1,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^2, x)","F",0
2,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c), x)","F",0
3,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3), x)","F",0
4,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3)*cos(d*x + c), x)","F",0
5,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3)*cos(d*x + c)^2, x)","F",0
6,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c)^2, x)","F",0
7,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c), x)","F",0
8,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(4/3), x)","F",0
9,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c), x)","F",0
10,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c)^2, x)","F",0
11,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(1/3), x)","F",0
12,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)/(b*sec(d*x + c))^(1/3), x)","F",0
13,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(b*sec(d*x + c))^(1/3), x)","F",0
14,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)/(b*sec(d*x + c))^(1/3), x)","F",0
15,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^2/(b*sec(d*x + c))^(1/3), x)","F",0
16,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(4/3), x)","F",0
17,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
18,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(b*sec(d*x + c))^(4/3), x)","F",0
19,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
20,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^2/(b*sec(d*x + c))^(4/3), x)","F",0
21,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c)^m, x)","F",0
22,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^m, x)","F",0
23,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^m, x)","F",0
24,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(1/3), x)","F",0
25,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(2/3), x)","F",0
26,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(4/3), x)","F",0
27,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sec(d*x + c)^m, x)","F",0
28,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sec(d*x + c)^2, x)","F",0
29,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sec(d*x + c), x)","F",0
30,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n, x)","F",0
31,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*cos(d*x + c), x)","F",0
32,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*cos(d*x + c)^2, x)","F",0
33,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*cos(d*x + c)^3, x)","F",0
34,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sec(d*x + c)^(5/2), x)","F",0
35,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sec(d*x + c)^(3/2), x)","F",0
36,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
37,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n/sqrt(sec(d*x + c)), x)","F",0
38,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(3/2), x)","F",0
39,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(5/2), x)","F",0
40,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^n*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c))^n*sec(d*x + c)^m, x)","F",0
41,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^2, x)","F",0
42,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c), x)","F",0
43,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3), x)","F",0
44,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*cos(d*x + c), x)","F",0
45,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*cos(d*x + c)^2, x)","F",0
46,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*cos(d*x + c)^3, x)","F",0
47,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c)^2, x)","F",0
48,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c), x)","F",0
49,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3), x)","F",0
50,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c), x)","F",0
51,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c)^2, x)","F",0
52,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c)^3, x)","F",0
53,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(2/3), x)","F",0
54,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(2/3), x)","F",0
55,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(b*sec(d*x + c))^(2/3), x)","F",0
56,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(2/3), x)","F",0
57,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(2/3), x)","F",0
58,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^3/(b*sec(d*x + c))^(2/3), x)","F",0
59,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(4/3), x)","F",0
60,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
61,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(b*sec(d*x + c))^(4/3), x)","F",0
62,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
63,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(4/3), x)","F",0
64,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^3/(b*sec(d*x + c))^(4/3), x)","F",0
65,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c)^m, x)","F",0
66,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^m, x)","F",0
67,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^m, x)","F",0
68,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(1/3), x)","F",0
69,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(2/3), x)","F",0
70,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(4/3), x)","F",0
71,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^m, x)","F",0
72,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^2, x)","F",0
73,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c), x)","F",0
74,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n, x)","F",0
75,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*cos(d*x + c), x)","F",0
76,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*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))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*cos(d*x + c)^3, x)","F",0
78,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^(5/2), x)","F",0
79,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^(3/2), x)","F",0
80,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
81,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sqrt(sec(d*x + c)), x)","F",0
82,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(3/2), x)","F",0
83,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(5/2), x)","F",0
84,1,218,0,0.327577," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, A a + 3 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, A a + 3 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(60 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 200 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 130 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 400 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 464 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 440 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 190 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 180 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 195 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(4*A*a + 3*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*A*a + 3*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(60*A*a*tan(1/2*d*x + 1/2*c)^9 + 45*C*a*tan(1/2*d*x + 1/2*c)^9 - 200*A*a*tan(1/2*d*x + 1/2*c)^7 - 130*C*a*tan(1/2*d*x + 1/2*c)^7 + 400*A*a*tan(1/2*d*x + 1/2*c)^5 + 464*C*a*tan(1/2*d*x + 1/2*c)^5 - 440*A*a*tan(1/2*d*x + 1/2*c)^3 - 190*C*a*tan(1/2*d*x + 1/2*c)^3 + 180*A*a*tan(1/2*d*x + 1/2*c) + 195*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
85,1,188,0,0.281239," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(4 \, A a + 3 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, A a + 3 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(12 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 49 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 84 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 31 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 39 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(4*A*a + 3*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*A*a + 3*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(12*A*a*tan(1/2*d*x + 1/2*c)^7 + 9*C*a*tan(1/2*d*x + 1/2*c)^7 - 60*A*a*tan(1/2*d*x + 1/2*c)^5 - 49*C*a*tan(1/2*d*x + 1/2*c)^5 + 84*A*a*tan(1/2*d*x + 1/2*c)^3 + 31*C*a*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*tan(1/2*d*x + 1/2*c) - 39*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
86,1,156,0,0.284421," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(2 \, A a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, A a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*A*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*A*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a*tan(1/2*d*x + 1/2*c)^5 + 3*C*a*tan(1/2*d*x + 1/2*c)^5 - 12*A*a*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*tan(1/2*d*x + 1/2*c)^3 + 6*A*a*tan(1/2*d*x + 1/2*c) + 9*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
87,1,105,0,0.250425," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} A a + {\left(2 \, A a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, A a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*A*a + (2*A*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*A*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(C*a*tan(1/2*d*x + 1/2*c)^3 - 3*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
88,1,119,0,0.251475," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} A a + C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((d*x + c)*A*a + C*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - C*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - C*a*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) - C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
89,1,99,0,1.100394," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(A a + 2 \, C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*C*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*C*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (A*a + 2*C*a)*(d*x + c) + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 + 3*A*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
90,1,125,0,0.250056," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(A a + 2 \, C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(3 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(A*a + 2*C*a)*(d*x + c) + 2*(3*A*a*tan(1/2*d*x + 1/2*c)^5 + 6*C*a*tan(1/2*d*x + 1/2*c)^5 + 4*A*a*tan(1/2*d*x + 1/2*c)^3 + 12*C*a*tan(1/2*d*x + 1/2*c)^3 + 9*A*a*tan(1/2*d*x + 1/2*c) + 6*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
91,1,156,0,0.777712," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a + 4 \, C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 49 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 84 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 39 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a + 4*C*a)*(d*x + c) + 2*(9*A*a*tan(1/2*d*x + 1/2*c)^7 + 12*C*a*tan(1/2*d*x + 1/2*c)^7 + 49*A*a*tan(1/2*d*x + 1/2*c)^5 + 60*C*a*tan(1/2*d*x + 1/2*c)^5 + 31*A*a*tan(1/2*d*x + 1/2*c)^3 + 84*C*a*tan(1/2*d*x + 1/2*c)^3 + 39*A*a*tan(1/2*d*x + 1/2*c) + 36*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
92,1,186,0,0.250379," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, A a + 4 \, C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(45 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 130 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 200 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 190 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 440 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 195 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*A*a + 4*C*a)*(d*x + c) + 2*(45*A*a*tan(1/2*d*x + 1/2*c)^9 + 60*C*a*tan(1/2*d*x + 1/2*c)^9 + 130*A*a*tan(1/2*d*x + 1/2*c)^7 + 200*C*a*tan(1/2*d*x + 1/2*c)^7 + 464*A*a*tan(1/2*d*x + 1/2*c)^5 + 400*C*a*tan(1/2*d*x + 1/2*c)^5 + 190*A*a*tan(1/2*d*x + 1/2*c)^3 + 440*C*a*tan(1/2*d*x + 1/2*c)^3 + 195*A*a*tan(1/2*d*x + 1/2*c) + 180*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
93,1,246,0,1.022611," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, A a^{2} + 3 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, A a^{2} + 3 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(60 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 280 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 210 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 560 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 432 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 520 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 270 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 180 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 195 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(15*(4*A*a^2 + 3*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*A*a^2 + 3*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(60*A*a^2*tan(1/2*d*x + 1/2*c)^9 + 45*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 280*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 210*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 560*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 432*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 520*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 270*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 180*A*a^2*tan(1/2*d*x + 1/2*c) + 195*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
94,1,212,0,0.316470," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(12 \, A a^{2} + 7 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(12 \, A a^{2} + 7 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(36 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 132 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 77 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 156 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 83 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 75 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(12*A*a^2 + 7*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(12*A*a^2 + 7*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(36*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 21*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 132*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 77*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 156*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 83*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 60*A*a^2*tan(1/2*d*x + 1/2*c) - 75*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
95,1,187,0,1.826173," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} A a^{2} + 3 \, {\left(2 \, A a^{2} + C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, A a^{2} + C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*A*a^2 + 3*(2*A*a^2 + C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*A*a^2 + C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 8*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^2*tan(1/2*d*x + 1/2*c) + 9*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
96,1,152,0,0.301419," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{4 \, {\left(d x + c\right)} A a^{2} + \frac{4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + {\left(2 \, A a^{2} + 3 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, A a^{2} + 3 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*A*a^2 + 4*A*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + (2*A*a^2 + 3*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*A*a^2 + 3*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
97,1,143,0,0.292470," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{4 \, C a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 4 \, C a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{4 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + {\left(3 \, A a^{2} + 2 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*C*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 4*C*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 4*C*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + (3*A*a^2 + 2*C*a^2)*(d*x + c) + 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
98,1,179,0,3.027013," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, C a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, C a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(A a^{2} + 2 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*C*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*C*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(A*a^2 + 2*C*a^2)*(d*x + c) + 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 8*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 9*A*a^2*tan(1/2*d*x + 1/2*c) + 3*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
99,1,176,0,0.846284," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(7 \, A a^{2} + 12 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(21 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 77 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 132 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 83 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 156 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 75 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(7*A*a^2 + 12*C*a^2)*(d*x + c) + 2*(21*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 36*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 77*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 132*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 83*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 156*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 75*A*a^2*tan(1/2*d*x + 1/2*c) + 60*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
100,1,210,0,0.261968," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, A a^{2} + 4 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(45 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 210 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 280 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 432 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 560 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 270 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 520 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 195 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(15*(3*A*a^2 + 4*C*a^2)*(d*x + c) + 2*(45*A*a^2*tan(1/2*d*x + 1/2*c)^9 + 60*C*a^2*tan(1/2*d*x + 1/2*c)^9 + 210*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 280*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 432*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 560*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 270*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 520*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 195*A*a^2*tan(1/2*d*x + 1/2*c) + 180*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
101,1,244,0,1.218420," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(11 \, A a^{2} + 14 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(165 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 210 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 935 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1190 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1986 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2580 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3006 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3180 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1305 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2330 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 795 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 750 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(11*A*a^2 + 14*C*a^2)*(d*x + c) + 2*(165*A*a^2*tan(1/2*d*x + 1/2*c)^11 + 210*C*a^2*tan(1/2*d*x + 1/2*c)^11 + 935*A*a^2*tan(1/2*d*x + 1/2*c)^9 + 1190*C*a^2*tan(1/2*d*x + 1/2*c)^9 + 1986*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 2580*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 3006*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 3180*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 1305*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 2330*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 795*A*a^2*tan(1/2*d*x + 1/2*c) + 750*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
102,1,280,0,0.382830," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(30 \, A a^{3} + 23 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(30 \, A a^{3} + 23 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(450 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 345 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 2550 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1955 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5940 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4554 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 7500 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5814 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5130 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3165 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1470 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1575 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(30*A*a^3 + 23*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(30*A*a^3 + 23*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(450*A*a^3*tan(1/2*d*x + 1/2*c)^11 + 345*C*a^3*tan(1/2*d*x + 1/2*c)^11 - 2550*A*a^3*tan(1/2*d*x + 1/2*c)^9 - 1955*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 5940*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 4554*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 7500*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 5814*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 5130*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 3165*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 1470*A*a^3*tan(1/2*d*x + 1/2*c) - 1575*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
103,1,246,0,0.383142," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(20 \, A a^{3} + 13 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(20 \, A a^{3} + 13 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(300 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 195 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1400 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 910 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2560 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1664 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1330 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 660 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 765 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(20*A*a^3 + 13*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(20*A*a^3 + 13*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(300*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 195*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 1400*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 910*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 2560*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 1664*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 2120*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 1330*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 660*A*a^3*tan(1/2*d*x + 1/2*c) + 765*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
104,1,222,0,0.349166," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, {\left(d x + c\right)} A a^{3} + {\left(28 \, A a^{3} + 15 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(28 \, A a^{3} + 15 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(20 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 68 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 55 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 76 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 73 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 49 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(8*(d*x + c)*A*a^3 + (28*A*a^3 + 15*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (28*A*a^3 + 15*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(20*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 68*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 55*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 76*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 73*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 28*A*a^3*tan(1/2*d*x + 1/2*c) - 49*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
105,1,219,0,0.428560," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{18 \, {\left(d x + c\right)} A a^{3} + \frac{12 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 3 \, {\left(6 \, A a^{3} + 5 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(6 \, A a^{3} + 5 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(18*(d*x + c)*A*a^3 + 12*A*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 3*(6*A*a^3 + 5*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(6*A*a^3 + 5*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 12*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*tan(1/2*d*x + 1/2*c) + 33*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
106,1,230,0,0.345789," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(7 \, A a^{3} + 2 \, C a^{3}\right)} {\left(d x + c\right)} + {\left(2 \, A a^{3} + 7 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, A a^{3} + 7 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(5 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((7*A*a^3 + 2*C*a^3)*(d*x + c) + (2*A*a^3 + 7*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*A*a^3 + 7*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(5*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 5*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 3*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 9*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 7*A*a^3*tan(1/2*d*x + 1/2*c) + 7*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","A",0
107,1,210,0,0.359678," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{18 \, C a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 18 \, C a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + 3 \, {\left(5 \, A a^{3} + 6 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(18*C*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 18*C*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 12*C*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 3*(5*A*a^3 + 6*C*a^3)*(d*x + c) + 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 33*A*a^3*tan(1/2*d*x + 1/2*c) + 6*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
108,1,213,0,0.339902," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, C a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 8 \, C a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(15 \, A a^{3} + 28 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 20 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 55 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 68 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 73 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 76 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 49 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 28 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(8*C*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 8*C*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (15*A*a^3 + 28*C*a^3)*(d*x + c) + 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 20*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 55*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 68*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 73*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 76*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 49*A*a^3*tan(1/2*d*x + 1/2*c) + 28*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
109,1,210,0,0.305391," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(13 \, A a^{3} + 20 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(195 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 300 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 910 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1400 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1664 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2560 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1330 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 765 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 660 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(13*A*a^3 + 20*C*a^3)*(d*x + c) + 2*(195*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 300*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 910*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 1400*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 1664*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 2560*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 1330*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 2120*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 765*A*a^3*tan(1/2*d*x + 1/2*c) + 660*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
110,1,244,0,0.354118," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(23 \, A a^{3} + 30 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(345 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1955 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2550 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4554 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5940 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5814 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7500 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5130 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1575 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1470 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(23*A*a^3 + 30*C*a^3)*(d*x + c) + 2*(345*A*a^3*tan(1/2*d*x + 1/2*c)^11 + 450*C*a^3*tan(1/2*d*x + 1/2*c)^11 + 1955*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 2550*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 4554*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 5940*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 5814*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 7500*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 3165*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 5130*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 1575*A*a^3*tan(1/2*d*x + 1/2*c) + 1470*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
111,1,314,0,1.015315," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(14 \, A a^{4} + 11 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(14 \, A a^{4} + 11 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(1470 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1155 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 9800 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 7700 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 27734 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 21791 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 43008 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 33792 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 39914 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31521 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21560 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 14700 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5250 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5565 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{420 \, d}"," ",0,"1/420*(105*(14*A*a^4 + 11*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(14*A*a^4 + 11*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(1470*A*a^4*tan(1/2*d*x + 1/2*c)^13 + 1155*C*a^4*tan(1/2*d*x + 1/2*c)^13 - 9800*A*a^4*tan(1/2*d*x + 1/2*c)^11 - 7700*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 27734*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 21791*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 43008*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 33792*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 39914*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 31521*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 21560*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 14700*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 5250*A*a^4*tan(1/2*d*x + 1/2*c) + 5565*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","A",0
112,1,280,0,0.365088," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(10 \, A a^{4} + 7 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(10 \, A a^{4} + 7 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(1050 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 735 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 5950 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4165 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 13860 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9702 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16860 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 11802 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10690 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7355 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2790 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3105 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(105*(10*A*a^4 + 7*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(10*A*a^4 + 7*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(1050*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 735*C*a^4*tan(1/2*d*x + 1/2*c)^11 - 5950*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 4165*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 13860*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 9702*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 16860*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 11802*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 10690*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 7355*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 2790*A*a^4*tan(1/2*d*x + 1/2*c) - 3105*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
113,1,257,0,0.571362," ","integrate((a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{30 \, {\left(d x + c\right)} A a^{4} + 15 \, {\left(12 \, A a^{4} + 7 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(12 \, A a^{4} + 7 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(150 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 105 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 680 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 490 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1180 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 896 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 920 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 790 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 270 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 375 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(30*(d*x + c)*A*a^4 + 15*(12*A*a^4 + 7*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(12*A*a^4 + 7*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(150*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 105*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 680*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 490*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 1180*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 896*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 920*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 790*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 270*A*a^4*tan(1/2*d*x + 1/2*c) + 375*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
114,1,253,0,0.400926," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{96 \, {\left(d x + c\right)} A a^{4} + \frac{48 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 3 \, {\left(52 \, A a^{4} + 35 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(52 \, A a^{4} + 35 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(84 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 276 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 385 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 300 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 511 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 108 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 279 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(96*(d*x + c)*A*a^4 + 48*A*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 3*(52*A*a^4 + 35*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(52*A*a^4 + 35*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(84*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 105*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 276*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 385*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 300*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 511*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 108*A*a^4*tan(1/2*d*x + 1/2*c) - 279*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
115,1,248,0,0.649908," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(13 \, A a^{4} + 2 \, C a^{4}\right)} {\left(d x + c\right)} + 12 \, {\left(2 \, A a^{4} + 3 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 12 \, {\left(2 \, A a^{4} + 3 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{6 \, {\left(7 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{4 \, {\left(3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 38 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(13*A*a^4 + 2*C*a^4)*(d*x + c) + 12*(2*A*a^4 + 3*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 12*(2*A*a^4 + 3*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 6*(7*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*A*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - 4*(3*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 15*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 38*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*tan(1/2*d*x + 1/2*c) + 27*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
116,1,248,0,0.336192," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{12 \, {\left(3 \, A a^{4} + 2 \, C a^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(2 \, A a^{4} + 13 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, A a^{4} + 13 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{6 \, {\left(7 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{4 \, {\left(15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 38 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*(3*A*a^4 + 2*C*a^4)*(d*x + c) + 3*(2*A*a^4 + 13*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*A*a^4 + 13*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 6*(7*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 9*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + 4*(15*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 38*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 27*A*a^4*tan(1/2*d*x + 1/2*c) + 3*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
117,1,244,0,0.531142," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{96 \, C a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 96 \, C a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{48 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + 3 \, {\left(35 \, A a^{4} + 52 \, C a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 84 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 385 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 276 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 511 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 300 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 279 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 108 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(96*C*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 96*C*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 48*C*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 3*(35*A*a^4 + 52*C*a^4)*(d*x + c) + 2*(105*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 84*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 385*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 276*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 511*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 300*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 279*A*a^4*tan(1/2*d*x + 1/2*c) + 108*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
118,1,248,0,0.362933," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{30 \, C a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 30 \, C a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 15 \, {\left(7 \, A a^{4} + 12 \, C a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 150 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 490 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 680 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 896 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1180 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 790 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 920 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 375 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 270 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(30*C*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 30*C*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 15*(7*A*a^4 + 12*C*a^4)*(d*x + c) + 2*(105*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 150*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 490*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 680*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 896*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 1180*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 790*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 920*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 375*A*a^4*tan(1/2*d*x + 1/2*c) + 270*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
119,1,244,0,0.335653," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(7 \, A a^{4} + 10 \, C a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(735 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1050 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 4165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5950 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 9702 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 13860 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 11802 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16860 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7355 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10690 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2790 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(105*(7*A*a^4 + 10*C*a^4)*(d*x + c) + 2*(735*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 1050*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 4165*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 5950*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 9702*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 13860*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 11802*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 16860*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 7355*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 10690*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 3105*A*a^4*tan(1/2*d*x + 1/2*c) + 2790*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
120,1,278,0,0.358998," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(11 \, A a^{4} + 14 \, C a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(1155 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1470 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 7700 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 9800 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 21791 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 27734 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 33792 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 43008 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 31521 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 39914 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 14700 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21560 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5565 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5250 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7}}}{420 \, d}"," ",0,"1/420*(105*(11*A*a^4 + 14*C*a^4)*(d*x + c) + 2*(1155*A*a^4*tan(1/2*d*x + 1/2*c)^13 + 1470*C*a^4*tan(1/2*d*x + 1/2*c)^13 + 7700*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 9800*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 21791*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 27734*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 33792*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 43008*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 31521*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 39914*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 14700*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 21560*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 5565*A*a^4*tan(1/2*d*x + 1/2*c) + 5250*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^7)/d","A",0
121,1,213,0,0.293866," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{9 \, {\left(4 \, A + 5 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{9 \, {\left(4 \, A + 5 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{24 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(36 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 75 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 84 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 115 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 109 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4} a}}{24 \, d}"," ",0,"1/24*(9*(4*A + 5*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - 9*(4*A + 5*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 24*(A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a + 2*(36*A*tan(1/2*d*x + 1/2*c)^7 + 75*C*tan(1/2*d*x + 1/2*c)^7 - 84*A*tan(1/2*d*x + 1/2*c)^5 - 115*C*tan(1/2*d*x + 1/2*c)^5 + 60*A*tan(1/2*d*x + 1/2*c)^3 + 109*C*tan(1/2*d*x + 1/2*c)^3 - 12*A*tan(1/2*d*x + 1/2*c) - 21*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^4*a))/d","A",0
122,1,185,0,0.435969," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, A + 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{3 \, {\left(2 \, A + 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{6 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a}}{6 \, d}"," ",0,"-1/6*(3*(2*A + 3*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - 3*(2*A + 3*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 6*(A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a + 2*(6*A*tan(1/2*d*x + 1/2*c)^5 + 15*C*tan(1/2*d*x + 1/2*c)^5 - 12*A*tan(1/2*d*x + 1/2*c)^3 - 16*C*tan(1/2*d*x + 1/2*c)^3 + 6*A*tan(1/2*d*x + 1/2*c) + 9*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a))/d","A",0
123,1,130,0,0.297513," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, A + 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{{\left(2 \, A + 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{2 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a}}{2 \, d}"," ",0,"1/2*((2*A + 3*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - (2*A + 3*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 2*(A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a + 2*(3*C*tan(1/2*d*x + 1/2*c)^3 - C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a))/d","A",0
124,1,101,0,0.533326," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} + \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a}}{d}"," ",0,"-(C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - (A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a + 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a))/d","A",0
125,1,80,0,0.713356," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} A}{a} + \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"((d*x + c)*A/a + C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - (A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a)/d","A",0
126,1,74,0,0.568974," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(d x + c\right)} A}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a}}{d}"," ",0,"-((d*x + c)*A/a - (A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a))/d","A",0
127,1,96,0,0.287725," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} {\left(3 \, A + 2 \, C\right)}}{a} - \frac{2 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a}}{2 \, d}"," ",0,"1/2*((d*x + c)*(3*A + 2*C)/a - 2*(A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*(3*A*tan(1/2*d*x + 1/2*c)^3 + A*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a))/d","A",0
128,1,152,0,0.337828," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)} {\left(3 \, A + 2 \, C\right)}}{a} - \frac{6 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a}}{6 \, d}"," ",0,"-1/6*(3*(d*x + c)*(3*A + 2*C)/a - 6*(A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*(15*A*tan(1/2*d*x + 1/2*c)^5 + 6*C*tan(1/2*d*x + 1/2*c)^5 + 16*A*tan(1/2*d*x + 1/2*c)^3 + 12*C*tan(1/2*d*x + 1/2*c)^3 + 9*A*tan(1/2*d*x + 1/2*c) + 6*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a))/d","A",0
129,1,180,0,0.732528," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{9 \, {\left(d x + c\right)} {\left(5 \, A + 4 \, C\right)}}{a} - \frac{24 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(75 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 115 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 84 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 109 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a}}{24 \, d}"," ",0,"1/24*(9*(d*x + c)*(5*A + 4*C)/a - 24*(A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*(75*A*tan(1/2*d*x + 1/2*c)^7 + 36*C*tan(1/2*d*x + 1/2*c)^7 + 115*A*tan(1/2*d*x + 1/2*c)^5 + 84*C*tan(1/2*d*x + 1/2*c)^5 + 109*A*tan(1/2*d*x + 1/2*c)^3 + 60*C*tan(1/2*d*x + 1/2*c)^3 + 21*A*tan(1/2*d*x + 1/2*c) + 12*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a))/d","A",0
130,1,225,0,1.523503," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(2 \, A + 5 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, {\left(2 \, A + 5 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{4 \, {\left(3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(6*(2*A + 5*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*(2*A + 5*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 4*(3*A*tan(1/2*d*x + 1/2*c)^5 + 15*C*tan(1/2*d*x + 1/2*c)^5 - 6*A*tan(1/2*d*x + 1/2*c)^3 - 20*C*tan(1/2*d*x + 1/2*c)^3 + 3*A*tan(1/2*d*x + 1/2*c) + 9*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^4*tan(1/2*d*x + 1/2*c) + 27*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
131,1,171,0,0.332200," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, A + 7 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{3 \, {\left(2 \, A + 7 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{6 \, {\left(5 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(2*A + 7*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 3*(2*A + 7*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 6*(5*C*tan(1/2*d*x + 1/2*c)^3 - 3*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*A*a^4*tan(1/2*d*x + 1/2*c) + 21*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
132,1,142,0,0.285613," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{12 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(12*C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 12*C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 12*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*tan(1/2*d*x + 1/2*c) + 15*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
133,1,112,0,0.662347," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 3*A*a^4*tan(1/2*d*x + 1/2*c) + 9*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
134,1,84,0,1.415511," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)} A}{a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*A/a^2 + (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 9*A*a^4*tan(1/2*d*x + 1/2*c) + 3*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
135,1,114,0,0.539013," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(d x + c\right)} A}{a^{2}} - \frac{12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(12*(d*x + c)*A/a^2 - 12*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^4*tan(1/2*d*x + 1/2*c) - 3*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
136,1,137,0,2.180593," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)} {\left(7 \, A + 2 \, C\right)}}{a^{2}} - \frac{6 \, {\left(5 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)*(7*A + 2*C)/a^2 - 6*(5*A*tan(1/2*d*x + 1/2*c)^3 + 3*A*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 21*A*a^4*tan(1/2*d*x + 1/2*c) - 9*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
137,1,191,0,0.280179," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(d x + c\right)} {\left(5 \, A + 2 \, C\right)}}{a^{2}} - \frac{4 \, {\left(15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 27 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c)*(5*A + 2*C)/a^2 - 4*(15*A*tan(1/2*d*x + 1/2*c)^5 + 3*C*tan(1/2*d*x + 1/2*c)^5 + 20*A*tan(1/2*d*x + 1/2*c)^3 + 6*C*tan(1/2*d*x + 1/2*c)^3 + 9*A*tan(1/2*d*x + 1/2*c) + 3*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 27*A*a^4*tan(1/2*d*x + 1/2*c) - 15*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
138,1,207,0,0.353079," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{30 \, {\left(2 \, A + 13 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{30 \, {\left(2 \, A + 13 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{60 \, {\left(7 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 465 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(30*(2*A + 13*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 30*(2*A + 13*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 60*(7*C*tan(1/2*d*x + 1/2*c)^3 - 5*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 20*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 40*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^12*tan(1/2*d*x + 1/2*c) + 465*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
139,1,178,0,0.338873," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{180 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{180 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{120 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 255 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(180*C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 180*C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 120*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 10*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 30*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^12*tan(1/2*d*x + 1/2*c) + 255*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
140,1,131,0,1.058380," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 20*C*a^12*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^12*tan(1/2*d*x + 1/2*c) + 105*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
141,1,89,0,1.117259," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, a^{3} d}"," ",0,"1/60*(3*A*tan(1/2*d*x + 1/2*c)^5 + 3*C*tan(1/2*d*x + 1/2*c)^5 - 10*A*tan(1/2*d*x + 1/2*c)^3 + 10*C*tan(1/2*d*x + 1/2*c)^3 + 15*A*tan(1/2*d*x + 1/2*c) + 15*C*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
142,1,104,0,0.386374," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(d x + c\right)} A}{a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 20 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*A/a^3 - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 20*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^12*tan(1/2*d*x + 1/2*c) - 15*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
143,1,151,0,0.279882," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{180 \, {\left(d x + c\right)} A}{a^{3}} - \frac{120 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(180*(d*x + c)*A/a^3 - 120*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 30*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 10*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 255*A*a^12*tan(1/2*d*x + 1/2*c) + 15*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
144,1,174,0,1.821576," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{30 \, {\left(d x + c\right)} {\left(13 \, A + 2 \, C\right)}}{a^{3}} - \frac{60 \, {\left(7 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 465 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(30*(d*x + c)*(13*A + 2*C)/a^3 - 60*(7*A*tan(1/2*d*x + 1/2*c)^3 + 5*A*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 40*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 20*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 465*A*a^12*tan(1/2*d*x + 1/2*c) + 105*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
145,1,228,0,0.303985," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(d x + c\right)} {\left(23 \, A + 6 \, C\right)}}{a^{3}} - \frac{20 \, {\left(51 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 76 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 50 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 735 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 255 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(30*(d*x + c)*(23*A + 6*C)/a^3 - 20*(51*A*tan(1/2*d*x + 1/2*c)^5 + 6*C*tan(1/2*d*x + 1/2*c)^5 + 76*A*tan(1/2*d*x + 1/2*c)^3 + 12*C*tan(1/2*d*x + 1/2*c)^3 + 33*A*tan(1/2*d*x + 1/2*c) + 6*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 50*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 30*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 735*A*a^12*tan(1/2*d*x + 1/2*c) + 255*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
146,1,241,0,1.511415," ","integrate(sec(d*x+c)^5*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{420 \, {\left(2 \, A + 21 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{420 \, {\left(2 \, A + 21 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{840 \, {\left(9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 189 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1365 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1575 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11655 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(420*(2*A + 21*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 420*(2*A + 21*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 840*(9*C*tan(1/2*d*x + 1/2*c)^3 - 7*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 105*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 189*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 385*A*a^24*tan(1/2*d*x + 1/2*c)^3 + 1365*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 1575*A*a^24*tan(1/2*d*x + 1/2*c) + 11655*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
147,1,212,0,0.341966," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3360 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{3360 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{1680 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 63 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 147 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 805 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5145 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(3360*C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 3360*C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 1680*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 63*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 147*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*A*a^24*tan(1/2*d*x + 1/2*c)^3 + 805*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^24*tan(1/2*d*x + 1/2*c) + 5145*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
148,1,182,0,0.314017," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{840 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 385 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1575 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 840*C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 21*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*C*a^24*tan(1/2*d*x + 1/2*c)^5 - 35*A*a^24*tan(1/2*d*x + 1/2*c)^3 + 385*C*a^24*tan(1/2*d*x + 1/2*c)^3 - 105*A*a^24*tan(1/2*d*x + 1/2*c) + 1575*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
149,1,117,0,1.889740," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 21 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 + 15*C*tan(1/2*d*x + 1/2*c)^7 - 21*A*tan(1/2*d*x + 1/2*c)^5 + 63*C*tan(1/2*d*x + 1/2*c)^5 - 35*A*tan(1/2*d*x + 1/2*c)^3 + 105*C*tan(1/2*d*x + 1/2*c)^3 + 105*A*tan(1/2*d*x + 1/2*c) + 105*C*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
150,1,117,0,0.632765," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 63 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"-1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 + 15*C*tan(1/2*d*x + 1/2*c)^7 - 63*A*tan(1/2*d*x + 1/2*c)^5 + 21*C*tan(1/2*d*x + 1/2*c)^5 + 105*A*tan(1/2*d*x + 1/2*c)^3 - 35*C*tan(1/2*d*x + 1/2*c)^3 - 105*A*tan(1/2*d*x + 1/2*c) - 105*C*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
151,1,154,0,0.252389," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, {\left(d x + c\right)} A}{a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1575 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*(d*x + c)*A/a^4 + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 - 105*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 21*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 385*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 35*C*a^24*tan(1/2*d*x + 1/2*c)^3 - 1575*A*a^24*tan(1/2*d*x + 1/2*c) + 105*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
152,1,184,0,0.501634," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3360 \, {\left(d x + c\right)} A}{a^{4}} - \frac{1680 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 147 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 63 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 805 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5145 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(3360*(d*x + c)*A/a^4 - 1680*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 - 147*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 63*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 805*A*a^24*tan(1/2*d*x + 1/2*c)^3 + 105*C*a^24*tan(1/2*d*x + 1/2*c)^3 - 5145*A*a^24*tan(1/2*d*x + 1/2*c) - 105*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
153,1,207,0,0.772316," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{420 \, {\left(d x + c\right)} {\left(21 \, A + 2 \, C\right)}}{a^{4}} - \frac{840 \, {\left(9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 189 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1365 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 385 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 11655 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1575 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(420*(d*x + c)*(21*A + 2*C)/a^4 - 840*(9*A*tan(1/2*d*x + 1/2*c)^3 + 7*A*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 - 189*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 105*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 1365*A*a^24*tan(1/2*d*x + 1/2*c)^3 + 385*C*a^24*tan(1/2*d*x + 1/2*c)^3 - 11655*A*a^24*tan(1/2*d*x + 1/2*c) - 1575*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
154,1,261,0,0.317393," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{1680 \, {\left(d x + c\right)} {\left(11 \, A + 2 \, C\right)}}{a^{4}} - \frac{560 \, {\left(39 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 62 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 231 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 147 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2065 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 805 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21945 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5145 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(1680*(d*x + c)*(11*A + 2*C)/a^4 - 560*(39*A*tan(1/2*d*x + 1/2*c)^5 + 3*C*tan(1/2*d*x + 1/2*c)^5 + 62*A*tan(1/2*d*x + 1/2*c)^3 + 6*C*tan(1/2*d*x + 1/2*c)^3 + 27*A*tan(1/2*d*x + 1/2*c) + 3*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 - 231*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 147*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 2065*A*a^24*tan(1/2*d*x + 1/2*c)^3 + 805*C*a^24*tan(1/2*d*x + 1/2*c)^3 - 21945*A*a^24*tan(1/2*d*x + 1/2*c) - 5145*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
