1,1,18,0,0.405378," ","integrate(sec(b*x+a),x, algorithm=""maxima"")","\frac{\log\left(\sec\left(b x + a\right) + \tan\left(b x + a\right)\right)}{b}"," ",0,"log(sec(b*x + a) + tan(b*x + a))/b","A",0
2,1,10,0,0.720328," ","integrate(sec(b*x+a)^2,x, algorithm=""maxima"")","\frac{\tan\left(b x + a\right)}{b}"," ",0,"tan(b*x + a)/b","A",0
3,1,46,0,0.474680," ","integrate(sec(b*x+a)^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, \sin\left(b x + a\right)}{\sin\left(b x + a\right)^{2} - 1} - \log\left(\sin\left(b x + a\right) + 1\right) + \log\left(\sin\left(b x + a\right) - 1\right)}{4 \, b}"," ",0,"-1/4*(2*sin(b*x + a)/(sin(b*x + a)^2 - 1) - log(sin(b*x + a) + 1) + log(sin(b*x + a) - 1))/b","A",0
4,1,22,0,0.328897," ","integrate(sec(b*x+a)^4,x, algorithm=""maxima"")","\frac{\tan\left(b x + a\right)^{3} + 3 \, \tan\left(b x + a\right)}{3 \, b}"," ",0,"1/3*(tan(b*x + a)^3 + 3*tan(b*x + a))/b","A",0
5,1,71,0,0.350670," ","integrate(sec(b*x+a)^5,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, \sin\left(b x + a\right)^{3} - 5 \, \sin\left(b x + a\right)\right)}}{\sin\left(b x + a\right)^{4} - 2 \, \sin\left(b x + a\right)^{2} + 1} - 3 \, \log\left(\sin\left(b x + a\right) + 1\right) + 3 \, \log\left(\sin\left(b x + a\right) - 1\right)}{16 \, b}"," ",0,"-1/16*(2*(3*sin(b*x + a)^3 - 5*sin(b*x + a))/(sin(b*x + a)^4 - 2*sin(b*x + a)^2 + 1) - 3*log(sin(b*x + a) + 1) + 3*log(sin(b*x + a) - 1))/b","A",0
6,1,34,0,0.422059," ","integrate(sec(b*x+a)^6,x, algorithm=""maxima"")","\frac{3 \, \tan\left(b x + a\right)^{5} + 10 \, \tan\left(b x + a\right)^{3} + 15 \, \tan\left(b x + a\right)}{15 \, b}"," ",0,"1/15*(3*tan(b*x + a)^5 + 10*tan(b*x + a)^3 + 15*tan(b*x + a))/b","A",0
7,1,91,0,0.429930," ","integrate(sec(b*x+a)^7,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(15 \, \sin\left(b x + a\right)^{5} - 40 \, \sin\left(b x + a\right)^{3} + 33 \, \sin\left(b x + a\right)\right)}}{\sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4} + 3 \, \sin\left(b x + a\right)^{2} - 1} - 15 \, \log\left(\sin\left(b x + a\right) + 1\right) + 15 \, \log\left(\sin\left(b x + a\right) - 1\right)}{96 \, b}"," ",0,"-1/96*(2*(15*sin(b*x + a)^5 - 40*sin(b*x + a)^3 + 33*sin(b*x + a))/(sin(b*x + a)^6 - 3*sin(b*x + a)^4 + 3*sin(b*x + a)^2 - 1) - 15*log(sin(b*x + a) + 1) + 15*log(sin(b*x + a) - 1))/b","A",0
8,1,44,0,0.340726," ","integrate(sec(b*x+a)^8,x, algorithm=""maxima"")","\frac{5 \, \tan\left(b x + a\right)^{7} + 21 \, \tan\left(b x + a\right)^{5} + 35 \, \tan\left(b x + a\right)^{3} + 35 \, \tan\left(b x + a\right)}{35 \, b}"," ",0,"1/35*(5*tan(b*x + a)^7 + 21*tan(b*x + a)^5 + 35*tan(b*x + a)^3 + 35*tan(b*x + a))/b","A",0
9,0,0,0,0.000000," ","integrate(sec(b*x+a)^(7/2),x, algorithm=""maxima"")","\int \sec\left(b x + a\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate(sec(b*x + a)^(7/2), x)","F",0
10,0,0,0,0.000000," ","integrate(sec(b*x+a)^(5/2),x, algorithm=""maxima"")","\int \sec\left(b x + a\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sec(b*x + a)^(5/2), x)","F",0
11,0,0,0,0.000000," ","integrate(sec(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \sec\left(b x + a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sec(b*x + a)^(3/2), x)","F",0
12,0,0,0,0.000000," ","integrate(sec(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\sec\left(b x + a\right)}\,{d x}"," ",0,"integrate(sqrt(sec(b*x + a)), x)","F",0
13,0,0,0,0.000000," ","integrate(1/sec(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\sec\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/sqrt(sec(b*x + a)), x)","F",0
14,0,0,0,0.000000," ","integrate(1/sec(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\sec\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(b*x + a)^(-3/2), x)","F",0
15,0,0,0,0.000000," ","integrate(1/sec(b*x+a)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\sec\left(b x + a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(b*x + a)^(-5/2), x)","F",0
16,0,0,0,0.000000," ","integrate(1/sec(b*x+a)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{\sec\left(b x + a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sec(b*x + a)^(-7/2), x)","F",0
17,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(7/2),x, algorithm=""maxima"")","\int \left(c \sec\left(b x + a\right)\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(7/2), x)","F",0
18,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(5/2), x)","F",0
19,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(3/2), x)","F",0
20,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c \sec\left(b x + a\right)}\,{d x}"," ",0,"integrate(sqrt(c*sec(b*x + a)), x)","F",0
21,0,0,0,0.000000," ","integrate(1/(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c \sec\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/sqrt(c*sec(b*x + a)), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(-3/2), x)","F",0
23,0,0,0,0.000000," ","integrate(1/(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(-5/2), x)","F",0
24,0,0,0,0.000000," ","integrate(1/(c*sec(b*x+a))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \sec\left(b x + a\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(-7/2), x)","F",0
25,0,0,0,0.000000," ","integrate(sec(b*x+a)^(4/3),x, algorithm=""maxima"")","\int \sec\left(b x + a\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate(sec(b*x + a)^(4/3), x)","F",0
26,0,0,0,0.000000," ","integrate(sec(b*x+a)^(2/3),x, algorithm=""maxima"")","\int \sec\left(b x + a\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(sec(b*x + a)^(2/3), x)","F",0
27,0,0,0,0.000000," ","integrate(sec(b*x+a)^(1/3),x, algorithm=""maxima"")","\int \sec\left(b x + a\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(sec(b*x + a)^(1/3), x)","F",0
28,0,0,0,0.000000," ","integrate(1/sec(b*x+a)^(1/3),x, algorithm=""maxima"")","\int \frac{1}{\sec\left(b x + a\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(b*x + a)^(-1/3), x)","F",0
29,0,0,0,0.000000," ","integrate(1/sec(b*x+a)^(2/3),x, algorithm=""maxima"")","\int \frac{1}{\sec\left(b x + a\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(sec(b*x + a)^(-2/3), x)","F",0
30,0,0,0,0.000000," ","integrate(1/sec(b*x+a)^(4/3),x, algorithm=""maxima"")","\int \frac{1}{\sec\left(b x + a\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sec(b*x + a)^(-4/3), x)","F",0
31,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(4/3),x, algorithm=""maxima"")","\int \left(c \sec\left(b x + a\right)\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(4/3), x)","F",0
32,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(2/3),x, algorithm=""maxima"")","\int \left(c \sec\left(b x + a\right)\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(2/3), x)","F",0
33,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(1/3),x, algorithm=""maxima"")","\int \left(c \sec\left(b x + a\right)\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(1/3), x)","F",0
34,0,0,0,0.000000," ","integrate(1/(c*sec(b*x+a))^(1/3),x, algorithm=""maxima"")","\int \frac{1}{\left(c \sec\left(b x + a\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(-1/3), x)","F",0
35,0,0,0,0.000000," ","integrate(1/(c*sec(b*x+a))^(2/3),x, algorithm=""maxima"")","\int \frac{1}{\left(c \sec\left(b x + a\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(-2/3), x)","F",0
36,0,0,0,0.000000," ","integrate(1/(c*sec(b*x+a))^(4/3),x, algorithm=""maxima"")","\int \frac{1}{\left(c \sec\left(b x + a\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(-4/3), x)","F",0
37,0,0,0,0.000000," ","integrate(sec(b*x+a)^n,x, algorithm=""maxima"")","\int \sec\left(b x + a\right)^{n}\,{d x}"," ",0,"integrate(sec(b*x + a)^n, x)","F",0
38,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^n,x, algorithm=""maxima"")","\int \left(c \sec\left(b x + a\right)\right)^{n}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^n, x)","F",0
39,1,42,0,0.894689," ","integrate((sec(x)^2)^(7/2),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\tan\left(x\right)^{2} + 1\right)}^{\frac{5}{2}} \tan\left(x\right) + \frac{5}{24} \, {\left(\tan\left(x\right)^{2} + 1\right)}^{\frac{3}{2}} \tan\left(x\right) + \frac{5}{16} \, \sqrt{\tan\left(x\right)^{2} + 1} \tan\left(x\right) + \frac{5}{16} \, \operatorname{arsinh}\left(\tan\left(x\right)\right)"," ",0,"1/6*(tan(x)^2 + 1)^(5/2)*tan(x) + 5/24*(tan(x)^2 + 1)^(3/2)*tan(x) + 5/16*sqrt(tan(x)^2 + 1)*tan(x) + 5/16*arcsinh(tan(x))","A",0
40,1,30,0,0.588823," ","integrate((sec(x)^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(\tan\left(x\right)^{2} + 1\right)}^{\frac{3}{2}} \tan\left(x\right) + \frac{3}{8} \, \sqrt{\tan\left(x\right)^{2} + 1} \tan\left(x\right) + \frac{3}{8} \, \operatorname{arsinh}\left(\tan\left(x\right)\right)"," ",0,"1/4*(tan(x)^2 + 1)^(3/2)*tan(x) + 3/8*sqrt(tan(x)^2 + 1)*tan(x) + 3/8*arcsinh(tan(x))","A",0
41,1,18,0,0.762672," ","integrate((sec(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{\tan\left(x\right)^{2} + 1} \tan\left(x\right) + \frac{1}{2} \, \operatorname{arsinh}\left(\tan\left(x\right)\right)"," ",0,"1/2*sqrt(tan(x)^2 + 1)*tan(x) + 1/2*arcsinh(tan(x))","A",0
42,1,3,0,0.457519," ","integrate((sec(x)^2)^(1/2),x, algorithm=""maxima"")","\operatorname{arsinh}\left(\tan\left(x\right)\right)"," ",0,"arcsinh(tan(x))","A",0
43,1,11,0,0.522192," ","integrate(1/(sec(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{\tan\left(x\right)}{\sqrt{\tan\left(x\right)^{2} + 1}}"," ",0,"tan(x)/sqrt(tan(x)^2 + 1)","A",0
