 - 3)*sin(b*x + a)^(7/2)/b","A",0
268,0,0,0,0.000000," ","integrate(cos(b*x+a)^4*csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{4} \sqrt{\csc\left(b x + a\right)}\,{d x}"," ",0,"integrate(cos(b*x + a)^4*sqrt(csc(b*x + a)), x)","F",0
269,0,0,0,0.000000," ","integrate(cos(b*x+a)^4/csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{4}}{\sqrt{\csc\left(b x + a\right)}}\,{d x}"," ",0,"integrate(cos(b*x + a)^4/sqrt(csc(b*x + a)), x)","F",0
270,1,6,0,1.131009," ","integrate(cos(x)*csc(x)^(7/3),x, algorithm=""maxima"")","-\frac{3}{4 \, \sin\left(x\right)^{\frac{4}{3}}}"," ",0,"-3/4/sin(x)^(4/3)","A",0
271,1,41,0,1.349108," ","integrate(csc(b*x+a)^(1/2)*sec(b*x+a),x, algorithm=""maxima"")","-\frac{2 \, \arctan\left(\frac{1}{\sqrt{\sin\left(b x + a\right)}}\right) - \log\left(\frac{1}{\sqrt{\sin\left(b x + a\right)}} + 1\right) + \log\left(\frac{1}{\sqrt{\sin\left(b x + a\right)}} - 1\right)}{2 \, b}"," ",0,"-1/2*(2*arctan(1/sqrt(sin(b*x + a))) - log(1/sqrt(sin(b*x + a)) + 1) + log(1/sqrt(sin(b*x + a)) - 1))/b","A",0
272,1,41,0,0.703812," ","integrate(sec(b*x+a)/csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \arctan\left(\frac{1}{\sqrt{\sin\left(b x + a\right)}}\right) + \log\left(\frac{1}{\sqrt{\sin\left(b x + a\right)}} + 1\right) - \log\left(\frac{1}{\sqrt{\sin\left(b x + a\right)}} - 1\right)}{2 \, b}"," ",0,"1/2*(2*arctan(1/sqrt(sin(b*x + a))) + log(1/sqrt(sin(b*x + a)) + 1) - log(1/sqrt(sin(b*x + a)) - 1))/b","A",0
273,0,0,0,0.000000," ","integrate(csc(b*x+a)^(1/2)*sec(b*x+a)^2,x, algorithm=""maxima"")","\int \sqrt{\csc\left(b x + a\right)} \sec\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sqrt(csc(b*x + a))*sec(b*x + a)^2, x)","F",0
274,0,0,0,0.000000," ","integrate(sec(b*x+a)^2/csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(b x + a\right)^{2}}{\sqrt{\csc\left(b x + a\right)}}\,{d x}"," ",0,"integrate(sec(b*x + a)^2/sqrt(csc(b*x + a)), x)","F",0
275,1,65,0,1.328081," ","integrate(csc(b*x+a)^(1/2)*sec(b*x+a)^3,x, algorithm=""maxima"")","\frac{\frac{4}{{\left(\frac{1}{\sin\left(b x + a\right)^{2}} - 1\right)} \sin\left(b x + a\right)^{\frac{3}{2}}} - 6 \, \arctan\left(\frac{1}{\sqrt{\sin\left(b x + a\right)}}\right) + 3 \, \log\left(\frac{1}{\sqrt{\sin\left(b x + a\right)}} + 1\right) - 3 \, \log\left(\frac{1}{\sqrt{\sin\left(b x + a\right)}} - 1\right)}{8 \, b}"," ",0,"1/8*(4/((1/sin(b*x + a)^2 - 1)*sin(b*x + a)^(3/2)) - 6*arctan(1/sqrt(sin(b*x + a))) + 3*log(1/sqrt(sin(b*x + a)) + 1) - 3*log(1/sqrt(sin(b*x + a)) - 1))/b","A",0
276,1,63,0,1.442713," ","integrate(sec(b*x+a)^3/csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\frac{\frac{4}{{\left(\frac{1}{\sin\left(b x + a\right)^{2}} - 1\right)} \sqrt{\sin\left(b x + a\right)}} + 2 \, \arctan\left(\frac{1}{\sqrt{\sin\left(b x + a\right)}}\right) + \log\left(\frac{1}{\sqrt{\sin\left(b x + a\right)}} + 1\right) - \log\left(\frac{1}{\sqrt{\sin\left(b x + a\right)}} - 1\right)}{8 \, b}"," ",0,"1/8*(4/((1/sin(b*x + a)^2 - 1)*sqrt(sin(b*x + a))) + 2*arctan(1/sqrt(sin(b*x + a))) + log(1/sqrt(sin(b*x + a)) + 1) - log(1/sqrt(sin(b*x + a)) - 1))/b","A",0
277,-1,0,0,0.000000," ","integrate(csc(b*x+a)^(1/2)*sec(b*x+a)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
278,0,0,0,0.000000," ","integrate(sec(b*x+a)^4/csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(b x + a\right)^{4}}{\sqrt{\csc\left(b x + a\right)}}\,{d x}"," ",0,"integrate(sec(b*x + a)^4/sqrt(csc(b*x + a)), x)","F",0
279,0,0,0,0.000000," ","integrate((d*cos(b*x+a))^(3/2)*csc(b*x+a)^p,x, algorithm=""maxima"")","\int \left(d \cos\left(b x + a\right)\right)^{\frac{3}{2}} \csc\left(b x + a\right)^{p}\,{d x}"," ",0,"integrate((d*cos(b*x + a))^(3/2)*csc(b*x + a)^p, x)","F",0