155,1,314,0,3.293489," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(3465 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3465 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(10395 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5775 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(15246 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 16170 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(14058 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8910 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(6633 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5885 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(891 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 755 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{3465 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"-2/3465*(3465*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 3465*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (10395*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 5775*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (15246*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 16170*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (14058*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 8910*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (6633*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 5885*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (891*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 755*sqrt(2)*C*a^6*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
156,1,256,0,1.310513," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left({\left(\sqrt{2} {\left(147 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 107 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, \sqrt{2} {\left(14 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 882 \, \sqrt{2} {\left(A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 420 \, \sqrt{2} {\left(2 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 315 \, \sqrt{2} {\left(A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"2/315*((((sqrt(2)*(147*A*a^5*sgn(cos(d*x + c)) + 107*C*a^5*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 36*sqrt(2)*(14*A*a^5*sgn(cos(d*x + c)) + 9*C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 882*sqrt(2)*(A*a^5*sgn(cos(d*x + c)) + C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 420*sqrt(2)*(2*A*a^5*sgn(cos(d*x + c)) + C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 315*sqrt(2)*(A*a^5*sgn(cos(d*x + c)) + C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
157,1,222,0,3.922470," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(105 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 105 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(245 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 105 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(175 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 147 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(35 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 27 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{105 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"-2/105*(105*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 105*sqrt(2)*C*a^4*sgn(cos(d*x + c)) - (245*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 105*sqrt(2)*C*a^4*sgn(cos(d*x + c)) - (175*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 147*sqrt(2)*C*a^4*sgn(cos(d*x + c)) - (35*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 27*sqrt(2)*C*a^4*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
158,1,168,0,1.194609," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(\sqrt{2} {\left(15 \, A a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7 \, C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, \sqrt{2} {\left(3 \, A a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, \sqrt{2} {\left(A a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{15 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"2/15*((sqrt(2)*(15*A*a^3*sgn(cos(d*x + c)) + 7*C*a^3*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 10*sqrt(2)*(3*A*a^3*sgn(cos(d*x + c)) + C*a^3*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 15*sqrt(2)*(A*a^3*sgn(cos(d*x + c)) + C*a^3*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","B",0
159,1,225,0,1.971421," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{3 \, A \sqrt{-a} a \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} - \frac{2 \, {\left(\sqrt{2} C a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{3 \, d}"," ",0,"-1/3*(3*A*sqrt(-a)*a*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) - 2*(sqrt(2)*C*a^2*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 3*sqrt(2)*C*a^2*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
160,1,362,0,5.552536," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{4 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} C a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + A \sqrt{-a} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - A \sqrt{-a} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + \frac{4 \, {\left(3 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \sqrt{2} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}}}{2 \, d}"," ",0,"-1/2*(4*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*C*a*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + A*sqrt(-a)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))*sgn(cos(d*x + c)) - A*sqrt(-a)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))*sgn(cos(d*x + c)) + 4*(3*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a*sgn(cos(d*x + c)) - sqrt(2)*A*sqrt(-a)*a^2*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2))/d","B",0
161,1,446,0,7.116783," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{{\left(3 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(3 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) - \frac{4 \, \sqrt{2} {\left(5 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 17 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((3*A*sqrt(-a)*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (3*A*sqrt(-a)*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) - 4*sqrt(2)*(5*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 19*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 17*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + A*sqrt(-a)*a^4*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2)/d","B",0
162,1,889,0,1.759234," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{3 \, {\left(5 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(5 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(63 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 72 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 369 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 888 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1638 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3024 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1074 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1776 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 171 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 360 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 13 \, \sqrt{2} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 24 \, \sqrt{2} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(3*(5*A*sqrt(-a)*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(5*A*sqrt(-a)*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(63*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 72*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a*sgn(cos(d*x + c)) - 369*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 888*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 1638*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 3024*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 1074*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 1776*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 171*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 360*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 13*sqrt(2)*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 24*sqrt(2)*C*sqrt(-a)*a^6*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3)/d","B",0
163,1,1080,0,1.899812," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{3 \, {\left(35 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 48 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(35 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 48 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) - \frac{4 \, \sqrt{2} {\left(279 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 240 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 285 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1968 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4605 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2640 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 37281 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 41616 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 35643 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 42288 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9175 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12528 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1311 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1392 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 43 \, A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 48 \, C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(3*(35*A*sqrt(-a)*sgn(cos(d*x + c)) + 48*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(35*A*sqrt(-a)*sgn(cos(d*x + c)) + 48*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) - 4*sqrt(2)*(279*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 240*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a*sgn(cos(d*x + c)) + 285*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 1968*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 4605*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 2640*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 37281*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 41616*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 35643*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 42288*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 9175*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 12528*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 1311*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 1392*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 43*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 48*C*sqrt(-a)*a^8*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^4)/d","B",0
164,1,305,0,9.284648," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{4 \, {\left({\left({\left({\left({\left(2 \, \sqrt{2} {\left(209 \, A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 161 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 11 \, \sqrt{2} {\left(209 \, A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 161 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 132 \, \sqrt{2} {\left(37 \, A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 28 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 154 \, \sqrt{2} {\left(37 \, A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 33 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 770 \, \sqrt{2} {\left(5 \, A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1155 \, \sqrt{2} {\left(A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{1155 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"4/1155*(((((2*sqrt(2)*(209*A*a^7*sgn(cos(d*x + c)) + 161*C*a^7*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 11*sqrt(2)*(209*A*a^7*sgn(cos(d*x + c)) + 161*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 132*sqrt(2)*(37*A*a^7*sgn(cos(d*x + c)) + 28*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 154*sqrt(2)*(37*A*a^7*sgn(cos(d*x + c)) + 33*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 770*sqrt(2)*(5*A*a^7*sgn(cos(d*x + c)) + 3*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 1155*sqrt(2)*(A*a^7*sgn(cos(d*x + c)) + C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
165,1,268,0,18.851583," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{4 \, {\left(315 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 315 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(945 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 525 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(1071 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 819 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(567 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 423 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2 \, {\left(63 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 47 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"4/315*(315*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 315*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (945*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 525*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (1071*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 819*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (567*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 423*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - 2*(63*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 47*sqrt(2)*C*a^6*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
166,1,214,0,6.950845," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{4 \, {\left({\left({\left(2 \, \sqrt{2} {\left(35 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, \sqrt{2} {\left(35 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 140 \, \sqrt{2} {\left(2 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \sqrt{2} {\left(A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{105 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"4/105*(((2*sqrt(2)*(35*A*a^5*sgn(cos(d*x + c)) + 19*C*a^5*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 7*sqrt(2)*(35*A*a^5*sgn(cos(d*x + c)) + 19*C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 140*sqrt(2)*(2*A*a^5*sgn(cos(d*x + c)) + C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 105*sqrt(2)*(A*a^5*sgn(cos(d*x + c)) + C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
167,1,301,0,15.971804," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{5 \, A \sqrt{-a} a^{2} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} - \frac{2 \, {\left({\left(\sqrt{2} {\left(5 \, A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, \sqrt{2} {\left(A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, \sqrt{2} {\left(A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{5 \, d}"," ",0,"-1/5*(5*A*sqrt(-a)*a^2*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) - 2*((sqrt(2)*(5*A*a^4*sgn(cos(d*x + c)) + 4*C*a^4*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 10*sqrt(2)*(A*a^4*sgn(cos(d*x + c)) + C*a^4*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 5*sqrt(2)*(A*a^4*sgn(cos(d*x + c)) + 2*C*a^4*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
168,1,374,0,11.003167," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, \sqrt{2} A \sqrt{-a} a^{3} {\left(\frac{3 \, \sqrt{2} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right)}{a {\left| a \right|}} + \frac{8 \, {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} a}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \frac{16 \, {\left(2 \, \sqrt{2} C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \sqrt{2} C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{12 \, d}"," ",0,"-1/12*(3*sqrt(2)*A*sqrt(-a)*a^3*(3*sqrt(2)*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))/(a*abs(a)) + 8*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*a))*sgn(cos(d*x + c)) - 16*(2*sqrt(2)*C*a^3*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 3*sqrt(2)*C*a^3*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
169,1,515,0,1.808947," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{16 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} C a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + {\left(7 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(7 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(7 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 95 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 53 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 5 \, A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(16*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*C*a^2*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + (7*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (7*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(7*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 95*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 53*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 5*A*sqrt(-a)*a^5*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2)/d","B",0
170,1,897,0,6.227839," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(11 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 24 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(11 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 24 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(33 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 72 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 303 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 888 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2394 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3024 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1806 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1776 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 309 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 360 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 19 \, \sqrt{2} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 24 \, \sqrt{2} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(3*(11*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 24*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(11*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 24*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(33*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 72*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 303*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 888*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 2394*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 3024*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 1806*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 1776*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 309*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 360*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 19*sqrt(2)*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 24*sqrt(2)*C*sqrt(-a)*a^7*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3)/d","B",0
171,1,1087,0,2.307596," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{{\left(75 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 112 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(75 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 112 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(75 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 112 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2087 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2864 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 11975 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 23344 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 42483 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 69360 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 33889 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 51536 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 8693 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 14736 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1101 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1808 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 49 \, A \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 80 \, C \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{4}}}{128 \, d}"," ",0,"-1/128*((75*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 112*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (75*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 112*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(75*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 112*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 2087*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 2864*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 11975*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 23344*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 42483*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 69360*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 33889*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 51536*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 8693*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 14736*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 1101*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 1808*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 49*A*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 80*C*sqrt(-a)*a^9*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^4)/d","B",0
172,1,1369,0,8.435895," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{15 \, {\left(133 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 176 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 15 \, {\left(133 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 176 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(1995 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2640 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 38505 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 55920 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 561660 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 582720 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2684100 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 3395520 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7371738 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9329760 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6407470 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 8110880 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2176620 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2882880 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 399860 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 498880 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 34035 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 42960 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1201 \, \sqrt{2} A \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1520 \, \sqrt{2} C \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{5}}}{3840 \, d}"," ",0,"-1/3840*(15*(133*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 176*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 15*(133*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 176*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(1995*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 2640*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 38505*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 55920*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 561660*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 582720*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 2684100*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 3395520*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 7371738*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 9329760*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 6407470*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 8110880*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 2176620*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 2882880*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 399860*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 498880*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 34035*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^10*sgn(cos(d*x + c)) + 42960*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 1201*sqrt(2)*A*sqrt(-a)*a^11*sgn(cos(d*x + c)) - 1520*sqrt(2)*C*sqrt(-a)*a^11*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^5)/d","B",0
173,1,351,0,2.289210," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, {\left({\left({\left({\left({\left(4 \, {\left(2 \, \sqrt{2} {\left(1859 \, A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1483 \, C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 13 \, \sqrt{2} {\left(1859 \, A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1483 \, C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 143 \, \sqrt{2} {\left(1859 \, A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1483 \, C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1716 \, \sqrt{2} {\left(228 \, A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 181 \, C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6006 \, \sqrt{2} {\left(57 \, A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 49 \, C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 60060 \, \sqrt{2} {\left(3 \, A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 45045 \, \sqrt{2} {\left(A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{45045 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{6} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"8/45045*(((((4*(2*sqrt(2)*(1859*A*a^9*sgn(cos(d*x + c)) + 1483*C*a^9*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 13*sqrt(2)*(1859*A*a^9*sgn(cos(d*x + c)) + 1483*C*a^9*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 143*sqrt(2)*(1859*A*a^9*sgn(cos(d*x + c)) + 1483*C*a^9*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 1716*sqrt(2)*(228*A*a^9*sgn(cos(d*x + c)) + 181*C*a^9*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 6006*sqrt(2)*(57*A*a^9*sgn(cos(d*x + c)) + 49*C*a^9*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 60060*sqrt(2)*(3*A*a^9*sgn(cos(d*x + c)) + 2*C*a^9*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 45045*sqrt(2)*(A*a^9*sgn(cos(d*x + c)) + C*a^9*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^6*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
174,1,314,0,2.120707," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{8 \, {\left(693 \, \sqrt{2} A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 693 \, \sqrt{2} C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(2541 \, \sqrt{2} A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1617 \, \sqrt{2} C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(3927 \, \sqrt{2} A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3003 \, \sqrt{2} C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(3267 \, \sqrt{2} A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2475 \, \sqrt{2} C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4 \, {\left(363 \, \sqrt{2} A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 275 \, \sqrt{2} C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2 \, {\left(33 \, \sqrt{2} A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 25 \, \sqrt{2} C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{693 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"-8/693*(693*sqrt(2)*A*a^8*sgn(cos(d*x + c)) + 693*sqrt(2)*C*a^8*sgn(cos(d*x + c)) - (2541*sqrt(2)*A*a^8*sgn(cos(d*x + c)) + 1617*sqrt(2)*C*a^8*sgn(cos(d*x + c)) - (3927*sqrt(2)*A*a^8*sgn(cos(d*x + c)) + 3003*sqrt(2)*C*a^8*sgn(cos(d*x + c)) - (3267*sqrt(2)*A*a^8*sgn(cos(d*x + c)) + 2475*sqrt(2)*C*a^8*sgn(cos(d*x + c)) - 4*(363*sqrt(2)*A*a^8*sgn(cos(d*x + c)) + 275*sqrt(2)*C*a^8*sgn(cos(d*x + c)) - 2*(33*sqrt(2)*A*a^8*sgn(cos(d*x + c)) + 25*sqrt(2)*C*a^8*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
175,1,261,0,2.125181," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, {\left({\left({\left(4 \, {\left(2 \, \sqrt{2} {\left(21 \, A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \sqrt{2} {\left(21 \, A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 63 \, \sqrt{2} {\left(21 \, A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 210 \, \sqrt{2} {\left(5 \, A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 315 \, \sqrt{2} {\left(A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"8/315*(((4*(2*sqrt(2)*(21*A*a^7*sgn(cos(d*x + c)) + 13*C*a^7*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 9*sqrt(2)*(21*A*a^7*sgn(cos(d*x + c)) + 13*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 63*sqrt(2)*(21*A*a^7*sgn(cos(d*x + c)) + 13*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 210*sqrt(2)*(5*A*a^7*sgn(cos(d*x + c)) + 3*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 315*sqrt(2)*(A*a^7*sgn(cos(d*x + c)) + C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
176,1,355,0,2.057321," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{21 \, A \sqrt{-a} a^{3} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} + \frac{2 \, {\left(63 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 84 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(175 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 140 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(161 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 112 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(49 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 32 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{21 \, d}"," ",0,"-1/21*(21*A*sqrt(-a)*a^3*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) + 2*(63*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 84*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (175*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 140*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (161*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 112*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (49*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 32*sqrt(2)*C*a^6*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
177,1,484,0,2.055131," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{75 \, A \sqrt{-a} a^{2} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 75 \, A \sqrt{-a} a^{2} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + \frac{60 \, {\left(3 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \sqrt{2} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}} - \frac{4 \, {\left(15 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 60 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(30 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 80 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(15 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 32 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{30 \, d}"," ",0,"-1/30*(75*A*sqrt(-a)*a^2*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))*sgn(cos(d*x + c)) - 75*A*sqrt(-a)*a^2*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))*sgn(cos(d*x + c)) + 60*(3*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - sqrt(2)*A*sqrt(-a)*a^4*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2) - 4*(15*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 60*sqrt(2)*C*a^5*sgn(cos(d*x + c)) - (30*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 80*sqrt(2)*C*a^5*sgn(cos(d*x + c)) - (15*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 32*sqrt(2)*C*a^5*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
178,1,554,0,2.163012," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(19 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(19 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) - \frac{16 \, {\left(7 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{12 \, \sqrt{2} {\left(19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 171 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 89 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 9 \, A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2}}}{24 \, d}"," ",0,"-1/24*(3*(19*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(19*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) - 16*(7*sqrt(2)*C*a^4*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 9*sqrt(2)*C*a^4*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) + 12*sqrt(2)*(19*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 171*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 89*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 9*A*sqrt(-a)*a^6*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2)/d","B",0
179,1,967,0,4.885259," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{96 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + 15 \, {\left(5 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 15 \, {\left(5 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(75 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 72 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1125 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 888 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6174 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3024 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4314 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1776 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 807 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 360 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 49 \, \sqrt{2} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 24 \, \sqrt{2} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(96*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*C*a^3*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + 15*(5*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 15*(5*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(75*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 72*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 1125*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 888*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 6174*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 3024*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 4314*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 1776*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 807*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 360*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 49*sqrt(2)*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 24*sqrt(2)*C*sqrt(-a)*a^8*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3)/d","B",0
180,1,1096,0,6.273438," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(163 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 304 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(163 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 304 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(489 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 912 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 10269 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 19152 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 69885 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 137424 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 259233 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 374544 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 209979 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 266928 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 55511 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 75888 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6687 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9456 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 299 \, A \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 432 \, C \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(3*(163*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 304*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(163*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 304*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(489*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 912*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 10269*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 19152*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 69885*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 137424*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 259233*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 374544*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 209979*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 266928*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 55511*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 75888*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 6687*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 9456*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 299*A*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 432*C*sqrt(-a)*a^10*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^4)/d","B",0
181,1,1377,0,3.420528," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{15 \, {\left(283 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 400 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 15 \, {\left(283 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 400 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(4245 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6000 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 114615 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 162000 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1298820 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1801920 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6176700 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 9764160 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 16394598 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 24060960 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 14042770 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 19910240 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4791060 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7135680 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 860300 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1268800 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 75885 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 111600 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2671 \, \sqrt{2} A \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 3920 \, \sqrt{2} C \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{5}}}{3840 \, d}"," ",0,"-1/3840*(15*(283*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 400*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 15*(283*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 400*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(4245*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 6000*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 114615*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 162000*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 1298820*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 1801920*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 6176700*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 9764160*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 16394598*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 24060960*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 14042770*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 19910240*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 4791060*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 7135680*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 860300*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 1268800*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^10*sgn(cos(d*x + c)) + 75885*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^11*sgn(cos(d*x + c)) + 111600*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^11*sgn(cos(d*x + c)) - 2671*sqrt(2)*A*sqrt(-a)*a^12*sgn(cos(d*x + c)) - 3920*sqrt(2)*C*sqrt(-a)*a^12*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^5)/d","B",0
182,1,1613,0,6.264408," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(1015 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1304 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(1015 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1304 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(3045 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{22} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3912 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{22} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 100485 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{20} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 129096 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{20} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1303699 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1693560 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 9936699 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 11951544 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 38257266 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 48800976 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 83779026 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 106200016 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 74917446 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 94661616 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 30850806 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 39751536 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7187801 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9070440 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 929817 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1176936 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 64887 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{13} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 82200 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{13} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1887 \, \sqrt{2} A \sqrt{-a} a^{14} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2392 \, \sqrt{2} C \sqrt{-a} a^{14} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{6}}}{3072 \, d}"," ",0,"-1/3072*(3*(1015*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 1304*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(1015*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 1304*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(3045*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^22*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 3912*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^22*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 100485*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^20*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 129096*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^20*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 1303699*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 1693560*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 9936699*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 11951544*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 38257266*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 48800976*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 83779026*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 106200016*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 74917446*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 94661616*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 30850806*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 39751536*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^10*sgn(cos(d*x + c)) + 7187801*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^11*sgn(cos(d*x + c)) + 9070440*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^11*sgn(cos(d*x + c)) - 929817*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^12*sgn(cos(d*x + c)) - 1176936*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^12*sgn(cos(d*x + c)) + 64887*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^13*sgn(cos(d*x + c)) + 82200*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^13*sgn(cos(d*x + c)) - 1887*sqrt(2)*A*sqrt(-a)*a^14*sgn(cos(d*x + c)) - 2392*sqrt(2)*C*sqrt(-a)*a^14*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^6)/d","B",0
183,1,412,0,4.723564," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{315 \, {\left(\sqrt{2} A + \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{2 \, {\left(315 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 315 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(1050 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 840 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(1512 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 1638 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(1134 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 936 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(357 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 383 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{315 \, d}"," ",0,"-1/315*(315*(sqrt(2)*A + sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 2*(315*sqrt(2)*A*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 315*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (1050*sqrt(2)*A*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 840*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (1512*sqrt(2)*A*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 1638*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (1134*sqrt(2)*A*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 936*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (357*sqrt(2)*A*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 383*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
184,1,247,0,2.248519," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{105 \, \sqrt{2} {\left(A + C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, {\left({\left(\frac{\sqrt{2} {\left(35 \, A a^{3} + 46 \, C a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{14 \, \sqrt{2} {\left(5 \, A a^{3} + 4 \, C a^{3}\right)}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{35 \, \sqrt{2} {\left(A a^{3} + 2 \, C a^{3}\right)}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{105 \, d}"," ",0,"1/105*(105*sqrt(2)*(A + C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*((sqrt(2)*(35*A*a^3 + 46*C*a^3)*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 14*sqrt(2)*(5*A*a^3 + 4*C*a^3)/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2 + 35*sqrt(2)*(A*a^3 + 2*C*a^3)/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^3/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
185,1,292,0,2.209707," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(\sqrt{2} A + \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{2 \, {\left(15 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 15 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(30 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 20 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(15 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 17 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{15 \, d}"," ",0,"-1/15*(15*(sqrt(2)*A + sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 2*(15*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 15*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (30*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 20*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (15*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 17*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
186,1,143,0,2.143714," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{4 \, \sqrt{2} C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{3 \, \sqrt{2} {\left(A + C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{3 \, d}"," ",0,"1/3*(4*sqrt(2)*C*a*tan(1/2*d*x + 1/2*c)^3/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 3*sqrt(2)*(A + C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
187,-2,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableDiscontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 1.22index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
188,1,383,0,2.029822," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} {\left(A + C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{A \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{A \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} - A \sqrt{-a} a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{2 \, d}"," ",0,"1/2*(sqrt(2)*(A + C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + A*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - A*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a) - A*sqrt(-a)*a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
189,1,494,0,2.438275," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{4 \, \sqrt{2} {\left(A + C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{{\left(7 \, A + 8 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left(7 \, A + 8 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(17 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} - 57 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a + 19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{2} - 3 \, A \sqrt{-a} a^{3}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"-1/8*(4*sqrt(2)*(A + C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + (7*A + 8*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - (7*A + 8*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(17*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a) - 57*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a + 19*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^2 - 3*A*sqrt(-a)*a^3)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
190,1,844,0,2.700034," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{24 \, \sqrt{2} {\left(A + C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{3 \, {\left(9 \, A + 8 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, {\left(9 \, A + 8 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(165 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} + 72 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} - 1323 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a - 888 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a + 3906 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{2} + 3024 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{2} - 2118 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{3} - 1776 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{3} + 393 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{4} + 360 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{4} - 31 \, A \sqrt{-a} a^{5} - 24 \, C \sqrt{-a} a^{5}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{48 \, d}"," ",0,"1/48*(24*sqrt(2)*(A + C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 3*(9*A + 8*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 3*(9*A + 8*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(165*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a) + 72*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a) - 1323*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a - 888*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a + 3906*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^2 + 3024*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^2 - 2118*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^3 - 1776*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^3 + 393*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^4 + 360*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^4 - 31*A*sqrt(-a)*a^5 - 24*C*sqrt(-a)*a^5)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
191,1,1040,0,2.968312," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{192 \, \sqrt{2} {\left(A + C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{3 \, {\left(107 \, A + 112 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, {\left(107 \, A + 112 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(1599 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} + 816 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} - 18219 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a - 12528 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a + 91467 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{2} + 64752 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{2} - 177735 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{3} - 124848 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{3} + 100413 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{4} + 70032 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{4} - 26881 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{5} - 19152 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{5} + 3321 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{6} + 2640 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{6} - 205 \, A \sqrt{-a} a^{7} - 144 \, C \sqrt{-a} a^{7}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{384 \, d}"," ",0,"-1/384*(192*sqrt(2)*(A + C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 3*(107*A + 112*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 3*(107*A + 112*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(1599*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a) + 816*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a) - 18219*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a - 12528*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a + 91467*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^2 + 64752*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^2 - 177735*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^3 - 124848*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^3 + 100413*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^4 + 70032*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^4 - 26881*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^5 - 19152*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^5 + 3321*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^6 + 2640*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^6 - 205*A*sqrt(-a)*a^7 - 144*C*sqrt(-a)*a^7)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
192,1,439,0,3.915779," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{105 \, {\left(11 \, \sqrt{2} A + 19 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left({\left({\left({\left(\frac{105 \, {\left(\sqrt{2} A a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3}} - \frac{4 \, {\left(455 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 877 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{14 \, {\left(305 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 517 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{140 \, {\left(25 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 47 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{105 \, {\left(9 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 17 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{420 \, d}"," ",0,"1/420*(105*(11*sqrt(2)*A + 19*sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - ((((105*(sqrt(2)*A*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a^3 - 4*(455*sqrt(2)*A*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 877*sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^3)*tan(1/2*d*x + 1/2*c)^2 + 14*(305*sqrt(2)*A*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 517*sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^3)*tan(1/2*d*x + 1/2*c)^2 - 140*(25*sqrt(2)*A*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 47*sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^3)*tan(1/2*d*x + 1/2*c)^2 + 105*(9*sqrt(2)*A*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 17*sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^3)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
193,1,311,0,2.355134," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{5 \, \sqrt{2} {\left(7 \, A + 15 \, C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left({\left({\left(\frac{5 \, \sqrt{2} {\left(A a^{3} + C a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(55 \, A a^{3} + 127 \, C a^{3}\right)}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{5 \, \sqrt{2} {\left(19 \, A a^{3} + 35 \, C a^{3}\right)}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{5 \, \sqrt{2} {\left(9 \, A a^{3} + 17 \, C a^{3}\right)}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{20 \, d}"," ",0,"-1/20*(5*sqrt(2)*(7*A + 15*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - (((5*sqrt(2)*(A*a^3 + C*a^3)*tan(1/2*d*x + 1/2*c)^2/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(55*A*a^3 + 127*C*a^3)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 5*sqrt(2)*(19*A*a^3 + 35*C*a^3)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 - 5*sqrt(2)*(9*A*a^3 + 17*C*a^3)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
194,1,295,0,2.835153," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(\frac{3 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a} - \frac{2 \, {\left(3 \, \sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 23 \, \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{3 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 9 \, \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{3 \, {\left(3 \, \sqrt{2} A + 11 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{12 \, d}"," ",0,"-1/12*(((3*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a - 2*(3*sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 23*sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a)*tan(1/2*d*x + 1/2*c)^2 + 3*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 9*sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) - 3*(3*sqrt(2)*A + 11*sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
195,1,186,0,2.012220," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(\frac{\sqrt{2} {\left(A a^{2} + C a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(A a^{2} + 9 \, C a^{2}\right)}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{\sqrt{2} {\left(A - 7 \, C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{4 \, d}"," ",0,"1/4*((sqrt(2)*(A*a^2 + C*a^2)*tan(1/2*d*x + 1/2*c)^2/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(A*a^2 + 9*C*a^2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(2)*(A - 7*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
196,-2,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableDiscontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 1.23index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
197,1,444,0,2.105458," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} {\left(9 \, A + C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{12 \, A \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right)}{\sqrt{-a} {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{16 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A - A a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"1/8*(sqrt(2)*(9*A + C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 12*A*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))/(sqrt(-a)*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^3 - 16*sqrt(2)*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A - A*a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
198,1,539,0,5.651196," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} {\left(13 \, A + 5 \, C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{{\left(19 \, A + 8 \, C\right)} \log\left(\frac{{\left| 147573952589676412928 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 295147905179352825856 \, \sqrt{2} {\left| a \right|} - 442721857769029238784 \, a \right|}}{{\left| 147573952589676412928 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 295147905179352825856 \, \sqrt{2} {\left| a \right|} - 442721857769029238784 \, a \right|}}\right)}{\sqrt{-a} {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{4 \, \sqrt{2} {\left(29 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A - 133 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A a + 55 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A a^{2} - 7 \, A a^{3}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"-1/8*(sqrt(2)*(13*A + 5*C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + (19*A + 8*C)*log(abs(147573952589676412928*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 295147905179352825856*sqrt(2)*abs(a) - 442721857769029238784*a)/abs(147573952589676412928*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 295147905179352825856*sqrt(2)*abs(a) - 442721857769029238784*a))/(sqrt(-a)*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^3 - 4*sqrt(2)*(29*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A - 133*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*a + 55*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*a^2 - 7*A*a^3)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
199,1,850,0,10.029363," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} {\left(17 \, A + 9 \, C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, {\left(47 \, A + 24 \, C\right)} \log\left(\frac{{\left| -1947111321950560360698936123457536 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 3894222643901120721397872246915072 \, \sqrt{2} {\left| a \right|} + 5841333965851681082096808370372608 \, a \right|}}{{\left| -1947111321950560360698936123457536 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 3894222643901120721397872246915072 \, \sqrt{2} {\left| a \right|} + 5841333965851681082096808370372608 \, a \right|}}\right)}{\sqrt{-a} {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{12 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{4 \, \sqrt{2} {\left(339 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A + 72 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C - 3165 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A a - 888 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C a + 9198 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A a^{2} + 3024 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C a^{2} - 4938 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A a^{3} - 1776 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C a^{3} + 975 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A a^{4} + 360 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C a^{4} - 73 \, A a^{5} - 24 \, C a^{5}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{48 \, d}"," ",0,"1/48*(6*sqrt(2)*(17*A + 9*C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 3*(47*A + 24*C)*log(abs(-1947111321950560360698936123457536*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 3894222643901120721397872246915072*sqrt(2)*abs(a) + 5841333965851681082096808370372608*a)/abs(-1947111321950560360698936123457536*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 3894222643901120721397872246915072*sqrt(2)*abs(a) + 5841333965851681082096808370372608*a))/(sqrt(-a)*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 12*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^3 - 4*sqrt(2)*(339*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A + 72*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C - 3165*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*a - 888*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*a + 9198*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*a^2 + 3024*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*a^2 - 4938*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*a^3 - 1776*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*a^3 + 975*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*a^4 + 360*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*a^4 - 73*A*a^5 - 24*C*a^5)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