44,1,25,0,0.482201," ","integrate(1/(sec(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{2 \, \tan\left(x\right)}{3 \, \sqrt{\tan\left(x\right)^{2} + 1}} + \frac{\tan\left(x\right)}{3 \, {\left(\tan\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}}"," ",0,"2/3*tan(x)/sqrt(tan(x)^2 + 1) + 1/3*tan(x)/(tan(x)^2 + 1)^(3/2)","A",0
45,1,37,0,0.418490," ","integrate(1/(sec(x)^2)^(5/2),x, algorithm=""maxima"")","\frac{8 \, \tan\left(x\right)}{15 \, \sqrt{\tan\left(x\right)^{2} + 1}} + \frac{4 \, \tan\left(x\right)}{15 \, {\left(\tan\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}} + \frac{\tan\left(x\right)}{5 \, {\left(\tan\left(x\right)^{2} + 1\right)}^{\frac{5}{2}}}"," ",0,"8/15*tan(x)/sqrt(tan(x)^2 + 1) + 4/15*tan(x)/(tan(x)^2 + 1)^(3/2) + 1/5*tan(x)/(tan(x)^2 + 1)^(5/2)","A",0
46,1,49,0,0.337055," ","integrate(1/(sec(x)^2)^(7/2),x, algorithm=""maxima"")","\frac{16 \, \tan\left(x\right)}{35 \, \sqrt{\tan\left(x\right)^{2} + 1}} + \frac{8 \, \tan\left(x\right)}{35 \, {\left(\tan\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}} + \frac{6 \, \tan\left(x\right)}{35 \, {\left(\tan\left(x\right)^{2} + 1\right)}^{\frac{5}{2}}} + \frac{\tan\left(x\right)}{7 \, {\left(\tan\left(x\right)^{2} + 1\right)}^{\frac{7}{2}}}"," ",0,"16/35*tan(x)/sqrt(tan(x)^2 + 1) + 8/35*tan(x)/(tan(x)^2 + 1)^(3/2) + 6/35*tan(x)/(tan(x)^2 + 1)^(5/2) + 1/7*tan(x)/(tan(x)^2 + 1)^(7/2)","A",0
47,1,2175,0,3.535619," ","integrate((a*sec(x)^2)^(7/2),x, algorithm=""maxima"")","\frac{{\left(2040 \, a^{3} \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 360 \, a^{3} \cos\left(x\right) \sin\left(2 \, x\right) - 360 \, a^{3} \cos\left(2 \, x\right) \sin\left(x\right) - 60 \, a^{3} \sin\left(x\right) + 4 \, {\left(15 \, a^{3} \sin\left(11 \, x\right) + 85 \, a^{3} \sin\left(9 \, x\right) + 198 \, a^{3} \sin\left(7 \, x\right) - 198 \, a^{3} \sin\left(5 \, x\right) - 85 \, a^{3} \sin\left(3 \, x\right) - 15 \, a^{3} \sin\left(x\right)\right)} \cos\left(12 \, x\right) - 60 \, {\left(6 \, a^{3} \sin\left(10 \, x\right) + 15 \, a^{3} \sin\left(8 \, x\right) + 20 \, a^{3} \sin\left(6 \, x\right) + 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \cos\left(11 \, x\right) + 24 \, {\left(85 \, a^{3} \sin\left(9 \, x\right) + 198 \, a^{3} \sin\left(7 \, x\right) - 198 \, a^{3} \sin\left(5 \, x\right) - 85 \, a^{3} \sin\left(3 \, x\right) - 15 \, a^{3} \sin\left(x\right)\right)} \cos\left(10 \, x\right) - 340 \, {\left(15 \, a^{3} \sin\left(8 \, x\right) + 20 \, a^{3} \sin\left(6 \, x\right) + 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \cos\left(9 \, x\right) + 60 \, {\left(198 \, a^{3} \sin\left(7 \, x\right) - 198 \, a^{3} \sin\left(5 \, x\right) - 85 \, a^{3} \sin\left(3 \, x\right) - 15 \, a^{3} \sin\left(x\right)\right)} \cos\left(8 \, x\right) - 792 \, {\left(20 \, a^{3} \sin\left(6 \, x\right) + 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \cos\left(7 \, x\right) - 80 \, {\left(198 \, a^{3} \sin\left(5 \, x\right) + 85 \, a^{3} \sin\left(3 \, x\right) + 15 \, a^{3} \sin\left(x\right)\right)} \cos\left(6 \, x\right) + 2376 \, {\left(5 \, a^{3} \sin\left(4 \, x\right) + 2 \, a^{3} \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) - 300 \, {\left(17 \, a^{3} \sin\left(3 \, x\right) + 3 \, a^{3} \sin\left(x\right)\right)} \cos\left(4 \, x\right) + 15 \, {\left(a^{3} \cos\left(12 \, x\right)^{2} + 36 \, a^{3} \cos\left(10 \, x\right)^{2} + 225 \, a^{3} \cos\left(8 \, x\right)^{2} + 400 \, a^{3} \cos\left(6 \, x\right)^{2} + 225 \, a^{3} \cos\left(4 \, x\right)^{2} + 36 \, a^{3} \cos\left(2 \, x\right)^{2} + a^{3} \sin\left(12 \, x\right)^{2} + 36 \, a^{3} \sin\left(10 \, x\right)^{2} + 225 \, a^{3} \sin\left(8 \, x\right)^{2} + 400 \, a^{3} \sin\left(6 \, x\right)^{2} + 225 \, a^{3} \sin\left(4 \, x\right)^{2} + 180 \, a^{3} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 36 \, a^{3} \sin\left(2 \, x\right)^{2} + 12 \, a^{3} \cos\left(2 \, x\right) + a^{3} + 2 \, {\left(6 \, a^{3} \cos\left(10 \, x\right) + 15 \, a^{3} \cos\left(8 \, x\right) + 20 \, a^{3} \cos\left(6 \, x\right) + 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(12 \, x\right) + 12 \, {\left(15 \, a^{3} \cos\left(8 \, x\right) + 20 \, a^{3} \cos\left(6 \, x\right) + 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(10 \, x\right) + 30 \, {\left(20 \, a^{3} \cos\left(6 \, x\right) + 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(8 \, x\right) + 40 \, {\left(15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(6 \, x\right) + 30 \, {\left(6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(4 \, x\right) + 2 \, {\left(6 \, a^{3} \sin\left(10 \, x\right) + 15 \, a^{3} \sin\left(8 \, x\right) + 20 \, a^{3} \sin\left(6 \, x\right) + 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(12 \, x\right) + 12 \, {\left(15 \, a^{3} \sin\left(8 \, x\right) + 20 \, a^{3} \sin\left(6 \, x\right) + 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(10 \, x\right) + 30 \, {\left(20 \, a^{3} \sin\left(6 \, x\right) + 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + 120 \, {\left(5 \, a^{3} \sin\left(4 \, x\right) + 2 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right)\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - 15 \, {\left(a^{3} \cos\left(12 \, x\right)^{2} + 36 \, a^{3} \cos\left(10 \, x\right)^{2} + 225 \, a^{3} \cos\left(8 \, x\right)^{2} + 400 \, a^{3} \cos\left(6 \, x\right)^{2} + 225 \, a^{3} \cos\left(4 \, x\right)^{2} + 36 \, a^{3} \cos\left(2 \, x\right)^{2} + a^{3} \sin\left(12 \, x\right)^{2} + 36 \, a^{3} \sin\left(10 \, x\right)^{2} + 225 \, a^{3} \sin\left(8 \, x\right)^{2} + 400 \, a^{3} \sin\left(6 \, x\right)^{2} + 225 \, a^{3} \sin\left(4 \, x\right)^{2} + 180 \, a^{3} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 36 \, a^{3} \sin\left(2 \, x\right)^{2} + 12 \, a^{3} \cos\left(2 \, x\right) + a^{3} + 2 \, {\left(6 \, a^{3} \cos\left(10 \, x\right) + 15 \, a^{3} \cos\left(8 \, x\right) + 20 \, a^{3} \cos\left(6 \, x\right) + 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(12 \, x\right) + 12 \, {\left(15 \, a^{3} \cos\left(8 \, x\right) + 20 \, a^{3} \cos\left(6 \, x\right) + 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(10 \, x\right) + 30 \, {\left(20 \, a^{3} \cos\left(6 \, x\right) + 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(8 \, x\right) + 40 \, {\left(15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(6 \, x\right) + 30 \, {\left(6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(4 \, x\right) + 2 \, {\left(6 \, a^{3} \sin\left(10 \, x\right) + 15 \, a^{3} \sin\left(8 \, x\right) + 20 \, a^{3} \sin\left(6 \, x\right) + 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(12 \, x\right) + 12 \, {\left(15 \, a^{3} \sin\left(8 \, x\right) + 20 \, a^{3} \sin\left(6 \, x\right) + 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(10 \, x\right) + 30 \, {\left(20 \, a^{3} \sin\left(6 \, x\right) + 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + 120 \, {\left(5 \, a^{3} \sin\left(4 \, x\right) + 2 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right)\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) - 4 \, {\left(15 \, a^{3} \cos\left(11 \, x\right) + 85 \, a^{3} \cos\left(9 \, x\right) + 198 \, a^{3} \cos\left(7 \, x\right) - 198 \, a^{3} \cos\left(5 \, x\right) - 85 \, a^{3} \cos\left(3 \, x\right) - 15 \, a^{3} \cos\left(x\right)\right)} \sin\left(12 \, x\right) + 60 \, {\left(6 \, a^{3} \cos\left(10 \, x\right) + 15 \, a^{3} \cos\left(8 \, x\right) + 20 \, a^{3} \cos\left(6 \, x\right) + 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \sin\left(11 \, x\right) - 24 \, {\left(85 \, a^{3} \cos\left(9 \, x\right) + 198 \, a^{3} \cos\left(7 \, x\right) - 198 \, a^{3} \cos\left(5 \, x\right) - 85 \, a^{3} \cos\left(3 \, x\right) - 15 \, a^{3} \cos\left(x\right)\right)} \sin\left(10 \, x\right) + 340 \, {\left(15 \, a^{3} \cos\left(8 \, x\right) + 20 \, a^{3} \cos\left(6 \, x\right) + 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \sin\left(9 \, x\right) - 60 \, {\left(198 \, a^{3} \cos\left(7 \, x\right) - 198 \, a^{3} \cos\left(5 \, x\right) - 85 \, a^{3} \cos\left(3 \, x\right) - 15 \, a^{3} \cos\left(x\right)\right)} \sin\left(8 \, x\right) + 792 \, {\left(20 \, a^{3} \cos\left(6 \, x\right) + 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \sin\left(7 \, x\right) + 80 \, {\left(198 \, a^{3} \cos\left(5 \, x\right) + 85 \, a^{3} \cos\left(3 \, x\right) + 15 \, a^{3} \cos\left(x\right)\right)} \sin\left(6 \, x\right) - 792 \, {\left(15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \sin\left(5 \, x\right) + 300 \, {\left(17 \, a^{3} \cos\left(3 \, x\right) + 3 \, a^{3} \cos\left(x\right)\right)} \sin\left(4 \, x\right) - 340 \, {\left(6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \sin\left(3 \, x\right)\right)} \sqrt{a}}{96 \, {\left(2 \, {\left(6 \, \cos\left(10 \, x\right) + 15 \, \cos\left(8 \, x\right) + 20 \, \cos\left(6 \, x\right) + 15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(12 \, x\right) + \cos\left(12 \, x\right)^{2} + 12 \, {\left(15 \, \cos\left(8 \, x\right) + 20 \, \cos\left(6 \, x\right) + 15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(10 \, x\right) + 36 \, \cos\left(10 \, x\right)^{2} + 30 \, {\left(20 \, \cos\left(6 \, x\right) + 15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(8 \, x\right) + 225 \, \cos\left(8 \, x\right)^{2} + 40 \, {\left(15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + 400 \, \cos\left(6 \, x\right)^{2} + 30 \, {\left(6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 225 \, \cos\left(4 \, x\right)^{2} + 36 \, \cos\left(2 \, x\right)^{2} + 2 \, {\left(6 \, \sin\left(10 \, x\right) + 15 \, \sin\left(8 \, x\right) + 20 \, \sin\left(6 \, x\right) + 15 \, \sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right)\right)} \sin\left(12 \, x\right) + \sin\left(12 \, x\right)^{2} + 12 \, {\left(15 \, \sin\left(8 \, x\right) + 20 \, \sin\left(6 \, x\right) + 15 \, \sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right)\right)} \sin\left(10 \, x\right) + 36 \, \sin\left(10 \, x\right)^{2} + 30 \, {\left(20 \, \sin\left(6 \, x\right) + 15 \, \sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + 225 \, \sin\left(8 \, x\right)^{2} + 120 \, {\left(5 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + 400 \, \sin\left(6 \, x\right)^{2} + 225 \, \sin\left(4 \, x\right)^{2} + 180 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 36 \, \sin\left(2 \, x\right)^{2} + 12 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"1/96*(2040*a^3*cos(3*x)*sin(2*x) + 360*a^3*cos(x)*sin(2*x) - 360*a^3*cos(2*x)*sin(x) - 60*a^3*sin(x) + 4*(15*a^3*sin(11*x) + 85*a^3*sin(9*x) + 198*a^3*sin(7*x) - 198*a^3*sin(5*x) - 85*a^3*sin(3*x) - 15*a^3*sin(x))*cos(12*x) - 60*(6*a^3*sin(10*x) + 15*a^3*sin(8*x) + 20*a^3*sin(6*x) + 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*cos(11*x) + 24*(85*a^3*sin(9*x) + 198*a^3*sin(7*x) - 198*a^3*sin(5*x) - 85*a^3*sin(3*x) - 15*a^3*sin(x))*cos(10*x) - 340*(15*a^3*sin(8*x) + 20*a^3*sin(6*x) + 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*cos(9*x) + 60*(198*a^3*sin(7*x) - 198*a^3*sin(5*x) - 85*a^3*sin(3*x) - 15*a^3*sin(x))*cos(8*x) - 792*(20*a^3*sin(6*x) + 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*cos(7*x) - 80*(198*a^3*sin(5*x) + 85*a^3*sin(3*x) + 15*a^3*sin(x))*cos(6*x) + 2376*(5*a^3*sin(4*x) + 2*a^3*sin(2*x))*cos(5*x) - 300*(17*a^3*sin(3*x) + 3*a^3*sin(x))*cos(4*x) + 15*(a^3*cos(12*x)^2 + 36*a^3*cos(10*x)^2 + 225*a^3*cos(8*x)^2 + 400*a^3*cos(6*x)^2 + 225*a^3*cos(4*x)^2 + 36*a^3*cos(2*x)^2 + a^3*sin(12*x)^2 + 36*a^3*sin(10*x)^2 + 225*a^3*sin(8*x)^2 + 400*a^3*sin(6*x)^2 + 225*a^3*sin(4*x)^2 + 180*a^3*sin(4*x)*sin(2*x) + 36*a^3*sin(2*x)^2 + 12*a^3*cos(2*x) + a^3 + 2*(6*a^3*cos(10*x) + 15*a^3*cos(8*x) + 20*a^3*cos(6*x) + 15*a^3*cos(4*x) + 6*a^3*cos(2*x) + a^3)*cos(12*x) + 12*(15*a^3*cos(8*x) + 20*a^3*cos(6*x) + 15*a^3*cos(4*x) + 6*a^3*cos(2*x) + a^3)*cos(10*x) + 30*(20*a^3*cos(6*x) + 15*a^3*cos(4*x) + 6*a^3*cos(2*x) + a^3)*cos(8*x) + 40*(15*a^3*cos(4*x) + 6*a^3*cos(2*x) + a^3)*cos(6*x) + 30*(6*a^3*cos(2*x) + a^3)*cos(4*x) + 2*(6*a^3*sin(10*x) + 15*a^3*sin(8*x) + 20*a^3*sin(6*x) + 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*sin(12*x) + 12*(15*a^3*sin(8*x) + 20*a^3*sin(6*x) + 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*sin(10*x) + 30*(20*a^3*sin(6*x) + 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*sin(8*x) + 120*(5*a^3*sin(4*x) + 2*a^3*sin(2*x))*sin(6*x))*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - 15*(a^3*cos(12*x)^2 + 36*a^3*cos(10*x)^2 + 225*a^3*cos(8*x)^2 + 400*a^3*cos(6*x)^2 + 225*a^3*cos(4*x)^2 + 36*a^3*cos(2*x)^2 + a^3*sin(12*x)^2 + 36*a^3*sin(10*x)^2 + 225*a^3*sin(8*x)^2 + 400*a^3*sin(6*x)^2 + 225*a^3*sin(4*x)^2 + 180*a^3*sin(4*x)*sin(2*x) + 36*a^3*sin(2*x)^2 + 12*a^3*cos(2*x) + a^3 + 2*(6*a^3*cos(10*x) + 15*a^3*cos(8*x) + 20*a^3*cos(6*x) + 15*a^3*cos(4*x) + 6*a^3*cos(2*x) + a^3)*cos(12*x) + 12*(15*a^3*cos(8*x) + 20*a^3*cos(6*x) + 15*a^3*cos(4*x) + 6*a^3*cos(2*x) + a^3)*cos(10*x) + 30*(20*a^3*cos(6*x) + 15*a^3*cos(4*x) + 6*a^3*cos(2*x) + a^3)*cos(8*x) + 40*(15*a^3*cos(4*x) + 6*a^3*cos(2*x) + a^3)*cos(6*x) + 30*(6*a^3*cos(2*x) + a^3)*cos(4*x) + 2*(6*a^3*sin(10*x) + 15*a^3*sin(8*x) + 20*a^3*sin(6*x) + 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*sin(12*x) + 12*(15*a^3*sin(8*x) + 20*a^3*sin(6*x) + 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*sin(10*x) + 30*(20*a^3*sin(6*x) + 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*sin(8*x) + 120*(5*a^3*sin(4*x) + 2*a^3*sin(2*x))*sin(6*x))*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) - 4*(15*a^3*cos(11*x) + 85*a^3*cos(9*x) + 198*a^3*cos(7*x) - 198*a^3*cos(5*x) - 85*a^3*cos(3*x) - 15*a^3*cos(x))*sin(12*x) + 60*(6*a^3*cos(10*x) + 15*a^3*cos(8*x) + 20*a^3*cos(6*x) + 15*a^3*cos(4*x) + 6*a^3*cos(2*x) + a^3)*sin(11*x) - 24*(85*a^3*cos(9*x) + 198*a^3*cos(7*x) - 198*a^3*cos(5*x) - 85*a^3*cos(3*x) - 15*a^3*cos(x))*sin(10*x) + 340*(15*a^3*cos(8*x) + 20*a^3*cos(6*x) + 15*a^3*cos(4*x) + 6*a^3*cos(2*x) + a^3)*sin(9*x) - 60*(198*a^3*cos(7*x) - 198*a^3*cos(5*x) - 85*a^3*cos(3*x) - 15*a^3*cos(x))*sin(8*x) + 792*(20*a^3*cos(6*x) + 15*a^3*cos(4*x) + 6*a^3*cos(2*x) + a^3)*sin(7*x) + 80*(198*a^3*cos(5*x) + 85*a^3*cos(3*x) + 15*a^3*cos(x))*sin(6*x) - 792*(15*a^3*cos(4*x) + 6*a^3*cos(2*x) + a^3)*sin(5*x) + 300*(17*a^3*cos(3*x) + 3*a^3*cos(x))*sin(4*x) - 340*(6*a^3*cos(2*x) + a^3)*sin(3*x))*sqrt(a)/(2*(6*cos(10*x) + 15*cos(8*x) + 20*cos(6*x) + 15*cos(4*x) + 6*cos(2*x) + 1)*cos(12*x) + cos(12*x)^2 + 12*(15*cos(8*x) + 20*cos(6*x) + 15*cos(4*x) + 6*cos(2*x) + 1)*cos(10*x) + 36*cos(10*x)^2 + 30*(20*cos(6*x) + 15*cos(4*x) + 6*cos(2*x) + 1)*cos(8*x) + 225*cos(8*x)^2 + 40*(15*cos(4*x) + 6*cos(2*x) + 1)*cos(6*x) + 400*cos(6*x)^2 + 30*(6*cos(2*x) + 1)*cos(4*x) + 225*cos(4*x)^2 + 36*cos(2*x)^2 + 2*(6*sin(10*x) + 15*sin(8*x) + 20*sin(6*x) + 15*sin(4*x) + 6*sin(2*x))*sin(12*x) + sin(12*x)^2 + 12*(15*sin(8*x) + 20*sin(6*x) + 15*sin(4*x) + 6*sin(2*x))*sin(10*x) + 36*sin(10*x)^2 + 30*(20*sin(6*x) + 15*sin(4*x) + 6*sin(2*x))*sin(8*x) + 225*sin(8*x)^2 + 120*(5*sin(4*x) + 2*sin(2*x))*sin(6*x) + 400*sin(6*x)^2 + 225*sin(4*x)^2 + 180*sin(4*x)*sin(2*x) + 36*sin(2*x)^2 + 12*cos(2*x) + 1)","B",0
48,1,1111,0,0.999896," ","integrate((a*sec(x)^2)^(5/2),x, algorithm=""maxima"")","\frac{{\left(176 \, a^{2} \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 48 \, a^{2} \cos\left(x\right) \sin\left(2 \, x\right) - 48 \, a^{2} \cos\left(2 \, x\right) \sin\left(x\right) - 12 \, a^{2} \sin\left(x\right) + 4 \, {\left(3 \, a^{2} \sin\left(7 \, x\right) + 11 \, a^{2} \sin\left(5 \, x\right) - 11 \, a^{2} \sin\left(3 \, x\right) - 3 \, a^{2} \sin\left(x\right)\right)} \cos\left(8 \, x\right) - 24 \, {\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)} \cos\left(7 \, x\right) + 16 \, {\left(11 \, a^{2} \sin\left(5 \, x\right) - 11 \, a^{2} \sin\left(3 \, x\right) - 3 \, a^{2} \sin\left(x\right)\right)} \cos\left(6 \, x\right) - 88 \, {\left(3 \, a^{2} \sin\left(4 \, x\right) + 2 \, a^{2} \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) - 24 \, {\left(11 \, a^{2} \sin\left(3 \, x\right) + 3 \, a^{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) + 3 \, {\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)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - 3 \, {\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)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) - 4 \, {\left(3 \, a^{2} \cos\left(7 \, x\right) + 11 \, a^{2} \cos\left(5 \, x\right) - 11 \, a^{2} \cos\left(3 \, x\right) - 3 \, a^{2} \cos\left(x\right)\right)} \sin\left(8 \, x\right) + 12 \, {\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)} \sin\left(7 \, x\right) - 16 \, {\left(11 \, a^{2} \cos\left(5 \, x\right) - 11 \, a^{2} \cos\left(3 \, x\right) - 3 \, a^{2} \cos\left(x\right)\right)} \sin\left(6 \, x\right) + 44 \, {\left(6 \, a^{2} \cos\left(4 \, x\right) + 4 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)} \sin\left(5 \, x\right) + 24 \, {\left(11 \, a^{2} \cos\left(3 \, x\right) + 3 \, a^{2} \cos\left(x\right)\right)} \sin\left(4 \, x\right) - 44 \, {\left(4 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)} \sin\left(3 \, x\right)\right)} \sqrt{a}}{16 \, {\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)}}"," ",0,"1/16*(176*a^2*cos(3*x)*sin(2*x) + 48*a^2*cos(x)*sin(2*x) - 48*a^2*cos(2*x)*sin(x) - 12*a^2*sin(x) + 4*(3*a^2*sin(7*x) + 11*a^2*sin(5*x) - 11*a^2*sin(3*x) - 3*a^2*sin(x))*cos(8*x) - 24*(2*a^2*sin(6*x) + 3*a^2*sin(4*x) + 2*a^2*sin(2*x))*cos(7*x) + 16*(11*a^2*sin(5*x) - 11*a^2*sin(3*x) - 3*a^2*sin(x))*cos(6*x) - 88*(3*a^2*sin(4*x) + 2*a^2*sin(2*x))*cos(5*x) - 24*(11*a^2*sin(3*x) + 3*a^2*sin(x))*cos(4*x) + 3*(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))*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - 3*(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))*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) - 4*(3*a^2*cos(7*x) + 11*a^2*cos(5*x) - 11*a^2*cos(3*x) - 3*a^2*cos(x))*sin(8*x) + 12*(4*a^2*cos(6*x) + 6*a^2*cos(4*x) + 4*a^2*cos(2*x) + a^2)*sin(7*x) - 16*(11*a^2*cos(5*x) - 11*a^2*cos(3*x) - 3*a^2*cos(x))*sin(6*x) + 44*(6*a^2*cos(4*x) + 4*a^2*cos(2*x) + a^2)*sin(5*x) + 24*(11*a^2*cos(3*x) + 3*a^2*cos(x))*sin(4*x) - 44*(4*a^2*cos(2*x) + a^2)*sin(3*x))*sqrt(a)/(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)","B",0
49,1,324,0,1.028091," ","integrate((a*sec(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(8 \, a \cos\left(3 \, x\right) \sin\left(2 \, x\right) - 8 \, a \cos\left(x\right) \sin\left(2 \, x\right) + 8 \, a \cos\left(2 \, x\right) \sin\left(x\right) - 4 \, {\left(a \sin\left(3 \, x\right) - a \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\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)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + {\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)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) + 4 \, {\left(a \cos\left(3 \, x\right) - a \cos\left(x\right)\right)} \sin\left(4 \, x\right) - 4 \, {\left(2 \, a \cos\left(2 \, x\right) + a\right)} \sin\left(3 \, x\right) + 4 \, a \sin\left(x\right)\right)} \sqrt{a}}{4 \, {\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)}}"," ",0,"-1/4*(8*a*cos(3*x)*sin(2*x) - 8*a*cos(x)*sin(2*x) + 8*a*cos(2*x)*sin(x) - 4*(a*sin(3*x) - a*sin(x))*cos(4*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)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + (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)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) + 4*(a*cos(3*x) - a*cos(x))*sin(4*x) - 4*(2*a*cos(2*x) + a)*sin(3*x) + 4*a*sin(x))*sqrt(a)/(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)","B",0