280,0,0,0,0.000000," ","integrate((d*cos(b*x+a))^(1/2)*csc(b*x+a)^p,x, algorithm=""maxima"")","\int \sqrt{d \cos\left(b x + a\right)} \csc\left(b x + a\right)^{p}\,{d x}"," ",0,"integrate(sqrt(d*cos(b*x + a))*csc(b*x + a)^p, x)","F",0
281,0,0,0,0.000000," ","integrate(csc(b*x+a)^p/(d*cos(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)^{p}}{\sqrt{d \cos\left(b x + a\right)}}\,{d x}"," ",0,"integrate(csc(b*x + a)^p/sqrt(d*cos(b*x + a)), x)","F",0
282,0,0,0,0.000000," ","integrate(csc(b*x+a)^p/(d*cos(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)^{p}}{\left(d \cos\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^p/(d*cos(b*x + a))^(3/2), x)","F",0
283,0,0,0,0.000000," ","integrate(csc(b*x+a)^p/(d*cos(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)^{p}}{\left(d \cos\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^p/(d*cos(b*x + a))^(5/2), x)","F",0
284,0,0,0,0.000000," ","integrate(cos(f*x+e)^m*csc(f*x+e)^n,x, algorithm=""maxima"")","\int \cos\left(f x + e\right)^{m} \csc\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate(cos(f*x + e)^m*csc(f*x + e)^n, x)","F",0
285,0,0,0,0.000000," ","integrate((a*cos(f*x+e))^m*csc(f*x+e)^n,x, algorithm=""maxima"")","\int \left(a \cos\left(f x + e\right)\right)^{m} \csc\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*cos(f*x + e))^m*csc(f*x + e)^n, x)","F",0
286,0,0,0,0.000000," ","integrate(cos(f*x+e)^m*(b*csc(f*x+e))^n,x, algorithm=""maxima"")","\int \left(b \csc\left(f x + e\right)\right)^{n} \cos\left(f x + e\right)^{m}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n*cos(f*x + e)^m, x)","F",0
287,0,0,0,0.000000," ","integrate((a*cos(f*x+e))^m*(b*csc(f*x+e))^n,x, algorithm=""maxima"")","\int \left(a \cos\left(f x + e\right)\right)^{m} \left(b \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*cos(f*x + e))^m*(b*csc(f*x + e))^n, x)","F",0
288,0,0,0,0.000000," ","integrate((a*cos(f*x+e))^m*(b*csc(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \left(b \csc\left(f x + e\right)\right)^{\frac{7}{2}} \left(a \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^(7/2)*(a*cos(f*x + e))^m, x)","F",0
289,0,0,0,0.000000," ","integrate((a*cos(f*x+e))^m*(b*csc(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \left(b \csc\left(f x + e\right)\right)^{\frac{5}{2}} \left(a \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^(5/2)*(a*cos(f*x + e))^m, x)","F",0
290,0,0,0,0.000000," ","integrate((a*cos(f*x+e))^m*(b*csc(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \left(b \csc\left(f x + e\right)\right)^{\frac{3}{2}} \left(a \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^(3/2)*(a*cos(f*x + e))^m, x)","F",0
291,0,0,0,0.000000," ","integrate((a*cos(f*x+e))^m*(b*csc(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \csc\left(f x + e\right)} \left(a \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate(sqrt(b*csc(f*x + e))*(a*cos(f*x + e))^m, x)","F",0
292,0,0,0,0.000000," ","integrate((a*cos(f*x+e))^m/(b*csc(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(a \cos\left(f x + e\right)\right)^{m}}{\sqrt{b \csc\left(f x + e\right)}}\,{d x}"," ",0,"integrate((a*cos(f*x + e))^m/sqrt(b*csc(f*x + e)), x)","F",0
293,0,0,0,0.000000," ","integrate((a*cos(f*x+e))^m/(b*csc(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(a \cos\left(f x + e\right)\right)^{m}}{\left(b \csc\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*cos(f*x + e))^m/(b*csc(f*x + e))^(3/2), x)","F",0
294,0,0,0,0.000000," ","integrate((a*cos(f*x+e))^m/(b*csc(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(a \cos\left(f x + e\right)\right)^{m}}{\left(b \csc\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*cos(f*x + e))^m/(b*csc(f*x + e))^(5/2), x)","F",0