200,1,438,0,2.958632," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left({\left(15 \, {\left(\frac{2 \, {\left(\sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2}} + \frac{13 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 29 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{1725 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 6733 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{5 \, {\left(549 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 1973 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{15 \, {\left(83 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 291 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{15 \, {\left(75 \, \sqrt{2} A + 283 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{480 \, d}"," ",0,"1/480*((((15*(2*(sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a^2 + (13*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 29*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^2)*tan(1/2*d*x + 1/2*c)^2 - (1725*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 6733*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^2)*tan(1/2*d*x + 1/2*c)^2 + 5*(549*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 1973*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^2)*tan(1/2*d*x + 1/2*c)^2 - 15*(83*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 291*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) - 15*(75*sqrt(2)*A + 283*sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
201,1,310,0,8.135863," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(3 \, {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{\sqrt{2} {\left(7 \, A a^{5} + 23 \, C a^{5}\right)}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{4 \, \sqrt{2} {\left(15 \, A a^{5} + 167 \, C a^{5}\right)}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{3 \, \sqrt{2} {\left(11 \, A a^{5} + 155 \, C a^{5}\right)}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{3 \, \sqrt{2} {\left(19 \, A + 163 \, C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{96 \, d}"," ",0,"-1/96*(((3*(2*sqrt(2)*(A*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + sqrt(2)*(7*A*a^5 + 23*C*a^5)/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 - 4*sqrt(2)*(15*A*a^5 + 167*C*a^5)/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 3*sqrt(2)*(11*A*a^5 + 155*C*a^5)/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) - 3*sqrt(2)*(19*A + 163*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
202,1,286,0,6.648753," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left(\frac{2 \, {\left(\sqrt{2} A a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} + \frac{\sqrt{2} A a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 17 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{3 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 83 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{5 \, {\left(\sqrt{2} A - 15 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"1/32*(((2*(sqrt(2)*A*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a^8 + (sqrt(2)*A*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 17*sqrt(2)*C*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^8)*tan(1/2*d*x + 1/2*c)^2 - (3*sqrt(2)*A*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 83*sqrt(2)*C*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^8)*tan(1/2*d*x + 1/2*c)/sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a) + 5*(sqrt(2)*A - 15*sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
203,1,190,0,2.394742," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(5 \, A a^{5} - 11 \, C a^{5}\right)}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{\sqrt{2} {\left(3 \, A + 19 \, C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"1/32*(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(5*A*a^5 - 11*C*a^5)/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + sqrt(2)*(3*A + 19*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
204,-2,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableDiscontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 1.42index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
205,1,492,0,2.892645," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(21 \, A a^{5} + 5 \, C a^{5}\right)}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{\sqrt{2} {\left(115 \, A + 3 \, C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{160 \, A \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right)}{\sqrt{-a} a {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{128 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A - A a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} \sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{64 \, d}"," ",0,"1/64*(2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(21*A*a^5 + 5*C*a^5)/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + sqrt(2)*(115*A + 3*C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 160*A*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))/(sqrt(-a)*a*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 128*sqrt(2)*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A - A*a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
206,1,586,0,4.149367," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(29 \, A a^{5} + 13 \, C a^{5}\right)}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{\sqrt{2} {\left(219 \, A + 43 \, C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{8 \, {\left(39 \, A + 8 \, C\right)} \log\left(\frac{{\left| 309485009821345068724781056 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 618970019642690137449562112 \, \sqrt{2} {\left| a \right|} - 928455029464035206174343168 \, a \right|}}{{\left| 309485009821345068724781056 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 618970019642690137449562112 \, \sqrt{2} {\left| a \right|} - 928455029464035206174343168 \, a \right|}}\right)}{\sqrt{-a} a {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{32 \, \sqrt{2} {\left(41 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A - 209 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A a + 91 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A a^{2} - 11 \, A a^{3}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2} \sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{64 \, d}"," ",0,"-1/64*(2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(29*A*a^5 + 13*C*a^5)/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + sqrt(2)*(219*A + 43*C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 8*(39*A + 8*C)*log(abs(309485009821345068724781056*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 618970019642690137449562112*sqrt(2)*abs(a) - 928455029464035206174343168*a)/abs(309485009821345068724781056*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 618970019642690137449562112*sqrt(2)*abs(a) - 928455029464035206174343168*a))/(sqrt(-a)*a*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 32*sqrt(2)*(41*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A - 209*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*a + 91*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*a^2 - 11*A*a^3)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2*sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
207,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
208,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
209,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
210,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
211,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
212,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
213,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(9/2), x)","F",0
214,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
215,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
216,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
217,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
218,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(5/2), x)","F",0
219,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(7/2), x)","F",0
220,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(9/2), x)","F",0
221,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(11/2), x)","F",0
222,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
223,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
224,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
225,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
226,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(5/2), x)","F",0
227,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(7/2), x)","F",0
228,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(9/2), x)","F",0
229,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(11/2), x)","F",0
230,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(13/2), x)","F",0
231,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
232,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
233,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
234,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
235,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
236,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
237,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
238,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
239,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
240,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
241,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
242,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
243,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a)^3, x)","F",0
244,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^3, x)","F",0
245,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^3, x)","F",0
246,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^3, x)","F",0
247,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
248,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
249,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
250,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
251,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
252,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
253,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
254,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
255,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
256,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
257,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(9/2), x)","F",0
258,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2), x)","F",0
259,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
260,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
261,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
262,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
263,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(5/2), x)","F",0
264,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(7/2), x)","F",0
265,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(9/2), x)","F",0
266,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(11/2), x)","F",0
267,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2), x)","F",0
268,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2), x)","F",0
269,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c)), x)","F",0
270,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
271,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(3/2), x)","F",0
272,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(5/2), x)","F",0
273,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(7/2), x)","F",0
274,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(9/2), x)","F",0
275,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(11/2), x)","F",0
276,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(13/2), x)","F",0
277,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
278,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
279,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(sec(d*x + c))/sqrt(a*sec(d*x + c) + a), x)","F",0
280,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{a \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(sqrt(a*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
281,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
282,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
283,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(7/2)), x)","F",0
284,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
285,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^(3/2), x)","F",0
286,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
287,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
288,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2)), x)","F",0
289,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
290,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
291,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^(5/2), x)","F",0
292,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
293,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
294,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
295,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(2/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(2/3), x)","F",0
296,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(a*sec(d*x + c) + a)^(1/3), x)","F",0
297,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(a*sec(d*x + c) + a)^(4/3), x)","F",0
298,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(7/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(a*sec(d*x + c) + a)^(7/3), x)","F",0
299,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(4/3), x)","F",0
300,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(1/3), x)","F",0
301,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(a*sec(d*x + c) + a)^(2/3), x)","F",0
302,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(a*sec(d*x + c) + a)^(5/3), x)","F",0
303,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(a+a*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^m, x)","F",0
304,0,0,0,0.000000," ","integrate(sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{-n - 1}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^(-n - 1), x)","F",0
305,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*(-a*A*n-a*C*(1+n)*sec(d*x+c))/a/(1+n)/(sec(d*x+c)^n)+sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{-n - 1} - \frac{{\left(C a {\left(n + 1\right)} \sec\left(d x + c\right) + A a n\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n}}{a {\left(n + 1\right)} \sec\left(d x + c\right)^{n}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^(-n - 1) - (C*a*(n + 1)*sec(d*x + c) + A*a*n)*(a*sec(d*x + c) + a)^n/(a*(n + 1)*sec(d*x + c)^n), x)","F",0
306,1,188,0,0.487277," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(4 \, B a + 3 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, B a + 3 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 28 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 49 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 52 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 31 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 39 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(4*B*a + 3*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*B*a + 3*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(12*B*a*tan(1/2*d*x + 1/2*c)^7 + 9*C*a*tan(1/2*d*x + 1/2*c)^7 - 28*B*a*tan(1/2*d*x + 1/2*c)^5 - 49*C*a*tan(1/2*d*x + 1/2*c)^5 + 52*B*a*tan(1/2*d*x + 1/2*c)^3 + 31*C*a*tan(1/2*d*x + 1/2*c)^3 - 36*B*a*tan(1/2*d*x + 1/2*c) - 39*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
307,1,154,0,0.275829," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*B*a*tan(1/2*d*x + 1/2*c)^5 + 3*C*a*tan(1/2*d*x + 1/2*c)^5 - 12*B*a*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*tan(1/2*d*x + 1/2*c)^3 + 9*B*a*tan(1/2*d*x + 1/2*c) + 9*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
308,1,124,0,1.598391," ","integrate((a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(2 \, B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((2*B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*B*a*tan(1/2*d*x + 1/2*c)^3 + C*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c) - 3*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
309,1,84,0,0.841906," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} B a + {\left(B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"((d*x + c)*B*a + (B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*C*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
310,1,79,0,0.265517," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(B a + C a\right)} {\left(d x + c\right)} + \frac{2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"(C*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - C*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (B*a + C*a)*(d*x + c) + 2*B*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
311,1,93,0,0.235469," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(B a + 2 \, C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((B*a + 2*C*a)*(d*x + c) + 2*(B*a*tan(1/2*d*x + 1/2*c)^3 + 2*C*a*tan(1/2*d*x + 1/2*c)^3 + 3*B*a*tan(1/2*d*x + 1/2*c) + 2*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
312,1,124,0,1.022700," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(B a + C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a + C*a)*(d*x + c) + 2*(3*B*a*tan(1/2*d*x + 1/2*c)^5 + 3*C*a*tan(1/2*d*x + 1/2*c)^5 + 4*B*a*tan(1/2*d*x + 1/2*c)^3 + 12*C*a*tan(1/2*d*x + 1/2*c)^3 + 9*B*a*tan(1/2*d*x + 1/2*c) + 9*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
313,1,156,0,0.265899," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, B a + 4 \, C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 49 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 28 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 52 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 39 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*B*a + 4*C*a)*(d*x + c) + 2*(9*B*a*tan(1/2*d*x + 1/2*c)^7 + 12*C*a*tan(1/2*d*x + 1/2*c)^7 + 49*B*a*tan(1/2*d*x + 1/2*c)^5 + 28*C*a*tan(1/2*d*x + 1/2*c)^5 + 31*B*a*tan(1/2*d*x + 1/2*c)^3 + 52*C*a*tan(1/2*d*x + 1/2*c)^3 + 39*B*a*tan(1/2*d*x + 1/2*c) + 36*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
314,1,246,0,0.322784," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(7 \, B a^{2} + 6 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(7 \, B a^{2} + 6 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(105 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 90 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 490 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 420 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 800 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 864 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 790 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 540 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 375 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 390 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(7*B*a^2 + 6*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(7*B*a^2 + 6*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(105*B*a^2*tan(1/2*d*x + 1/2*c)^9 + 90*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 490*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 420*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 800*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 864*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 790*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 540*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 375*B*a^2*tan(1/2*d*x + 1/2*c) + 390*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
315,1,212,0,0.374261," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(8 \, B a^{2} + 7 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, B a^{2} + 7 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 88 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 77 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 136 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 83 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 75 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(8*B*a^2 + 7*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*B*a^2 + 7*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(24*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 21*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 88*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 77*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 136*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 83*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 72*B*a^2*tan(1/2*d*x + 1/2*c) - 75*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
316,1,178,0,0.288709," ","integrate((a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, B a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, B a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(9 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(3*B*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*B*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(9*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 24*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 16*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 15*B*a^2*tan(1/2*d*x + 1/2*c) + 18*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
317,1,154,0,0.302306," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} B a^{2} + {\left(4 \, B a^{2} + 3 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(4 \, B a^{2} + 3 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*B*a^2 + (4*B*a^2 + 3*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (4*B*a^2 + 3*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 3*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^2*tan(1/2*d*x + 1/2*c) - 5*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
318,1,157,0,0.304018," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(2 \, B a^{2} + C a^{2}\right)} {\left(d x + c\right)} + {\left(B a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(B a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((2*B*a^2 + C*a^2)*(d*x + c) + (B*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (B*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(B*a^2*tan(1/2*d*x + 1/2*c)^3 - C*a^2*tan(1/2*d*x + 1/2*c)^3 - B*a^2*tan(1/2*d*x + 1/2*c) - C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
319,1,145,0,0.715292," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, C a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, C a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(3 \, B a^{2} + 4 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*C*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*C*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (3*B*a^2 + 4*C*a^2)*(d*x + c) + 2*(3*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 2*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^2*tan(1/2*d*x + 1/2*c) + 2*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
320,1,142,0,0.260406," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(2 \, B a^{2} + 3 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*B*a^2 + 3*C*a^2)*(d*x + c) + 2*(6*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 9*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 16*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 18*B*a^2*tan(1/2*d*x + 1/2*c) + 15*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
321,1,176,0,0.637601," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(7 \, B a^{2} + 8 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(21 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 77 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 88 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 83 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 136 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 75 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(7*B*a^2 + 8*C*a^2)*(d*x + c) + 2*(21*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 24*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 77*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 88*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 83*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 136*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 75*B*a^2*tan(1/2*d*x + 1/2*c) + 72*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
322,1,210,0,0.585077," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(6 \, B a^{2} + 7 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(90 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 105 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 420 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 490 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 864 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 800 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 540 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 790 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 390 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 375 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(6*B*a^2 + 7*C*a^2)*(d*x + c) + 2*(90*B*a^2*tan(1/2*d*x + 1/2*c)^9 + 105*C*a^2*tan(1/2*d*x + 1/2*c)^9 + 420*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 490*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 864*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 800*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 540*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 790*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 390*B*a^2*tan(1/2*d*x + 1/2*c) + 375*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
323,1,246,0,0.399718," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(15 \, B a^{3} + 13 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(15 \, B a^{3} + 13 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(225 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 195 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1050 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 910 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1920 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1664 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1830 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1330 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 735 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 765 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(15*B*a^3 + 13*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(15*B*a^3 + 13*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(225*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 195*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 1050*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 910*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 1920*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 1664*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 1830*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 1330*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 735*B*a^3*tan(1/2*d*x + 1/2*c) + 765*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
324,1,212,0,0.855799," ","integrate((a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, B a^{3} + 3 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, B a^{3} + 3 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(60 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 45 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 220 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 165 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 292 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 219 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 132 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 147 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(15*(4*B*a^3 + 3*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*B*a^3 + 3*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(60*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 45*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 220*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 165*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 292*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 219*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 132*B*a^3*tan(1/2*d*x + 1/2*c) - 147*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
325,1,189,0,0.341948," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} B a^{3} + 3 \, {\left(7 \, B a^{3} + 5 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(7 \, B a^{3} + 5 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*B*a^3 + 3*(7*B*a^3 + 5*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(7*B*a^3 + 5*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(15*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 36*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 21*B*a^3*tan(1/2*d*x + 1/2*c) + 33*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
326,1,192,0,1.096579," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{4 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 2 \, {\left(3 \, B a^{3} + C a^{3}\right)} {\left(d x + c\right)} + {\left(6 \, B a^{3} + 7 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(6 \, B a^{3} + 7 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*B*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(3*B*a^3 + C*a^3)*(d*x + c) + (6*B*a^3 + 7*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (6*B*a^3 + 7*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 5*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^3*tan(1/2*d*x + 1/2*c) - 7*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
327,1,192,0,0.317742," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{4 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - {\left(7 \, B a^{3} + 6 \, C a^{3}\right)} {\left(d x + c\right)} - 2 \, {\left(B a^{3} + 3 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 2 \, {\left(B a^{3} + 3 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(5 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(4*C*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (7*B*a^3 + 6*C*a^3)*(d*x + c) - 2*(B*a^3 + 3*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 2*(B*a^3 + 3*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(5*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 2*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 7*B*a^3*tan(1/2*d*x + 1/2*c) + 2*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
328,1,180,0,0.787284," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{6 \, C a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6 \, C a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(5 \, B a^{3} + 7 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*C*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6*C*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(5*B*a^3 + 7*C*a^3)*(d*x + c) + 2*(15*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 33*B*a^3*tan(1/2*d*x + 1/2*c) + 21*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
329,1,176,0,0.333141," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, B a^{3} + 4 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(45 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 165 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 220 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 219 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 292 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 147 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 132 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(15*(3*B*a^3 + 4*C*a^3)*(d*x + c) + 2*(45*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 165*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 220*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 219*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 292*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 147*B*a^3*tan(1/2*d*x + 1/2*c) + 132*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
330,1,210,0,0.471880," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(13 \, B a^{3} + 15 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(195 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 225 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 910 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1050 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1664 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1920 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1330 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1830 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 765 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 735 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(13*B*a^3 + 15*C*a^3)*(d*x + c) + 2*(195*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 225*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 910*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 1050*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 1664*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 1920*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 1330*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 1830*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 765*B*a^3*tan(1/2*d*x + 1/2*c) + 735*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
331,1,244,0,0.403475," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(23 \, B a^{3} + 26 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(345 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 390 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1955 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2210 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4554 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5148 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5814 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5988 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3165 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4190 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1575 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1530 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(23*B*a^3 + 26*C*a^3)*(d*x + c) + 2*(345*B*a^3*tan(1/2*d*x + 1/2*c)^11 + 390*C*a^3*tan(1/2*d*x + 1/2*c)^11 + 1955*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 2210*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 4554*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 5148*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 5814*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 5988*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 3165*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 4190*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 1575*B*a^3*tan(1/2*d*x + 1/2*c) + 1530*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
332,1,182,0,0.329296," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{9 \, {\left(B - C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{9 \, {\left(B - C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{6 \, {\left(B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a}}{6 \, d}"," ",0,"1/6*(9*(B - C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - 9*(B - C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 6*(B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a + 2*(9*B*tan(1/2*d*x + 1/2*c)^5 - 15*C*tan(1/2*d*x + 1/2*c)^5 - 12*B*tan(1/2*d*x + 1/2*c)^3 + 16*C*tan(1/2*d*x + 1/2*c)^3 + 3*B*tan(1/2*d*x + 1/2*c) - 9*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a))/d","A",0
333,1,156,0,1.304926," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, B - 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{{\left(2 \, B - 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{2 \, {\left(B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a}}{2 \, d}"," ",0,"-1/2*((2*B - 3*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - (2*B - 3*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 2*(B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a + 2*(2*B*tan(1/2*d*x + 1/2*c)^3 - 3*C*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a))/d","A",0
334,1,109,0,0.293227," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(B - C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{{\left(B - C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a}}{d}"," ",0,"((B - C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - (B - C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - (B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a - 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a))/d","A",0
335,1,70,0,0.297172," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} + \frac{B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"(C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a + (B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a)/d","A",0
336,1,44,0,0.250468," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} B}{a} - \frac{B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"((d*x + c)*B/a - (B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a)/d","A",0
337,1,79,0,0.383348," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(d x + c\right)} {\left(B - C\right)}}{a} - \frac{B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a}}{d}"," ",0,"-((d*x + c)*(B - C)/a - (B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a - 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a))/d","A",0
338,1,123,0,0.243632," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} {\left(3 \, B - 2 \, C\right)}}{a} - \frac{2 \, {\left(B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a}}{2 \, d}"," ",0,"1/2*((d*x + c)*(3*B - 2*C)/a - 2*(B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a - 2*(3*B*tan(1/2*d*x + 1/2*c)^3 - 2*C*tan(1/2*d*x + 1/2*c)^3 + B*tan(1/2*d*x + 1/2*c) - 2*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a))/d","A",0
339,1,151,0,1.305789," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{9 \, {\left(d x + c\right)} {\left(B - C\right)}}{a} - \frac{6 \, {\left(B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a}}{6 \, d}"," ",0,"-1/6*(9*(d*x + c)*(B - C)/a - 6*(B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a - 2*(15*B*tan(1/2*d*x + 1/2*c)^5 - 9*C*tan(1/2*d*x + 1/2*c)^5 + 16*B*tan(1/2*d*x + 1/2*c)^3 - 12*C*tan(1/2*d*x + 1/2*c)^3 + 9*B*tan(1/2*d*x + 1/2*c) - 3*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a))/d","A",0
340,1,198,0,0.333765," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(4 \, B - 7 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{3 \, {\left(4 \, B - 7 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{6 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}} - \frac{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(3*(4*B - 7*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 3*(4*B - 7*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 6*(2*B*tan(1/2*d*x + 1/2*c)^3 - 5*C*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c) + 3*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2) - (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 + 15*B*a^4*tan(1/2*d*x + 1/2*c) - 21*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
341,1,151,0,0.269665," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(B - 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, {\left(B - 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{2}} - \frac{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(B - 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*(B - 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - 12*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^2) - (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*B*a^4*tan(1/2*d*x + 1/2*c) - 15*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
342,1,112,0,0.289128," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^4*tan(1/2*d*x + 1/2*c) - 9*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
343,1,60,0,0.250015," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{6 \, a^{2} d}"," ",0,"-1/6*(B*tan(1/2*d*x + 1/2*c)^3 - C*tan(1/2*d*x + 1/2*c)^3 - 3*B*tan(1/2*d*x + 1/2*c) - 3*C*tan(1/2*d*x + 1/2*c))/(a^2*d)","A",0
344,1,85,0,0.238142," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)} B}{a^{2}} + \frac{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*B/a^2 + (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 - 9*B*a^4*tan(1/2*d*x + 1/2*c) + 3*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
345,1,121,0,0.320228," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(d x + c\right)} {\left(2 \, B - C\right)}}{a^{2}} - \frac{12 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{2}} + \frac{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c)*(2*B - C)/a^2 - 12*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^2) + (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 - 15*B*a^4*tan(1/2*d*x + 1/2*c) + 9*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
346,1,164,0,0.598229," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)} {\left(7 \, B - 4 \, C\right)}}{a^{2}} - \frac{6 \, {\left(5 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}} + \frac{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)*(7*B - 4*C)/a^2 - 6*(5*B*tan(1/2*d*x + 1/2*c)^3 - 2*C*tan(1/2*d*x + 1/2*c)^3 + 3*B*tan(1/2*d*x + 1/2*c) - 2*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2) + (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 - 21*B*a^4*tan(1/2*d*x + 1/2*c) + 15*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
347,1,192,0,0.341403," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)} {\left(10 \, B - 7 \, C\right)}}{a^{2}} - \frac{2 \, {\left(30 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{2}} + \frac{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 27 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(3*(d*x + c)*(10*B - 7*C)/a^2 - 2*(30*B*tan(1/2*d*x + 1/2*c)^5 - 15*C*tan(1/2*d*x + 1/2*c)^5 + 40*B*tan(1/2*d*x + 1/2*c)^3 - 24*C*tan(1/2*d*x + 1/2*c)^3 + 18*B*tan(1/2*d*x + 1/2*c) - 9*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^2) + (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 - 27*B*a^4*tan(1/2*d*x + 1/2*c) + 21*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
348,1,233,0,0.701445," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(6 \, B - 13 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{30 \, {\left(6 \, B - 13 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{60 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}} - \frac{3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 465 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(30*(6*B - 13*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 30*(6*B - 13*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 60*(2*B*tan(1/2*d*x + 1/2*c)^3 - 7*C*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c) + 5*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^3) - (3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 30*B*a^12*tan(1/2*d*x + 1/2*c)^3 - 40*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 255*B*a^12*tan(1/2*d*x + 1/2*c) - 465*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
349,1,186,0,1.207928," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(B - 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, {\left(B - 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{120 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{3}} - \frac{3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 255 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(B - 3*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*(B - 3*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - 120*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^3) - (3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 20*B*a^12*tan(1/2*d*x + 1/2*c)^3 - 30*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*B*a^12*tan(1/2*d*x + 1/2*c) - 255*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
350,1,147,0,0.338934," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + (3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 10*B*a^12*tan(1/2*d*x + 1/2*c)^3 - 20*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 15*B*a^12*tan(1/2*d*x + 1/2*c) - 105*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
351,1,75,0,1.019458," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, a^{3} d}"," ",0,"-1/60*(3*B*tan(1/2*d*x + 1/2*c)^5 - 3*C*tan(1/2*d*x + 1/2*c)^5 - 10*C*tan(1/2*d*x + 1/2*c)^3 - 15*B*tan(1/2*d*x + 1/2*c) - 15*C*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
352,1,75,0,1.590482," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, a^{3} d}"," ",0,"1/60*(3*B*tan(1/2*d*x + 1/2*c)^5 - 3*C*tan(1/2*d*x + 1/2*c)^5 - 10*B*tan(1/2*d*x + 1/2*c)^3 + 15*B*tan(1/2*d*x + 1/2*c) + 15*C*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
353,1,121,0,0.302182," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(d x + c\right)} B}{a^{3}} - \frac{3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 20 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*B/a^3 - (3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 20*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 10*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*B*a^12*tan(1/2*d*x + 1/2*c) - 15*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
354,1,157,0,0.476980," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(d x + c\right)} {\left(3 \, B - C\right)}}{a^{3}} - \frac{120 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}} - \frac{3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(60*(d*x + c)*(3*B - C)/a^3 - 120*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3) - (3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 30*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 20*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 255*B*a^12*tan(1/2*d*x + 1/2*c) - 105*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
355,1,200,0,0.360010," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{30 \, {\left(d x + c\right)} {\left(13 \, B - 6 \, C\right)}}{a^{3}} - \frac{60 \, {\left(7 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}} - \frac{3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 465 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 255 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(30*(d*x + c)*(13*B - 6*C)/a^3 - 60*(7*B*tan(1/2*d*x + 1/2*c)^3 - 2*C*tan(1/2*d*x + 1/2*c)^3 + 5*B*tan(1/2*d*x + 1/2*c) - 2*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3) - (3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 40*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 30*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 465*B*a^12*tan(1/2*d*x + 1/2*c) - 255*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
356,1,314,0,3.598057," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(3465 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3465 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(8085 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5775 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(14322 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 16170 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(13266 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8910 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(4741 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5885 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(1177 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 755 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{3465 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"-2/3465*(3465*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 3465*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (8085*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 5775*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (14322*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 16170*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (13266*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 8910*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (4741*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 5885*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (1177*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 755*sqrt(2)*C*a^6*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
357,1,268,0,8.779852," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(315 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 315 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(630 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 420 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(756 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 882 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(522 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 324 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(81 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 107 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"2/315*(315*sqrt(2)*B*a^5*sgn(cos(d*x + c)) + 315*sqrt(2)*C*a^5*sgn(cos(d*x + c)) - (630*sqrt(2)*B*a^5*sgn(cos(d*x + c)) + 420*sqrt(2)*C*a^5*sgn(cos(d*x + c)) - (756*sqrt(2)*B*a^5*sgn(cos(d*x + c)) + 882*sqrt(2)*C*a^5*sgn(cos(d*x + c)) - (522*sqrt(2)*B*a^5*sgn(cos(d*x + c)) + 324*sqrt(2)*C*a^5*sgn(cos(d*x + c)) - (81*sqrt(2)*B*a^5*sgn(cos(d*x + c)) + 107*sqrt(2)*C*a^5*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
358,1,222,0,1.682364," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(105 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 105 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(175 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 105 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(119 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 147 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(49 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 27 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{105 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"-2/105*(105*sqrt(2)*B*a^4*sgn(cos(d*x + c)) + 105*sqrt(2)*C*a^4*sgn(cos(d*x + c)) - (175*sqrt(2)*B*a^4*sgn(cos(d*x + c)) + 105*sqrt(2)*C*a^4*sgn(cos(d*x + c)) - (119*sqrt(2)*B*a^4*sgn(cos(d*x + c)) + 147*sqrt(2)*C*a^4*sgn(cos(d*x + c)) - (49*sqrt(2)*B*a^4*sgn(cos(d*x + c)) + 27*sqrt(2)*C*a^4*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
359,1,176,0,4.975428," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(15 \, \sqrt{2} B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 15 \, \sqrt{2} C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(20 \, \sqrt{2} B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 10 \, \sqrt{2} C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(5 \, \sqrt{2} B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7 \, \sqrt{2} C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{15 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"2/15*(15*sqrt(2)*B*a^3*sgn(cos(d*x + c)) + 15*sqrt(2)*C*a^3*sgn(cos(d*x + c)) - (20*sqrt(2)*B*a^3*sgn(cos(d*x + c)) + 10*sqrt(2)*C*a^3*sgn(cos(d*x + c)) - (5*sqrt(2)*B*a^3*sgn(cos(d*x + c)) + 7*sqrt(2)*C*a^3*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
360,1,129,0,3.984921," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(3 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + \sqrt{2} C a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"-2/3*(3*sqrt(2)*B*a^2*sgn(cos(d*x + c)) + 3*sqrt(2)*C*a^2*sgn(cos(d*x + c)) - (3*sqrt(2)*B*a^2*sgn(cos(d*x + c)) + sqrt(2)*C*a^2*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","B",0
361,1,193,0,3.121326," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{2 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} C a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + \frac{B \sqrt{-a} a \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}}}{d}"," ",0,"-(2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*C*a*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + B*sqrt(-a)*a*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a))/d","B",0
362,1,336,0,1.580795," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{{\left(B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(3 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \sqrt{2} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}}}{2 \, d}"," ",0,"-1/2*((B*sqrt(-a)*sgn(cos(d*x + c)) + 2*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (B*sqrt(-a)*sgn(cos(d*x + c)) + 2*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(3*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a*sgn(cos(d*x + c)) - sqrt(2)*B*sqrt(-a)*a^2*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2))/d","B",0
363,1,630,0,4.843904," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{{\left(3 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(3 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) - \frac{4 \, \sqrt{2} {\left(5 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 17 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((3*B*sqrt(-a)*sgn(cos(d*x + c)) + 4*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (3*B*sqrt(-a)*sgn(cos(d*x + c)) + 4*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) - 4*sqrt(2)*(5*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a*sgn(cos(d*x + c)) - 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a*sgn(cos(d*x + c)) + 19*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 17*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) + B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 4*C*sqrt(-a)*a^4*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2)/d","B",0
364,1,889,0,1.814941," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{3 \, {\left(5 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(5 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(63 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 30 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 369 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 66 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1638 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 756 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1074 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 732 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 171 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 138 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 13 \, \sqrt{2} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6 \, \sqrt{2} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(3*(5*B*sqrt(-a)*sgn(cos(d*x + c)) + 6*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(5*B*sqrt(-a)*sgn(cos(d*x + c)) + 6*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(63*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a*sgn(cos(d*x + c)) - 30*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a*sgn(cos(d*x + c)) - 369*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 66*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 1638*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 756*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 1074*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 732*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 171*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 138*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 13*sqrt(2)*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 6*sqrt(2)*C*sqrt(-a)*a^6*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3)/d","B",0
365,1,305,0,2.946224," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{4 \, {\left({\left({\left({\left({\left(2 \, \sqrt{2} {\left(517 \, B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 483 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 11 \, \sqrt{2} {\left(517 \, B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 483 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 198 \, \sqrt{2} {\left(69 \, B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 56 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 462 \, \sqrt{2} {\left(32 \, B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 33 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2310 \, \sqrt{2} {\left(4 \, B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3465 \, \sqrt{2} {\left(B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{3465 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"4/3465*(((((2*sqrt(2)*(517*B*a^7*sgn(cos(d*x + c)) + 483*C*a^7*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 11*sqrt(2)*(517*B*a^7*sgn(cos(d*x + c)) + 483*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 198*sqrt(2)*(69*B*a^7*sgn(cos(d*x + c)) + 56*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 462*sqrt(2)*(32*B*a^7*sgn(cos(d*x + c)) + 33*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 2310*sqrt(2)*(4*B*a^7*sgn(cos(d*x + c)) + 3*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 3465*sqrt(2)*(B*a^7*sgn(cos(d*x + c)) + C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
366,1,258,0,3.568727," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{4 \, {\left({\left({\left({\left(2 \, \sqrt{2} {\left(57 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 47 \, C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \sqrt{2} {\left(57 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 47 \, C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 819 \, \sqrt{2} {\left(B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \sqrt{2} {\left(7 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5 \, C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 315 \, \sqrt{2} {\left(B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"4/315*((((2*sqrt(2)*(57*B*a^6*sgn(cos(d*x + c)) + 47*C*a^6*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 9*sqrt(2)*(57*B*a^6*sgn(cos(d*x + c)) + 47*C*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 819*sqrt(2)*(B*a^6*sgn(cos(d*x + c)) + C*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 105*sqrt(2)*(7*B*a^6*sgn(cos(d*x + c)) + 5*C*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 315*sqrt(2)*(B*a^6*sgn(cos(d*x + c)) + C*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
367,1,215,0,9.219499," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{4 \, {\left({\left({\left(2 \, \sqrt{2} {\left(21 \, B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, \sqrt{2} {\left(21 \, B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 70 \, \sqrt{2} {\left(3 \, B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \sqrt{2} {\left(B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{105 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"4/105*(((2*sqrt(2)*(21*B*a^5*sgn(cos(d*x + c)) + 19*C*a^5*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 7*sqrt(2)*(21*B*a^5*sgn(cos(d*x + c)) + 19*C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 70*sqrt(2)*(3*B*a^5*sgn(cos(d*x + c)) + 2*C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 105*sqrt(2)*(B*a^5*sgn(cos(d*x + c)) + C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
368,1,170,0,2.912080," ","integrate((a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{4 \, {\left({\left(2 \, \sqrt{2} {\left(5 \, B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5 \, \sqrt{2} {\left(5 \, B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, \sqrt{2} {\left(B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{15 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"4/15*((2*sqrt(2)*(5*B*a^4*sgn(cos(d*x + c)) + 3*C*a^4*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 5*sqrt(2)*(5*B*a^4*sgn(cos(d*x + c)) + 3*C*a^4*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 15*sqrt(2)*(B*a^4*sgn(cos(d*x + c)) + C*a^4*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
369,1,263,0,5.053877," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{3 \, B \sqrt{-a} a^{2} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} + \frac{2 \, {\left(3 \, \sqrt{2} B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6 \, \sqrt{2} C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(3 \, \sqrt{2} B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, \sqrt{2} C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{3 \, d}"," ",0,"-1/3*(3*B*sqrt(-a)*a^2*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) + 2*(3*sqrt(2)*B*a^3*sgn(cos(d*x + c)) + 6*sqrt(2)*C*a^3*sgn(cos(d*x + c)) - (3*sqrt(2)*B*a^3*sgn(cos(d*x + c)) + 4*sqrt(2)*C*a^3*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
370,1,406,0,19.792964," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{4 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} C a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + {\left(3 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(3 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(3 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \sqrt{2} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}}}{2 \, d}"," ",0,"-1/2*(4*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*C*a^2*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + (3*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 2*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (3*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 2*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(3*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) - sqrt(2)*B*sqrt(-a)*a^3*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2))/d","B",0
371,1,639,0,11.481699," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{{\left(7 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(7 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(7 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 95 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 53 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 5 \, B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4 \, C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((7*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 12*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (7*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 12*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(7*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 95*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 53*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 5*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 4*C*sqrt(-a)*a^5*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2)/d","B",0
372,1,897,0,7.933694," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(11 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 14 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(11 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 14 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(33 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 42 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 303 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 822 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2394 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3780 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1806 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2508 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 309 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 498 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 19 \, \sqrt{2} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 30 \, \sqrt{2} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(3*(11*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 14*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(11*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 14*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(33*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 42*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 303*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 822*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 2394*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 3780*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 1806*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 2508*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 309*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 498*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 19*sqrt(2)*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 30*sqrt(2)*C*sqrt(-a)*a^7*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3)/d","B",0