50,1,38,0,0.888053," ","integrate((a*sec(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{a} {\left(\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)\right)}"," ",0,"1/2*sqrt(a)*(log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1))","A",0
51,1,6,0,0.915364," ","integrate(1/(a*sec(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{\sin\left(x\right)}{\sqrt{a}}"," ",0,"sin(x)/sqrt(a)","A",0
52,1,14,0,1.002144," ","integrate(1/(a*sec(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{\sin\left(3 \, x\right) + 9 \, \sin\left(x\right)}{12 \, a^{\frac{3}{2}}}"," ",0,"1/12*(sin(3*x) + 9*sin(x))/a^(3/2)","A",0
53,1,22,0,0.678526," ","integrate(1/(a*sec(x)^2)^(5/2),x, algorithm=""maxima"")","\frac{3 \, \sin\left(5 \, x\right) + 25 \, \sin\left(3 \, x\right) + 150 \, \sin\left(x\right)}{240 \, a^{\frac{5}{2}}}"," ",0,"1/240*(3*sin(5*x) + 25*sin(3*x) + 150*sin(x))/a^(5/2)","A",0
54,1,28,0,0.563364," ","integrate(1/(a*sec(x)^2)^(7/2),x, algorithm=""maxima"")","\frac{5 \, \sin\left(7 \, x\right) + 49 \, \sin\left(5 \, x\right) + 245 \, \sin\left(3 \, x\right) + 1225 \, \sin\left(x\right)}{2240 \, a^{\frac{7}{2}}}"," ",0,"1/2240*(5*sin(7*x) + 49*sin(5*x) + 245*sin(3*x) + 1225*sin(x))/a^(7/2)","A",0
55,0,0,0,0.000000," ","integrate((a*sec(x)^3)^(5/2),x, algorithm=""maxima"")","\int \left(a \sec\left(x\right)^{3}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(x)^3)^(5/2), x)","F",0
56,0,0,0,0.000000," ","integrate((a*sec(x)^3)^(3/2),x, algorithm=""maxima"")","\int \left(a \sec\left(x\right)^{3}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(x)^3)^(3/2), x)","F",0
57,0,0,0,0.000000," ","integrate((a*sec(x)^3)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(x\right)^{3}}\,{d x}"," ",0,"integrate(sqrt(a*sec(x)^3), x)","F",0
58,0,0,0,0.000000," ","integrate(1/(a*sec(x)^3)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sec\left(x\right)^{3}}}\,{d x}"," ",0,"integrate(1/sqrt(a*sec(x)^3), x)","F",0
59,0,0,0,0.000000," ","integrate(1/(a*sec(x)^3)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(a \sec\left(x\right)^{3}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(x)^3)^(-3/2), x)","F",0
60,0,0,0,0.000000," ","integrate(1/(a*sec(x)^3)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(a \sec\left(x\right)^{3}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(x)^3)^(-5/2), x)","F",0
61,1,61,0,1.136136," ","integrate((a*sec(x)^4)^(7/2),x, algorithm=""maxima"")","\frac{1}{13} \, a^{\frac{7}{2}} \tan\left(x\right)^{13} + \frac{6}{11} \, a^{\frac{7}{2}} \tan\left(x\right)^{11} + \frac{5}{3} \, a^{\frac{7}{2}} \tan\left(x\right)^{9} + \frac{20}{7} \, a^{\frac{7}{2}} \tan\left(x\right)^{7} + 3 \, a^{\frac{7}{2}} \tan\left(x\right)^{5} + 2 \, a^{\frac{7}{2}} \tan\left(x\right)^{3} + a^{\frac{7}{2}} \tan\left(x\right)"," ",0,"1/13*a^(7/2)*tan(x)^13 + 6/11*a^(7/2)*tan(x)^11 + 5/3*a^(7/2)*tan(x)^9 + 20/7*a^(7/2)*tan(x)^7 + 3*a^(7/2)*tan(x)^5 + 2*a^(7/2)*tan(x)^3 + a^(7/2)*tan(x)","A",0
62,1,43,0,0.753039," ","integrate((a*sec(x)^4)^(5/2),x, algorithm=""maxima"")","\frac{1}{9} \, a^{\frac{5}{2}} \tan\left(x\right)^{9} + \frac{4}{7} \, a^{\frac{5}{2}} \tan\left(x\right)^{7} + \frac{6}{5} \, a^{\frac{5}{2}} \tan\left(x\right)^{5} + \frac{4}{3} \, a^{\frac{5}{2}} \tan\left(x\right)^{3} + a^{\frac{5}{2}} \tan\left(x\right)"," ",0,"1/9*a^(5/2)*tan(x)^9 + 4/7*a^(5/2)*tan(x)^7 + 6/5*a^(5/2)*tan(x)^5 + 4/3*a^(5/2)*tan(x)^3 + a^(5/2)*tan(x)","A",0
63,1,25,0,0.440057," ","integrate((a*sec(x)^4)^(3/2),x, algorithm=""maxima"")","\frac{1}{5} \, a^{\frac{3}{2}} \tan\left(x\right)^{5} + \frac{2}{3} \, a^{\frac{3}{2}} \tan\left(x\right)^{3} + a^{\frac{3}{2}} \tan\left(x\right)"," ",0,"1/5*a^(3/2)*tan(x)^5 + 2/3*a^(3/2)*tan(x)^3 + a^(3/2)*tan(x)","A",0
64,1,6,0,0.700395," ","integrate((a*sec(x)^4)^(1/2),x, algorithm=""maxima"")","\sqrt{a} \tan\left(x\right)"," ",0,"sqrt(a)*tan(x)","A",0
65,1,25,0,0.652484," ","integrate(1/(a*sec(x)^4)^(1/2),x, algorithm=""maxima"")","\frac{x}{2 \, \sqrt{a}} + \frac{\tan\left(x\right)}{2 \, {\left(\sqrt{a} \tan\left(x\right)^{2} + \sqrt{a}\right)}}"," ",0,"1/2*x/sqrt(a) + 1/2*tan(x)/(sqrt(a)*tan(x)^2 + sqrt(a))","A",0
66,1,58,0,0.693833," ","integrate(1/(a*sec(x)^4)^(3/2),x, algorithm=""maxima"")","\frac{15 \, \tan\left(x\right)^{5} + 40 \, \tan\left(x\right)^{3} + 33 \, \tan\left(x\right)}{48 \, {\left(a^{\frac{3}{2}} \tan\left(x\right)^{6} + 3 \, a^{\frac{3}{2}} \tan\left(x\right)^{4} + 3 \, a^{\frac{3}{2}} \tan\left(x\right)^{2} + a^{\frac{3}{2}}\right)}} + \frac{5 \, x}{16 \, a^{\frac{3}{2}}}"," ",0,"1/48*(15*tan(x)^5 + 40*tan(x)^3 + 33*tan(x))/(a^(3/2)*tan(x)^6 + 3*a^(3/2)*tan(x)^4 + 3*a^(3/2)*tan(x)^2 + a^(3/2)) + 5/16*x/a^(3/2)","A",0
67,1,88,0,0.693757," ","integrate(1/(a*sec(x)^4)^(5/2),x, algorithm=""maxima"")","\frac{315 \, \tan\left(x\right)^{9} + 1470 \, \tan\left(x\right)^{7} + 2688 \, \tan\left(x\right)^{5} + 2370 \, \tan\left(x\right)^{3} + 965 \, \tan\left(x\right)}{1280 \, {\left(a^{\frac{5}{2}} \tan\left(x\right)^{10} + 5 \, a^{\frac{5}{2}} \tan\left(x\right)^{8} + 10 \, a^{\frac{5}{2}} \tan\left(x\right)^{6} + 10 \, a^{\frac{5}{2}} \tan\left(x\right)^{4} + 5 \, a^{\frac{5}{2}} \tan\left(x\right)^{2} + a^{\frac{5}{2}}\right)}} + \frac{63 \, x}{256 \, a^{\frac{5}{2}}}"," ",0,"1/1280*(315*tan(x)^9 + 1470*tan(x)^7 + 2688*tan(x)^5 + 2370*tan(x)^3 + 965*tan(x))/(a^(5/2)*tan(x)^10 + 5*a^(5/2)*tan(x)^8 + 10*a^(5/2)*tan(x)^6 + 10*a^(5/2)*tan(x)^4 + 5*a^(5/2)*tan(x)^2 + a^(5/2)) + 63/256*x/a^(5/2)","A",0
68,0,0,0,0.000000," ","integrate(((b*sec(d*x+c))^p)^n,x, algorithm=""maxima"")","\int {\left(\left(b \sec\left(d x + c\right)\right)^{p}\right)}^{n}\,{d x}"," ",0,"integrate(((b*sec(d*x + c))^p)^n, x)","F",0
69,0,0,0,0.000000," ","integrate((a*(b*sec(d*x+c))^p)^n,x, algorithm=""maxima"")","\int \left(\left(b \sec\left(d x + c\right)\right)^{p} a\right)^{n}\,{d x}"," ",0,"integrate(((b*sec(d*x + c))^p*a)^n, x)","F",0
70,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right)} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c))*sec(d*x + c)^4, x)","F",0
71,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right)} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c))*sec(d*x + c)^3, x)","F",0
72,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right)} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c))*sec(d*x + c)^2, x)","F",0
73,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right)} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c))*sec(d*x + c), x)","F",0
74,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c)), x)","F",0
75,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right)} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c))*cos(d*x + c), x)","F",0
76,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right)} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c))*cos(d*x + c)^2, x)","F",0
77,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right)} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c))*cos(d*x + c)^3, x)","F",0
78,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right)} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c))*cos(d*x + c)^4, x)","F",0
79,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right)} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c))*cos(d*x + c)^5, x)","F",0
80,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(3/2)*sec(d*x + c)^3, x)","F",0
81,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(3/2)*sec(d*x + c)^2, x)","F",0
82,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(3/2)*sec(d*x + c), x)","F",0
83,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(3/2), x)","F",0
84,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(3/2)*cos(d*x + c), x)","F",0
85,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(3/2)*cos(d*x + c)^2, x)","F",0
86,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(3/2)*cos(d*x + c)^3, x)","F",0
87,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(3/2)*cos(d*x + c)^4, x)","F",0
88,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(3/2)*cos(d*x + c)^5, x)","F",0
89,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(3/2)*cos(d*x + c)^6, x)","F",0
90,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(5/2)*sec(d*x + c)^2, x)","F",0
91,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(5/2)*sec(d*x + c), x)","F",0
92,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(5/2), x)","F",0
93,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(5/2)*cos(d*x + c), x)","F",0
94,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(5/2)*cos(d*x + c)^2, x)","F",0
95,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(5/2)*cos(d*x + c)^3, x)","F",0
96,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(5/2)*cos(d*x + c)^4, x)","F",0
97,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(5/2)*cos(d*x + c)^5, x)","F",0
98,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(5/2)*cos(d*x + c)^6, x)","F",0