373,1,1088,0,5.714378," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(75 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 88 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(75 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 88 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(225 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 264 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6261 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4008 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 35925 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 33960 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 127449 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 131784 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 101667 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 108312 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 26079 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 29432 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3303 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3384 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 147 \, B \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 152 \, C \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(3*(75*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 88*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(75*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 88*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(225*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 264*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 6261*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 4008*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 35925*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 33960*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 127449*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 131784*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 101667*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 108312*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 26079*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 29432*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 3303*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 3384*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 147*B*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 152*C*sqrt(-a)*a^9*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^4)/d","B",0
374,1,351,0,2.385188," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, {\left({\left({\left({\left({\left(4 \, {\left(2 \, \sqrt{2} {\left(1625 \, B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1483 \, C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 13 \, \sqrt{2} {\left(1625 \, B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1483 \, C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 143 \, \sqrt{2} {\left(1625 \, B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1483 \, C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 858 \, \sqrt{2} {\left(415 \, B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 362 \, C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6006 \, \sqrt{2} {\left(50 \, B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 49 \, C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 30030 \, \sqrt{2} {\left(5 \, B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 45045 \, \sqrt{2} {\left(B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{45045 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{6} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"8/45045*(((((4*(2*sqrt(2)*(1625*B*a^9*sgn(cos(d*x + c)) + 1483*C*a^9*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 13*sqrt(2)*(1625*B*a^9*sgn(cos(d*x + c)) + 1483*C*a^9*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 143*sqrt(2)*(1625*B*a^9*sgn(cos(d*x + c)) + 1483*C*a^9*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 858*sqrt(2)*(415*B*a^9*sgn(cos(d*x + c)) + 362*C*a^9*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 6006*sqrt(2)*(50*B*a^9*sgn(cos(d*x + c)) + 49*C*a^9*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 30030*sqrt(2)*(5*B*a^9*sgn(cos(d*x + c)) + 4*C*a^9*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 45045*sqrt(2)*(B*a^9*sgn(cos(d*x + c)) + C*a^9*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^6*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
375,1,306,0,3.993139," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, {\left({\left({\left({\left(4 \, {\left(2 \, \sqrt{2} {\left(143 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 125 \, C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 11 \, \sqrt{2} {\left(143 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 125 \, C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 99 \, \sqrt{2} {\left(143 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 125 \, C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 231 \, \sqrt{2} {\left(69 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 65 \, C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1155 \, \sqrt{2} {\left(9 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7 \, C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3465 \, \sqrt{2} {\left(B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{3465 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"8/3465*((((4*(2*sqrt(2)*(143*B*a^8*sgn(cos(d*x + c)) + 125*C*a^8*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 11*sqrt(2)*(143*B*a^8*sgn(cos(d*x + c)) + 125*C*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 99*sqrt(2)*(143*B*a^8*sgn(cos(d*x + c)) + 125*C*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 231*sqrt(2)*(69*B*a^8*sgn(cos(d*x + c)) + 65*C*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 1155*sqrt(2)*(9*B*a^8*sgn(cos(d*x + c)) + 7*C*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 3465*sqrt(2)*(B*a^8*sgn(cos(d*x + c)) + C*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
376,1,261,0,2.124128," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, {\left({\left({\left(4 \, {\left(2 \, \sqrt{2} {\left(15 \, B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \sqrt{2} {\left(15 \, B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 63 \, \sqrt{2} {\left(15 \, B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 210 \, \sqrt{2} {\left(4 \, B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 315 \, \sqrt{2} {\left(B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"8/315*(((4*(2*sqrt(2)*(15*B*a^7*sgn(cos(d*x + c)) + 13*C*a^7*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 9*sqrt(2)*(15*B*a^7*sgn(cos(d*x + c)) + 13*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 63*sqrt(2)*(15*B*a^7*sgn(cos(d*x + c)) + 13*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 210*sqrt(2)*(4*B*a^7*sgn(cos(d*x + c)) + 3*C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 315*sqrt(2)*(B*a^7*sgn(cos(d*x + c)) + C*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
377,1,216,0,1.855660," ","integrate((a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, {\left({\left(4 \, {\left(2 \, \sqrt{2} {\left(7 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5 \, C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, \sqrt{2} {\left(7 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5 \, C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, \sqrt{2} {\left(7 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5 \, C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \sqrt{2} {\left(B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{105 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"8/105*((4*(2*sqrt(2)*(7*B*a^6*sgn(cos(d*x + c)) + 5*C*a^6*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 7*sqrt(2)*(7*B*a^6*sgn(cos(d*x + c)) + 5*C*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 35*sqrt(2)*(7*B*a^6*sgn(cos(d*x + c)) + 5*C*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 105*sqrt(2)*(B*a^6*sgn(cos(d*x + c)) + C*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
378,1,309,0,7.644263," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{15 \, B \sqrt{-a} a^{3} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} - \frac{2 \, {\left(45 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 60 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(80 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 80 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(35 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 32 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{15 \, d}"," ",0,"-1/15*(15*B*sqrt(-a)*a^3*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) - 2*(45*sqrt(2)*B*a^5*sgn(cos(d*x + c)) + 60*sqrt(2)*C*a^5*sgn(cos(d*x + c)) - (80*sqrt(2)*B*a^5*sgn(cos(d*x + c)) + 80*sqrt(2)*C*a^5*sgn(cos(d*x + c)) - (35*sqrt(2)*B*a^5*sgn(cos(d*x + c)) + 32*sqrt(2)*C*a^5*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
379,1,480,0,5.140211," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(5 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(5 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(3 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(3 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{12 \, {\left(3 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \sqrt{2} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}}}{6 \, d}"," ",0,"-1/6*(3*(5*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 2*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(5*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 2*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(3*sqrt(2)*B*a^4*sgn(cos(d*x + c)) + 9*sqrt(2)*C*a^4*sgn(cos(d*x + c)) - (3*sqrt(2)*B*a^4*sgn(cos(d*x + c)) + 7*sqrt(2)*C*a^4*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) + 12*(3*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - sqrt(2)*B*sqrt(-a)*a^4*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2))/d","B",0
380,1,709,0,3.131259," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{16 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + {\left(19 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 20 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(19 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 20 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 171 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 89 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 9 \, B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4 \, C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(16*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*C*a^3*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + (19*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 20*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (19*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 20*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(19*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 171*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 89*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 9*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 4*C*sqrt(-a)*a^6*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2)/d","B",0
381,1,905,0,3.000090," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(25 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 38 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(25 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 38 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(75 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 114 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1125 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1710 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6174 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6804 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4314 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4284 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 807 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 858 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 49 \, \sqrt{2} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 54 \, \sqrt{2} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(3*(25*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 38*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(25*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 38*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(75*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 114*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 1125*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 1710*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 6174*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 6804*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 4314*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 4284*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 807*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 858*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 49*sqrt(2)*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 54*sqrt(2)*C*sqrt(-a)*a^8*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3)/d","B",0
382,1,1096,0,4.318908," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(163 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 200 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(163 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 200 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(489 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 600 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 10269 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 12600 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 69885 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 103992 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 259233 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 339864 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 209979 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 262920 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 55511 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 73640 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6687 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8808 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 299 \, B \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 392 \, C \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(3*(163*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 200*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(163*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 200*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(489*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 600*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 10269*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 12600*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 69885*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 103992*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 259233*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 339864*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 209979*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 262920*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 55511*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 73640*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 6687*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 8808*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 299*B*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 392*C*sqrt(-a)*a^10*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^4)/d","B",0
383,1,1377,0,4.701258," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{15 \, {\left(283 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 326 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 15 \, {\left(283 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 326 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(4245 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4890 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 114615 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 132030 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1298820 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1319880 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6176700 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6888120 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 16394598 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 18352620 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 14042770 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 15746180 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4791060 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5497320 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 860300 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 959320 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 75885 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 84810 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2671 \, \sqrt{2} B \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2990 \, \sqrt{2} C \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{5}}}{3840 \, d}"," ",0,"-1/3840*(15*(283*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 326*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 15*(283*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 326*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(4245*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 4890*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 114615*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 132030*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 1298820*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 1319880*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 6176700*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 6888120*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 16394598*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 18352620*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 14042770*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 15746180*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 4791060*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 5497320*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 860300*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 959320*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^10*sgn(cos(d*x + c)) + 75885*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^11*sgn(cos(d*x + c)) + 84810*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^11*sgn(cos(d*x + c)) - 2671*sqrt(2)*B*sqrt(-a)*a^12*sgn(cos(d*x + c)) - 2990*sqrt(2)*C*sqrt(-a)*a^12*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^5)/d","B",0
384,1,391,0,2.538908," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{315 \, {\left(\sqrt{2} B - \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(\frac{315 \, \sqrt{2} C a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + {\left(420 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 840 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(756 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 1638 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(612 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 936 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(276 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 383 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{315 \, d}"," ",0,"1/315*(315*(sqrt(2)*B - sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(315*sqrt(2)*C*a^4/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + (420*sqrt(2)*B*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 840*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (756*sqrt(2)*B*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 1638*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (612*sqrt(2)*B*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 936*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (276*sqrt(2)*B*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 383*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
385,1,287,0,2.324119," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{105 \, \sqrt{2} {\left(B - C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(\frac{105 \, \sqrt{2} B a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - {\left({\left(\frac{\sqrt{2} {\left(119 \, B a^{3} - 92 \, C a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{7 \, \sqrt{2} {\left(37 \, B a^{3} - 16 \, C a^{3}\right)}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{35 \, \sqrt{2} {\left(7 \, B a^{3} - 4 \, C a^{3}\right)}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{105 \, d}"," ",0,"-1/105*(105*sqrt(2)*(B - C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(105*sqrt(2)*B*a^3/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - ((sqrt(2)*(119*B*a^3 - 92*C*a^3)*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 7*sqrt(2)*(37*B*a^3 - 16*C*a^3)/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2 + 35*sqrt(2)*(7*B*a^3 - 4*C*a^3)/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
386,1,271,0,2.971138," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(\sqrt{2} B - \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left({\left(10 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 20 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(10 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 17 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{15 \, \sqrt{2} C a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{15 \, d}"," ",0,"1/15*(15*(sqrt(2)*B - sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*((10*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 20*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (10*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 17*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2 + 15*sqrt(2)*C*a^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
387,1,186,0,2.745956," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{3 \, \sqrt{2} {\left(B - C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{2 \, {\left(\frac{\sqrt{2} {\left(3 \, B a - 2 \, C a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, \sqrt{2} B a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{3 \, d}"," ",0,"-1/3*(3*sqrt(2)*(B - C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 2*(sqrt(2)*(3*B*a - 2*C*a)*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*sqrt(2)*B*a/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
388,1,144,0,2.168559," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{{\left(\sqrt{2} B - \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{d}"," ",0,"(2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*C*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + (sqrt(2)*B - sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
389,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableDiscontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 1.28index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
390,1,393,0,3.296955," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} {\left(B - C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{{\left(B - 2 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left(B - 2 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} - B \sqrt{-a} a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{2 \, d}"," ",0,"1/2*(sqrt(2)*(B - C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + (B - 2*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - (B - 2*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a) - B*sqrt(-a)*a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
391,1,649,0,3.040238," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{4 \, \sqrt{2} {\left(B - C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{{\left(7 \, B - 4 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left(7 \, B - 4 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(17 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} - 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} - 57 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a + 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a + 19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{2} - 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{2} - 3 \, B \sqrt{-a} a^{3} + 4 \, C \sqrt{-a} a^{3}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"-1/8*(4*sqrt(2)*(B - C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + (7*B - 4*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - (7*B - 4*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(17*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a) - 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a) - 57*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a + 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a + 19*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^2 - 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^2 - 3*B*sqrt(-a)*a^3 + 4*C*sqrt(-a)*a^3)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
392,1,846,0,2.999549," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{24 \, \sqrt{2} {\left(B - C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{3 \, {\left(9 \, B - 14 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, {\left(9 \, B - 14 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(165 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} - 102 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} - 1323 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a + 954 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a + 3906 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{2} - 2268 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{2} - 2118 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{3} + 1044 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{3} + 393 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{4} - 222 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{4} - 31 \, B \sqrt{-a} a^{5} + 18 \, C \sqrt{-a} a^{5}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{48 \, d}"," ",0,"1/48*(24*sqrt(2)*(B - C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 3*(9*B - 14*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 3*(9*B - 14*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(165*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a) - 102*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a) - 1323*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a + 954*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a + 3906*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^2 - 2268*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^2 - 2118*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^3 + 1044*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^3 + 393*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^4 - 222*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^4 - 31*B*sqrt(-a)*a^5 + 18*C*sqrt(-a)*a^5)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
393,1,439,0,4.774559," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(15 \, \sqrt{2} B - 19 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left({\left({\left({\left(\frac{105 \, {\left(\sqrt{2} B a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3}} - \frac{4 \, {\left(693 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 877 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{14 \, {\left(453 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 517 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{140 \, {\left(39 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 47 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{1785 \, {\left(\sqrt{2} B a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{420 \, d}"," ",0,"-1/420*(105*(15*sqrt(2)*B - 19*sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - ((((105*(sqrt(2)*B*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a^3 - 4*(693*sqrt(2)*B*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 877*sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^3)*tan(1/2*d*x + 1/2*c)^2 + 14*(453*sqrt(2)*B*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 517*sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^3)*tan(1/2*d*x + 1/2*c)^2 - 140*(39*sqrt(2)*B*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 47*sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^3)*tan(1/2*d*x + 1/2*c)^2 + 1785*(sqrt(2)*B*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^3)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
394,1,312,0,2.595633," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{15 \, \sqrt{2} {\left(11 \, B - 15 \, C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left({\left({\left(\frac{15 \, \sqrt{2} {\left(B a^{3} - C a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(245 \, B a^{3} - 381 \, C a^{3}\right)}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{5 \, \sqrt{2} {\left(73 \, B a^{3} - 105 \, C a^{3}\right)}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{15 \, \sqrt{2} {\left(9 \, B a^{3} - 17 \, C a^{3}\right)}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{60 \, d}"," ",0,"1/60*(15*sqrt(2)*(11*B - 15*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - (((15*sqrt(2)*(B*a^3 - C*a^3)*tan(1/2*d*x + 1/2*c)^2/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(245*B*a^3 - 381*C*a^3)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 5*sqrt(2)*(73*B*a^3 - 105*C*a^3)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 - 15*sqrt(2)*(9*B*a^3 - 17*C*a^3)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
395,1,296,0,2.339930," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left(\frac{3 \, {\left(\sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a} - \frac{2 \, {\left(15 \, \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 23 \, \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{27 \, {\left(\sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{3 \, {\left(7 \, \sqrt{2} B - 11 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{12 \, d}"," ",0,"1/12*(((3*(sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a - 2*(15*sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 23*sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a)*tan(1/2*d*x + 1/2*c)^2 + 27*(sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) - 3*(7*sqrt(2)*B - 11*sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
396,1,190,0,2.095942," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left(\frac{\sqrt{2} {\left(B a^{2} - C a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(B a^{2} - 9 \, C a^{2}\right)}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{\sqrt{2} {\left(3 \, B - 7 \, C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{4 \, d}"," ",0,"-1/4*((sqrt(2)*(B*a^2 - C*a^2)*tan(1/2*d*x + 1/2*c)^2/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(B*a^2 - 9*C*a^2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a) - sqrt(2)*(3*B - 7*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
397,1,154,0,1.967724," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(\sqrt{2} B + 3 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left(\sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}}}{4 \, d}"," ",0,"1/4*((sqrt(2)*B + 3*sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - (sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^3)/d","B",0
398,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableDiscontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 1.56index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
399,1,453,0,3.411889," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} {\left(9 \, B - 5 \, C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{4 \, {\left(3 \, B - 2 \, C\right)} \log\left(\frac{{\left| -17179869184 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 34359738368 \, \sqrt{2} {\left| a \right|} + 51539607552 \, a \right|}}{{\left| -17179869184 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 34359738368 \, \sqrt{2} {\left| a \right|} + 51539607552 \, a \right|}}\right)}{\sqrt{-a} {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(\sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{16 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B - B a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"1/8*(sqrt(2)*(9*B - 5*C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 4*(3*B - 2*C)*log(abs(-17179869184*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 34359738368*sqrt(2)*abs(a) + 51539607552*a)/abs(-17179869184*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 34359738368*sqrt(2)*abs(a) + 51539607552*a))/(sqrt(-a)*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^3 - 16*sqrt(2)*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B - B*a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
400,1,673,0,3.553948," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} {\left(13 \, B - 9 \, C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{{\left(19 \, B - 12 \, C\right)} \log\left(\frac{{\left| 147573952589676412928 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 295147905179352825856 \, \sqrt{2} {\left| a \right|} - 442721857769029238784 \, a \right|}}{{\left| 147573952589676412928 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 295147905179352825856 \, \sqrt{2} {\left| a \right|} - 442721857769029238784 \, a \right|}}\right)}{\sqrt{-a} {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(\sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{4 \, \sqrt{2} {\left(29 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B - 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C - 133 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B a + 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C a + 55 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B a^{2} - 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C a^{2} - 7 \, B a^{3} + 4 \, C a^{3}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"-1/8*(sqrt(2)*(13*B - 9*C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + (19*B - 12*C)*log(abs(147573952589676412928*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 295147905179352825856*sqrt(2)*abs(a) - 442721857769029238784*a)/abs(147573952589676412928*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 295147905179352825856*sqrt(2)*abs(a) - 442721857769029238784*a))/(sqrt(-a)*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^3 - 4*sqrt(2)*(29*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B - 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C - 133*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*a + 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*a + 55*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*a^2 - 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*a^2 - 7*B*a^3 + 4*C*a^3)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
401,1,439,0,3.531485," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{{\left({\left({\left(15 \, {\left(\frac{2 \, {\left(\sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2}} + \frac{21 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 29 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{3685 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 6733 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{5 \, {\left(1133 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 1973 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{15 \, {\left(155 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 291 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{15 \, {\left(163 \, \sqrt{2} B - 283 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{480 \, d}"," ",0,"-1/480*((((15*(2*(sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a^2 + (21*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 29*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^2)*tan(1/2*d*x + 1/2*c)^2 - (3685*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 6733*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^2)*tan(1/2*d*x + 1/2*c)^2 + 5*(1133*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 1973*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^2)*tan(1/2*d*x + 1/2*c)^2 - 15*(155*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 291*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) - 15*(163*sqrt(2)*B - 283*sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
402,1,311,0,3.026960," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left(3 \, {\left(\frac{2 \, \sqrt{2} {\left(B a^{5} - C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{\sqrt{2} {\left(15 \, B a^{5} - 23 \, C a^{5}\right)}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{4 \, \sqrt{2} {\left(75 \, B a^{5} - 167 \, C a^{5}\right)}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{3 \, \sqrt{2} {\left(83 \, B a^{5} - 155 \, C a^{5}\right)}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{3 \, \sqrt{2} {\left(75 \, B - 163 \, C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{96 \, d}"," ",0,"1/96*(((3*(2*sqrt(2)*(B*a^5 - C*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + sqrt(2)*(15*B*a^5 - 23*C*a^5)/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 - 4*sqrt(2)*(75*B*a^5 - 167*C*a^5)/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 3*sqrt(2)*(83*B*a^5 - 155*C*a^5)/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) - 3*sqrt(2)*(75*B - 163*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
403,1,289,0,2.912985," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(\frac{2 \, {\left(\sqrt{2} B a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} C a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} + \frac{9 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 17 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{11 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 83 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{{\left(19 \, \sqrt{2} B - 75 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"-1/32*(((2*(sqrt(2)*B*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*C*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a^8 + (9*sqrt(2)*B*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 17*sqrt(2)*C*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^8)*tan(1/2*d*x + 1/2*c)^2 - (11*sqrt(2)*B*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 83*sqrt(2)*C*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^8)*tan(1/2*d*x + 1/2*c)/sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a) - (19*sqrt(2)*B - 75*sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
404,1,191,0,2.609536," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(B a^{5} - C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{\sqrt{2} {\left(3 \, B a^{5} - 11 \, C a^{5}\right)}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{\sqrt{2} {\left(5 \, B + 19 \, C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"-1/32*(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(B*a^5 - C*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + sqrt(2)*(3*B*a^5 - 11*C*a^5)/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) - sqrt(2)*(5*B + 19*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
405,1,191,0,2.168809," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(B a^{5} - C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(5 \, B a^{5} + 3 \, C a^{5}\right)}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{\sqrt{2} {\left(3 \, B + 5 \, C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"1/32*(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(B*a^5 - C*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(5*B*a^5 + 3*C*a^5)/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + sqrt(2)*(3*B + 5*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
406,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableDiscontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 2.14index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
407,1,499,0,4.515334," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(B a^{5} - C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(21 \, B a^{5} - 13 \, C a^{5}\right)}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{\sqrt{2} {\left(115 \, B - 43 \, C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{32 \, {\left(5 \, B - 2 \, C\right)} \log\left(\frac{{\left| -562949953421312 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 1125899906842624 \, \sqrt{2} {\left| a \right|} + 1688849860263936 \, a \right|}}{{\left| -562949953421312 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 1125899906842624 \, \sqrt{2} {\left| a \right|} + 1688849860263936 \, a \right|}}\right)}{\sqrt{-a} a {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{128 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B - B a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} \sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{64 \, d}"," ",0,"1/64*(2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(B*a^5 - C*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(21*B*a^5 - 13*C*a^5)/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + sqrt(2)*(115*B - 43*C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 32*(5*B - 2*C)*log(abs(-562949953421312*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 1125899906842624*sqrt(2)*abs(a) + 1688849860263936*a)/abs(-562949953421312*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 1125899906842624*sqrt(2)*abs(a) + 1688849860263936*a))/(sqrt(-a)*a*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 128*sqrt(2)*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B - B*a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
408,1,299,0,0.297248," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, A a + 3 \, B a + 3 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, A a + 3 \, B a + 3 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(60 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 200 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 290 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 130 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 400 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 464 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 440 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 350 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 190 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 180 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 195 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 195 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(4*A*a + 3*B*a + 3*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*A*a + 3*B*a + 3*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(60*A*a*tan(1/2*d*x + 1/2*c)^9 + 45*B*a*tan(1/2*d*x + 1/2*c)^9 + 45*C*a*tan(1/2*d*x + 1/2*c)^9 - 200*A*a*tan(1/2*d*x + 1/2*c)^7 - 290*B*a*tan(1/2*d*x + 1/2*c)^7 - 130*C*a*tan(1/2*d*x + 1/2*c)^7 + 400*A*a*tan(1/2*d*x + 1/2*c)^5 + 400*B*a*tan(1/2*d*x + 1/2*c)^5 + 464*C*a*tan(1/2*d*x + 1/2*c)^5 - 440*A*a*tan(1/2*d*x + 1/2*c)^3 - 350*B*a*tan(1/2*d*x + 1/2*c)^3 - 190*C*a*tan(1/2*d*x + 1/2*c)^3 + 180*A*a*tan(1/2*d*x + 1/2*c) + 195*B*a*tan(1/2*d*x + 1/2*c) + 195*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
409,1,254,0,0.271055," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(4 \, A a + 4 \, B a + 3 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, A a + 4 \, B a + 3 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(12 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 28 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 49 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 84 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 52 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 31 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 39 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(4*A*a + 4*B*a + 3*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*A*a + 4*B*a + 3*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(12*A*a*tan(1/2*d*x + 1/2*c)^7 + 12*B*a*tan(1/2*d*x + 1/2*c)^7 + 9*C*a*tan(1/2*d*x + 1/2*c)^7 - 60*A*a*tan(1/2*d*x + 1/2*c)^5 - 28*B*a*tan(1/2*d*x + 1/2*c)^5 - 49*C*a*tan(1/2*d*x + 1/2*c)^5 + 84*A*a*tan(1/2*d*x + 1/2*c)^3 + 52*B*a*tan(1/2*d*x + 1/2*c)^3 + 31*C*a*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*tan(1/2*d*x + 1/2*c) - 36*B*a*tan(1/2*d*x + 1/2*c) - 39*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
410,1,205,0,0.267952," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(2 \, A a + B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, A a + B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*A*a + B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*A*a + B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a*tan(1/2*d*x + 1/2*c)^5 + 3*B*a*tan(1/2*d*x + 1/2*c)^5 + 3*C*a*tan(1/2*d*x + 1/2*c)^5 - 12*A*a*tan(1/2*d*x + 1/2*c)^3 - 12*B*a*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*tan(1/2*d*x + 1/2*c)^3 + 6*A*a*tan(1/2*d*x + 1/2*c) + 9*B*a*tan(1/2*d*x + 1/2*c) + 9*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
411,1,141,0,0.235136," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} A a + {\left(2 \, A a + 2 \, B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, A a + 2 \, B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*A*a + (2*A*a + 2*B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*A*a + 2*B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*B*a*tan(1/2*d*x + 1/2*c)^3 + C*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c) - 3*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
412,1,134,0,0.218464," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(A a + B a\right)} {\left(d x + c\right)} + {\left(B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((A*a + B*a)*(d*x + c) + (B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - C*a*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) - C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
413,1,131,0,0.239451," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(A a + 2 \, B a + 2 \, C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*C*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*C*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (A*a + 2*B*a + 2*C*a)*(d*x + c) + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 + 2*B*a*tan(1/2*d*x + 1/2*c)^3 + 3*A*a*tan(1/2*d*x + 1/2*c) + 2*B*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
414,1,171,0,0.215725," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(A a + B a + 2 \, C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(3 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(A*a + B*a + 2*C*a)*(d*x + c) + 2*(3*A*a*tan(1/2*d*x + 1/2*c)^5 + 3*B*a*tan(1/2*d*x + 1/2*c)^5 + 6*C*a*tan(1/2*d*x + 1/2*c)^5 + 4*A*a*tan(1/2*d*x + 1/2*c)^3 + 12*B*a*tan(1/2*d*x + 1/2*c)^3 + 12*C*a*tan(1/2*d*x + 1/2*c)^3 + 9*A*a*tan(1/2*d*x + 1/2*c) + 9*B*a*tan(1/2*d*x + 1/2*c) + 6*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
415,1,218,0,0.215161," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a + 4 \, B a + 4 \, C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 49 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 28 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 52 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 84 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 39 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a + 4*B*a + 4*C*a)*(d*x + c) + 2*(9*A*a*tan(1/2*d*x + 1/2*c)^7 + 12*B*a*tan(1/2*d*x + 1/2*c)^7 + 12*C*a*tan(1/2*d*x + 1/2*c)^7 + 49*A*a*tan(1/2*d*x + 1/2*c)^5 + 28*B*a*tan(1/2*d*x + 1/2*c)^5 + 60*C*a*tan(1/2*d*x + 1/2*c)^5 + 31*A*a*tan(1/2*d*x + 1/2*c)^3 + 52*B*a*tan(1/2*d*x + 1/2*c)^3 + 84*C*a*tan(1/2*d*x + 1/2*c)^3 + 39*A*a*tan(1/2*d*x + 1/2*c) + 36*B*a*tan(1/2*d*x + 1/2*c) + 36*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
416,1,263,0,0.239391," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, A a + 3 \, B a + 4 \, C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(45 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 130 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 290 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 200 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 190 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 350 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 440 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 195 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 195 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*A*a + 3*B*a + 4*C*a)*(d*x + c) + 2*(45*A*a*tan(1/2*d*x + 1/2*c)^9 + 45*B*a*tan(1/2*d*x + 1/2*c)^9 + 60*C*a*tan(1/2*d*x + 1/2*c)^9 + 130*A*a*tan(1/2*d*x + 1/2*c)^7 + 290*B*a*tan(1/2*d*x + 1/2*c)^7 + 200*C*a*tan(1/2*d*x + 1/2*c)^7 + 464*A*a*tan(1/2*d*x + 1/2*c)^5 + 400*B*a*tan(1/2*d*x + 1/2*c)^5 + 400*C*a*tan(1/2*d*x + 1/2*c)^5 + 190*A*a*tan(1/2*d*x + 1/2*c)^3 + 350*B*a*tan(1/2*d*x + 1/2*c)^3 + 440*C*a*tan(1/2*d*x + 1/2*c)^3 + 195*A*a*tan(1/2*d*x + 1/2*c) + 195*B*a*tan(1/2*d*x + 1/2*c) + 180*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
417,1,392,0,0.338019," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(14 \, A a^{2} + 12 \, B a^{2} + 11 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(14 \, A a^{2} + 12 \, B a^{2} + 11 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(210 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 180 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 165 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1190 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1020 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 935 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2580 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2568 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1986 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3180 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2808 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3006 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2330 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1860 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1305 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 750 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 780 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 795 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(14*A*a^2 + 12*B*a^2 + 11*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(14*A*a^2 + 12*B*a^2 + 11*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(210*A*a^2*tan(1/2*d*x + 1/2*c)^11 + 180*B*a^2*tan(1/2*d*x + 1/2*c)^11 + 165*C*a^2*tan(1/2*d*x + 1/2*c)^11 - 1190*A*a^2*tan(1/2*d*x + 1/2*c)^9 - 1020*B*a^2*tan(1/2*d*x + 1/2*c)^9 - 935*C*a^2*tan(1/2*d*x + 1/2*c)^9 + 2580*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 2568*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 1986*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 3180*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 2808*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 3006*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 2330*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 1860*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 1305*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 750*A*a^2*tan(1/2*d*x + 1/2*c) - 780*B*a^2*tan(1/2*d*x + 1/2*c) - 795*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
418,1,341,0,0.321185," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(8 \, A a^{2} + 7 \, B a^{2} + 6 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(8 \, A a^{2} + 7 \, B a^{2} + 6 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 105 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 90 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 560 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 490 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 420 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1120 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 800 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 864 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1040 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 790 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 540 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 360 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 375 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 390 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(8*A*a^2 + 7*B*a^2 + 6*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(8*A*a^2 + 7*B*a^2 + 6*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*A*a^2*tan(1/2*d*x + 1/2*c)^9 + 105*B*a^2*tan(1/2*d*x + 1/2*c)^9 + 90*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 560*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 490*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 420*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 1120*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 800*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 864*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 1040*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 790*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 540*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 360*A*a^2*tan(1/2*d*x + 1/2*c) + 375*B*a^2*tan(1/2*d*x + 1/2*c) + 390*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
419,1,290,0,0.320309," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(12 \, A a^{2} + 8 \, B a^{2} + 7 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(12 \, A a^{2} + 8 \, B a^{2} + 7 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(36 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 132 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 88 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 77 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 156 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 136 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 83 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 75 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(12*A*a^2 + 8*B*a^2 + 7*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(12*A*a^2 + 8*B*a^2 + 7*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(36*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 24*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 21*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 132*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 88*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 77*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 156*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 136*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 83*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 60*A*a^2*tan(1/2*d*x + 1/2*c) - 72*B*a^2*tan(1/2*d*x + 1/2*c) - 75*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
420,1,250,0,0.373283," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} A a^{2} + 3 \, {\left(4 \, A a^{2} + 3 \, B a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, A a^{2} + 3 \, B a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*A*a^2 + 3*(4*A*a^2 + 3*B*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*A*a^2 + 3*B*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 12*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 16*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 15*B*a^2*tan(1/2*d*x + 1/2*c) + 18*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
421,1,204,0,0.300517," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 2 \, {\left(2 \, A a^{2} + B a^{2}\right)} {\left(d x + c\right)} + {\left(2 \, A a^{2} + 4 \, B a^{2} + 3 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, A a^{2} + 4 \, B a^{2} + 3 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*A*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(2*A*a^2 + B*a^2)*(d*x + c) + (2*A*a^2 + 4*B*a^2 + 3*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*A*a^2 + 4*B*a^2 + 3*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 3*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^2*tan(1/2*d*x + 1/2*c) - 5*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
422,1,198,0,0.272305," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{4 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - {\left(3 \, A a^{2} + 4 \, B a^{2} + 2 \, C a^{2}\right)} {\left(d x + c\right)} - 2 \, {\left(B a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 2 \, {\left(B a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(4*C*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (3*A*a^2 + 4*B*a^2 + 2*C*a^2)*(d*x + c) - 2*(B*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 2*(B*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^2*tan(1/2*d*x + 1/2*c) + 2*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
423,1,235,0,0.294930," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{6 \, C a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6 \, C a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(2 \, A a^{2} + 3 \, B a^{2} + 4 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*C*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6*C*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(2*A*a^2 + 3*B*a^2 + 4*C*a^2)*(d*x + c) + 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 16*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 18*A*a^2*tan(1/2*d*x + 1/2*c) + 15*B*a^2*tan(1/2*d*x + 1/2*c) + 6*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
424,1,248,0,0.249943," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(7 \, A a^{2} + 8 \, B a^{2} + 12 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(21 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 77 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 88 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 132 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 83 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 136 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 156 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 75 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(7*A*a^2 + 8*B*a^2 + 12*C*a^2)*(d*x + c) + 2*(21*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 24*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 36*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 77*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 88*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 132*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 83*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 136*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 156*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 75*A*a^2*tan(1/2*d*x + 1/2*c) + 72*B*a^2*tan(1/2*d*x + 1/2*c) + 60*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
425,1,299,0,0.284692," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(6 \, A a^{2} + 7 \, B a^{2} + 8 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(90 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 105 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 420 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 490 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 560 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 864 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 800 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 540 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 790 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1040 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 390 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 375 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(6*A*a^2 + 7*B*a^2 + 8*C*a^2)*(d*x + c) + 2*(90*A*a^2*tan(1/2*d*x + 1/2*c)^9 + 105*B*a^2*tan(1/2*d*x + 1/2*c)^9 + 120*C*a^2*tan(1/2*d*x + 1/2*c)^9 + 420*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 490*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 560*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 864*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 800*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 1120*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 540*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 790*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 1040*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 390*A*a^2*tan(1/2*d*x + 1/2*c) + 375*B*a^2*tan(1/2*d*x + 1/2*c) + 360*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
426,1,350,0,0.325871," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(11 \, A a^{2} + 12 \, B a^{2} + 14 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(165 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 180 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 210 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 935 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1020 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1190 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1986 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2568 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2580 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3006 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2808 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3180 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1305 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1860 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2330 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 795 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 780 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 750 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(11*A*a^2 + 12*B*a^2 + 14*C*a^2)*(d*x + c) + 2*(165*A*a^2*tan(1/2*d*x + 1/2*c)^11 + 180*B*a^2*tan(1/2*d*x + 1/2*c)^11 + 210*C*a^2*tan(1/2*d*x + 1/2*c)^11 + 935*A*a^2*tan(1/2*d*x + 1/2*c)^9 + 1020*B*a^2*tan(1/2*d*x + 1/2*c)^9 + 1190*C*a^2*tan(1/2*d*x + 1/2*c)^9 + 1986*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 2568*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 2580*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 3006*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 2808*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 3180*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 1305*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 1860*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 2330*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 795*A*a^2*tan(1/2*d*x + 1/2*c) + 780*B*a^2*tan(1/2*d*x + 1/2*c) + 750*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
427,1,443,0,0.402266," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(26 \, A a^{3} + 23 \, B a^{3} + 21 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(26 \, A a^{3} + 23 \, B a^{3} + 21 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2730 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2415 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2205 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 18200 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 16100 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 14700 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 51506 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45563 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 41601 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 77952 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72576 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 62592 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 71246 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 62853 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63231 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40040 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 33180 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25620 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10710 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11025 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11235 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{1680 \, d}"," ",0,"1/1680*(105*(26*A*a^3 + 23*B*a^3 + 21*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(26*A*a^3 + 23*B*a^3 + 21*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2730*A*a^3*tan(1/2*d*x + 1/2*c)^13 + 2415*B*a^3*tan(1/2*d*x + 1/2*c)^13 + 2205*C*a^3*tan(1/2*d*x + 1/2*c)^13 - 18200*A*a^3*tan(1/2*d*x + 1/2*c)^11 - 16100*B*a^3*tan(1/2*d*x + 1/2*c)^11 - 14700*C*a^3*tan(1/2*d*x + 1/2*c)^11 + 51506*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 45563*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 41601*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 77952*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 72576*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 62592*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 71246*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 62853*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 63231*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 40040*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 33180*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 25620*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 10710*A*a^3*tan(1/2*d*x + 1/2*c) + 11025*B*a^3*tan(1/2*d*x + 1/2*c) + 11235*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","A",0
428,1,392,0,0.389895," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(30 \, A a^{3} + 26 \, B a^{3} + 23 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(30 \, A a^{3} + 26 \, B a^{3} + 23 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(450 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 390 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 345 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 2550 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2210 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1955 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5940 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5148 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4554 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 7500 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5988 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5814 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5130 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4190 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3165 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1470 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1530 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1575 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(30*A*a^3 + 26*B*a^3 + 23*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(30*A*a^3 + 26*B*a^3 + 23*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(450*A*a^3*tan(1/2*d*x + 1/2*c)^11 + 390*B*a^3*tan(1/2*d*x + 1/2*c)^11 + 345*C*a^3*tan(1/2*d*x + 1/2*c)^11 - 2550*A*a^3*tan(1/2*d*x + 1/2*c)^9 - 2210*B*a^3*tan(1/2*d*x + 1/2*c)^9 - 1955*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 5940*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 5148*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 4554*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 7500*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 5988*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 5814*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 5130*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 4190*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 3165*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 1470*A*a^3*tan(1/2*d*x + 1/2*c) - 1530*B*a^3*tan(1/2*d*x + 1/2*c) - 1575*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
429,1,341,0,0.353588," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(20 \, A a^{3} + 15 \, B a^{3} + 13 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(20 \, A a^{3} + 15 \, B a^{3} + 13 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(300 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 225 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 195 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1400 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1050 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 910 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2560 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1920 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1664 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1830 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1330 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 660 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 735 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 765 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(20*A*a^3 + 15*B*a^3 + 13*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(20*A*a^3 + 15*B*a^3 + 13*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(300*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 225*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 195*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 1400*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 1050*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 910*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 2560*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 1920*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 1664*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 2120*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 1830*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 1330*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 660*A*a^3*tan(1/2*d*x + 1/2*c) + 735*B*a^3*tan(1/2*d*x + 1/2*c) + 765*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
430,1,301,0,0.334712," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{24 \, {\left(d x + c\right)} A a^{3} + 3 \, {\left(28 \, A a^{3} + 20 \, B a^{3} + 15 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(28 \, A a^{3} + 20 \, B a^{3} + 15 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(60 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 45 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 204 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 220 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 165 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 228 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 292 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 219 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 84 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 132 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 147 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*(d*x + c)*A*a^3 + 3*(28*A*a^3 + 20*B*a^3 + 15*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(28*A*a^3 + 20*B*a^3 + 15*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(60*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 45*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 204*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 220*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 165*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 228*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 292*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 219*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 84*A*a^3*tan(1/2*d*x + 1/2*c) - 132*B*a^3*tan(1/2*d*x + 1/2*c) - 147*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
431,1,288,0,0.414213," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{12 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 6 \, {\left(3 \, A a^{3} + B a^{3}\right)} {\left(d x + c\right)} + 3 \, {\left(6 \, A a^{3} + 7 \, B a^{3} + 5 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(6 \, A a^{3} + 7 \, B a^{3} + 5 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*A*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 6*(3*A*a^3 + B*a^3)*(d*x + c) + 3*(6*A*a^3 + 7*B*a^3 + 5*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(6*A*a^3 + 7*B*a^3 + 5*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 12*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*tan(1/2*d*x + 1/2*c) + 21*B*a^3*tan(1/2*d*x + 1/2*c) + 33*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
432,1,280,0,0.336590," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(7 \, A a^{3} + 6 \, B a^{3} + 2 \, C a^{3}\right)} {\left(d x + c\right)} + {\left(2 \, A a^{3} + 6 \, B a^{3} + 7 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, A a^{3} + 6 \, B a^{3} + 7 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(5 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((7*A*a^3 + 6*B*a^3 + 2*C*a^3)*(d*x + c) + (2*A*a^3 + 6*B*a^3 + 7*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*A*a^3 + 6*B*a^3 + 7*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(5*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 5*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 3*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 4*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 9*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 7*A*a^3*tan(1/2*d*x + 1/2*c) + 4*B*a^3*tan(1/2*d*x + 1/2*c) + 7*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","A",0
433,1,281,0,0.345368," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, {\left(5 \, A a^{3} + 7 \, B a^{3} + 6 \, C a^{3}\right)} {\left(d x + c\right)} - 6 \, {\left(B a^{3} + 3 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 6 \, {\left(B a^{3} + 3 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(12*C*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*(5*A*a^3 + 7*B*a^3 + 6*C*a^3)*(d*x + c) - 6*(B*a^3 + 3*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 6*(B*a^3 + 3*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 36*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 33*A*a^3*tan(1/2*d*x + 1/2*c) + 21*B*a^3*tan(1/2*d*x + 1/2*c) + 6*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
434,1,286,0,0.339340," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{24 \, C a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 24 \, C a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(15 \, A a^{3} + 20 \, B a^{3} + 28 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(45 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 220 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 204 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 219 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 292 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 228 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 147 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 132 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 84 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*C*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 24*C*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(15*A*a^3 + 20*B*a^3 + 28*C*a^3)*(d*x + c) + 2*(45*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 165*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 220*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 204*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 219*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 292*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 228*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 147*A*a^3*tan(1/2*d*x + 1/2*c) + 132*B*a^3*tan(1/2*d*x + 1/2*c) + 84*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
435,1,299,0,0.303717," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(13 \, A a^{3} + 15 \, B a^{3} + 20 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(195 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 225 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 300 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 910 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1050 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1400 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1664 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1920 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2560 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1330 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1830 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 765 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 735 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 660 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(13*A*a^3 + 15*B*a^3 + 20*C*a^3)*(d*x + c) + 2*(195*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 225*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 300*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 910*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 1050*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 1400*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 1664*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 1920*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 2560*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 1330*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 1830*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 2120*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 765*A*a^3*tan(1/2*d*x + 1/2*c) + 735*B*a^3*tan(1/2*d*x + 1/2*c) + 660*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
436,1,350,0,0.326545," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(23 \, A a^{3} + 26 \, B a^{3} + 30 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(345 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 390 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1955 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2210 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2550 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4554 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5148 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5940 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5814 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5988 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7500 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4190 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5130 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1575 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1530 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1470 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(23*A*a^3 + 26*B*a^3 + 30*C*a^3)*(d*x + c) + 2*(345*A*a^3*tan(1/2*d*x + 1/2*c)^11 + 390*B*a^3*tan(1/2*d*x + 1/2*c)^11 + 450*C*a^3*tan(1/2*d*x + 1/2*c)^11 + 1955*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 2210*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 2550*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 4554*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 5148*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 5940*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 5814*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 5988*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 7500*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 3165*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 4190*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 5130*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 1575*A*a^3*tan(1/2*d*x + 1/2*c) + 1530*B*a^3*tan(1/2*d*x + 1/2*c) + 1470*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
437,1,401,0,0.337800," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(21 \, A a^{3} + 23 \, B a^{3} + 26 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(2205 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2415 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2730 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 14700 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 16100 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 18200 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 41601 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45563 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 51506 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 62592 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72576 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 77952 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 63231 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 62853 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 71246 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25620 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33180 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40040 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11235 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11025 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10710 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7}}}{1680 \, d}"," ",0,"1/1680*(105*(21*A*a^3 + 23*B*a^3 + 26*C*a^3)*(d*x + c) + 2*(2205*A*a^3*tan(1/2*d*x + 1/2*c)^13 + 2415*B*a^3*tan(1/2*d*x + 1/2*c)^13 + 2730*C*a^3*tan(1/2*d*x + 1/2*c)^13 + 14700*A*a^3*tan(1/2*d*x + 1/2*c)^11 + 16100*B*a^3*tan(1/2*d*x + 1/2*c)^11 + 18200*C*a^3*tan(1/2*d*x + 1/2*c)^11 + 41601*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 45563*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 51506*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 62592*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 72576*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 77952*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 63231*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 62853*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 71246*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 25620*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 33180*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 40040*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 11235*A*a^3*tan(1/2*d*x + 1/2*c) + 11025*B*a^3*tan(1/2*d*x + 1/2*c) + 10710*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^7)/d","A",0
438,1,443,0,0.403840," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(56 \, A a^{4} + 49 \, B a^{4} + 44 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(56 \, A a^{4} + 49 \, B a^{4} + 44 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(5880 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5145 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 4620 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 39200 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 34300 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 30800 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 110936 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 97069 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 87164 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 172032 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 150528 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 135168 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 159656 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 134099 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 126084 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 86240 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 73220 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 58800 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21000 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21735 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 22260 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{1680 \, d}"," ",0,"1/1680*(105*(56*A*a^4 + 49*B*a^4 + 44*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(56*A*a^4 + 49*B*a^4 + 44*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(5880*A*a^4*tan(1/2*d*x + 1/2*c)^13 + 5145*B*a^4*tan(1/2*d*x + 1/2*c)^13 + 4620*C*a^4*tan(1/2*d*x + 1/2*c)^13 - 39200*A*a^4*tan(1/2*d*x + 1/2*c)^11 - 34300*B*a^4*tan(1/2*d*x + 1/2*c)^11 - 30800*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 110936*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 97069*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 87164*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 172032*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 150528*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 135168*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 159656*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 134099*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 126084*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 86240*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 73220*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 58800*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 21000*A*a^4*tan(1/2*d*x + 1/2*c) + 21735*B*a^4*tan(1/2*d*x + 1/2*c) + 22260*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","A",0
439,1,392,0,0.424462," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(10 \, A a^{4} + 8 \, B a^{4} + 7 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(10 \, A a^{4} + 8 \, B a^{4} + 7 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(1050 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 840 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 735 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 5950 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4760 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4165 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 13860 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 11088 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9702 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16860 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 13488 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 11802 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10690 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9320 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7355 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2790 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3000 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3105 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(105*(10*A*a^4 + 8*B*a^4 + 7*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(10*A*a^4 + 8*B*a^4 + 7*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(1050*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 840*B*a^4*tan(1/2*d*x + 1/2*c)^11 + 735*C*a^4*tan(1/2*d*x + 1/2*c)^11 - 5950*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 4760*B*a^4*tan(1/2*d*x + 1/2*c)^9 - 4165*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 13860*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 11088*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 9702*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 16860*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 13488*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 11802*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 10690*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 9320*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 7355*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 2790*A*a^4*tan(1/2*d*x + 1/2*c) - 3000*B*a^4*tan(1/2*d*x + 1/2*c) - 3105*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
440,1,352,0,0.369972," ","integrate((a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{120 \, {\left(d x + c\right)} A a^{4} + 15 \, {\left(48 \, A a^{4} + 35 \, B a^{4} + 28 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(48 \, A a^{4} + 35 \, B a^{4} + 28 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(600 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 525 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 420 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2720 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2450 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1960 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4720 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4480 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3584 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3680 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3950 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3160 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1080 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1395 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1500 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(120*(d*x + c)*A*a^4 + 15*(48*A*a^4 + 35*B*a^4 + 28*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(48*A*a^4 + 35*B*a^4 + 28*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(600*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 525*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 420*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 2720*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 2450*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 1960*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 4720*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 4480*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 3584*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 3680*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 3950*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 3160*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 1080*A*a^4*tan(1/2*d*x + 1/2*c) + 1395*B*a^4*tan(1/2*d*x + 1/2*c) + 1500*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
441,1,339,0,0.430563," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{48 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 24 \, {\left(4 \, A a^{4} + B a^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(52 \, A a^{4} + 48 \, B a^{4} + 35 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(52 \, A a^{4} + 48 \, B a^{4} + 35 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(84 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 276 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 424 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 385 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 300 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 520 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 511 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 108 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 216 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 279 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(48*A*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 24*(4*A*a^4 + B*a^4)*(d*x + c) + 3*(52*A*a^4 + 48*B*a^4 + 35*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(52*A*a^4 + 48*B*a^4 + 35*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(84*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 120*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 105*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 276*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 424*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 385*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 300*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 520*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 511*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 108*A*a^4*tan(1/2*d*x + 1/2*c) - 216*B*a^4*tan(1/2*d*x + 1/2*c) - 279*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
442,1,347,0,0.397312," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(13 \, A a^{4} + 8 \, B a^{4} + 2 \, C a^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(8 \, A a^{4} + 13 \, B a^{4} + 12 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, A a^{4} + 13 \, B a^{4} + 12 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{6 \, {\left(7 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{2 \, {\left(6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 76 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 54 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(13*A*a^4 + 8*B*a^4 + 2*C*a^4)*(d*x + c) + 3*(8*A*a^4 + 13*B*a^4 + 12*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*A*a^4 + 13*B*a^4 + 12*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 6*(7*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*A*a^4*tan(1/2*d*x + 1/2*c) + 2*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - 2*(6*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 21*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 30*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 12*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 48*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 76*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^4*tan(1/2*d*x + 1/2*c) + 27*B*a^4*tan(1/2*d*x + 1/2*c) + 54*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
443,1,347,0,0.366534," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(12 \, A a^{4} + 13 \, B a^{4} + 8 \, C a^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(2 \, A a^{4} + 8 \, B a^{4} + 13 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, A a^{4} + 8 \, B a^{4} + 13 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{6 \, {\left(2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{2 \, {\left(30 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 76 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 54 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(12*A*a^4 + 13*B*a^4 + 8*C*a^4)*(d*x + c) + 3*(2*A*a^4 + 8*B*a^4 + 13*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*A*a^4 + 8*B*a^4 + 13*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 6*(2*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 7*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^4*tan(1/2*d*x + 1/2*c) - 9*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + 2*(30*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 21*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 76*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 48*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 54*A*a^4*tan(1/2*d*x + 1/2*c) + 27*B*a^4*tan(1/2*d*x + 1/2*c) + 6*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
444,1,332,0,0.340230," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{48 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, {\left(35 \, A a^{4} + 48 \, B a^{4} + 52 \, C a^{4}\right)} {\left(d x + c\right)} - 24 \, {\left(B a^{4} + 4 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 24 \, {\left(B a^{4} + 4 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 84 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 385 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 424 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 276 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 511 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 520 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 300 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 279 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 216 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 108 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"-1/24*(48*C*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*(35*A*a^4 + 48*B*a^4 + 52*C*a^4)*(d*x + c) - 24*(B*a^4 + 4*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 24*(B*a^4 + 4*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(105*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 120*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 84*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 385*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 424*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 276*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 511*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 520*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 300*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 279*A*a^4*tan(1/2*d*x + 1/2*c) + 216*B*a^4*tan(1/2*d*x + 1/2*c) + 108*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
445,1,337,0,0.354254," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{120 \, C a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 120 \, C a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 15 \, {\left(28 \, A a^{4} + 35 \, B a^{4} + 48 \, C a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(420 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 525 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 600 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1960 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2450 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2720 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3584 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4480 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4720 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3160 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3950 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3680 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1500 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1395 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1080 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(120*C*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 120*C*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 15*(28*A*a^4 + 35*B*a^4 + 48*C*a^4)*(d*x + c) + 2*(420*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 525*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 600*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 1960*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 2450*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 2720*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 3584*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 4480*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 4720*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 3160*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 3950*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 3680*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 1500*A*a^4*tan(1/2*d*x + 1/2*c) + 1395*B*a^4*tan(1/2*d*x + 1/2*c) + 1080*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
446,1,350,0,0.343683," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(7 \, A a^{4} + 8 \, B a^{4} + 10 \, C a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(735 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 840 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1050 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 4165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4760 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5950 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 9702 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 11088 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 13860 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 11802 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 13488 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16860 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7355 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9320 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10690 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3000 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2790 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(105*(7*A*a^4 + 8*B*a^4 + 10*C*a^4)*(d*x + c) + 2*(735*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 840*B*a^4*tan(1/2*d*x + 1/2*c)^11 + 1050*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 4165*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 4760*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 5950*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 9702*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 11088*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 13860*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 11802*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 13488*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 16860*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 7355*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 9320*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 10690*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 3105*A*a^4*tan(1/2*d*x + 1/2*c) + 3000*B*a^4*tan(1/2*d*x + 1/2*c) + 2790*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
447,1,401,0,0.354726," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(44 \, A a^{4} + 49 \, B a^{4} + 56 \, C a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(4620 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5145 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5880 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 30800 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 34300 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 39200 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 87164 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 97069 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 110936 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 135168 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 150528 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 172032 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 126084 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 134099 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 159656 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 58800 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 73220 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 86240 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 22260 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21735 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21000 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7}}}{1680 \, d}"," ",0,"1/1680*(105*(44*A*a^4 + 49*B*a^4 + 56*C*a^4)*(d*x + c) + 2*(4620*A*a^4*tan(1/2*d*x + 1/2*c)^13 + 5145*B*a^4*tan(1/2*d*x + 1/2*c)^13 + 5880*C*a^4*tan(1/2*d*x + 1/2*c)^13 + 30800*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 34300*B*a^4*tan(1/2*d*x + 1/2*c)^11 + 39200*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 87164*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 97069*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 110936*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 135168*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 150528*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 172032*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 126084*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 134099*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 159656*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 58800*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 73220*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 86240*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 22260*A*a^4*tan(1/2*d*x + 1/2*c) + 21735*B*a^4*tan(1/2*d*x + 1/2*c) + 21000*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^7)/d","A",0
448,1,452,0,0.358171," ","integrate(cos(d*x+c)^8*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(323 \, A a^{4} + 352 \, B a^{4} + 392 \, C a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(33915 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 36960 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 41160 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 260015 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 283360 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 315560 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 865963 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 943712 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1050952 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1632119 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1778656 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1980776 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1872009 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2090016 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2277016 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1442133 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1479072 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1658552 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 528465 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 648480 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 759640 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 181125 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 178080 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 173880 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{8}}}{13440 \, d}"," ",0,"1/13440*(105*(323*A*a^4 + 352*B*a^4 + 392*C*a^4)*(d*x + c) + 2*(33915*A*a^4*tan(1/2*d*x + 1/2*c)^15 + 36960*B*a^4*tan(1/2*d*x + 1/2*c)^15 + 41160*C*a^4*tan(1/2*d*x + 1/2*c)^15 + 260015*A*a^4*tan(1/2*d*x + 1/2*c)^13 + 283360*B*a^4*tan(1/2*d*x + 1/2*c)^13 + 315560*C*a^4*tan(1/2*d*x + 1/2*c)^13 + 865963*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 943712*B*a^4*tan(1/2*d*x + 1/2*c)^11 + 1050952*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 1632119*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 1778656*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 1980776*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 1872009*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 2090016*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 2277016*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 1442133*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 1479072*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 1658552*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 528465*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 648480*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 759640*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 181125*A*a^4*tan(1/2*d*x + 1/2*c) + 178080*B*a^4*tan(1/2*d*x + 1/2*c) + 173880*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^8)/d","A",0
449,1,285,0,0.275738," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{9 \, {\left(4 \, A - 4 \, B + 5 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{9 \, {\left(4 \, A - 4 \, B + 5 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{24 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(36 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 75 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 84 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 124 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 115 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 100 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 109 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4} a}}{24 \, d}"," ",0,"1/24*(9*(4*A - 4*B + 5*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - 9*(4*A - 4*B + 5*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 24*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a + 2*(36*A*tan(1/2*d*x + 1/2*c)^7 - 60*B*tan(1/2*d*x + 1/2*c)^7 + 75*C*tan(1/2*d*x + 1/2*c)^7 - 84*A*tan(1/2*d*x + 1/2*c)^5 + 124*B*tan(1/2*d*x + 1/2*c)^5 - 115*C*tan(1/2*d*x + 1/2*c)^5 + 60*A*tan(1/2*d*x + 1/2*c)^3 - 100*B*tan(1/2*d*x + 1/2*c)^3 + 109*C*tan(1/2*d*x + 1/2*c)^3 - 12*A*tan(1/2*d*x + 1/2*c) + 36*B*tan(1/2*d*x + 1/2*c) - 21*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^4*a))/d","A",0
450,1,243,0,0.296597," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, A - 3 \, B + 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{3 \, {\left(2 \, A - 3 \, B + 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{6 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a}}{6 \, d}"," ",0,"-1/6*(3*(2*A - 3*B + 3*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - 3*(2*A - 3*B + 3*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 6*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a + 2*(6*A*tan(1/2*d*x + 1/2*c)^5 - 9*B*tan(1/2*d*x + 1/2*c)^5 + 15*C*tan(1/2*d*x + 1/2*c)^5 - 12*A*tan(1/2*d*x + 1/2*c)^3 + 12*B*tan(1/2*d*x + 1/2*c)^3 - 16*C*tan(1/2*d*x + 1/2*c)^3 + 6*A*tan(1/2*d*x + 1/2*c) - 3*B*tan(1/2*d*x + 1/2*c) + 9*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a))/d","A",0
451,1,173,0,0.244215," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, A - 2 \, B + 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{{\left(2 \, A - 2 \, B + 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{2 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a}}{2 \, d}"," ",0,"1/2*((2*A - 2*B + 3*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - (2*A - 2*B + 3*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 2*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*(2*B*tan(1/2*d*x + 1/2*c)^3 - 3*C*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a))/d","A",0
452,1,119,0,0.264869," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(B - C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{{\left(B - C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} + \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a}}{d}"," ",0,"((B - C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - (B - C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a + (A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a))/d","A",0
453,1,92,0,0.236917," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} A}{a} + \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"((d*x + c)*A/a + C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - (A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a)/d","A",0
454,1,90,0,0.202583," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(d x + c\right)} {\left(A - B\right)}}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a}}{d}"," ",0,"-((d*x + c)*(A - B)/a - (A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a))/d","A",0
455,1,137,0,0.201869," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} {\left(3 \, A - 2 \, B + 2 \, C\right)}}{a} - \frac{2 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a}}{2 \, d}"," ",0,"1/2*((d*x + c)*(3*A - 2*B + 2*C)/a - 2*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*(3*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 + A*tan(1/2*d*x + 1/2*c) - 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a))/d","A",0
456,1,207,0,0.225333," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)} {\left(3 \, A - 3 \, B + 2 \, C\right)}}{a} - \frac{6 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a}}{6 \, d}"," ",0,"-1/6*(3*(d*x + c)*(3*A - 3*B + 2*C)/a - 6*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*(15*A*tan(1/2*d*x + 1/2*c)^5 - 9*B*tan(1/2*d*x + 1/2*c)^5 + 6*C*tan(1/2*d*x + 1/2*c)^5 + 16*A*tan(1/2*d*x + 1/2*c)^3 - 12*B*tan(1/2*d*x + 1/2*c)^3 + 12*C*tan(1/2*d*x + 1/2*c)^3 + 9*A*tan(1/2*d*x + 1/2*c) - 3*B*tan(1/2*d*x + 1/2*c) + 6*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a))/d","A",0
457,1,249,0,0.222381," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{9 \, {\left(d x + c\right)} {\left(5 \, A - 4 \, B + 4 \, C\right)}}{a} - \frac{24 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(75 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 115 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 124 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 84 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 109 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 100 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a}}{24 \, d}"," ",0,"1/24*(9*(d*x + c)*(5*A - 4*B + 4*C)/a - 24*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*(75*A*tan(1/2*d*x + 1/2*c)^7 - 60*B*tan(1/2*d*x + 1/2*c)^7 + 36*C*tan(1/2*d*x + 1/2*c)^7 + 115*A*tan(1/2*d*x + 1/2*c)^5 - 124*B*tan(1/2*d*x + 1/2*c)^5 + 84*C*tan(1/2*d*x + 1/2*c)^5 + 109*A*tan(1/2*d*x + 1/2*c)^3 - 100*B*tan(1/2*d*x + 1/2*c)^3 + 60*C*tan(1/2*d*x + 1/2*c)^3 + 21*A*tan(1/2*d*x + 1/2*c) - 36*B*tan(1/2*d*x + 1/2*c) + 12*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a))/d","A",0
458,1,303,0,0.306179," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(4 \, A - 7 \, B + 10 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{3 \, {\left(4 \, A - 7 \, B + 10 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{2 \, {\left(6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(3*(4*A - 7*B + 10*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 3*(4*A - 7*B + 10*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 2*(6*A*tan(1/2*d*x + 1/2*c)^5 - 15*B*tan(1/2*d*x + 1/2*c)^5 + 30*C*tan(1/2*d*x + 1/2*c)^5 - 12*A*tan(1/2*d*x + 1/2*c)^3 + 24*B*tan(1/2*d*x + 1/2*c)^3 - 40*C*tan(1/2*d*x + 1/2*c)^3 + 6*A*tan(1/2*d*x + 1/2*c) - 9*B*tan(1/2*d*x + 1/2*c) + 18*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^4*tan(1/2*d*x + 1/2*c) - 21*B*a^4*tan(1/2*d*x + 1/2*c) + 27*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
459,1,235,0,0.302355," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, A - 4 \, B + 7 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{3 \, {\left(2 \, A - 4 \, B + 7 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{6 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(2*A - 4*B + 7*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 3*(2*A - 4*B + 7*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - 6*(2*B*tan(1/2*d*x + 1/2*c)^3 - 5*C*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c) + 3*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*A*a^4*tan(1/2*d*x + 1/2*c) - 15*B*a^4*tan(1/2*d*x + 1/2*c) + 21*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
460,1,181,0,0.276470," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(B - 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, {\left(B - 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(B - 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*(B - 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - 12*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*tan(1/2*d*x + 1/2*c) - 9*B*a^4*tan(1/2*d*x + 1/2*c) + 15*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
461,1,144,0,0.269952," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 3*A*a^4*tan(1/2*d*x + 1/2*c) - 3*B*a^4*tan(1/2*d*x + 1/2*c) + 9*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
462,1,116,0,0.201331," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)} A}{a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*A/a^2 + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 9*A*a^4*tan(1/2*d*x + 1/2*c) + 3*B*a^4*tan(1/2*d*x + 1/2*c) + 3*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
463,1,152,0,0.233200," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(d x + c\right)} {\left(2 \, A - B\right)}}{a^{2}} - \frac{12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c)*(2*A - B)/a^2 - 12*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^4*tan(1/2*d*x + 1/2*c) + 9*B*a^4*tan(1/2*d*x + 1/2*c) - 3*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
464,1,198,0,0.241094," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)} {\left(7 \, A - 4 \, B + 2 \, C\right)}}{a^{2}} - \frac{6 \, {\left(5 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)*(7*A - 4*B + 2*C)/a^2 - 6*(5*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 + 3*A*tan(1/2*d*x + 1/2*c) - 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 21*A*a^4*tan(1/2*d*x + 1/2*c) + 15*B*a^4*tan(1/2*d*x + 1/2*c) - 9*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
465,1,266,0,0.249230," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)} {\left(10 \, A - 7 \, B + 4 \, C\right)}}{a^{2}} - \frac{2 \, {\left(30 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 27 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(3*(d*x + c)*(10*A - 7*B + 4*C)/a^2 - 2*(30*A*tan(1/2*d*x + 1/2*c)^5 - 15*B*tan(1/2*d*x + 1/2*c)^5 + 6*C*tan(1/2*d*x + 1/2*c)^5 + 40*A*tan(1/2*d*x + 1/2*c)^3 - 24*B*tan(1/2*d*x + 1/2*c)^3 + 12*C*tan(1/2*d*x + 1/2*c)^3 + 18*A*tan(1/2*d*x + 1/2*c) - 9*B*tan(1/2*d*x + 1/2*c) + 6*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 27*A*a^4*tan(1/2*d*x + 1/2*c) + 21*B*a^4*tan(1/2*d*x + 1/2*c) - 15*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
466,1,288,0,0.341189," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{30 \, {\left(2 \, A - 6 \, B + 13 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{30 \, {\left(2 \, A - 6 \, B + 13 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{60 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 255 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 465 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(30*(2*A - 6*B + 13*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 30*(2*A - 6*B + 13*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - 60*(2*B*tan(1/2*d*x + 1/2*c)^3 - 7*C*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c) + 5*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 20*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 30*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 40*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^12*tan(1/2*d*x + 1/2*c) - 255*B*a^12*tan(1/2*d*x + 1/2*c) + 465*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
467,1,234,0,0.331545," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(B - 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, {\left(B - 3 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{120 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{3}} + \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 255 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(B - 3*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*(B - 3*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - 120*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^3) + (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 10*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 20*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 30*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^12*tan(1/2*d*x + 1/2*c) - 105*B*a^12*tan(1/2*d*x + 1/2*c) + 255*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
468,1,180,0,0.356130," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 10*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 20*C*a^12*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^12*tan(1/2*d*x + 1/2*c) - 15*B*a^12*tan(1/2*d*x + 1/2*c) + 105*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
469,1,115,0,0.286235," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, a^{3} d}"," ",0,"1/60*(3*A*tan(1/2*d*x + 1/2*c)^5 - 3*B*tan(1/2*d*x + 1/2*c)^5 + 3*C*tan(1/2*d*x + 1/2*c)^5 - 10*A*tan(1/2*d*x + 1/2*c)^3 + 10*C*tan(1/2*d*x + 1/2*c)^3 + 15*A*tan(1/2*d*x + 1/2*c) + 15*B*tan(1/2*d*x + 1/2*c) + 15*C*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
470,1,153,0,0.261644," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(d x + c\right)} A}{a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 20 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*A/a^3 - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 20*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 10*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^12*tan(1/2*d*x + 1/2*c) - 15*B*a^12*tan(1/2*d*x + 1/2*c) - 15*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
471,1,206,0,0.262281," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(d x + c\right)} {\left(3 \, A - B\right)}}{a^{3}} - \frac{120 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(60*(d*x + c)*(3*A - B)/a^3 - 120*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 30*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 20*B*a^12*tan(1/2*d*x + 1/2*c)^3 - 10*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 255*A*a^12*tan(1/2*d*x + 1/2*c) - 105*B*a^12*tan(1/2*d*x + 1/2*c) + 15*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
472,1,252,0,0.288444," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{30 \, {\left(d x + c\right)} {\left(13 \, A - 6 \, B + 2 \, C\right)}}{a^{3}} - \frac{60 \, {\left(7 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 465 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 255 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(30*(d*x + c)*(13*A - 6*B + 2*C)/a^3 - 60*(7*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 + 5*A*tan(1/2*d*x + 1/2*c) - 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 40*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 30*B*a^12*tan(1/2*d*x + 1/2*c)^3 - 20*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 465*A*a^12*tan(1/2*d*x + 1/2*c) - 255*B*a^12*tan(1/2*d*x + 1/2*c) + 105*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
473,1,320,0,0.289534," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(d x + c\right)} {\left(23 \, A - 13 \, B + 6 \, C\right)}}{a^{3}} - \frac{20 \, {\left(51 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 76 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 50 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 735 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 465 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 255 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(30*(d*x + c)*(23*A - 13*B + 6*C)/a^3 - 20*(51*A*tan(1/2*d*x + 1/2*c)^5 - 21*B*tan(1/2*d*x + 1/2*c)^5 + 6*C*tan(1/2*d*x + 1/2*c)^5 + 76*A*tan(1/2*d*x + 1/2*c)^3 - 36*B*tan(1/2*d*x + 1/2*c)^3 + 12*C*tan(1/2*d*x + 1/2*c)^3 + 33*A*tan(1/2*d*x + 1/2*c) - 15*B*tan(1/2*d*x + 1/2*c) + 6*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 50*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 40*B*a^12*tan(1/2*d*x + 1/2*c)^3 - 30*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 735*A*a^12*tan(1/2*d*x + 1/2*c) - 465*B*a^12*tan(1/2*d*x + 1/2*c) + 255*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
474,1,339,0,0.363189," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{420 \, {\left(2 \, A - 8 \, B + 21 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{420 \, {\left(2 \, A - 8 \, B + 21 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{840 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 147 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 189 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 805 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1365 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1575 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5145 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11655 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(420*(2*A - 8*B + 21*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 420*(2*A - 8*B + 21*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - 840*(2*B*tan(1/2*d*x + 1/2*c)^3 - 9*C*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c) + 7*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 105*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 147*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 189*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 385*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 805*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 1365*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 1575*A*a^24*tan(1/2*d*x + 1/2*c) - 5145*B*a^24*tan(1/2*d*x + 1/2*c) + 11655*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
475,1,285,0,0.325553," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, {\left(B - 4 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{840 \, {\left(B - 4 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{1680 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 63 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 147 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 385 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 805 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1575 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5145 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*(B - 4*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 840*(B - 4*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - 1680*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 63*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 105*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 147*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 385*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 805*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^24*tan(1/2*d*x + 1/2*c) - 1575*B*a^24*tan(1/2*d*x + 1/2*c) + 5145*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
476,1,248,0,0.337701," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{840 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 63 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 385 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1575 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 840*C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 21*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 63*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*C*a^24*tan(1/2*d*x + 1/2*c)^5 - 35*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 105*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 385*C*a^24*tan(1/2*d*x + 1/2*c)^3 - 105*A*a^24*tan(1/2*d*x + 1/2*c) - 105*B*a^24*tan(1/2*d*x + 1/2*c) + 1575*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
477,1,171,0,0.279415," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 21 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 - 15*B*tan(1/2*d*x + 1/2*c)^7 + 15*C*tan(1/2*d*x + 1/2*c)^7 - 21*A*tan(1/2*d*x + 1/2*c)^5 - 21*B*tan(1/2*d*x + 1/2*c)^5 + 63*C*tan(1/2*d*x + 1/2*c)^5 - 35*A*tan(1/2*d*x + 1/2*c)^3 + 35*B*tan(1/2*d*x + 1/2*c)^3 + 105*C*tan(1/2*d*x + 1/2*c)^3 + 105*A*tan(1/2*d*x + 1/2*c) + 105*B*tan(1/2*d*x + 1/2*c) + 105*C*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
478,1,171,0,0.296344," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 63 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"-1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 - 15*B*tan(1/2*d*x + 1/2*c)^7 + 15*C*tan(1/2*d*x + 1/2*c)^7 - 63*A*tan(1/2*d*x + 1/2*c)^5 + 21*B*tan(1/2*d*x + 1/2*c)^5 + 21*C*tan(1/2*d*x + 1/2*c)^5 + 105*A*tan(1/2*d*x + 1/2*c)^3 + 35*B*tan(1/2*d*x + 1/2*c)^3 - 35*C*tan(1/2*d*x + 1/2*c)^3 - 105*A*tan(1/2*d*x + 1/2*c) - 105*B*tan(1/2*d*x + 1/2*c) - 105*C*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
479,1,220,0,0.260025," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, {\left(d x + c\right)} A}{a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1575 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*(d*x + c)*A/a^4 + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 - 105*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 63*B*a^24*tan(1/2*d*x + 1/2*c)^5 - 21*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 385*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 105*B*a^24*tan(1/2*d*x + 1/2*c)^3 - 35*C*a^24*tan(1/2*d*x + 1/2*c)^3 - 1575*A*a^24*tan(1/2*d*x + 1/2*c) + 105*B*a^24*tan(1/2*d*x + 1/2*c) + 105*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
480,1,256,0,0.279570," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{840 \, {\left(d x + c\right)} {\left(4 \, A - B\right)}}{a^{4}} - \frac{1680 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 147 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 63 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 805 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 385 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5145 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1575 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(840*(d*x + c)*(4*A - B)/a^4 - 1680*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 - 147*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*B*a^24*tan(1/2*d*x + 1/2*c)^5 - 63*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 805*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 385*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 105*C*a^24*tan(1/2*d*x + 1/2*c)^3 - 5145*A*a^24*tan(1/2*d*x + 1/2*c) + 1575*B*a^24*tan(1/2*d*x + 1/2*c) - 105*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
481,1,302,0,0.302227," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{420 \, {\left(d x + c\right)} {\left(21 \, A - 8 \, B + 2 \, C\right)}}{a^{4}} - \frac{840 \, {\left(9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 189 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 147 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1365 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 805 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 385 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 11655 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5145 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1575 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(420*(d*x + c)*(21*A - 8*B + 2*C)/a^4 - 840*(9*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 + 7*A*tan(1/2*d*x + 1/2*c) - 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 - 189*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 147*B*a^24*tan(1/2*d*x + 1/2*c)^5 - 105*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 1365*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 805*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 385*C*a^24*tan(1/2*d*x + 1/2*c)^3 - 11655*A*a^24*tan(1/2*d*x + 1/2*c) + 5145*B*a^24*tan(1/2*d*x + 1/2*c) - 1575*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
482,1,410,0,1.617033," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(3465 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3465 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3465 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(10395 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8085 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5775 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(15246 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 14322 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 16170 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(14058 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13266 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8910 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(6633 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4741 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5885 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(891 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1177 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 755 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{3465 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"-2/3465*(3465*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 3465*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 3465*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (10395*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 8085*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 5775*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (15246*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 14322*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 16170*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (14058*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 13266*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 8910*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (6633*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 4741*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 5885*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (891*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 1177*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 755*sqrt(2)*C*a^6*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