99,0,0,0,0.000000," ","integrate(cos(d*x+c)^7*(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}} \cos\left(d x + c\right)^{7}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(5/2)*cos(d*x + c)^7, x)","F",0
100,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(7/2), x)","F",0
101,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{5}}{\sqrt{b \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/sqrt(b*sec(d*x + c)), x)","F",0
102,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{4}}{\sqrt{b \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/sqrt(b*sec(d*x + c)), x)","F",0
103,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/sqrt(b*sec(d*x + c)), x)","F",0
104,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/sqrt(b*sec(d*x + c)), x)","F",0
105,0,0,0,0.000000," ","integrate(sec(d*x+c)/(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sec(d*x + c)/sqrt(b*sec(d*x + c)), x)","F",0
106,0,0,0,0.000000," ","integrate(1/(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/sqrt(b*sec(d*x + c)), x)","F",0
107,0,0,0,0.000000," ","integrate(cos(d*x+c)/(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(cos(d*x + c)/sqrt(b*sec(d*x + c)), x)","F",0
108,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/sqrt(b*sec(d*x + c)), x)","F",0
109,0,0,0,0.000000," ","integrate(cos(d*x+c)^3/(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3/sqrt(b*sec(d*x + c)), x)","F",0
110,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4}}{\sqrt{b \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/sqrt(b*sec(d*x + c)), x)","F",0
111,0,0,0,0.000000," ","integrate(sec(d*x+c)^6/(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{6}}{\left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^6/(b*sec(d*x + c))^(3/2), x)","F",0
112,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{5}}{\left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/(b*sec(d*x + c))^(3/2), x)","F",0
113,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{4}}{\left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(b*sec(d*x + c))^(3/2), x)","F",0
114,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*sec(d*x + c))^(3/2), x)","F",0
115,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sec(d*x + c))^(3/2), x)","F",0
116,0,0,0,0.000000," ","integrate(sec(d*x+c)/(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c))^(3/2), x)","F",0
117,0,0,0,0.000000," ","integrate(1/(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(-3/2), x)","F",0
118,0,0,0,0.000000," ","integrate(cos(d*x+c)/(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*sec(d*x + c))^(3/2), x)","F",0
119,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*sec(d*x + c))^(3/2), x)","F",0
120,0,0,0,0.000000," ","integrate(cos(d*x+c)^3/(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{3}}{\left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3/(b*sec(d*x + c))^(3/2), x)","F",0
121,0,0,0,0.000000," ","integrate(sec(d*x+c)^7/(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{7}}{\left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^7/(b*sec(d*x + c))^(5/2), x)","F",0
122,0,0,0,0.000000," ","integrate(sec(d*x+c)^6/(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{6}}{\left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^6/(b*sec(d*x + c))^(5/2), x)","F",0
123,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{5}}{\left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/(b*sec(d*x + c))^(5/2), x)","F",0
124,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{4}}{\left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(b*sec(d*x + c))^(5/2), x)","F",0
125,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*sec(d*x + c))^(5/2), x)","F",0
126,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sec(d*x + c))^(5/2), x)","F",0
127,0,0,0,0.000000," ","integrate(sec(d*x+c)/(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c))^(5/2), x)","F",0
128,0,0,0,0.000000," ","integrate(1/(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(-5/2), x)","F",0
129,0,0,0,0.000000," ","integrate(cos(d*x+c)/(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*sec(d*x + c))^(5/2), x)","F",0
130,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*sec(d*x + c))^(5/2), x)","F",0
131,0,0,0,0.000000," ","integrate(1/(b*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{\left(b \sec\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(-7/2), x)","F",0
132,1,1656,0,1.057954," ","integrate(sec(d*x+c)^(9/2)*(b*sec(d*x+c))^(1/2),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
133,1,294,0,0.829751," ","integrate(sec(d*x+c)^(7/2)*(b*sec(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)} \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
134,1,661,0,0.967191," ","integrate(sec(d*x+c)^(5/2)*(b*sec(d*x+c))^(1/2),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
135,1,54,0,1.053198," ","integrate(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^(1/2),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
136,1,65,0,1.024770," ","integrate(sec(d*x+c)^(1/2)*(b*sec(d*x+c))^(1/2),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
137,1,26,0,0.500906," ","integrate((b*sec(d*x+c))^(1/2)/sec(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
138,1,13,0,0.628588," ","integrate((b*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{b} \sin\left(d x + c\right)}{d}"," ",0,"sqrt(b)*sin(d*x + c)/d","A",0
139,1,25,0,0.795130," ","integrate((b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),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
140,1,42,0,1.046874," ","integrate((b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),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
141,1,49,0,0.782480," ","integrate((b*sec(d*x+c))^(1/2)/sec(d*x+c)^(9/2),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
142,1,1742,0,1.183651," ","integrate(sec(d*x+c)^(7/2)*(b*sec(d*x+c))^(3/2),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
143,1,299,0,1.001605," ","integrate(sec(d*x+c)^(5/2)*(b*sec(d*x+c))^(3/2),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
144,1,691,0,0.920276," ","integrate(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^(3/2),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
145,1,54,0,0.728734," ","integrate(sec(d*x+c)^(1/2)*(b*sec(d*x+c))^(3/2),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
146,1,68,0,0.781017," ","integrate((b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),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
147,1,26,0,0.774070," ","integrate((b*sec(d*x+c))^(3/2)/sec(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
148,1,13,0,0.687012," ","integrate((b*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/2),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
149,1,28,0,0.668955," ","integrate((b*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/2),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
150,1,45,0,0.737321," ","integrate((b*sec(d*x+c))^(3/2)/sec(d*x+c)^(9/2),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
151,1,53,0,1.019955," ","integrate((b*sec(d*x+c))^(3/2)/sec(d*x+c)^(11/2),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
152,1,705,0,1.177197," ","integrate(sec(d*x+c)^(7/2)*(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{16 \, {\left(5 \, {\left(2 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(10 \, d x + 10 \, c\right) + 25 \, {\left(2 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 50 \, {\left(2 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - {\left(10 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \sin\left(10 \, d x + 10 \, c\right) - 5 \, {\left(10 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \sin\left(8 \, d x + 8 \, c\right) - 10 \, {\left(10 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \sqrt{b}}{15 \, {\left(2 \, {\left(5 \, \cos\left(8 \, d x + 8 \, c\right) + 10 \, \cos\left(6 \, d x + 6 \, c\right) + 10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(10 \, d x + 10 \, c\right) + \cos\left(10 \, d x + 10 \, c\right)^{2} + 10 \, {\left(10 \, \cos\left(6 \, d x + 6 \, c\right) + 10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + 25 \, \cos\left(8 \, d x + 8 \, c\right)^{2} + 20 \, {\left(10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 100 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 20 \, {\left(5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 100 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 10 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 2 \, \sin\left(6 \, d x + 6 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + \sin\left(10 \, d x + 10 \, c\right)^{2} + 50 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 25 \, \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, {\left(2 \, \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) + 100 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-16/15*(5*(2*b^2*sin(4*d*x + 4*c) + b^2*sin(2*d*x + 2*c))*cos(10*d*x + 10*c) + 25*(2*b^2*sin(4*d*x + 4*c) + b^2*sin(2*d*x + 2*c))*cos(8*d*x + 8*c) + 50*(2*b^2*sin(4*d*x + 4*c) + b^2*sin(2*d*x + 2*c))*cos(6*d*x + 6*c) - (10*b^2*cos(4*d*x + 4*c) + 5*b^2*cos(2*d*x + 2*c) + b^2)*sin(10*d*x + 10*c) - 5*(10*b^2*cos(4*d*x + 4*c) + 5*b^2*cos(2*d*x + 2*c) + b^2)*sin(8*d*x + 8*c) - 10*(10*b^2*cos(4*d*x + 4*c) + 5*b^2*cos(2*d*x + 2*c) + b^2)*sin(6*d*x + 6*c))*sqrt(b)/((2*(5*cos(8*d*x + 8*c) + 10*cos(6*d*x + 6*c) + 10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(10*d*x + 10*c) + cos(10*d*x + 10*c)^2 + 10*(10*cos(6*d*x + 6*c) + 10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + 25*cos(8*d*x + 8*c)^2 + 20*(10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 100*cos(6*d*x + 6*c)^2 + 20*(5*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 100*cos(4*d*x + 4*c)^2 + 25*cos(2*d*x + 2*c)^2 + 10*(sin(8*d*x + 8*c) + 2*sin(6*d*x + 6*c) + 2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + sin(10*d*x + 10*c)^2 + 50*(2*sin(6*d*x + 6*c) + 2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 25*sin(8*d*x + 8*c)^2 + 100*(2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 100*sin(6*d*x + 6*c)^2 + 100*sin(4*d*x + 4*c)^2 + 100*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*sin(2*d*x + 2*c)^2 + 10*cos(2*d*x + 2*c) + 1)*d)","B",0