483,1,323,0,1.464473," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left({\left(\sqrt{2} {\left(147 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 81 \, B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 107 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 18 \, \sqrt{2} {\left(28 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 29 \, B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 18 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 126 \, \sqrt{2} {\left(7 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6 \, B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 210 \, \sqrt{2} {\left(4 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 315 \, \sqrt{2} {\left(A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"2/315*((((sqrt(2)*(147*A*a^5*sgn(cos(d*x + c)) + 81*B*a^5*sgn(cos(d*x + c)) + 107*C*a^5*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 18*sqrt(2)*(28*A*a^5*sgn(cos(d*x + c)) + 29*B*a^5*sgn(cos(d*x + c)) + 18*C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 126*sqrt(2)*(7*A*a^5*sgn(cos(d*x + c)) + 6*B*a^5*sgn(cos(d*x + c)) + 7*C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 210*sqrt(2)*(4*A*a^5*sgn(cos(d*x + c)) + 3*B*a^5*sgn(cos(d*x + c)) + 2*C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 315*sqrt(2)*(A*a^5*sgn(cos(d*x + c)) + B*a^5*sgn(cos(d*x + c)) + C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
484,1,286,0,1.393482," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(105 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 105 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 105 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(245 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 175 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 105 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(175 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 119 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 147 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(35 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 49 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 27 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{105 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"-2/105*(105*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 105*sqrt(2)*B*a^4*sgn(cos(d*x + c)) + 105*sqrt(2)*C*a^4*sgn(cos(d*x + c)) - (245*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 175*sqrt(2)*B*a^4*sgn(cos(d*x + c)) + 105*sqrt(2)*C*a^4*sgn(cos(d*x + c)) - (175*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 119*sqrt(2)*B*a^4*sgn(cos(d*x + c)) + 147*sqrt(2)*C*a^4*sgn(cos(d*x + c)) - (35*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 49*sqrt(2)*B*a^4*sgn(cos(d*x + c)) + 27*sqrt(2)*C*a^4*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","B",0
485,1,206,0,1.264532," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(\sqrt{2} {\left(15 \, A a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5 \, B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7 \, C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, \sqrt{2} {\left(3 \, A a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, \sqrt{2} {\left(A a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{15 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"2/15*((sqrt(2)*(15*A*a^3*sgn(cos(d*x + c)) + 5*B*a^3*sgn(cos(d*x + c)) + 7*C*a^3*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 10*sqrt(2)*(3*A*a^3*sgn(cos(d*x + c)) + 2*B*a^3*sgn(cos(d*x + c)) + C*a^3*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 15*sqrt(2)*(A*a^3*sgn(cos(d*x + c)) + B*a^3*sgn(cos(d*x + c)) + C*a^3*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","B",0
486,1,260,0,1.443672," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{3 \, A \sqrt{-a} a \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} + \frac{2 \, {\left(3 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(3 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + \sqrt{2} C a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{3 \, d}"," ",0,"-1/3*(3*A*sqrt(-a)*a*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) + 2*(3*sqrt(2)*B*a^2*sgn(cos(d*x + c)) + 3*sqrt(2)*C*a^2*sgn(cos(d*x + c)) - (3*sqrt(2)*B*a^2*sgn(cos(d*x + c)) + sqrt(2)*C*a^2*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
487,1,396,0,1.580410," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{4 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} C a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + {\left(A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(3 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \sqrt{2} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}}}{2 \, d}"," ",0,"-1/2*(4*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*C*a*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + (A*sqrt(-a)*sgn(cos(d*x + c)) + 2*B*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (A*sqrt(-a)*sgn(cos(d*x + c)) + 2*B*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(3*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a*sgn(cos(d*x + c)) - sqrt(2)*A*sqrt(-a)*a^2*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2))/d","B",0
488,1,660,0,1.695511," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{{\left(3 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(3 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) - \frac{4 \, \sqrt{2} {\left(5 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 17 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((3*A*sqrt(-a)*sgn(cos(d*x + c)) + 4*B*sqrt(-a)*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (3*A*sqrt(-a)*sgn(cos(d*x + c)) + 4*B*sqrt(-a)*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) - 4*sqrt(2)*(5*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a*sgn(cos(d*x + c)) - 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 19*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 17*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 4*B*sqrt(-a)*a^4*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2)/d","B",0
489,1,1233,0,2.018622," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{3 \, {\left(5 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(5 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(63 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 30 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 72 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 369 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 66 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 888 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1638 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 756 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3024 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1074 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 732 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1776 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 171 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 138 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 360 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 13 \, \sqrt{2} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6 \, \sqrt{2} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 24 \, \sqrt{2} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(3*(5*A*sqrt(-a)*sgn(cos(d*x + c)) + 6*B*sqrt(-a)*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(5*A*sqrt(-a)*sgn(cos(d*x + c)) + 6*B*sqrt(-a)*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(63*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a*sgn(cos(d*x + c)) - 30*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 72*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a*sgn(cos(d*x + c)) - 369*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 66*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 888*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 1638*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 756*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 3024*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 1074*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 732*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 1776*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 171*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 138*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 360*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 13*sqrt(2)*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 6*sqrt(2)*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 24*sqrt(2)*C*sqrt(-a)*a^6*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3)/d","B",0
490,1,1518,0,2.143461," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{3 \, {\left(35 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 40 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 48 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(35 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 40 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 48 \, C \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) - \frac{4 \, \sqrt{2} {\left(279 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 504 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 240 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 285 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5976 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1968 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4605 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 31320 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2640 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 37281 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 90168 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 41616 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 35643 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 66024 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 42288 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9175 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 16904 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12528 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1311 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1992 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1392 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 43 \, A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 104 \, B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 48 \, C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(3*(35*A*sqrt(-a)*sgn(cos(d*x + c)) + 40*B*sqrt(-a)*sgn(cos(d*x + c)) + 48*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(35*A*sqrt(-a)*sgn(cos(d*x + c)) + 40*B*sqrt(-a)*sgn(cos(d*x + c)) + 48*C*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) - 4*sqrt(2)*(279*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a*sgn(cos(d*x + c)) - 504*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 240*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a*sgn(cos(d*x + c)) + 285*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 5976*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 1968*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 4605*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 31320*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 2640*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 37281*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 90168*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 41616*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 35643*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 66024*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 42288*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 9175*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 16904*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 12528*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 1311*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 1992*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 1392*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 43*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 104*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 48*C*sqrt(-a)*a^8*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^4)/d","B",0
491,1,410,0,2.278496," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{4 \, {\left(3465 \, \sqrt{2} A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3465 \, \sqrt{2} B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3465 \, \sqrt{2} C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(11550 \, \sqrt{2} A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9240 \, \sqrt{2} B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6930 \, \sqrt{2} C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(17094 \, \sqrt{2} A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 14784 \, \sqrt{2} B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 15246 \, \sqrt{2} C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(14652 \, \sqrt{2} A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13662 \, \sqrt{2} B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 11088 \, \sqrt{2} C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(6897 \, \sqrt{2} A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5687 \, \sqrt{2} B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5313 \, \sqrt{2} C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2 \, {\left(627 \, \sqrt{2} A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 517 \, \sqrt{2} B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 483 \, \sqrt{2} C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{3465 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"-4/3465*(3465*sqrt(2)*A*a^7*sgn(cos(d*x + c)) + 3465*sqrt(2)*B*a^7*sgn(cos(d*x + c)) + 3465*sqrt(2)*C*a^7*sgn(cos(d*x + c)) - (11550*sqrt(2)*A*a^7*sgn(cos(d*x + c)) + 9240*sqrt(2)*B*a^7*sgn(cos(d*x + c)) + 6930*sqrt(2)*C*a^7*sgn(cos(d*x + c)) - (17094*sqrt(2)*A*a^7*sgn(cos(d*x + c)) + 14784*sqrt(2)*B*a^7*sgn(cos(d*x + c)) + 15246*sqrt(2)*C*a^7*sgn(cos(d*x + c)) - (14652*sqrt(2)*A*a^7*sgn(cos(d*x + c)) + 13662*sqrt(2)*B*a^7*sgn(cos(d*x + c)) + 11088*sqrt(2)*C*a^7*sgn(cos(d*x + c)) - (6897*sqrt(2)*A*a^7*sgn(cos(d*x + c)) + 5687*sqrt(2)*B*a^7*sgn(cos(d*x + c)) + 5313*sqrt(2)*C*a^7*sgn(cos(d*x + c)) - 2*(627*sqrt(2)*A*a^7*sgn(cos(d*x + c)) + 517*sqrt(2)*B*a^7*sgn(cos(d*x + c)) + 483*sqrt(2)*C*a^7*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
492,1,324,0,2.057226," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{4 \, {\left({\left({\left({\left(2 \, \sqrt{2} {\left(63 \, A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 57 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 47 \, C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \sqrt{2} {\left(63 \, A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 57 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 47 \, C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 63 \, \sqrt{2} {\left(17 \, A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13 \, C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \sqrt{2} {\left(9 \, A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5 \, C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 315 \, \sqrt{2} {\left(A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"4/315*((((2*sqrt(2)*(63*A*a^6*sgn(cos(d*x + c)) + 57*B*a^6*sgn(cos(d*x + c)) + 47*C*a^6*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 9*sqrt(2)*(63*A*a^6*sgn(cos(d*x + c)) + 57*B*a^6*sgn(cos(d*x + c)) + 47*C*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 63*sqrt(2)*(17*A*a^6*sgn(cos(d*x + c)) + 13*B*a^6*sgn(cos(d*x + c)) + 13*C*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 105*sqrt(2)*(9*A*a^6*sgn(cos(d*x + c)) + 7*B*a^6*sgn(cos(d*x + c)) + 5*C*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 315*sqrt(2)*(A*a^6*sgn(cos(d*x + c)) + B*a^6*sgn(cos(d*x + c)) + C*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
493,1,286,0,1.842837," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{4 \, {\left(105 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 105 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 105 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(280 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 210 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 140 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(245 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 147 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 133 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2 \, {\left(35 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 21 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{105 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"-4/105*(105*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 105*sqrt(2)*B*a^5*sgn(cos(d*x + c)) + 105*sqrt(2)*C*a^5*sgn(cos(d*x + c)) - (280*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 210*sqrt(2)*B*a^5*sgn(cos(d*x + c)) + 140*sqrt(2)*C*a^5*sgn(cos(d*x + c)) - (245*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 147*sqrt(2)*B*a^5*sgn(cos(d*x + c)) + 133*sqrt(2)*C*a^5*sgn(cos(d*x + c)) - 2*(35*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 21*sqrt(2)*B*a^5*sgn(cos(d*x + c)) + 19*sqrt(2)*C*a^5*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","B",0
494,1,342,0,1.999501," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{15 \, A \sqrt{-a} a^{2} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} - \frac{2 \, {\left({\left(\sqrt{2} {\left(15 \, A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 20 \, B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12 \, C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, \sqrt{2} {\left(3 \, A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5 \, B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, \sqrt{2} {\left(A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{15 \, d}"," ",0,"-1/15*(15*A*sqrt(-a)*a^2*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) - 2*((sqrt(2)*(15*A*a^4*sgn(cos(d*x + c)) + 20*B*a^4*sgn(cos(d*x + c)) + 12*C*a^4*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 10*sqrt(2)*(3*A*a^4*sgn(cos(d*x + c)) + 5*B*a^4*sgn(cos(d*x + c)) + 3*C*a^4*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 15*sqrt(2)*(A*a^4*sgn(cos(d*x + c)) + 2*B*a^4*sgn(cos(d*x + c)) + 2*C*a^4*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
495,1,472,0,1.999064," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(3 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(3 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(3 \, \sqrt{2} B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6 \, \sqrt{2} C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(3 \, \sqrt{2} B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, \sqrt{2} C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{12 \, {\left(3 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \sqrt{2} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}}}{6 \, d}"," ",0,"-1/6*(3*(3*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 2*B*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(3*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 2*B*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(3*sqrt(2)*B*a^3*sgn(cos(d*x + c)) + 6*sqrt(2)*C*a^3*sgn(cos(d*x + c)) - (3*sqrt(2)*B*a^3*sgn(cos(d*x + c)) + 4*sqrt(2)*C*a^3*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) + 12*(3*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) - sqrt(2)*A*sqrt(-a)*a^3*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2))/d","B",0
496,1,733,0,2.149546," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{16 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} C a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + {\left(7 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(7 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(7 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 95 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 53 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 5 \, A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4 \, B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(16*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*C*a^2*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + (7*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 12*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (7*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 12*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(7*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 95*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 53*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 5*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 4*B*sqrt(-a)*a^5*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2)/d","B",0
497,1,1245,0,2.683907," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(11 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 14 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 24 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(11 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 14 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 24 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(33 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 42 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 72 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 303 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 822 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 888 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2394 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3780 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3024 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1806 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2508 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1776 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 309 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 498 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 360 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 19 \, \sqrt{2} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 30 \, \sqrt{2} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 24 \, \sqrt{2} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(3*(11*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 14*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 24*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(11*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 14*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 24*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(33*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 42*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 72*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 303*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 822*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 888*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 2394*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 3780*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 3024*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 1806*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 2508*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 1776*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 309*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 498*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 360*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 19*sqrt(2)*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 30*sqrt(2)*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 24*sqrt(2)*C*sqrt(-a)*a^7*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3)/d","B",0
498,1,1530,0,3.037927," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(75 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 88 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 112 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(75 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 88 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 112 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(225 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 264 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 336 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6261 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4008 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 8592 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 35925 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 33960 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 70032 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 127449 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 131784 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 208080 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 101667 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 108312 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 154608 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 26079 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 29432 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 44208 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3303 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3384 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5424 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 147 \, A \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 152 \, B \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 240 \, C \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(3*(75*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 88*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 112*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(75*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 88*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 112*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(225*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 264*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 336*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 6261*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 4008*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 8592*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 35925*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 33960*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 70032*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 127449*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 131784*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 208080*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 101667*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 108312*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 154608*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 26079*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 29432*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 44208*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 3303*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 3384*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 5424*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 147*A*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 152*B*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 240*C*sqrt(-a)*a^9*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^4)/d","B",0
499,1,1953,0,3.317665," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{15 \, {\left(133 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 150 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 176 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 15 \, {\left(133 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 150 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 176 \, C \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(1995 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2250 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2640 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 38505 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 76110 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 55920 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 561660 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 737160 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 582720 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2684100 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 3492600 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 3395520 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7371738 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9022860 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9329760 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6407470 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 7635300 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 8110880 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2176620 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2614440 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2882880 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 399860 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 460440 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 498880 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 34035 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 41850 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 42960 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1201 \, \sqrt{2} A \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1470 \, \sqrt{2} B \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1520 \, \sqrt{2} C \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{5}}}{3840 \, d}"," ",0,"-1/3840*(15*(133*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 150*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 176*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 15*(133*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 150*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 176*C*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(1995*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 2250*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 2640*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*C*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 38505*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 76110*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 55920*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 561660*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 737160*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 582720*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 2684100*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 3492600*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 3395520*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 7371738*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 9022860*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 9329760*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 6407470*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 7635300*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 8110880*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 2176620*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 2614440*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 2882880*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 399860*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 460440*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 498880*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 34035*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^10*sgn(cos(d*x + c)) + 41850*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^10*sgn(cos(d*x + c)) + 42960*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 1201*sqrt(2)*A*sqrt(-a)*a^11*sgn(cos(d*x + c)) - 1470*sqrt(2)*B*sqrt(-a)*a^11*sgn(cos(d*x + c)) - 1520*sqrt(2)*C*sqrt(-a)*a^11*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^5)/d","B",0
500,1,472,0,3.074376," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, {\left(45045 \, \sqrt{2} A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 45045 \, \sqrt{2} B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 45045 \, \sqrt{2} C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(180180 \, \sqrt{2} A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 150150 \, \sqrt{2} B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 120120 \, \sqrt{2} C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(342342 \, \sqrt{2} A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 300300 \, \sqrt{2} B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 294294 \, \sqrt{2} C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(391248 \, \sqrt{2} A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 356070 \, \sqrt{2} B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 310596 \, \sqrt{2} C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(265837 \, \sqrt{2} A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 232375 \, \sqrt{2} B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 212069 \, \sqrt{2} C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4 \, {\left(24167 \, \sqrt{2} A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 21125 \, \sqrt{2} B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19279 \, \sqrt{2} C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2 \, {\left(1859 \, \sqrt{2} A a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1625 \, \sqrt{2} B a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1483 \, \sqrt{2} C a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{45045 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{6} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"8/45045*(45045*sqrt(2)*A*a^9*sgn(cos(d*x + c)) + 45045*sqrt(2)*B*a^9*sgn(cos(d*x + c)) + 45045*sqrt(2)*C*a^9*sgn(cos(d*x + c)) - (180180*sqrt(2)*A*a^9*sgn(cos(d*x + c)) + 150150*sqrt(2)*B*a^9*sgn(cos(d*x + c)) + 120120*sqrt(2)*C*a^9*sgn(cos(d*x + c)) - (342342*sqrt(2)*A*a^9*sgn(cos(d*x + c)) + 300300*sqrt(2)*B*a^9*sgn(cos(d*x + c)) + 294294*sqrt(2)*C*a^9*sgn(cos(d*x + c)) - (391248*sqrt(2)*A*a^9*sgn(cos(d*x + c)) + 356070*sqrt(2)*B*a^9*sgn(cos(d*x + c)) + 310596*sqrt(2)*C*a^9*sgn(cos(d*x + c)) - (265837*sqrt(2)*A*a^9*sgn(cos(d*x + c)) + 232375*sqrt(2)*B*a^9*sgn(cos(d*x + c)) + 212069*sqrt(2)*C*a^9*sgn(cos(d*x + c)) - 4*(24167*sqrt(2)*A*a^9*sgn(cos(d*x + c)) + 21125*sqrt(2)*B*a^9*sgn(cos(d*x + c)) + 19279*sqrt(2)*C*a^9*sgn(cos(d*x + c)) - 2*(1859*sqrt(2)*A*a^9*sgn(cos(d*x + c)) + 1625*sqrt(2)*B*a^9*sgn(cos(d*x + c)) + 1483*sqrt(2)*C*a^9*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^6*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
501,1,383,0,2.902152," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, {\left({\left({\left({\left(4 \, {\left(2 \, \sqrt{2} {\left(165 \, A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 143 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 125 \, C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 11 \, \sqrt{2} {\left(165 \, A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 143 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 125 \, C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 99 \, \sqrt{2} {\left(165 \, A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 143 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 125 \, C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 231 \, \sqrt{2} {\left(85 \, A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 69 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 65 \, C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1155 \, \sqrt{2} {\left(11 \, A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7 \, C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3465 \, \sqrt{2} {\left(A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + C a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{3465 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"8/3465*((((4*(2*sqrt(2)*(165*A*a^8*sgn(cos(d*x + c)) + 143*B*a^8*sgn(cos(d*x + c)) + 125*C*a^8*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 11*sqrt(2)*(165*A*a^8*sgn(cos(d*x + c)) + 143*B*a^8*sgn(cos(d*x + c)) + 125*C*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 99*sqrt(2)*(165*A*a^8*sgn(cos(d*x + c)) + 143*B*a^8*sgn(cos(d*x + c)) + 125*C*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 231*sqrt(2)*(85*A*a^8*sgn(cos(d*x + c)) + 69*B*a^8*sgn(cos(d*x + c)) + 65*C*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 1155*sqrt(2)*(11*A*a^8*sgn(cos(d*x + c)) + 9*B*a^8*sgn(cos(d*x + c)) + 7*C*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 3465*sqrt(2)*(A*a^8*sgn(cos(d*x + c)) + B*a^8*sgn(cos(d*x + c)) + C*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
502,1,348,0,2.835465," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, {\left(315 \, \sqrt{2} A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 315 \, \sqrt{2} B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 315 \, \sqrt{2} C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(1050 \, \sqrt{2} A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 840 \, \sqrt{2} B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 630 \, \sqrt{2} C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(1323 \, \sqrt{2} A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 945 \, \sqrt{2} B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 819 \, \sqrt{2} C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4 \, {\left(189 \, \sqrt{2} A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 135 \, \sqrt{2} B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 117 \, \sqrt{2} C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2 \, {\left(21 \, \sqrt{2} A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 15 \, \sqrt{2} B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13 \, \sqrt{2} C a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"8/315*(315*sqrt(2)*A*a^7*sgn(cos(d*x + c)) + 315*sqrt(2)*B*a^7*sgn(cos(d*x + c)) + 315*sqrt(2)*C*a^7*sgn(cos(d*x + c)) - (1050*sqrt(2)*A*a^7*sgn(cos(d*x + c)) + 840*sqrt(2)*B*a^7*sgn(cos(d*x + c)) + 630*sqrt(2)*C*a^7*sgn(cos(d*x + c)) - (1323*sqrt(2)*A*a^7*sgn(cos(d*x + c)) + 945*sqrt(2)*B*a^7*sgn(cos(d*x + c)) + 819*sqrt(2)*C*a^7*sgn(cos(d*x + c)) - 4*(189*sqrt(2)*A*a^7*sgn(cos(d*x + c)) + 135*sqrt(2)*B*a^7*sgn(cos(d*x + c)) + 117*sqrt(2)*C*a^7*sgn(cos(d*x + c)) - 2*(21*sqrt(2)*A*a^7*sgn(cos(d*x + c)) + 15*sqrt(2)*B*a^7*sgn(cos(d*x + c)) + 13*sqrt(2)*C*a^7*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","B",0
503,1,419,0,2.555262," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{105 \, A \sqrt{-a} a^{3} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} + \frac{2 \, {\left(315 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 420 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 420 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(875 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 980 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 700 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(805 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 784 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 560 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(245 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 224 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 160 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{105 \, d}"," ",0,"-1/105*(105*A*sqrt(-a)*a^3*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) + 2*(315*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 420*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 420*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (875*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 980*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 700*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (805*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 784*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 560*sqrt(2)*C*a^6*sgn(cos(d*x + c)) - (245*sqrt(2)*A*a^6*sgn(cos(d*x + c)) + 224*sqrt(2)*B*a^6*sgn(cos(d*x + c)) + 160*sqrt(2)*C*a^6*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
504,1,559,0,2.411230," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{15 \, {\left(5 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 15 \, {\left(5 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{60 \, {\left(3 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \sqrt{2} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}} - \frac{4 \, {\left({\left(\sqrt{2} {\left(15 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 35 \, B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 32 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, \sqrt{2} {\left(3 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, \sqrt{2} {\left(A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, C a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{30 \, d}"," ",0,"-1/30*(15*(5*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 2*B*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 15*(5*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 2*B*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 60*(3*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - sqrt(2)*A*sqrt(-a)*a^4*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2) - 4*((sqrt(2)*(15*A*a^5*sgn(cos(d*x + c)) + 35*B*a^5*sgn(cos(d*x + c)) + 32*C*a^5*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 10*sqrt(2)*(3*A*a^5*sgn(cos(d*x + c)) + 8*B*a^5*sgn(cos(d*x + c)) + 8*C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 15*sqrt(2)*(A*a^5*sgn(cos(d*x + c)) + 3*B*a^5*sgn(cos(d*x + c)) + 4*C*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
505,1,811,0,2.536976," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(19 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 20 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(19 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 20 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{16 \, {\left(3 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(3 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{12 \, \sqrt{2} {\left(19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 171 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 89 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 9 \, A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4 \, B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2}}}{24 \, d}"," ",0,"-1/24*(3*(19*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 20*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(19*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 20*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 8*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 16*(3*sqrt(2)*B*a^4*sgn(cos(d*x + c)) + 9*sqrt(2)*C*a^4*sgn(cos(d*x + c)) - (3*sqrt(2)*B*a^4*sgn(cos(d*x + c)) + 7*sqrt(2)*C*a^4*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) + 12*sqrt(2)*(19*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 171*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 89*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 9*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 4*B*sqrt(-a)*a^6*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2)/d","B",0
506,1,1319,0,3.419746," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{96 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} C a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + 3 \, {\left(25 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 38 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 40 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(25 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 38 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 40 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(75 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 114 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 72 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1125 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1710 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 888 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6174 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6804 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3024 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4314 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4284 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1776 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 807 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 858 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 360 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 49 \, \sqrt{2} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 54 \, \sqrt{2} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 24 \, \sqrt{2} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(96*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*C*a^3*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + 3*(25*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 38*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 40*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(25*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 38*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 40*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(75*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 114*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 72*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 1125*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 1710*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 888*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 6174*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 6804*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 3024*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 4314*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 4284*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 1776*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 807*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 858*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 360*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 49*sqrt(2)*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 54*sqrt(2)*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 24*sqrt(2)*C*sqrt(-a)*a^8*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3)/d","B",0
507,1,1542,0,4.051579," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, {\left(163 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 200 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 304 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(163 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 200 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 304 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(489 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 600 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 912 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 10269 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 12600 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 19152 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 69885 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 103992 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 137424 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 259233 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 339864 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 374544 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 209979 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 262920 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 266928 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 55511 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 73640 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 75888 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6687 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8808 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9456 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 299 \, A \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 392 \, B \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 432 \, C \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(3*(163*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 200*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 304*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(163*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 200*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 304*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(489*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 600*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 912*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 10269*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 12600*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 19152*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 69885*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 103992*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 137424*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 259233*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 339864*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 374544*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 209979*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 262920*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 266928*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 55511*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 73640*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 75888*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 6687*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 8808*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 9456*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 299*A*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 392*B*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 432*C*sqrt(-a)*a^10*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^4)/d","B",0
508,1,1965,0,4.340600," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{15 \, {\left(283 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 326 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 400 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 15 \, {\left(283 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 326 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 400 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(4245 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4890 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6000 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 114615 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 132030 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 162000 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1298820 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1319880 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1801920 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6176700 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6888120 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 9764160 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 16394598 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 18352620 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 24060960 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 14042770 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 15746180 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 19910240 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4791060 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5497320 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7135680 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 860300 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 959320 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1268800 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 75885 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 84810 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 111600 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2671 \, \sqrt{2} A \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2990 \, \sqrt{2} B \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 3920 \, \sqrt{2} C \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{5}}}{3840 \, d}"," ",0,"-1/3840*(15*(283*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 326*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 400*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 15*(283*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 326*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 400*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(4245*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 4890*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 6000*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 114615*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 132030*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 162000*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 1298820*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 1319880*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 1801920*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 6176700*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 6888120*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 9764160*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 16394598*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 18352620*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 24060960*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 14042770*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 15746180*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 19910240*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 4791060*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 5497320*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 7135680*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 860300*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 959320*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 1268800*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^10*sgn(cos(d*x + c)) + 75885*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^11*sgn(cos(d*x + c)) + 84810*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^11*sgn(cos(d*x + c)) + 111600*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^11*sgn(cos(d*x + c)) - 2671*sqrt(2)*A*sqrt(-a)*a^12*sgn(cos(d*x + c)) - 2990*sqrt(2)*B*sqrt(-a)*a^12*sgn(cos(d*x + c)) - 3920*sqrt(2)*C*sqrt(-a)*a^12*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^5)/d","B",0
509,1,2319,0,4.953273," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{15 \, {\left(1015 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1132 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1304 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 15 \, {\left(1015 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1132 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1304 \, C \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(15225 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{22} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 16980 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{22} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19560 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{22} C \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 502425 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{20} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 560340 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{20} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 645480 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{20} C \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6518495 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7963020 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8467800 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} C \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 49683495 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 56336940 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 59757720 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} C \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 191286330 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 219014472 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 244004880 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 418895130 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 474348232 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 531000080 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 374587230 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 421769112 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 473308080 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 154254030 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 174597720 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 198757680 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 35939005 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 40114980 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 45352200 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4649085 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 5273124 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 5884680 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 324435 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{13} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 367644 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{13} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 411000 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{13} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 9435 \, \sqrt{2} A \sqrt{-a} a^{14} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 10684 \, \sqrt{2} B \sqrt{-a} a^{14} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 11960 \, \sqrt{2} C \sqrt{-a} a^{14} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{6}}}{15360 \, d}"," ",0,"-1/15360*(15*(1015*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 1132*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 1304*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 15*(1015*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 1132*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 1304*C*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(15225*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^22*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 16980*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^22*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 19560*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^22*C*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 502425*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^20*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 560340*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^20*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 645480*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^20*C*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 6518495*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 7963020*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 8467800*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*C*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 49683495*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 56336940*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 59757720*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*C*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 191286330*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 219014472*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 244004880*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 418895130*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 474348232*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 531000080*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 374587230*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 421769112*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 473308080*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 154254030*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 174597720*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 198757680*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^10*sgn(cos(d*x + c)) + 35939005*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^11*sgn(cos(d*x + c)) + 40114980*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^11*sgn(cos(d*x + c)) + 45352200*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^11*sgn(cos(d*x + c)) - 4649085*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^12*sgn(cos(d*x + c)) - 5273124*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^12*sgn(cos(d*x + c)) - 5884680*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^12*sgn(cos(d*x + c)) + 324435*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^13*sgn(cos(d*x + c)) + 367644*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^13*sgn(cos(d*x + c)) + 411000*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^13*sgn(cos(d*x + c)) - 9435*sqrt(2)*A*sqrt(-a)*a^14*sgn(cos(d*x + c)) - 10684*sqrt(2)*B*sqrt(-a)*a^14*sgn(cos(d*x + c)) - 11960*sqrt(2)*C*sqrt(-a)*a^14*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^6)/d","B",0
510,1,510,0,2.884720," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{315 \, {\left(\sqrt{2} A - \sqrt{2} B + \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{2 \, {\left(315 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 315 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(1050 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 420 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 840 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(1512 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 756 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 1638 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(1134 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 612 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 936 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(357 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 276 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 383 \, \sqrt{2} C a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{315 \, d}"," ",0,"-1/315*(315*(sqrt(2)*A - sqrt(2)*B + sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 2*(315*sqrt(2)*A*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 315*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (1050*sqrt(2)*A*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 420*sqrt(2)*B*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 840*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (1512*sqrt(2)*A*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 756*sqrt(2)*B*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 1638*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (1134*sqrt(2)*A*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 612*sqrt(2)*B*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 936*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (357*sqrt(2)*A*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 276*sqrt(2)*B*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 383*sqrt(2)*C*a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
511,1,305,0,2.589860," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{105 \, \sqrt{2} {\left(A - B + C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{2 \, {\left(\frac{105 \, \sqrt{2} B a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + {\left({\left(\frac{\sqrt{2} {\left(70 \, A a^{3} - 119 \, B a^{3} + 92 \, C a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{7 \, \sqrt{2} {\left(20 \, A a^{3} - 37 \, B a^{3} + 16 \, C a^{3}\right)}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{35 \, \sqrt{2} {\left(2 \, A a^{3} - 7 \, B a^{3} + 4 \, C a^{3}\right)}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{105 \, d}"," ",0,"1/105*(105*sqrt(2)*(A - B + C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 2*(105*sqrt(2)*B*a^3/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + ((sqrt(2)*(70*A*a^3 - 119*B*a^3 + 92*C*a^3)*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 7*sqrt(2)*(20*A*a^3 - 37*B*a^3 + 16*C*a^3)/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2 + 35*sqrt(2)*(2*A*a^3 - 7*B*a^3 + 4*C*a^3)/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
512,1,344,0,2.572048," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(\sqrt{2} A - \sqrt{2} B + \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{2 \, {\left(15 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 15 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(30 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 10 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 20 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(15 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 10 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 17 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{15 \, d}"," ",0,"-1/15*(15*(sqrt(2)*A - sqrt(2)*B + sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 2*(15*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 15*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (30*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 10*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 20*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (15*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 10*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 17*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
513,1,187,0,2.375270," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{3 \, \sqrt{2} {\left(A - B + C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(\frac{\sqrt{2} {\left(3 \, B a - 2 \, C a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, \sqrt{2} B a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{3 \, d}"," ",0,"1/3*(3*sqrt(2)*(A - B + C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(sqrt(2)*(3*B*a - 2*C*a)*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*sqrt(2)*B*a/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
514,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableDiscontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 1.4index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
515,1,394,0,2.081540," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} {\left(A - B + C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{{\left(A - 2 \, B\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left(A - 2 \, B\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} - A \sqrt{-a} a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{2 \, d}"," ",0,"1/2*(sqrt(2)*(A - B + C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + (A - 2*B)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - (A - 2*B)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a) - A*sqrt(-a)*a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
516,1,656,0,2.706650," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{4 \, \sqrt{2} {\left(A - B + C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{{\left(7 \, A - 4 \, B + 8 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left(7 \, A - 4 \, B + 8 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(17 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} - 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} - 57 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a + 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a + 19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{2} - 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{2} - 3 \, A \sqrt{-a} a^{3} + 4 \, B \sqrt{-a} a^{3}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"-1/8*(4*sqrt(2)*(A - B + C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + (7*A - 4*B + 8*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - (7*A - 4*B + 8*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(17*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a) - 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a) - 57*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a + 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a + 19*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^2 - 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^2 - 3*A*sqrt(-a)*a^3 + 4*B*sqrt(-a)*a^3)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
517,1,1104,0,2.965264," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{24 \, \sqrt{2} {\left(A - B + C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{3 \, {\left(9 \, A - 14 \, B + 8 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, {\left(9 \, A - 14 \, B + 8 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(165 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} - 102 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} + 72 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} - 1323 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a + 954 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a - 888 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a + 3906 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{2} - 2268 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{2} + 3024 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{2} - 2118 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{3} + 1044 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{3} - 1776 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{3} + 393 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{4} - 222 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{4} + 360 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{4} - 31 \, A \sqrt{-a} a^{5} + 18 \, B \sqrt{-a} a^{5} - 24 \, C \sqrt{-a} a^{5}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{48 \, d}"," ",0,"1/48*(24*sqrt(2)*(A - B + C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 3*(9*A - 14*B + 8*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 3*(9*A - 14*B + 8*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(165*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a) - 102*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a) + 72*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a) - 1323*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a + 954*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a - 888*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a + 3906*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^2 - 2268*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^2 + 3024*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^2 - 2118*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^3 + 1044*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^3 - 1776*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^3 + 393*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^4 - 222*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^4 + 360*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^4 - 31*A*sqrt(-a)*a^5 + 18*B*sqrt(-a)*a^5 - 24*C*sqrt(-a)*a^5)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
518,1,1398,0,3.415156," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{192 \, \sqrt{2} {\left(A - B + C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{3 \, {\left(107 \, A - 72 \, B + 112 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, {\left(107 \, A - 72 \, B + 112 \, C\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(1599 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} - 1320 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} + 816 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{-a} - 18219 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a + 18504 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a - 12528 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C \sqrt{-a} a + 91467 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{2} - 96072 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{2} + 64752 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{-a} a^{2} - 177735 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{3} + 215016 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{3} - 124848 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C \sqrt{-a} a^{3} + 100413 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{4} - 136056 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{4} + 70032 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C \sqrt{-a} a^{4} - 26881 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{5} + 36056 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{5} - 19152 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C \sqrt{-a} a^{5} + 3321 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{6} - 4632 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{6} + 2640 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C \sqrt{-a} a^{6} - 205 \, A \sqrt{-a} a^{7} + 248 \, B \sqrt{-a} a^{7} - 144 \, C \sqrt{-a} a^{7}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{384 \, d}"," ",0,"-1/384*(192*sqrt(2)*(A - B + C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 3*(107*A - 72*B + 112*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 3*(107*A - 72*B + 112*C)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(1599*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a) - 1320*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a) + 816*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(-a) - 18219*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a + 18504*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a - 12528*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*sqrt(-a)*a + 91467*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^2 - 96072*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^2 + 64752*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(-a)*a^2 - 177735*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^3 + 215016*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^3 - 124848*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*sqrt(-a)*a^3 + 100413*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^4 - 136056*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^4 + 70032*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*sqrt(-a)*a^4 - 26881*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^5 + 36056*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^5 - 19152*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*sqrt(-a)*a^5 + 3321*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^6 - 4632*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^6 + 2640*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*sqrt(-a)*a^6 - 205*A*sqrt(-a)*a^7 + 248*B*sqrt(-a)*a^7 - 144*C*sqrt(-a)*a^7)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
519,1,560,0,3.018667," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{105 \, {\left(11 \, \sqrt{2} A - 15 \, \sqrt{2} B + 19 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left({\left({\left({\left(\frac{105 \, {\left(\sqrt{2} A a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3}} - \frac{4 \, {\left(455 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 693 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 877 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{14 \, {\left(305 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 453 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 517 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{140 \, {\left(25 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 39 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 47 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{105 \, {\left(9 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 17 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 17 \, \sqrt{2} C a^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{420 \, d}"," ",0,"1/420*(105*(11*sqrt(2)*A - 15*sqrt(2)*B + 19*sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - ((((105*(sqrt(2)*A*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a^3 - 4*(455*sqrt(2)*A*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 693*sqrt(2)*B*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 877*sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^3)*tan(1/2*d*x + 1/2*c)^2 + 14*(305*sqrt(2)*A*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 453*sqrt(2)*B*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 517*sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^3)*tan(1/2*d*x + 1/2*c)^2 - 140*(25*sqrt(2)*A*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 39*sqrt(2)*B*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 47*sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^3)*tan(1/2*d*x + 1/2*c)^2 + 105*(9*sqrt(2)*A*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 17*sqrt(2)*B*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 17*sqrt(2)*C*a^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^3)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
520,1,338,0,2.868218," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{15 \, \sqrt{2} {\left(7 \, A - 11 \, B + 15 \, C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left({\left({\left(\frac{15 \, \sqrt{2} {\left(A a^{3} - B a^{3} + C a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(165 \, A a^{3} - 245 \, B a^{3} + 381 \, C a^{3}\right)}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{5 \, \sqrt{2} {\left(57 \, A a^{3} - 73 \, B a^{3} + 105 \, C a^{3}\right)}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{15 \, \sqrt{2} {\left(9 \, A a^{3} - 9 \, B a^{3} + 17 \, C a^{3}\right)}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{60 \, d}"," ",0,"-1/60*(15*sqrt(2)*(7*A - 11*B + 15*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - (((15*sqrt(2)*(A*a^3 - B*a^3 + C*a^3)*tan(1/2*d*x + 1/2*c)^2/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(165*A*a^3 - 245*B*a^3 + 381*C*a^3)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 5*sqrt(2)*(57*A*a^3 - 73*B*a^3 + 105*C*a^3)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 - 15*sqrt(2)*(9*A*a^3 - 9*B*a^3 + 17*C*a^3)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
521,1,364,0,2.691923," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(\frac{3 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a} - \frac{2 \, {\left(3 \, \sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 15 \, \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 23 \, \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{3 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 9 \, \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 9 \, \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{3 \, {\left(3 \, \sqrt{2} A - 7 \, \sqrt{2} B + 11 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{12 \, d}"," ",0,"-1/12*(((3*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a - 2*(3*sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 15*sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 23*sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a)*tan(1/2*d*x + 1/2*c)^2 + 3*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 9*sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 9*sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) - 3*(3*sqrt(2)*A - 7*sqrt(2)*B + 11*sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
522,1,201,0,2.256074," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(\frac{\sqrt{2} {\left(A a^{2} - B a^{2} + C a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(A a^{2} - B a^{2} + 9 \, C a^{2}\right)}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{\sqrt{2} {\left(A + 3 \, B - 7 \, C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{4 \, d}"," ",0,"1/4*((sqrt(2)*(A*a^2 - B*a^2 + C*a^2)*tan(1/2*d*x + 1/2*c)^2/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(A*a^2 - B*a^2 + 9*C*a^2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(2)*(A + 3*B - 7*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
523,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableDiscontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 1.4index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
524,1,474,0,3.087775," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} {\left(9 \, A - 5 \, B + C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{4 \, {\left(3 \, A - 2 \, B\right)} \log\left(\frac{{\left| -17179869184 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 34359738368 \, \sqrt{2} {\left| a \right|} + 51539607552 \, a \right|}}{{\left| -17179869184 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 34359738368 \, \sqrt{2} {\left| a \right|} + 51539607552 \, a \right|}}\right)}{\sqrt{-a} {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{16 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A - A a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"1/8*(sqrt(2)*(9*A - 5*B + C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 4*(3*A - 2*B)*log(abs(-17179869184*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 34359738368*sqrt(2)*abs(a) + 51539607552*a)/abs(-17179869184*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 34359738368*sqrt(2)*abs(a) + 51539607552*a))/(sqrt(-a)*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^3 - 16*sqrt(2)*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A - A*a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
525,1,699,0,3.951402," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} {\left(13 \, A - 9 \, B + 5 \, C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{{\left(19 \, A - 12 \, B + 8 \, C\right)} \log\left(\frac{{\left| 147573952589676412928 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 295147905179352825856 \, \sqrt{2} {\left| a \right|} - 442721857769029238784 \, a \right|}}{{\left| 147573952589676412928 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 295147905179352825856 \, \sqrt{2} {\left| a \right|} - 442721857769029238784 \, a \right|}}\right)}{\sqrt{-a} {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{4 \, \sqrt{2} {\left(29 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A - 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B - 133 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A a + 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B a + 55 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A a^{2} - 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B a^{2} - 7 \, A a^{3} + 4 \, B a^{3}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"-1/8*(sqrt(2)*(13*A - 9*B + 5*C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + (19*A - 12*B + 8*C)*log(abs(147573952589676412928*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 295147905179352825856*sqrt(2)*abs(a) - 442721857769029238784*a)/abs(147573952589676412928*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 295147905179352825856*sqrt(2)*abs(a) - 442721857769029238784*a))/(sqrt(-a)*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^3 - 4*sqrt(2)*(29*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A - 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B - 133*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*a + 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*a + 55*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*a^2 - 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*a^2 - 7*A*a^3 + 4*B*a^3)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
526,1,1098,0,6.098900," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} {\left(17 \, A - 13 \, B + 9 \, C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, {\left(47 \, A - 38 \, B + 24 \, C\right)} \log\left(\frac{{\left| -1947111321950560360698936123457536 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 3894222643901120721397872246915072 \, \sqrt{2} {\left| a \right|} + 5841333965851681082096808370372608 \, a \right|}}{{\left| -1947111321950560360698936123457536 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 3894222643901120721397872246915072 \, \sqrt{2} {\left| a \right|} + 5841333965851681082096808370372608 \, a \right|}}\right)}{\sqrt{-a} {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{12 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{4 \, \sqrt{2} {\left(339 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A - 174 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B + 72 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C - 3165 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A a + 1842 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B a - 888 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C a + 9198 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A a^{2} - 5292 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B a^{2} + 3024 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C a^{2} - 4938 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A a^{3} + 2820 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B a^{3} - 1776 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C a^{3} + 975 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A a^{4} - 582 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B a^{4} + 360 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C a^{4} - 73 \, A a^{5} + 42 \, B a^{5} - 24 \, C a^{5}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{48 \, d}"," ",0,"1/48*(6*sqrt(2)*(17*A - 13*B + 9*C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 3*(47*A - 38*B + 24*C)*log(abs(-1947111321950560360698936123457536*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 3894222643901120721397872246915072*sqrt(2)*abs(a) + 5841333965851681082096808370372608*a)/abs(-1947111321950560360698936123457536*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 3894222643901120721397872246915072*sqrt(2)*abs(a) + 5841333965851681082096808370372608*a))/(sqrt(-a)*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 12*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^3 - 4*sqrt(2)*(339*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A - 174*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B + 72*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C - 3165*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*a + 1842*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*a - 888*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*a + 9198*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*a^2 - 5292*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*a^2 + 3024*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*a^2 - 4938*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*a^3 + 2820*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*a^3 - 1776*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*a^3 + 975*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*a^4 - 582*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*a^4 + 360*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*a^4 - 73*A*a^5 + 42*B*a^5 - 24*C*a^5)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
527,1,559,0,4.099496," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left({\left(15 \, {\left(\frac{2 \, {\left(\sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2}} + \frac{13 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 21 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 29 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{1725 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 3685 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 6733 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{5 \, {\left(549 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 1133 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 1973 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{15 \, {\left(83 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 155 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 291 \, \sqrt{2} C a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{15 \, {\left(75 \, \sqrt{2} A - 163 \, \sqrt{2} B + 283 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{480 \, d}"," ",0,"1/480*((((15*(2*(sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a^2 + (13*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 21*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 29*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^2)*tan(1/2*d*x + 1/2*c)^2 - (1725*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 3685*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 6733*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^2)*tan(1/2*d*x + 1/2*c)^2 + 5*(549*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 1133*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 1973*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^2)*tan(1/2*d*x + 1/2*c)^2 - 15*(83*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 155*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 291*sqrt(2)*C*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) - 15*(75*sqrt(2)*A - 163*sqrt(2)*B + 283*sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
528,1,337,0,3.614234," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(3 \, {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{\sqrt{2} {\left(7 \, A a^{5} - 15 \, B a^{5} + 23 \, C a^{5}\right)}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{4 \, \sqrt{2} {\left(15 \, A a^{5} - 75 \, B a^{5} + 167 \, C a^{5}\right)}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{3 \, \sqrt{2} {\left(11 \, A a^{5} - 83 \, B a^{5} + 155 \, C a^{5}\right)}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{3 \, \sqrt{2} {\left(19 \, A - 75 \, B + 163 \, C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{96 \, d}"," ",0,"-1/96*(((3*(2*sqrt(2)*(A*a^5 - B*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + sqrt(2)*(7*A*a^5 - 15*B*a^5 + 23*C*a^5)/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 - 4*sqrt(2)*(15*A*a^5 - 75*B*a^5 + 167*C*a^5)/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 3*sqrt(2)*(11*A*a^5 - 83*B*a^5 + 155*C*a^5)/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) - 3*sqrt(2)*(19*A - 75*B + 163*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
529,1,361,0,3.397923," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left(\frac{2 \, {\left(\sqrt{2} A a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + \sqrt{2} C a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} + \frac{\sqrt{2} A a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 9 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 17 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{3 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 11 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + 83 \, \sqrt{2} C a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{{\left(5 \, \sqrt{2} A + 19 \, \sqrt{2} B - 75 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"1/32*(((2*(sqrt(2)*A*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + sqrt(2)*C*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a^8 + (sqrt(2)*A*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 9*sqrt(2)*B*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 17*sqrt(2)*C*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^8)*tan(1/2*d*x + 1/2*c)^2 - (3*sqrt(2)*A*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 11*sqrt(2)*B*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + 83*sqrt(2)*C*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^8)*tan(1/2*d*x + 1/2*c)/sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a) + (5*sqrt(2)*A + 19*sqrt(2)*B - 75*sqrt(2)*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
530,1,205,0,2.811818," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(5 \, A a^{5} + 3 \, B a^{5} - 11 \, C a^{5}\right)}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{\sqrt{2} {\left(3 \, A + 5 \, B + 19 \, C\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"1/32*(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(5*A*a^5 + 3*B*a^5 - 11*C*a^5)/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + sqrt(2)*(3*A + 5*B + 19*C)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
531,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableDiscontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 1.79index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
532,1,513,0,3.905702," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(21 \, A a^{5} - 13 \, B a^{5} + 5 \, C a^{5}\right)}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{\sqrt{2} {\left(115 \, A - 43 \, B + 3 \, C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{32 \, {\left(5 \, A - 2 \, B\right)} \log\left(\frac{{\left| -562949953421312 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 1125899906842624 \, \sqrt{2} {\left| a \right|} + 1688849860263936 \, a \right|}}{{\left| -562949953421312 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 1125899906842624 \, \sqrt{2} {\left| a \right|} + 1688849860263936 \, a \right|}}\right)}{\sqrt{-a} a {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{128 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A - A a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} \sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{64 \, d}"," ",0,"1/64*(2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(21*A*a^5 - 13*B*a^5 + 5*C*a^5)/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + sqrt(2)*(115*A - 43*B + 3*C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 32*(5*A - 2*B)*log(abs(-562949953421312*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 1125899906842624*sqrt(2)*abs(a) + 1688849860263936*a)/abs(-562949953421312*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 1125899906842624*sqrt(2)*abs(a) + 1688849860263936*a))/(sqrt(-a)*a*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 128*sqrt(2)*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A - A*a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
533,1,737,0,5.077618," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(29 \, A a^{5} - 21 \, B a^{5} + 13 \, C a^{5}\right)}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{\sqrt{2} {\left(219 \, A - 115 \, B + 43 \, C\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{8 \, {\left(39 \, A - 20 \, B + 8 \, C\right)} \log\left(\frac{{\left| 309485009821345068724781056 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 618970019642690137449562112 \, \sqrt{2} {\left| a \right|} - 928455029464035206174343168 \, a \right|}}{{\left| 309485009821345068724781056 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 618970019642690137449562112 \, \sqrt{2} {\left| a \right|} - 928455029464035206174343168 \, a \right|}}\right)}{\sqrt{-a} a {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{32 \, \sqrt{2} {\left(41 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A - 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B - 209 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A a + 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B a + 91 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A a^{2} - 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B a^{2} - 11 \, A a^{3} + 4 \, B a^{3}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2} \sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{64 \, d}"," ",0,"-1/64*(2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(29*A*a^5 - 21*B*a^5 + 13*C*a^5)/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + sqrt(2)*(219*A - 115*B + 43*C)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 8*(39*A - 20*B + 8*C)*log(abs(309485009821345068724781056*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 618970019642690137449562112*sqrt(2)*abs(a) - 928455029464035206174343168*a)/abs(309485009821345068724781056*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 618970019642690137449562112*sqrt(2)*abs(a) - 928455029464035206174343168*a))/(sqrt(-a)*a*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 32*sqrt(2)*(41*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A - 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B - 209*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*a + 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*a + 91*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*a^2 - 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*a^2 - 11*A*a^3 + 4*B*a^3)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2*sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
534,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
535,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
536,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
537,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
538,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
539,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
540,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(9/2), x)","F",0
541,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
542,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
543,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
544,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
545,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(5/2), x)","F",0
546,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(7/2), x)","F",0
547,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(9/2), x)","F",0
548,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(11/2), x)","F",0
549,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
550,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
551,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
552,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
553,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(5/2), x)","F",0
554,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(7/2), x)","F",0
555,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(9/2), x)","F",0
556,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(11/2), x)","F",0
557,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(13/2), x)","F",0
558,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
559,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
560,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
561,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
562,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
563,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
564,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(7/2)), x)","F",0
565,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
566,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
567,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
568,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
569,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
570,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
571,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a)^3, x)","F",0
572,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^3, x)","F",0
573,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^3, x)","F",0
574,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^3, x)","F",0
575,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
576,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
577,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
578,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
579,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
580,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
581,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
582,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
583,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
584,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
585,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(9/2), x)","F",0
586,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2), x)","F",0
587,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
588,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
589,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
590,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
591,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(5/2), x)","F",0
592,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(7/2), x)","F",0
593,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(9/2), x)","F",0
594,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(11/2), x)","F",0
595,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2), x)","F",0
596,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2), x)","F",0
597,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c)), x)","F",0
598,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
599,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(3/2), x)","F",0
600,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(5/2), x)","F",0
601,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(7/2), x)","F",0
602,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(9/2), x)","F",0
603,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(11/2), x)","F",0
604,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(13/2), x)","F",0
605,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
606,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
607,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/sqrt(a*sec(d*x + c) + a), x)","F",0
608,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
609,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
610,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
611,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(7/2)), x)","F",0
612,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*sec(d*x+c)+b*B*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B b \sec\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sqrt(sec(d*x + c))/sqrt(a*sec(d*x + c) + a), x)","F",0
613,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
614,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
615,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^(3/2), x)","F",0
616,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
617,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
618,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2)), x)","F",0
619,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
620,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
621,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^(5/2), x)","F",0
622,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
623,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
624,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
625,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(2/3), x)","F",0
626,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(1/3), x)","F",0
627,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(4/3), x)","F",0
628,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(7/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(7/3), x)","F",0
629,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(4/3), x)","F",0
630,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(1/3), x)","F",0
631,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(2/3), x)","F",0
632,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(5/3), x)","F",0
633,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^m, x)","F",0
634,0,0,0,0.000000," ","integrate(sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{-n - 1}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^(-n - 1), x)","F",0
635,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*(-a*(A*n+B*n+B)-a*C*(1+n)*sec(d*x+c))/a/(1+n)/(sec(d*x+c)^n)+sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{-n - 1} - \frac{{\left(C a {\left(n + 1\right)} \sec\left(d x + c\right) + {\left(A n + B n + B\right)} a\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n}}{a {\left(n + 1\right)} \sec\left(d x + c\right)^{n}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^(-n - 1) - (C*a*(n + 1)*sec(d*x + c) + (A*n + B*n + B)*a)*(a*sec(d*x + c) + a)^n/(a*(n + 1)*sec(d*x + c)^n), x)","F",0
636,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^m*(B-C+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + B - C\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + B - C)*(a*sec(d*x + c) + a)^m, x)","F",0
637,1,334,0,0.252442," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, A a + 3 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, A a + 3 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(60 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 75 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 160 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 400 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 464 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 75 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(4*A*a + 3*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*A*a + 3*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(60*A*a*tan(1/2*d*x + 1/2*c)^9 + 75*C*a*tan(1/2*d*x + 1/2*c)^9 - 120*A*b*tan(1/2*d*x + 1/2*c)^9 - 120*C*b*tan(1/2*d*x + 1/2*c)^9 - 120*A*a*tan(1/2*d*x + 1/2*c)^7 - 30*C*a*tan(1/2*d*x + 1/2*c)^7 + 320*A*b*tan(1/2*d*x + 1/2*c)^7 + 160*C*b*tan(1/2*d*x + 1/2*c)^7 - 400*A*b*tan(1/2*d*x + 1/2*c)^5 - 464*C*b*tan(1/2*d*x + 1/2*c)^5 + 120*A*a*tan(1/2*d*x + 1/2*c)^3 + 30*C*a*tan(1/2*d*x + 1/2*c)^3 + 320*A*b*tan(1/2*d*x + 1/2*c)^3 + 160*C*b*tan(1/2*d*x + 1/2*c)^3 - 60*A*a*tan(1/2*d*x + 1/2*c) - 75*C*a*tan(1/2*d*x + 1/2*c) - 120*A*b*tan(1/2*d*x + 1/2*c) - 120*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
638,1,304,0,0.227867," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(4 \, A b + 3 \, C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, A b + 3 \, C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(24 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(4*A*b + 3*C*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*A*b + 3*C*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(24*A*a*tan(1/2*d*x + 1/2*c)^7 + 24*C*a*tan(1/2*d*x + 1/2*c)^7 - 12*A*b*tan(1/2*d*x + 1/2*c)^7 - 15*C*b*tan(1/2*d*x + 1/2*c)^7 - 72*A*a*tan(1/2*d*x + 1/2*c)^5 - 40*C*a*tan(1/2*d*x + 1/2*c)^5 + 12*A*b*tan(1/2*d*x + 1/2*c)^5 - 9*C*b*tan(1/2*d*x + 1/2*c)^5 + 72*A*a*tan(1/2*d*x + 1/2*c)^3 + 40*C*a*tan(1/2*d*x + 1/2*c)^3 + 12*A*b*tan(1/2*d*x + 1/2*c)^3 - 9*C*b*tan(1/2*d*x + 1/2*c)^3 - 24*A*a*tan(1/2*d*x + 1/2*c) - 24*C*a*tan(1/2*d*x + 1/2*c) - 12*A*b*tan(1/2*d*x + 1/2*c) - 15*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
639,1,184,0,0.241654," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(2 \, A a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, A a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*A*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*A*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(3*C*a*tan(1/2*d*x + 1/2*c)^5 - 6*A*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*b*tan(1/2*d*x + 1/2*c)^3 + 4*C*b*tan(1/2*d*x + 1/2*c)^3 - 3*C*a*tan(1/2*d*x + 1/2*c) - 6*A*b*tan(1/2*d*x + 1/2*c) - 6*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
640,1,134,0,0.218017," ","integrate((a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} A a + {\left(2 \, A b + C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, A b + C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*A*a + (2*A*b + C*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*A*b + C*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*C*a*tan(1/2*d*x + 1/2*c)^3 - C*b*tan(1/2*d*x + 1/2*c)^3 - 2*C*a*tan(1/2*d*x + 1/2*c) - C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
641,1,119,0,0.207298," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} A b + C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((d*x + c)*A*b + C*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - C*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - C*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) - C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
642,1,127,0,0.209297," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, C b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, C b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(A a + 2 \, C a\right)} {\left(d x + c\right)} - \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*C*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*C*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (A*a + 2*C*a)*(d*x + c) - 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*A*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) - 2*A*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
643,1,153,0,0.178169," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(A b + 2 \, C b\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(A*b + 2*C*b)*(d*x + c) + 2*(6*A*a*tan(1/2*d*x + 1/2*c)^5 + 6*C*a*tan(1/2*d*x + 1/2*c)^5 - 3*A*b*tan(1/2*d*x + 1/2*c)^5 + 4*A*a*tan(1/2*d*x + 1/2*c)^3 + 12*C*a*tan(1/2*d*x + 1/2*c)^3 + 6*A*a*tan(1/2*d*x + 1/2*c) + 6*C*a*tan(1/2*d*x + 1/2*c) + 3*A*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
644,1,272,0,0.186085," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a + 4 \, C a\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a + 4*C*a)*(d*x + c) - 2*(15*A*a*tan(1/2*d*x + 1/2*c)^7 + 12*C*a*tan(1/2*d*x + 1/2*c)^7 - 24*A*b*tan(1/2*d*x + 1/2*c)^7 - 24*C*b*tan(1/2*d*x + 1/2*c)^7 - 9*A*a*tan(1/2*d*x + 1/2*c)^5 + 12*C*a*tan(1/2*d*x + 1/2*c)^5 - 40*A*b*tan(1/2*d*x + 1/2*c)^5 - 72*C*b*tan(1/2*d*x + 1/2*c)^5 + 9*A*a*tan(1/2*d*x + 1/2*c)^3 - 12*C*a*tan(1/2*d*x + 1/2*c)^3 - 40*A*b*tan(1/2*d*x + 1/2*c)^3 - 72*C*b*tan(1/2*d*x + 1/2*c)^3 - 15*A*a*tan(1/2*d*x + 1/2*c) - 12*C*a*tan(1/2*d*x + 1/2*c) - 24*A*b*tan(1/2*d*x + 1/2*c) - 24*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
645,1,302,0,0.188066," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, A b + 4 \, C b\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*A*b + 4*C*b)*(d*x + c) + 2*(120*A*a*tan(1/2*d*x + 1/2*c)^9 + 120*C*a*tan(1/2*d*x + 1/2*c)^9 - 75*A*b*tan(1/2*d*x + 1/2*c)^9 - 60*C*b*tan(1/2*d*x + 1/2*c)^9 + 160*A*a*tan(1/2*d*x + 1/2*c)^7 + 320*C*a*tan(1/2*d*x + 1/2*c)^7 - 30*A*b*tan(1/2*d*x + 1/2*c)^7 - 120*C*b*tan(1/2*d*x + 1/2*c)^7 + 464*A*a*tan(1/2*d*x + 1/2*c)^5 + 400*C*a*tan(1/2*d*x + 1/2*c)^5 + 160*A*a*tan(1/2*d*x + 1/2*c)^3 + 320*C*a*tan(1/2*d*x + 1/2*c)^3 + 30*A*b*tan(1/2*d*x + 1/2*c)^3 + 120*C*b*tan(1/2*d*x + 1/2*c)^3 + 120*A*a*tan(1/2*d*x + 1/2*c) + 120*C*a*tan(1/2*d*x + 1/2*c) + 75*A*b*tan(1/2*d*x + 1/2*c) + 60*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
646,1,532,0,0.291104," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, A a b + 3 \, C a b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, A a b + 3 \, C a b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(60 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 160 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 160 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 80 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 200 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 200 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 232 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(15*(4*A*a*b + 3*C*a*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*A*a*b + 3*C*a*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(60*A*a^2*tan(1/2*d*x + 1/2*c)^9 + 60*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 60*A*a*b*tan(1/2*d*x + 1/2*c)^9 - 75*C*a*b*tan(1/2*d*x + 1/2*c)^9 + 60*A*b^2*tan(1/2*d*x + 1/2*c)^9 + 60*C*b^2*tan(1/2*d*x + 1/2*c)^9 - 240*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 160*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 120*A*a*b*tan(1/2*d*x + 1/2*c)^7 + 30*C*a*b*tan(1/2*d*x + 1/2*c)^7 - 160*A*b^2*tan(1/2*d*x + 1/2*c)^7 - 80*C*b^2*tan(1/2*d*x + 1/2*c)^7 + 360*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 200*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 200*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 232*C*b^2*tan(1/2*d*x + 1/2*c)^5 - 240*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 160*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 120*A*a*b*tan(1/2*d*x + 1/2*c)^3 - 30*C*a*b*tan(1/2*d*x + 1/2*c)^3 - 160*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 80*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 60*A*a^2*tan(1/2*d*x + 1/2*c) + 60*C*a^2*tan(1/2*d*x + 1/2*c) + 60*A*a*b*tan(1/2*d*x + 1/2*c) + 75*C*a*b*tan(1/2*d*x + 1/2*c) + 60*A*b^2*tan(1/2*d*x + 1/2*c) + 60*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
647,1,426,0,0.279298," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(8 \, A a^{2} + 4 \, C a^{2} + 4 \, A b^{2} + 3 \, C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, A a^{2} + 4 \, C a^{2} + 4 \, A b^{2} + 3 \, C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 144 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 80 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 144 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(8*A*a^2 + 4*C*a^2 + 4*A*b^2 + 3*C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*A*a^2 + 4*C*a^2 + 4*A*b^2 + 3*C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(12*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 48*A*a*b*tan(1/2*d*x + 1/2*c)^7 - 48*C*a*b*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^7 + 15*C*b^2*tan(1/2*d*x + 1/2*c)^7 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 144*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 80*C*a*b*tan(1/2*d*x + 1/2*c)^5 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 9*C*b^2*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 144*A*a*b*tan(1/2*d*x + 1/2*c)^3 - 80*C*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 9*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^2*tan(1/2*d*x + 1/2*c) + 48*A*a*b*tan(1/2*d*x + 1/2*c) + 48*C*a*b*tan(1/2*d*x + 1/2*c) + 12*A*b^2*tan(1/2*d*x + 1/2*c) + 15*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
648,1,262,0,0.264996," ","integrate((a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} A a^{2} + 3 \, {\left(2 \, A a b + C a b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, A a b + C a b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*A*a^2 + 3*(2*A*a*b + C*a*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*A*a*b + C*a*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 3*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 6*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 2*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*C*a^2*tan(1/2*d*x + 1/2*c) + 3*C*a*b*tan(1/2*d*x + 1/2*c) + 3*A*b^2*tan(1/2*d*x + 1/2*c) + 3*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
649,1,191,0,0.265158," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{4 \, {\left(d x + c\right)} A a b + \frac{4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + {\left(2 \, C a^{2} + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, C a^{2} + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(4 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*A*a*b + 4*A*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + (2*C*a^2 + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*C*a^2 + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(4*C*a*b*tan(1/2*d*x + 1/2*c)^3 - C*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*b*tan(1/2*d*x + 1/2*c) - C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
650,1,175,0,0.246322," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{4 \, C a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 4 \, C a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + {\left(A a^{2} + 2 \, C a^{2} + 2 \, A b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*C*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 4*C*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 4*C*b^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + (A*a^2 + 2*C*a^2 + 2*A*b^2)*(d*x + c) - 2*(A*a^2*tan(1/2*d*x + 1/2*c)^3 - 4*A*a*b*tan(1/2*d*x + 1/2*c)^3 - A*a^2*tan(1/2*d*x + 1/2*c) - 4*A*a*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
651,1,256,0,0.262114," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, C b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, C b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(A a b + 2 \, C a b\right)} {\left(d x + c\right)} + \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*C*b^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*C*b^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(A*a*b + 2*C*a*b)*(d*x + c) + 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 3*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 2*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^2*tan(1/2*d*x + 1/2*c) + 3*C*a^2*tan(1/2*d*x + 1/2*c) + 3*A*a*b*tan(1/2*d*x + 1/2*c) + 3*A*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
652,1,378,0,0.227750," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a^{2} + 4 \, C a^{2} + 4 \, A b^{2} + 8 \, C b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 80 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 144 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 144 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a^2 + 4*C*a^2 + 4*A*b^2 + 8*C*b^2)*(d*x + c) - 2*(15*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 48*A*a*b*tan(1/2*d*x + 1/2*c)^7 - 48*C*a*b*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^7 - 9*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 80*A*a*b*tan(1/2*d*x + 1/2*c)^5 - 144*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 80*A*a*b*tan(1/2*d*x + 1/2*c)^3 - 144*C*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^2*tan(1/2*d*x + 1/2*c) - 12*C*a^2*tan(1/2*d*x + 1/2*c) - 48*A*a*b*tan(1/2*d*x + 1/2*c) - 48*C*a*b*tan(1/2*d*x + 1/2*c) - 12*A*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
653,1,498,0,0.238459," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, A a b + 4 \, C a b\right)} {\left(d x + c\right)} + \frac{2 \, {\left(60 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 80 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 160 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 160 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 232 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 200 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 200 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 360 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 80 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(15*(3*A*a*b + 4*C*a*b)*(d*x + c) + 2*(60*A*a^2*tan(1/2*d*x + 1/2*c)^9 + 60*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 75*A*a*b*tan(1/2*d*x + 1/2*c)^9 - 60*C*a*b*tan(1/2*d*x + 1/2*c)^9 + 60*A*b^2*tan(1/2*d*x + 1/2*c)^9 + 60*C*b^2*tan(1/2*d*x + 1/2*c)^9 + 80*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 160*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 30*A*a*b*tan(1/2*d*x + 1/2*c)^7 - 120*C*a*b*tan(1/2*d*x + 1/2*c)^7 + 160*A*b^2*tan(1/2*d*x + 1/2*c)^7 + 240*C*b^2*tan(1/2*d*x + 1/2*c)^7 + 232*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 200*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 200*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 360*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 80*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 160*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 30*A*a*b*tan(1/2*d*x + 1/2*c)^3 + 120*C*a*b*tan(1/2*d*x + 1/2*c)^3 + 160*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 240*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 60*A*a^2*tan(1/2*d*x + 1/2*c) + 60*C*a^2*tan(1/2*d*x + 1/2*c) + 75*A*a*b*tan(1/2*d*x + 1/2*c) + 60*C*a*b*tan(1/2*d*x + 1/2*c) + 60*A*b^2*tan(1/2*d*x + 1/2*c) + 60*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
654,1,932,0,0.353313," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(24 \, A a^{2} b + 18 \, C a^{2} b + 6 \, A b^{3} + 5 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(24 \, A a^{2} b + 18 \, C a^{2} b + 6 \, A b^{3} + 5 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(240 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 240 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 360 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 450 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 720 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 150 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 165 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1200 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 880 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1080 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 630 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2640 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1680 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 210 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 25 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2400 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1440 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 720 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4320 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3744 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 450 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2400 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1440 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 720 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4320 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3744 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 450 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 880 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1080 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 630 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2640 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1680 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 210 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 360 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 450 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 150 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 165 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(24*A*a^2*b + 18*C*a^2*b + 6*A*b^3 + 5*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(24*A*a^2*b + 18*C*a^2*b + 6*A*b^3 + 5*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(240*A*a^3*tan(1/2*d*x + 1/2*c)^11 + 240*C*a^3*tan(1/2*d*x + 1/2*c)^11 - 360*A*a^2*b*tan(1/2*d*x + 1/2*c)^11 - 450*C*a^2*b*tan(1/2*d*x + 1/2*c)^11 + 720*A*a*b^2*tan(1/2*d*x + 1/2*c)^11 + 720*C*a*b^2*tan(1/2*d*x + 1/2*c)^11 - 150*A*b^3*tan(1/2*d*x + 1/2*c)^11 - 165*C*b^3*tan(1/2*d*x + 1/2*c)^11 - 1200*A*a^3*tan(1/2*d*x + 1/2*c)^9 - 880*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 1080*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 630*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 2640*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 1680*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 210*A*b^3*tan(1/2*d*x + 1/2*c)^9 - 25*C*b^3*tan(1/2*d*x + 1/2*c)^9 + 2400*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 1440*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 720*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 180*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 4320*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 3744*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 60*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 450*C*b^3*tan(1/2*d*x + 1/2*c)^7 - 2400*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 1440*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 720*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 180*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 4320*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 3744*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 60*A*b^3*tan(1/2*d*x + 1/2*c)^5 - 450*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 1200*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 880*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 1080*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 630*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 2640*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 1680*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 210*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 25*C*b^3*tan(1/2*d*x + 1/2*c)^3 - 240*A*a^3*tan(1/2*d*x + 1/2*c) - 240*C*a^3*tan(1/2*d*x + 1/2*c) - 360*A*a^2*b*tan(1/2*d*x + 1/2*c) - 450*C*a^2*b*tan(1/2*d*x + 1/2*c) - 720*A*a*b^2*tan(1/2*d*x + 1/2*c) - 720*C*a*b^2*tan(1/2*d*x + 1/2*c) - 150*A*b^3*tan(1/2*d*x + 1/2*c) - 165*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
655,1,656,0,0.324933," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(8 \, A a^{3} + 4 \, C a^{3} + 12 \, A a b^{2} + 9 \, C a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(8 \, A a^{3} + 4 \, C a^{3} + 12 \, A a b^{2} + 9 \, C a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 180 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 225 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1440 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 90 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 160 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2160 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1200 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 400 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 464 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1440 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 960 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 90 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 360 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 180 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 225 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(8*A*a^3 + 4*C*a^3 + 12*A*a*b^2 + 9*C*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(8*A*a^3 + 4*C*a^3 + 12*A*a*b^2 + 9*C*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(60*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 360*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 360*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 180*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 225*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 120*A*b^3*tan(1/2*d*x + 1/2*c)^9 - 120*C*b^3*tan(1/2*d*x + 1/2*c)^9 - 120*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 1440*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 960*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 360*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 90*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 320*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 160*C*b^3*tan(1/2*d*x + 1/2*c)^7 - 2160*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 1200*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 400*A*b^3*tan(1/2*d*x + 1/2*c)^5 - 464*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 120*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 1440*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 960*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 360*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 90*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 320*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 160*C*b^3*tan(1/2*d*x + 1/2*c)^3 - 60*C*a^3*tan(1/2*d*x + 1/2*c) - 360*A*a^2*b*tan(1/2*d*x + 1/2*c) - 360*C*a^2*b*tan(1/2*d*x + 1/2*c) - 180*A*a*b^2*tan(1/2*d*x + 1/2*c) - 225*C*a*b^2*tan(1/2*d*x + 1/2*c) - 120*A*b^3*tan(1/2*d*x + 1/2*c) - 120*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
656,1,526,0,0.300980," ","integrate((a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, {\left(d x + c\right)} A a^{3} + {\left(24 \, A a^{2} b + 12 \, C a^{2} b + 4 \, A b^{3} + 3 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(24 \, A a^{2} b + 12 \, C a^{2} b + 4 \, A b^{3} + 3 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(8 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(8*(d*x + c)*A*a^3 + (24*A*a^2*b + 12*C*a^2*b + 4*A*b^3 + 3*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (24*A*a^2*b + 12*C*a^2*b + 4*A*b^3 + 3*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(8*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 12*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 24*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 24*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 4*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 5*C*b^3*tan(1/2*d*x + 1/2*c)^7 - 24*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 72*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 40*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*A*b^3*tan(1/2*d*x + 1/2*c)^5 - 3*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 24*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 72*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 40*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*C*b^3*tan(1/2*d*x + 1/2*c)^3 - 8*C*a^3*tan(1/2*d*x + 1/2*c) - 12*C*a^2*b*tan(1/2*d*x + 1/2*c) - 24*A*a*b^2*tan(1/2*d*x + 1/2*c) - 24*C*a*b^2*tan(1/2*d*x + 1/2*c) - 4*A*b^3*tan(1/2*d*x + 1/2*c) - 5*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
657,1,322,0,0.318781," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{18 \, {\left(d x + c\right)} A a^{2} b + \frac{12 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 3 \, {\left(2 \, C a^{3} + 6 \, A a b^{2} + 3 \, C a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, C a^{3} + 6 \, A a b^{2} + 3 \, C a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(18*(d*x + c)*A*a^2*b + 12*A*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 3*(2*C*a^3 + 6*A*a*b^2 + 3*C*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*C*a^3 + 6*A*a*b^2 + 3*C*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(18*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 9*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^3*tan(1/2*d*x + 1/2*c)^5 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 4*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^2*b*tan(1/2*d*x + 1/2*c) + 9*C*a*b^2*tan(1/2*d*x + 1/2*c) + 6*A*b^3*tan(1/2*d*x + 1/2*c) + 6*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