153,1,311,0,0.667156," ","integrate(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^(5/2),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
154,1,747,0,0.938436," ","integrate(sec(d*x+c)^(1/2)*(b*sec(d*x+c))^(5/2),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
155,1,54,0,1.196131," ","integrate((b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),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
156,1,72,0,1.042883," ","integrate((b*sec(d*x+c))^(5/2)/sec(d*x+c)^(3/2),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
157,1,26,0,0.763288," ","integrate((b*sec(d*x+c))^(5/2)/sec(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
158,1,13,0,0.990509," ","integrate((b*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/2),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
159,1,32,0,0.690594," ","integrate((b*sec(d*x+c))^(5/2)/sec(d*x+c)^(9/2),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
160,1,49,0,0.876360," ","integrate((b*sec(d*x+c))^(5/2)/sec(d*x+c)^(11/2),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
161,1,661,0,1.075073," ","integrate(sec(d*x+c)^(7/2)/(b*sec(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
162,1,59,0,0.961995," ","integrate(sec(d*x+c)^(5/2)/(b*sec(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
163,1,65,0,1.067867," ","integrate(sec(d*x+c)^(3/2)/(b*sec(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
164,1,26,0,0.524848," ","integrate(sec(d*x+c)^(1/2)/(b*sec(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
165,1,13,0,0.940224," ","integrate(1/sec(d*x+c)^(1/2)/(b*sec(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
166,1,25,0,0.946401," ","integrate(1/sec(d*x+c)^(3/2)/(b*sec(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
167,1,42,0,0.665849," ","integrate(1/sec(d*x+c)^(5/2)/(b*sec(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
168,1,670,0,0.770594," ","integrate(sec(d*x+c)^(9/2)/(b*sec(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
169,1,67,0,0.846602," ","integrate(sec(d*x+c)^(7/2)/(b*sec(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
170,1,65,0,0.867352," ","integrate(sec(d*x+c)^(5/2)/(b*sec(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
171,1,26,0,0.712746," ","integrate(sec(d*x+c)^(3/2)/(b*sec(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
172,1,13,0,1.036299," ","integrate(sec(d*x+c)^(1/2)/(b*sec(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
173,1,25,0,0.884146," ","integrate(1/sec(d*x+c)^(1/2)/(b*sec(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
174,1,42,0,0.723423," ","integrate(1/sec(d*x+c)^(3/2)/(b*sec(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
175,1,49,0,0.972106," ","integrate(1/sec(d*x+c)^(5/2)/(b*sec(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
176,1,688,0,0.837466," ","integrate(sec(d*x+c)^(11/2)/(b*sec(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
177,1,67,0,0.721143," ","integrate(sec(d*x+c)^(9/2)/(b*sec(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
178,1,65,0,0.904499," ","integrate(sec(d*x+c)^(7/2)/(b*sec(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
179,1,26,0,0.822765," ","integrate(sec(d*x+c)^(5/2)/(b*sec(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
180,1,13,0,0.903754," ","integrate(sec(d*x+c)^(3/2)/(b*sec(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
181,1,25,0,0.964789," ","integrate(sec(d*x+c)^(1/2)/(b*sec(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
182,1,42,0,1.037121," ","integrate(1/sec(d*x+c)^(1/2)/(b*sec(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
183,1,49,0,1.138819," ","integrate(1/sec(d*x+c)^(3/2)/(b*sec(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
184,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(1/3)*sec(d*x + c)^2, x)","F",0
185,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(1/3)*sec(d*x + c), x)","F",0
186,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(1/3), x)","F",0
187,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(1/3)*cos(d*x + c), x)","F",0
188,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(1/3)*cos(d*x + c)^2, x)","F",0
189,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(4/3)*sec(d*x + c)^2, x)","F",0
190,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(4/3)*sec(d*x + c), x)","F",0
191,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(4/3), x)","F",0
192,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(4/3)*cos(d*x + c), x)","F",0
193,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(4/3)*cos(d*x + c)^2, x)","F",0
194,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sec(d*x + c))^(1/3), x)","F",0
195,0,0,0,0.000000," ","integrate(sec(d*x+c)/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c))^(1/3), x)","F",0
196,0,0,0,0.000000," ","integrate(1/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{1}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(-1/3), x)","F",0
197,0,0,0,0.000000," ","integrate(cos(d*x+c)/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*sec(d*x + c))^(1/3), x)","F",0
198,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*sec(d*x + c))^(1/3), x)","F",0
199,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sec(d*x + c))^(4/3), x)","F",0
200,0,0,0,0.000000," ","integrate(sec(d*x+c)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
201,0,0,0,0.000000," ","integrate(1/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{1}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(-4/3), x)","F",0
202,0,0,0,0.000000," ","integrate(cos(d*x+c)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
203,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*sec(d*x + c))^(4/3), x)","F",0
204,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(4/3)*sec(d*x + c)^m, x)","F",0
205,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(2/3)*sec(d*x + c)^m, x)","F",0
206,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^(1/3)*sec(d*x + c)^m, x)","F",0
207,0,0,0,0.000000," ","integrate(sec(d*x+c)^m/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^m/(b*sec(d*x + c))^(1/3), x)","F",0
208,0,0,0,0.000000," ","integrate(sec(d*x+c)^m/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^m/(b*sec(d*x + c))^(2/3), x)","F",0
209,0,0,0,0.000000," ","integrate(sec(d*x+c)^m/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^m/(b*sec(d*x + c))^(4/3), x)","F",0
210,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^n*sec(d*x + c)^m, x)","F",0
211,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^n*sec(d*x + c)^2, x)","F",0
212,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c))^n*sec(d*x + c), x)","F",0
213,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^n, x)","F",0
214,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c))^n*cos(d*x + c), x)","F",0
215,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^n*cos(d*x + c)^2, x)","F",0
216,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^n*cos(d*x + c)^3, x)","F",0
217,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(b*sec(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^n*sec(d*x + c)^(5/2), x)","F",0
218,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^n*sec(d*x + c)^(3/2), x)","F",0
219,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \left(b \sec\left(d x + c\right)\right)^{n} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
220,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(b \sec\left(d x + c\right)\right)^{n}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^n/sqrt(sec(d*x + c)), x)","F",0
221,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^n/sec(d*x + c)^(3/2), x)","F",0
222,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c))^n/sec(d*x + c)^(5/2), x)","F",0
223,1,23,0,0.722423," ","integrate((d*sec(b*x+a))^(7/2)*sin(b*x+a),x, algorithm=""maxima"")","\frac{2 \, \left(\frac{d}{\cos\left(b x + a\right)}\right)^{\frac{7}{2}} \cos\left(b x + a\right)}{5 \, b}"," ",0,"2/5*(d/cos(b*x + a))^(7/2)*cos(b*x + a)/b","A",0
224,1,23,0,0.390069," ","integrate((d*sec(b*x+a))^(5/2)*sin(b*x+a),x, algorithm=""maxima"")","\frac{2 \, \left(\frac{d}{\cos\left(b x + a\right)}\right)^{\frac{5}{2}} \cos\left(b x + a\right)}{3 \, b}"," ",0,"2/3*(d/cos(b*x + a))^(5/2)*cos(b*x + a)/b","A",0
225,1,23,0,0.613535," ","integrate((d*sec(b*x+a))^(3/2)*sin(b*x+a),x, algorithm=""maxima"")","\frac{2 \, \left(\frac{d}{\cos\left(b x + a\right)}\right)^{\frac{3}{2}} \cos\left(b x + a\right)}{b}"," ",0,"2*(d/cos(b*x + a))^(3/2)*cos(b*x + a)/b","A",0
226,1,23,0,0.469921," ","integrate((d*sec(b*x+a))^(1/2)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{\frac{d}{\cos\left(b x + a\right)}} \cos\left(b x + a\right)}{b}"," ",0,"-2*sqrt(d/cos(b*x + a))*cos(b*x + a)/b","A",0
227,1,23,0,0.377349," ","integrate(sin(b*x+a)/(d*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \cos\left(b x + a\right)}{3 \, b \sqrt{\frac{d}{\cos\left(b x + a\right)}}}"," ",0,"-2/3*cos(b*x + a)/(b*sqrt(d/cos(b*x + a)))","A",0
228,1,36,0,0.639580," ","integrate((d*sec(b*x+a))^(5/2)*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{3 \, d^{2}}{\sqrt{\frac{d}{\cos\left(b x + a\right)}}} + \left(\frac{d}{\cos\left(b x + a\right)}\right)^{\frac{3}{2}}\right)} d}{3 \, b}"," ",0,"2/3*(3*d^2/sqrt(d/cos(b*x + a)) + (d/cos(b*x + a))^(3/2))*d/b","A",0
229,1,38,0,0.343803," ","integrate((d*sec(b*x+a))^(9/2)*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(7 \, d^{2} \left(\frac{d}{\cos\left(b x + a\right)}\right)^{\frac{3}{2}} - 3 \, \left(\frac{d}{\cos\left(b x + a\right)}\right)^{\frac{7}{2}}\right)} d}{21 \, b}"," ",0,"-2/21*(7*d^2*(d/cos(b*x + a))^(3/2) - 3*(d/cos(b*x + a))^(7/2))*d/b","A",0
230,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(9/2)*(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \left(d \csc\left(b x + a\right)\right)^{\frac{9}{2}} \sqrt{c \sec\left(b x + a\right)}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(9/2)*sqrt(c*sec(b*x + a)), x)","F",0
231,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(7/2)*(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \left(d \csc\left(b x + a\right)\right)^{\frac{7}{2}} \sqrt{c \sec\left(b x + a\right)}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(7/2)*sqrt(c*sec(b*x + a)), x)","F",0
232,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(5/2)*(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \left(d \csc\left(b x + a\right)\right)^{\frac{5}{2}} \sqrt{c \sec\left(b x + a\right)}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(5/2)*sqrt(c*sec(b*x + a)), x)","F",0
233,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(3/2)*(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \left(d \csc\left(b x + a\right)\right)^{\frac{3}{2}} \sqrt{c \sec\left(b x + a\right)}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(3/2)*sqrt(c*sec(b*x + a)), x)","F",0
234,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(1/2)*(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \sqrt{d \csc\left(b x + a\right)} \sqrt{c \sec\left(b x + a\right)}\,{d x}"," ",0,"integrate(sqrt(d*csc(b*x + a))*sqrt(c*sec(b*x + a)), x)","F",0
235,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(1/2)/(d*csc(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c \sec\left(b x + a\right)}}{\sqrt{d \csc\left(b x + a\right)}}\,{d x}"," ",0,"integrate(sqrt(c*sec(b*x + a))/sqrt(d*csc(b*x + a)), x)","F",0
236,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(1/2)/(d*csc(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c \sec\left(b x + a\right)}}{\left(d \csc\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*sec(b*x + a))/(d*csc(b*x + a))^(3/2), x)","F",0
237,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(1/2)/(d*csc(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c \sec\left(b x + a\right)}}{\left(d \csc\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*sec(b*x + a))/(d*csc(b*x + a))^(5/2), x)","F",0
238,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(9/2)*(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \left(d \csc\left(b x + a\right)\right)^{\frac{9}{2}} \left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(9/2)*(c*sec(b*x + a))^(3/2), x)","F",0
239,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(7/2)*(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \left(d \csc\left(b x + a\right)\right)^{\frac{7}{2}} \left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(7/2)*(c*sec(b*x + a))^(3/2), x)","F",0
240,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(5/2)*(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \left(d \csc\left(b x + a\right)\right)^{\frac{5}{2}} \left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(5/2)*(c*sec(b*x + a))^(3/2), x)","F",0
241,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(3/2)*(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \left(d \csc\left(b x + a\right)\right)^{\frac{3}{2}} \left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(3/2)*(c*sec(b*x + a))^(3/2), x)","F",0
242,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(1/2)*(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \sqrt{d \csc\left(b x + a\right)} \left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(d*csc(b*x + a))*(c*sec(b*x + a))^(3/2), x)","F",0
243,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(3/2)/(d*csc(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}}{\sqrt{d \csc\left(b x + a\right)}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(3/2)/sqrt(d*csc(b*x + a)), x)","F",0
244,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(3/2)/(d*csc(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}}{\left(d \csc\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(3/2)/(d*csc(b*x + a))^(3/2), x)","F",0
245,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(3/2)/(d*csc(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}}{\left(d \csc\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(3/2)/(d*csc(b*x + a))^(5/2), x)","F",0
246,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(9/2)*(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \left(d \csc\left(b x + a\right)\right)^{\frac{9}{2}} \left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(9/2)*(c*sec(b*x + a))^(5/2), x)","F",0
247,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(7/2)*(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \left(d \csc\left(b x + a\right)\right)^{\frac{7}{2}} \left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(7/2)*(c*sec(b*x + a))^(5/2), x)","F",0
248,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(5/2)*(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \left(d \csc\left(b x + a\right)\right)^{\frac{5}{2}} \left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(5/2)*(c*sec(b*x + a))^(5/2), x)","F",0
249,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(3/2)*(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \left(d \csc\left(b x + a\right)\right)^{\frac{3}{2}} \left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(3/2)*(c*sec(b*x + a))^(5/2), x)","F",0
250,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(1/2)*(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \sqrt{d \csc\left(b x + a\right)} \left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(d*csc(b*x + a))*(c*sec(b*x + a))^(5/2), x)","F",0
251,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(5/2)/(d*csc(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}}{\sqrt{d \csc\left(b x + a\right)}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(5/2)/sqrt(d*csc(b*x + a)), x)","F",0
252,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(5/2)/(d*csc(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}}{\left(d \csc\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(5/2)/(d*csc(b*x + a))^(3/2), x)","F",0
253,0,0,0,0.000000," ","integrate((c*sec(b*x+a))^(5/2)/(d*csc(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}}{\left(d \csc\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*sec(b*x + a))^(5/2)/(d*csc(b*x + a))^(5/2), x)","F",0
254,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(9/2)/(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(b x + a\right)\right)^{\frac{9}{2}}}{\sqrt{c \sec\left(b x + a\right)}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(9/2)/sqrt(c*sec(b*x + a)), x)","F",0
255,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(7/2)/(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(b x + a\right)\right)^{\frac{7}{2}}}{\sqrt{c \sec\left(b x + a\right)}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(7/2)/sqrt(c*sec(b*x + a)), x)","F",0
256,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(5/2)/(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(b x + a\right)\right)^{\frac{5}{2}}}{\sqrt{c \sec\left(b x + a\right)}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(5/2)/sqrt(c*sec(b*x + a)), x)","F",0
257,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(3/2)/(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(b x + a\right)\right)^{\frac{3}{2}}}{\sqrt{c \sec\left(b x + a\right)}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(3/2)/sqrt(c*sec(b*x + a)), x)","F",0
258,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(1/2)/(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d \csc\left(b x + a\right)}}{\sqrt{c \sec\left(b x + a\right)}}\,{d x}"," ",0,"integrate(sqrt(d*csc(b*x + a))/sqrt(c*sec(b*x + a)), x)","F",0
259,0,0,0,0.000000," ","integrate(1/(d*csc(b*x+a))^(1/2)/(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{d \csc\left(b x + a\right)} \sqrt{c \sec\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(d*csc(b*x + a))*sqrt(c*sec(b*x + a))), x)","F",0
260,0,0,0,0.000000," ","integrate(1/(d*csc(b*x+a))^(3/2)/(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\left(d \csc\left(b x + a\right)\right)^{\frac{3}{2}} \sqrt{c \sec\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/((d*csc(b*x + a))^(3/2)*sqrt(c*sec(b*x + a))), x)","F",0
261,0,0,0,0.000000," ","integrate(1/(d*csc(b*x+a))^(5/2)/(c*sec(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\left(d \csc\left(b x + a\right)\right)^{\frac{5}{2}} \sqrt{c \sec\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/((d*csc(b*x + a))^(5/2)*sqrt(c*sec(b*x + a))), x)","F",0
262,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(11/2)/(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(b x + a\right)\right)^{\frac{11}{2}}}{\left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(11/2)/(c*sec(b*x + a))^(3/2), x)","F",0
263,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(9/2)/(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(b x + a\right)\right)^{\frac{9}{2}}}{\left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(9/2)/(c*sec(b*x + a))^(3/2), x)","F",0
264,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(7/2)/(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(b x + a\right)\right)^{\frac{7}{2}}}{\left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(7/2)/(c*sec(b*x + a))^(3/2), x)","F",0
265,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(5/2)/(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(b x + a\right)\right)^{\frac{5}{2}}}{\left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(5/2)/(c*sec(b*x + a))^(3/2), x)","F",0
266,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(3/2)/(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(b x + a\right)\right)^{\frac{3}{2}}}{\left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(3/2)/(c*sec(b*x + a))^(3/2), x)","F",0
267,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(1/2)/(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d \csc\left(b x + a\right)}}{\left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*csc(b*x + a))/(c*sec(b*x + a))^(3/2), x)","F",0
268,0,0,0,0.000000," ","integrate(1/(d*csc(b*x+a))^(1/2)/(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{d \csc\left(b x + a\right)} \left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(d*csc(b*x + a))*(c*sec(b*x + a))^(3/2)), x)","F",0
269,0,0,0,0.000000," ","integrate(1/(d*csc(b*x+a))^(3/2)/(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(d \csc\left(b x + a\right)\right)^{\frac{3}{2}} \left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((d*csc(b*x + a))^(3/2)*(c*sec(b*x + a))^(3/2)), x)","F",0
270,0,0,0,0.000000," ","integrate(1/(d*csc(b*x+a))^(5/2)/(c*sec(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(d \csc\left(b x + a\right)\right)^{\frac{5}{2}} \left(c \sec\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((d*csc(b*x + a))^(5/2)*(c*sec(b*x + a))^(3/2)), x)","F",0
271,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(9/2)/(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(b x + a\right)\right)^{\frac{9}{2}}}{\left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(9/2)/(c*sec(b*x + a))^(5/2), x)","F",0
272,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(7/2)/(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(b x + a\right)\right)^{\frac{7}{2}}}{\left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(7/2)/(c*sec(b*x + a))^(5/2), x)","F",0
273,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(5/2)/(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(b x + a\right)\right)^{\frac{5}{2}}}{\left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(5/2)/(c*sec(b*x + a))^(5/2), x)","F",0
274,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(3/2)/(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(b x + a\right)\right)^{\frac{3}{2}}}{\left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*csc(b*x + a))^(3/2)/(c*sec(b*x + a))^(5/2), x)","F",0
275,0,0,0,0.000000," ","integrate((d*csc(b*x+a))^(1/2)/(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d \csc\left(b x + a\right)}}{\left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*csc(b*x + a))/(c*sec(b*x + a))^(5/2), x)","F",0
276,0,0,0,0.000000," ","integrate(1/(d*csc(b*x+a))^(1/2)/(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{d \csc\left(b x + a\right)} \left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(d*csc(b*x + a))*(c*sec(b*x + a))^(5/2)), x)","F",0
277,0,0,0,0.000000," ","integrate(1/(d*csc(b*x+a))^(3/2)/(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(d \csc\left(b x + a\right)\right)^{\frac{3}{2}} \left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((d*csc(b*x + a))^(3/2)*(c*sec(b*x + a))^(5/2)), x)","F",0
278,0,0,0,0.000000," ","integrate(1/(d*csc(b*x+a))^(5/2)/(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(d \csc\left(b x + a\right)\right)^{\frac{5}{2}} \left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((d*csc(b*x + a))^(5/2)*(c*sec(b*x + a))^(5/2)), x)","F",0
279,0,0,0,0.000000," ","integrate(1/(d*csc(b*x+a))^(7/2)/(c*sec(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(d \csc\left(b x + a\right)\right)^{\frac{7}{2}} \left(c \sec\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((d*csc(b*x + a))^(7/2)*(c*sec(b*x + a))^(5/2)), x)","F",0
280,0,0,0,0.000000," ","integrate(csc(f*x+e)^n*sec(f*x+e)^m,x, algorithm=""maxima"")","\int \csc\left(f x + e\right)^{n} \sec\left(f x + e\right)^{m}\,{d x}"," ",0,"integrate(csc(f*x + e)^n*sec(f*x + e)^m, x)","F",0
281,0,0,0,0.000000," ","integrate(csc(f*x+e)^n*(a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int \left(a \sec\left(f x + e\right)\right)^{m} \csc\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e))^m*csc(f*x + e)^n, x)","F",0
282,0,0,0,0.000000," ","integrate((b*csc(f*x+e))^n*sec(f*x+e)^m,x, algorithm=""maxima"")","\int \left(b \csc\left(f x + e\right)\right)^{n} \sec\left(f x + e\right)^{m}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n*sec(f*x + e)^m, x)","F",0
283,0,0,0,0.000000," ","integrate((b*csc(f*x+e))^n*(a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int \left(b \csc\left(f x + e\right)\right)^{n} \left(a \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n*(a*sec(f*x + e))^m, x)","F",0
284,0,0,0,0.000000," ","integrate((b*csc(f*x+e))^n*sec(f*x+e)^5,x, algorithm=""maxima"")","\int \left(b \csc\left(f x + e\right)\right)^{n} \sec\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n*sec(f*x + e)^5, x)","F",0
285,0,0,0,0.000000," ","integrate((b*csc(f*x+e))^n*sec(f*x+e)^3,x, algorithm=""maxima"")","\int \left(b \csc\left(f x + e\right)\right)^{n} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n*sec(f*x + e)^3, x)","F",0
286,0,0,0,0.000000," ","integrate((b*csc(f*x+e))^n*sec(f*x+e),x, algorithm=""maxima"")","\int \left(b \csc\left(f x + e\right)\right)^{n} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n*sec(f*x + e), x)","F",0
287,1,29,0,0.711001," ","integrate(cos(f*x+e)*(b*csc(f*x+e))^n,x, algorithm=""maxima"")","-\frac{b^{n} \sin\left(f x + e\right)^{-n} \sin\left(f x + e\right)}{f {\left(n - 1\right)}}"," ",0,"-b^n*sin(f*x + e)^(-n)*sin(f*x + e)/(f*(n - 1))","A",0
288,1,58,0,0.709647," ","integrate(cos(f*x+e)^3*(b*csc(f*x+e))^n,x, algorithm=""maxima"")","\frac{\frac{b^{n} \sin\left(f x + e\right)^{-n} \sin\left(f x + e\right)^{3}}{n - 3} - \frac{b^{n} \sin\left(f x + e\right)^{-n} \sin\left(f x + e\right)}{n - 1}}{f}"," ",0,"(b^n*sin(f*x + e)^(-n)*sin(f*x + e)^3/(n - 3) - b^n*sin(f*x + e)^(-n)*sin(f*x + e)/(n - 1))/f","A",0
289,1,86,0,0.687426," ","integrate(cos(f*x+e)^5*(b*csc(f*x+e))^n,x, algorithm=""maxima"")","-\frac{\frac{b^{n} \sin\left(f x + e\right)^{-n} \sin\left(f x + e\right)^{5}}{n - 5} - \frac{2 \, b^{n} \sin\left(f x + e\right)^{-n} \sin\left(f x + e\right)^{3}}{n - 3} + \frac{b^{n} \sin\left(f x + e\right)^{-n} \sin\left(f x + e\right)}{n - 1}}{f}"," ",0,"-(b^n*sin(f*x + e)^(-n)*sin(f*x + e)^5/(n - 5) - 2*b^n*sin(f*x + e)^(-n)*sin(f*x + e)^3/(n - 3) + b^n*sin(f*x + e)^(-n)*sin(f*x + e)/(n - 1))/f","A",0
290,0,0,0,0.000000," ","integrate((b*csc(f*x+e))^n*sec(f*x+e)^6,x, algorithm=""maxima"")","\int \left(b \csc\left(f x + e\right)\right)^{n} \sec\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n*sec(f*x + e)^6, x)","F",0
291,0,0,0,0.000000," ","integrate((b*csc(f*x+e))^n*sec(f*x+e)^4,x, algorithm=""maxima"")","\int \left(b \csc\left(f x + e\right)\right)^{n} \sec\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n*sec(f*x + e)^4, x)","F",0
292,0,0,0,0.000000," ","integrate((b*csc(f*x+e))^n*sec(f*x+e)^2,x, algorithm=""maxima"")","\int \left(b \csc\left(f x + e\right)\right)^{n} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n*sec(f*x + e)^2, x)","F",0
293,0,0,0,0.000000," ","integrate((b*csc(f*x+e))^n,x, algorithm=""maxima"")","\int \left(b \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n, x)","F",0
294,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(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)^{2}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n*cos(f*x + e)^2, x)","F",0
295,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(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)^{4}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n*cos(f*x + e)^4, x)","F",0
296,0,0,0,0.000000," ","integrate((b*csc(f*x+e))^n*(c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \left(c \sec\left(f x + e\right)\right)^{\frac{3}{2}} \left(b \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((c*sec(f*x + e))^(3/2)*(b*csc(f*x + e))^n, x)","F",0
297,0,0,0,0.000000," ","integrate((b*csc(f*x+e))^n*(c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c \sec\left(f x + e\right)} \left(b \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(c*sec(f*x + e))*(b*csc(f*x + e))^n, x)","F",0
298,0,0,0,0.000000," ","integrate((b*csc(f*x+e))^n/(c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(b \csc\left(f x + e\right)\right)^{n}}{\sqrt{c \sec\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n/sqrt(c*sec(f*x + e)), x)","F",0
299,0,0,0,0.000000," ","integrate((b*csc(f*x+e))^n/(c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(b \csc\left(f x + e\right)\right)^{n}}{\left(c \sec\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*csc(f*x + e))^n/(c*sec(f*x + e))^(3/2), x)","F",0