658,1,387,0,0.321552," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(A a^{3} + 2 \, C a^{3} + 6 \, A a b^{2}\right)} {\left(d x + c\right)} + {\left(6 \, C a^{2} b + 2 \, A b^{3} + C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(6 \, C a^{2} b + 2 \, A b^{3} + C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((A*a^3 + 2*C*a^3 + 6*A*a*b^2)*(d*x + c) + (6*C*a^2*b + 2*A*b^3 + C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (6*C*a^2*b + 2*A*b^3 + C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(A*a^3*tan(1/2*d*x + 1/2*c)^7 - 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 6*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - C*b^3*tan(1/2*d*x + 1/2*c)^7 - 3*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 6*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 6*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 3*C*b^3*tan(1/2*d*x + 1/2*c)^3 - A*a^3*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b*tan(1/2*d*x + 1/2*c) - 6*C*a*b^2*tan(1/2*d*x + 1/2*c) - C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","B",0
659,1,306,0,0.287957," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{18 \, C a b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 18 \, C a b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{12 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + 3 \, {\left(3 \, A a^{2} b + 6 \, C a^{2} b + 2 \, A b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(18*C*a*b^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 18*C*a*b^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 12*C*b^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 3*(3*A*a^2*b + 6*C*a^2*b + 2*A*b^3)*(d*x + c) + 2*(6*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*tan(1/2*d*x + 1/2*c) + 6*C*a^3*tan(1/2*d*x + 1/2*c) + 9*A*a^2*b*tan(1/2*d*x + 1/2*c) + 18*A*a*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
660,1,503,0,0.303529," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, C b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 8 \, C b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(3 \, A a^{3} + 4 \, C a^{3} + 12 \, A a b^{2} + 24 \, C a b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(5 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(8*C*b^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 8*C*b^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (3*A*a^3 + 4*C*a^3 + 12*A*a*b^2 + 24*C*a*b^2)*(d*x + c) - 2*(5*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 4*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 24*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 8*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 3*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 4*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 40*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 24*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 24*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 5*A*a^3*tan(1/2*d*x + 1/2*c) - 4*C*a^3*tan(1/2*d*x + 1/2*c) - 24*A*a^2*b*tan(1/2*d*x + 1/2*c) - 24*C*a^2*b*tan(1/2*d*x + 1/2*c) - 12*A*a*b^2*tan(1/2*d*x + 1/2*c) - 8*A*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
661,1,606,0,0.295327," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(9 \, A a^{2} b + 12 \, C a^{2} b + 4 \, A b^{3} + 8 \, C b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 225 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 90 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1440 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2160 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 90 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1440 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 225 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(9*A*a^2*b + 12*C*a^2*b + 4*A*b^3 + 8*C*b^3)*(d*x + c) + 2*(120*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 120*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 225*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 180*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*A*b^3*tan(1/2*d*x + 1/2*c)^9 + 160*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 320*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 90*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 360*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 1440*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 120*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 464*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 400*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 1200*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 2160*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 160*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 320*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 90*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 360*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 1440*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^3*tan(1/2*d*x + 1/2*c) + 120*C*a^3*tan(1/2*d*x + 1/2*c) + 225*A*a^2*b*tan(1/2*d*x + 1/2*c) + 180*C*a^2*b*tan(1/2*d*x + 1/2*c) + 360*A*a*b^2*tan(1/2*d*x + 1/2*c) + 360*C*a*b^2*tan(1/2*d*x + 1/2*c) + 60*A*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
662,1,882,0,0.303468," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(5 \, A a^{3} + 6 \, C a^{3} + 18 \, A a b^{2} + 24 \, C a b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 150 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 25 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 210 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1680 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2640 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 630 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1080 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 880 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1200 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 450 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3744 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4320 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 180 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1440 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2400 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 450 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3744 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4320 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 180 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1440 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2400 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1680 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2640 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 630 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1080 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 880 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1200 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 150 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 450 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(5*A*a^3 + 6*C*a^3 + 18*A*a*b^2 + 24*C*a*b^2)*(d*x + c) - 2*(165*A*a^3*tan(1/2*d*x + 1/2*c)^11 + 150*C*a^3*tan(1/2*d*x + 1/2*c)^11 - 720*A*a^2*b*tan(1/2*d*x + 1/2*c)^11 - 720*C*a^2*b*tan(1/2*d*x + 1/2*c)^11 + 450*A*a*b^2*tan(1/2*d*x + 1/2*c)^11 + 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^11 - 240*A*b^3*tan(1/2*d*x + 1/2*c)^11 - 240*C*b^3*tan(1/2*d*x + 1/2*c)^11 - 25*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 210*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 1680*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 2640*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 630*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 1080*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 880*A*b^3*tan(1/2*d*x + 1/2*c)^9 - 1200*C*b^3*tan(1/2*d*x + 1/2*c)^9 + 450*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 3744*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 4320*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 180*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 720*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 1440*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 2400*C*b^3*tan(1/2*d*x + 1/2*c)^7 - 450*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 60*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 3744*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 4320*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 180*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 720*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 1440*A*b^3*tan(1/2*d*x + 1/2*c)^5 - 2400*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 25*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 210*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 1680*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 2640*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 630*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 1080*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 880*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 1200*C*b^3*tan(1/2*d*x + 1/2*c)^3 - 165*A*a^3*tan(1/2*d*x + 1/2*c) - 150*C*a^3*tan(1/2*d*x + 1/2*c) - 720*A*a^2*b*tan(1/2*d*x + 1/2*c) - 720*C*a^2*b*tan(1/2*d*x + 1/2*c) - 450*A*a*b^2*tan(1/2*d*x + 1/2*c) - 360*C*a*b^2*tan(1/2*d*x + 1/2*c) - 240*A*b^3*tan(1/2*d*x + 1/2*c) - 240*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","B",0
663,1,1280,0,0.392310," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(8 \, A a^{3} b + 6 \, C a^{3} b + 6 \, A a b^{3} + 5 \, C a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(8 \, A a^{3} b + 6 \, C a^{3} b + 6 \, A a b^{3} + 5 \, C a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(420 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 420 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 840 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1050 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2520 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2520 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1050 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1155 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 420 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 420 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 2520 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1960 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3360 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 2520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 11760 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 8400 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 2520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 980 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1400 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 840 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 6300 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4060 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4200 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1890 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 24360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 18984 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1890 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2975 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3164 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3612 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 8400 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5040 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30240 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 26208 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4368 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2544 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6300 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4060 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4200 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1890 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18984 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1890 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2975 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3164 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3612 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2520 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1960 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3360 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 11760 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8400 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 980 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1400 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 840 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 420 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 420 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 840 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1050 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2520 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2520 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1050 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1155 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 420 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 420 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{420 \, d}"," ",0,"1/420*(105*(8*A*a^3*b + 6*C*a^3*b + 6*A*a*b^3 + 5*C*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(8*A*a^3*b + 6*C*a^3*b + 6*A*a*b^3 + 5*C*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(420*A*a^4*tan(1/2*d*x + 1/2*c)^13 + 420*C*a^4*tan(1/2*d*x + 1/2*c)^13 - 840*A*a^3*b*tan(1/2*d*x + 1/2*c)^13 - 1050*C*a^3*b*tan(1/2*d*x + 1/2*c)^13 + 2520*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 + 2520*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 - 1050*A*a*b^3*tan(1/2*d*x + 1/2*c)^13 - 1155*C*a*b^3*tan(1/2*d*x + 1/2*c)^13 + 420*A*b^4*tan(1/2*d*x + 1/2*c)^13 + 420*C*b^4*tan(1/2*d*x + 1/2*c)^13 - 2520*A*a^4*tan(1/2*d*x + 1/2*c)^11 - 1960*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 3360*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 2520*C*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 11760*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 8400*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 2520*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 980*C*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 1400*A*b^4*tan(1/2*d*x + 1/2*c)^11 - 840*C*b^4*tan(1/2*d*x + 1/2*c)^11 + 6300*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 4060*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 4200*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 1890*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 24360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 18984*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 1890*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 2975*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 3164*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 3612*C*b^4*tan(1/2*d*x + 1/2*c)^9 - 8400*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 5040*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 30240*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 26208*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 4368*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 2544*C*b^4*tan(1/2*d*x + 1/2*c)^7 + 6300*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 4060*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 4200*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 1890*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 24360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 18984*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 1890*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 2975*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 3164*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 3612*C*b^4*tan(1/2*d*x + 1/2*c)^5 - 2520*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 1960*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 3360*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 2520*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 11760*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 8400*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 2520*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 980*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 1400*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 840*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 420*A*a^4*tan(1/2*d*x + 1/2*c) + 420*C*a^4*tan(1/2*d*x + 1/2*c) + 840*A*a^3*b*tan(1/2*d*x + 1/2*c) + 1050*C*a^3*b*tan(1/2*d*x + 1/2*c) + 2520*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 2520*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 1050*A*a*b^3*tan(1/2*d*x + 1/2*c) + 1155*C*a*b^3*tan(1/2*d*x + 1/2*c) + 420*A*b^4*tan(1/2*d*x + 1/2*c) + 420*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","B",0
664,1,1100,0,0.366262," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(16 \, A a^{4} + 8 \, C a^{4} + 48 \, A a^{2} b^{2} + 36 \, C a^{2} b^{2} + 6 \, A b^{4} + 5 \, C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(16 \, A a^{4} + 8 \, C a^{4} + 48 \, A a^{2} b^{2} + 36 \, C a^{2} b^{2} + 6 \, A b^{4} + 5 \, C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 900 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 150 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 165 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 360 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4800 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2160 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1260 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2240 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 210 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 25 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 240 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9600 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1440 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4992 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 450 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9600 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5760 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1440 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 360 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4992 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 450 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 360 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4800 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2160 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1260 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 25 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 900 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 150 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 165 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(16*A*a^4 + 8*C*a^4 + 48*A*a^2*b^2 + 36*C*a^2*b^2 + 6*A*b^4 + 5*C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(16*A*a^4 + 8*C*a^4 + 48*A*a^2*b^2 + 36*C*a^2*b^2 + 6*A*b^4 + 5*C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(120*C*a^4*tan(1/2*d*x + 1/2*c)^11 - 960*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 960*C*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 900*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 960*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 960*C*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 150*A*b^4*tan(1/2*d*x + 1/2*c)^11 + 165*C*b^4*tan(1/2*d*x + 1/2*c)^11 - 360*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 4800*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 3520*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 2160*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 1260*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 2240*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 210*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 25*C*b^4*tan(1/2*d*x + 1/2*c)^9 + 240*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 9600*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 5760*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 1440*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 360*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 4992*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 60*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 450*C*b^4*tan(1/2*d*x + 1/2*c)^7 + 240*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 9600*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 5760*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 1440*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 360*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 4992*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 60*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 450*C*b^4*tan(1/2*d*x + 1/2*c)^5 - 360*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 4800*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 3520*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 2160*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 1260*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 2240*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 210*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 25*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 120*C*a^4*tan(1/2*d*x + 1/2*c) + 960*A*a^3*b*tan(1/2*d*x + 1/2*c) + 960*C*a^3*b*tan(1/2*d*x + 1/2*c) + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 900*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 960*A*a*b^3*tan(1/2*d*x + 1/2*c) + 960*C*a*b^3*tan(1/2*d*x + 1/2*c) + 150*A*b^4*tan(1/2*d*x + 1/2*c) + 165*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
665,1,778,0,0.324843," ","integrate((a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{30 \, {\left(d x + c\right)} A a^{4} + 15 \, {\left(8 \, A a^{3} b + 4 \, C a^{3} b + 4 \, A a b^{3} + 3 \, C a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(8 \, A a^{3} b + 4 \, C a^{3} b + 4 \, A a b^{3} + 3 \, C a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(30 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 180 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 180 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 30 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 30 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 80 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 40 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 180 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1080 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 600 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 100 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 116 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(30*(d*x + c)*A*a^4 + 15*(8*A*a^3*b + 4*C*a^3*b + 4*A*a*b^3 + 3*C*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(8*A*a^3*b + 4*C*a^3*b + 4*A*a*b^3 + 3*C*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(30*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 60*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 180*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 180*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 75*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 30*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 30*C*b^4*tan(1/2*d*x + 1/2*c)^9 - 120*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 120*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 480*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 120*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 30*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 80*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 40*C*b^4*tan(1/2*d*x + 1/2*c)^7 + 180*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 1080*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 600*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 100*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 116*C*b^4*tan(1/2*d*x + 1/2*c)^5 - 120*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 120*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 480*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 30*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 80*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 40*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 30*C*a^4*tan(1/2*d*x + 1/2*c) + 60*C*a^3*b*tan(1/2*d*x + 1/2*c) + 180*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 180*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 60*A*a*b^3*tan(1/2*d*x + 1/2*c) + 75*C*a*b^3*tan(1/2*d*x + 1/2*c) + 30*A*b^4*tan(1/2*d*x + 1/2*c) + 30*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
666,1,590,0,0.337398," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{96 \, {\left(d x + c\right)} A a^{3} b + \frac{48 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 3 \, {\left(8 \, C a^{4} + 48 \, A a^{2} b^{2} + 24 \, C a^{2} b^{2} + 4 \, A b^{4} + 3 \, C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, C a^{4} + 48 \, A a^{2} b^{2} + 24 \, C a^{2} b^{2} + 4 \, A b^{4} + 3 \, C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(96*(d*x + c)*A*a^3*b + 48*A*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 3*(8*C*a^4 + 48*A*a^2*b^2 + 24*C*a^2*b^2 + 4*A*b^4 + 3*C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*C*a^4 + 48*A*a^2*b^2 + 24*C*a^2*b^2 + 4*A*b^4 + 3*C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(96*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 96*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 96*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 12*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 15*C*b^4*tan(1/2*d*x + 1/2*c)^7 - 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 160*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*b^4*tan(1/2*d*x + 1/2*c)^5 - 9*C*b^4*tan(1/2*d*x + 1/2*c)^5 + 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 160*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 9*C*b^4*tan(1/2*d*x + 1/2*c)^3 - 96*C*a^3*b*tan(1/2*d*x + 1/2*c) - 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c) - 96*A*a*b^3*tan(1/2*d*x + 1/2*c) - 96*C*a*b^3*tan(1/2*d*x + 1/2*c) - 12*A*b^4*tan(1/2*d*x + 1/2*c) - 15*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
667,1,397,0,0.353357," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(A a^{4} + 2 \, C a^{4} + 12 \, A a^{2} b^{2}\right)} {\left(d x + c\right)} + 12 \, {\left(2 \, C a^{3} b + 2 \, A a b^{3} + C a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 12 \, {\left(2 \, C a^{3} b + 2 \, A a b^{3} + C a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{6 \, {\left(A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{4 \, {\left(18 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(A*a^4 + 2*C*a^4 + 12*A*a^2*b^2)*(d*x + c) + 12*(2*C*a^3*b + 2*A*a*b^3 + C*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 12*(2*C*a^3*b + 2*A*a*b^3 + C*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 6*(A*a^4*tan(1/2*d*x + 1/2*c)^3 - 8*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - A*a^4*tan(1/2*d*x + 1/2*c) - 8*A*a^3*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - 4*(18*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*C*b^4*tan(1/2*d*x + 1/2*c)^5 - 36*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 6*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 2*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 6*C*a*b^3*tan(1/2*d*x + 1/2*c) + 3*A*b^4*tan(1/2*d*x + 1/2*c) + 3*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
668,1,398,0,0.330827," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{12 \, {\left(A a^{3} b + 2 \, C a^{3} b + 2 \, A a b^{3}\right)} {\left(d x + c\right)} + 3 \, {\left(12 \, C a^{2} b^{2} + 2 \, A b^{4} + C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(12 \, C a^{2} b^{2} + 2 \, A b^{4} + C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{6 \, {\left(8 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{4 \, {\left(3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*(A*a^3*b + 2*C*a^3*b + 2*A*a*b^3)*(d*x + c) + 3*(12*C*a^2*b^2 + 2*A*b^4 + C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(12*C*a^2*b^2 + 2*A*b^4 + C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 6*(8*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 - C*b^4*tan(1/2*d*x + 1/2*c)^3 - 8*C*a*b^3*tan(1/2*d*x + 1/2*c) - C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + 4*(3*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 18*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 2*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 36*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*tan(1/2*d*x + 1/2*c) + 3*C*a^4*tan(1/2*d*x + 1/2*c) + 6*A*a^3*b*tan(1/2*d*x + 1/2*c) + 18*A*a^2*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
669,1,558,0,0.325141," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{96 \, C a b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 96 \, C a b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{48 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + 3 \, {\left(3 \, A a^{4} + 4 \, C a^{4} + 24 \, A a^{2} b^{2} + 48 \, C a^{2} b^{2} + 8 \, A b^{4}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(96*C*a*b^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 96*C*a*b^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 48*C*b^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 3*(3*A*a^4 + 4*C*a^4 + 24*A*a^2*b^2 + 48*C*a^2*b^2 + 8*A*b^4)*(d*x + c) - 2*(15*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 96*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 96*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 96*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 9*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 160*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 160*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^4*tan(1/2*d*x + 1/2*c) - 12*C*a^4*tan(1/2*d*x + 1/2*c) - 96*A*a^3*b*tan(1/2*d*x + 1/2*c) - 96*C*a^3*b*tan(1/2*d*x + 1/2*c) - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c) - 96*A*a*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
670,1,753,0,0.324537," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{30 \, C b^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 30 \, C b^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 15 \, {\left(3 \, A a^{3} b + 4 \, C a^{3} b + 4 \, A a b^{3} + 8 \, C a b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(30 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 30 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 180 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 180 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 30 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 40 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 80 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 116 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 100 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 600 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1080 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 180 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(30*C*b^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 30*C*b^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 15*(3*A*a^3*b + 4*C*a^3*b + 4*A*a*b^3 + 8*C*a*b^3)*(d*x + c) + 2*(30*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 30*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 75*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 60*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 180*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 180*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 30*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 40*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 80*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 30*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 120*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 480*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 120*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 116*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 100*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 600*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 1080*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 180*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 40*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 80*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 30*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 120*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 480*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 30*A*a^4*tan(1/2*d*x + 1/2*c) + 30*C*a^4*tan(1/2*d*x + 1/2*c) + 75*A*a^3*b*tan(1/2*d*x + 1/2*c) + 60*C*a^3*b*tan(1/2*d*x + 1/2*c) + 180*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 180*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 60*A*a*b^3*tan(1/2*d*x + 1/2*c) + 30*A*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
671,1,1034,0,0.317633," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(5 \, A a^{4} + 6 \, C a^{4} + 36 \, A a^{2} b^{2} + 48 \, C a^{2} b^{2} + 8 \, A b^{4} + 16 \, C b^{4}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 150 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 900 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 25 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 210 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2240 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1260 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2160 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4800 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 450 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4992 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1440 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9600 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 450 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4992 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5760 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1440 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9600 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1260 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2160 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4800 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 150 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 900 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(5*A*a^4 + 6*C*a^4 + 36*A*a^2*b^2 + 48*C*a^2*b^2 + 8*A*b^4 + 16*C*b^4)*(d*x + c) - 2*(165*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 150*C*a^4*tan(1/2*d*x + 1/2*c)^11 - 960*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 960*C*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 900*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 960*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 960*C*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^11 - 25*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 210*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 2240*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 3520*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 1260*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 2160*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 4800*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 360*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 450*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 60*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 4992*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 5760*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 1440*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 9600*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 240*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 450*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 60*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 4992*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 5760*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 1440*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 9600*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 240*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 25*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 210*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 2240*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 3520*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 1260*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 2160*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 4800*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 360*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 165*A*a^4*tan(1/2*d*x + 1/2*c) - 150*C*a^4*tan(1/2*d*x + 1/2*c) - 960*A*a^3*b*tan(1/2*d*x + 1/2*c) - 960*C*a^3*b*tan(1/2*d*x + 1/2*c) - 900*A*a^2*b^2*tan(1/2*d*x + 1/2*c) - 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c) - 960*A*a*b^3*tan(1/2*d*x + 1/2*c) - 960*C*a*b^3*tan(1/2*d*x + 1/2*c) - 120*A*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","B",0
672,1,1228,0,0.334277," ","integrate(cos(d*x+c)^7*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(5 \, A a^{3} b + 6 \, C a^{3} b + 6 \, A a b^{3} + 8 \, C a b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(420 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 420 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1155 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1050 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2520 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2520 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1050 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 840 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 420 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 420 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 840 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1400 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 980 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 2520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 8400 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 11760 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 2520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 3360 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1960 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 2520 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3612 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3164 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2975 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1890 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 18984 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 24360 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1890 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4200 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4060 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 6300 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2544 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4368 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 26208 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30240 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5040 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 8400 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3612 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3164 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2975 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1890 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18984 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24360 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1890 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4200 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4060 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6300 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 840 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1400 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 980 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8400 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11760 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3360 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1960 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2520 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 420 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 420 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1155 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1050 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2520 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2520 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1050 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 840 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 420 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 420 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7}}}{420 \, d}"," ",0,"1/420*(105*(5*A*a^3*b + 6*C*a^3*b + 6*A*a*b^3 + 8*C*a*b^3)*(d*x + c) + 2*(420*A*a^4*tan(1/2*d*x + 1/2*c)^13 + 420*C*a^4*tan(1/2*d*x + 1/2*c)^13 - 1155*A*a^3*b*tan(1/2*d*x + 1/2*c)^13 - 1050*C*a^3*b*tan(1/2*d*x + 1/2*c)^13 + 2520*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 + 2520*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 - 1050*A*a*b^3*tan(1/2*d*x + 1/2*c)^13 - 840*C*a*b^3*tan(1/2*d*x + 1/2*c)^13 + 420*A*b^4*tan(1/2*d*x + 1/2*c)^13 + 420*C*b^4*tan(1/2*d*x + 1/2*c)^13 + 840*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 1400*C*a^4*tan(1/2*d*x + 1/2*c)^11 - 980*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 2520*C*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 8400*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 11760*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 2520*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 3360*C*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 1960*A*b^4*tan(1/2*d*x + 1/2*c)^11 + 2520*C*b^4*tan(1/2*d*x + 1/2*c)^11 + 3612*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 3164*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 2975*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 1890*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 18984*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 24360*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 1890*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 4200*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 4060*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 6300*C*b^4*tan(1/2*d*x + 1/2*c)^9 + 2544*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 4368*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 26208*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 30240*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 5040*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 8400*C*b^4*tan(1/2*d*x + 1/2*c)^7 + 3612*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 3164*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 2975*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 1890*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 18984*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 24360*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 1890*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 4200*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 4060*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 6300*C*b^4*tan(1/2*d*x + 1/2*c)^5 + 840*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 1400*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 980*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 2520*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 8400*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 11760*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 2520*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 3360*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 1960*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 2520*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 420*A*a^4*tan(1/2*d*x + 1/2*c) + 420*C*a^4*tan(1/2*d*x + 1/2*c) + 1155*A*a^3*b*tan(1/2*d*x + 1/2*c) + 1050*C*a^3*b*tan(1/2*d*x + 1/2*c) + 2520*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 2520*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 1050*A*a*b^3*tan(1/2*d*x + 1/2*c) + 840*C*a*b^3*tan(1/2*d*x + 1/2*c) + 420*A*b^4*tan(1/2*d*x + 1/2*c) + 420*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^7)/d","B",0
673,1,379,0,0.309440," ","integrate((a+b*sec(d*x+c))^3*(a^2-b^2*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, {\left(d x + c\right)} a^{5} + {\left(24 \, a^{4} b - 8 \, a^{2} b^{3} - 3 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(24 \, a^{4} b - 8 \, a^{2} b^{3} - 3 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(16 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 8 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(8*(d*x + c)*a^5 + (24*a^4*b - 8*a^2*b^3 - 3*b^5)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (24*a^4*b - 8*a^2*b^3 - 3*b^5)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(16*a^3*b^2*tan(1/2*d*x + 1/2*c)^7 + 8*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 - 24*a*b^4*tan(1/2*d*x + 1/2*c)^7 + 5*b^5*tan(1/2*d*x + 1/2*c)^7 - 48*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 8*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 40*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*b^5*tan(1/2*d*x + 1/2*c)^5 + 48*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 8*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 40*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 3*b^5*tan(1/2*d*x + 1/2*c)^3 - 16*a^3*b^2*tan(1/2*d*x + 1/2*c) + 8*a^2*b^3*tan(1/2*d*x + 1/2*c) + 24*a*b^4*tan(1/2*d*x + 1/2*c) + 5*b^5*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
674,1,168,0,0.241259," ","integrate((a+b*sec(d*x+c))^2*(a^2-b^2*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a^{4} + 3 \, {\left(2 \, a^{3} b - a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, a^{3} b - a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*a^4 + 3*(2*a^3*b - a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*a^3*b - a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 3*b^4*tan(1/2*d*x + 1/2*c)^5 + 2*b^4*tan(1/2*d*x + 1/2*c)^3 - 3*a*b^3*tan(1/2*d*x + 1/2*c) - 3*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
675,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(a^2-b^2*sec(d*x+c)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
676,1,372,0,8.944727," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, C a^{3} + 2 \, A a b^{2} + C a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} - \frac{3 \, {\left(2 \, C a^{3} + 2 \, A a b^{2} + C a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{12 \, {\left(C a^{4} + A a^{2} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} b^{4}} + \frac{2 \, {\left(6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"-1/6*(3*(2*C*a^3 + 2*A*a*b^2 + C*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - 3*(2*C*a^3 + 2*A*a*b^2 + C*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - 12*(C*a^4 + A*a^2*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*b^4) + 2*(6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^2*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*tan(1/2*d*x + 1/2*c) - 3*C*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c) + 6*C*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*b^3))/d","B",0
677,1,242,0,0.314675," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, C a^{2} + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} - \frac{{\left(2 \, C a^{2} + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}} - \frac{4 \, {\left(C a^{3} + A a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} b^{3}} + \frac{2 \, {\left(2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} b^{2}}}{2 \, d}"," ",0,"1/2*((2*C*a^2 + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 - (2*C*a^2 + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3 - 4*(C*a^3 + A*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*b^3) + 2*(2*C*a*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 - 2*C*a*tan(1/2*d*x + 1/2*c) + C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*b^2))/d","A",0
678,1,163,0,0.274712," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{2}} - \frac{C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{2}} + \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b} + \frac{2 \, {\left(C a^{2} + A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} b^{2}}}{d}"," ",0,"-(C*a*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^2 - C*a*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^2 + 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b) + 2*(C*a^2 + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*b^2))/d","A",0
679,1,144,0,0.261024," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} A}{a} + \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b} - \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b} - \frac{2 \, {\left(C a^{2} + A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a b}}{d}"," ",0,"((d*x + c)*A/a + C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b - C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b - 2*(C*a^2 + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a*b))/d","A",0
680,1,136,0,0.227219," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(d x + c\right)} A b}{a^{2}} - \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a} - \frac{2 \, {\left(C a^{2} + A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{2}}}{d}"," ",0,"-((d*x + c)*A*b/a^2 - 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a) - 2*(C*a^2 + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^2))/d","A",0
681,1,199,0,0.246905," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(A a^{2} + 2 \, C a^{2} + 2 \, A b^{2}\right)} {\left(d x + c\right)}}{a^{3}} - \frac{4 \, {\left(C a^{2} b + A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{3}} - \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"1/2*((A*a^2 + 2*C*a^2 + 2*A*b^2)*(d*x + c)/a^3 - 4*(C*a^2*b + A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^3) - 2*(A*a*tan(1/2*d*x + 1/2*c)^3 + 2*A*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) + 2*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2))/d","A",0
682,1,326,0,0.255387," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(A a^{2} b + 2 \, C a^{2} b + 2 \, A b^{3}\right)} {\left(d x + c\right)}}{a^{4}} - \frac{12 \, {\left(C a^{2} b^{2} + A b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{4}} - \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}}}{6 \, d}"," ",0,"-1/6*(3*(A*a^2*b + 2*C*a^2*b + 2*A*b^3)*(d*x + c)/a^4 - 12*(C*a^2*b^2 + A*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^4) - 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 6*C*a^2*tan(1/2*d*x + 1/2*c) - 3*A*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3))/d","B",0
683,1,574,0,0.280572," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(3 \, A a^{4} + 4 \, C a^{4} + 4 \, A a^{2} b^{2} + 8 \, C a^{2} b^{2} + 8 \, A b^{4}\right)} {\left(d x + c\right)}}{a^{5}} - \frac{48 \, {\left(C a^{2} b^{3} + A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{5}} - \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a^4 + 4*C*a^4 + 4*A*a^2*b^2 + 8*C*a^2*b^2 + 8*A*b^4)*(d*x + c)/a^5 - 48*(C*a^2*b^3 + A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^5) - 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 24*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 24*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 24*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 9*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 40*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 72*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^3*tan(1/2*d*x + 1/2*c) - 12*C*a^3*tan(1/2*d*x + 1/2*c) + 24*A*a^2*b*tan(1/2*d*x + 1/2*c) + 24*C*a^2*b*tan(1/2*d*x + 1/2*c) - 12*A*a*b^2*tan(1/2*d*x + 1/2*c) + 24*A*b^3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^4))/d","B",0
684,1,358,0,0.342991," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(3 \, C a^{5} + A a^{3} b^{2} - 4 \, C a^{3} b^{2} - 2 \, A a b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{4 \, {\left(C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} - \frac{{\left(6 \, C a^{2} + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} + \frac{{\left(6 \, C a^{2} + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{2 \, {\left(4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} b^{3}}}{2 \, d}"," ",0,"-1/2*(4*(3*C*a^5 + A*a^3*b^2 - 4*C*a^3*b^2 - 2*A*a*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) - 4*(C*a^4*tan(1/2*d*x + 1/2*c) + A*a^2*b^2*tan(1/2*d*x + 1/2*c))/((a^2*b^3 - b^5)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) - (6*C*a^2 + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 + (6*C*a^2 + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - 2*(4*C*a*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*tan(1/2*d*x + 1/2*c) + C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*b^3))/d","A",0
685,1,382,0,0.302264," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(2 \, C a^{4} - 3 \, C a^{2} b^{2} - A b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} + \frac{C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}} - \frac{2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} {\left(a^{2} b^{2} - b^{4}\right)}}\right)}}{d}"," ",0,"2*((2*C*a^4 - 3*C*a^2*b^2 - A*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^2*b^3 - b^5)*sqrt(-a^2 + b^2)) - C*a*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 + C*a*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3 - (2*C*a^3*tan(1/2*d*x + 1/2*c)^3 - C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + C*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^3*tan(1/2*d*x + 1/2*c) - C*a^2*b*tan(1/2*d*x + 1/2*c) - A*a*b^2*tan(1/2*d*x + 1/2*c) + C*a*b^2*tan(1/2*d*x + 1/2*c) + C*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)*(a^2*b^2 - b^4)))/d","B",0
686,1,231,0,0.297200," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(C a^{3} - A a b^{2} - 2 \, C a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{2} b^{2} - b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{2}} - \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{2}} + \frac{2 \, {\left(C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b - b^{3}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}}}{d}"," ",0,"(2*(C*a^3 - A*a*b^2 - 2*C*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^2*b^2 - b^4)*sqrt(-a^2 + b^2)) + C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^2 - C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^2 + 2*(C*a^2*tan(1/2*d*x + 1/2*c) + A*b^2*tan(1/2*d*x + 1/2*c))/((a^2*b - b^3)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)))/d","A",0
687,1,205,0,0.241497," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(2 \, A a^{2} b + C a^{2} b - A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - a^{2} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{{\left(d x + c\right)} A}{a^{2}} + \frac{2 \, {\left(C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{3} - a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}}}{d}"," ",0,"-(2*(2*A*a^2*b + C*a^2*b - A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - a^2*b^2)*sqrt(-a^2 + b^2)) - (d*x + c)*A/a^2 + 2*(C*a^2*tan(1/2*d*x + 1/2*c) + A*b^2*tan(1/2*d*x + 1/2*c))/((a^3 - a*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)))/d","A",0
688,1,988,0,0.453182," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(C a^{8} - 2 \, A a^{7} b + 5 \, A a^{6} b^{2} - C a^{6} b^{2} + 4 \, A a^{5} b^{3} - 9 \, A a^{4} b^{4} - 2 \, A a^{3} b^{5} + 4 \, A a^{2} b^{6} + C a^{3} {\left| -a^{5} + a^{3} b^{2} \right|} + 2 \, A a^{2} b {\left| -a^{5} + a^{3} b^{2} \right|} + A a b^{2} {\left| -a^{5} + a^{3} b^{2} \right|} - 2 \, A b^{3} {\left| -a^{5} + a^{3} b^{2} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{4} b - a^{2} b^{3} + \sqrt{{\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} {\left(a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}\right)} + {\left(a^{4} b - a^{2} b^{3}\right)}^{2}}}{a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}}}}\right)\right)}}{a^{4} b {\left| -a^{5} + a^{3} b^{2} \right|} - a^{2} b^{3} {\left| -a^{5} + a^{3} b^{2} \right|} + {\left(a^{5} - a^{3} b^{2}\right)}^{2}} - \frac{{\left(\sqrt{-a^{2} + b^{2}} C a^{3} {\left| -a^{5} + a^{3} b^{2} \right|} {\left| -a + b \right|} + {\left(2 \, a^{2} b + a b^{2} - 2 \, b^{3}\right)} \sqrt{-a^{2} + b^{2}} A {\left| -a^{5} + a^{3} b^{2} \right|} {\left| -a + b \right|} + {\left(2 \, a^{7} b - 5 \, a^{6} b^{2} - 4 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 2 \, a^{3} b^{5} - 4 \, a^{2} b^{6}\right)} \sqrt{-a^{2} + b^{2}} A {\left| -a + b \right|} - {\left(a^{8} - a^{6} b^{2}\right)} \sqrt{-a^{2} + b^{2}} C {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{4} b - a^{2} b^{3} - \sqrt{{\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} {\left(a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}\right)} + {\left(a^{4} b - a^{2} b^{3}\right)}^{2}}}{a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}}}}\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} - {\left(a^{6} b - 2 \, a^{5} b^{2} + 2 \, a^{3} b^{4} - a^{2} b^{5}\right)} {\left| -a^{5} + a^{3} b^{2} \right|}} + \frac{2 \, {\left(A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} {\left(a^{4} - a^{2} b^{2}\right)}}}{d}"," ",0,"((C*a^8 - 2*A*a^7*b + 5*A*a^6*b^2 - C*a^6*b^2 + 4*A*a^5*b^3 - 9*A*a^4*b^4 - 2*A*a^3*b^5 + 4*A*a^2*b^6 + C*a^3*abs(-a^5 + a^3*b^2) + 2*A*a^2*b*abs(-a^5 + a^3*b^2) + A*a*b^2*abs(-a^5 + a^3*b^2) - 2*A*b^3*abs(-a^5 + a^3*b^2))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^4*b - a^2*b^3 + sqrt((a^5 + a^4*b - a^3*b^2 - a^2*b^3)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3) + (a^4*b - a^2*b^3)^2))/(a^5 - a^4*b - a^3*b^2 + a^2*b^3))))/(a^4*b*abs(-a^5 + a^3*b^2) - a^2*b^3*abs(-a^5 + a^3*b^2) + (a^5 - a^3*b^2)^2) - (sqrt(-a^2 + b^2)*C*a^3*abs(-a^5 + a^3*b^2)*abs(-a + b) + (2*a^2*b + a*b^2 - 2*b^3)*sqrt(-a^2 + b^2)*A*abs(-a^5 + a^3*b^2)*abs(-a + b) + (2*a^7*b - 5*a^6*b^2 - 4*a^5*b^3 + 9*a^4*b^4 + 2*a^3*b^5 - 4*a^2*b^6)*sqrt(-a^2 + b^2)*A*abs(-a + b) - (a^8 - a^6*b^2)*sqrt(-a^2 + b^2)*C*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^4*b - a^2*b^3 - sqrt((a^5 + a^4*b - a^3*b^2 - a^2*b^3)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3) + (a^4*b - a^2*b^3)^2))/(a^5 - a^4*b - a^3*b^2 + a^2*b^3))))/((a^5 - a^3*b^2)^2*(a^2 - 2*a*b + b^2) - (a^6*b - 2*a^5*b^2 + 2*a^3*b^4 - a^2*b^5)*abs(-a^5 + a^3*b^2)) + 2*(A*a^3*tan(1/2*d*x + 1/2*c)^3 - A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^3*tan(1/2*d*x + 1/2*c)^3 - A*a^3*tan(1/2*d*x + 1/2*c) - A*a^2*b*tan(1/2*d*x + 1/2*c) + C*a^2*b*tan(1/2*d*x + 1/2*c) + A*a*b^2*tan(1/2*d*x + 1/2*c) + 2*A*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)*(a^4 - a^2*b^2)))/d","B",0
689,1,315,0,0.245255," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(2 \, C a^{4} b + 4 \, A a^{2} b^{3} - C a^{2} b^{3} - 3 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{4 \, {\left(C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} - \frac{{\left(A a^{2} + 2 \, C a^{2} + 6 \, A b^{2}\right)} {\left(d x + c\right)}}{a^{4}} + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}}}{2 \, d}"," ",0,"-1/2*(4*(2*C*a^4*b + 4*A*a^2*b^3 - C*a^2*b^3 - 3*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - a^4*b^2)*sqrt(-a^2 + b^2)) + 4*(C*a^2*b^2*tan(1/2*d*x + 1/2*c) + A*b^4*tan(1/2*d*x + 1/2*c))/((a^5 - a^3*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) - (A*a^2 + 2*C*a^2 + 6*A*b^2)*(d*x + c)/a^4 + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 + 4*A*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) + 4*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3))/d","A",0
690,1,441,0,0.271678," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(3 \, C a^{4} b^{2} + 5 \, A a^{2} b^{4} - 2 \, C a^{2} b^{4} - 4 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{7} - a^{5} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{6 \, {\left(C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} - \frac{3 \, {\left(A a^{2} b + 2 \, C a^{2} b + 4 \, A b^{3}\right)} {\left(d x + c\right)}}{a^{5}} + \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{4}}}{3 \, d}"," ",0,"1/3*(6*(3*C*a^4*b^2 + 5*A*a^2*b^4 - 2*C*a^2*b^4 - 4*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^7 - a^5*b^2)*sqrt(-a^2 + b^2)) + 6*(C*a^2*b^3*tan(1/2*d*x + 1/2*c) + A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - a^4*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) - 3*(A*a^2*b + 2*C*a^2*b + 4*A*b^3)*(d*x + c)/a^5 + 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 9*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 2*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 18*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^2*tan(1/2*d*x + 1/2*c) + 3*C*a^2*tan(1/2*d*x + 1/2*c) - 3*A*a*b*tan(1/2*d*x + 1/2*c) + 9*A*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^4))/d","A",0
691,1,1187,0,0.470962," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(12 \, C a^{7} + 2 \, A a^{5} b^{2} - 29 \, C a^{5} b^{2} - 5 \, A a^{3} b^{4} + 20 \, C a^{3} b^{4} + 6 \, A a b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, {\left(12 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 67 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 29 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 26 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 13 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}} - \frac{{\left(12 \, C a^{2} + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{5}} + \frac{{\left(12 \, C a^{2} + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{5}}}{2 \, d}"," ",0,"-1/2*(2*(12*C*a^7 + 2*A*a^5*b^2 - 29*C*a^5*b^2 - 5*A*a^3*b^4 + 20*C*a^3*b^4 + 6*A*a*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4*b^5 - 2*a^2*b^7 + b^9)*sqrt(-a^2 + b^2)) - 2*(12*C*a^7*tan(1/2*d*x + 1/2*c)^7 - 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^7 + 2*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 17*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 5*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 2*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 + 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 13*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^7 + C*b^7*tan(1/2*d*x + 1/2*c)^7 - 36*C*a^7*tan(1/2*d*x + 1/2*c)^5 + 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 67*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 29*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 15*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 26*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 5*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^5 + 3*C*b^7*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^7*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 67*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 26*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 5*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 3*C*b^7*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^7*tan(1/2*d*x + 1/2*c) - 18*C*a^6*b*tan(1/2*d*x + 1/2*c) - 2*A*a^5*b^2*tan(1/2*d*x + 1/2*c) + 17*C*a^5*b^2*tan(1/2*d*x + 1/2*c) - 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c) + 33*C*a^4*b^3*tan(1/2*d*x + 1/2*c) + 5*A*a^3*b^4*tan(1/2*d*x + 1/2*c) + 2*C*a^3*b^4*tan(1/2*d*x + 1/2*c) + 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c) - 13*C*a^2*b^5*tan(1/2*d*x + 1/2*c) - 4*C*a*b^6*tan(1/2*d*x + 1/2*c) + C*b^7*tan(1/2*d*x + 1/2*c))/((a^4*b^4 - 2*a^2*b^6 + b^8)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)^2) - (12*C*a^2 + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^5 + (12*C*a^2 + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^5)/d","B",0
692,1,521,0,0.478262," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(6 \, C a^{6} - 15 \, C a^{4} b^{2} + A a^{2} b^{4} + 12 \, C a^{2} b^{4} + 2 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{3 \, C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} + \frac{3 \, C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{4 \, C a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} - \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b^{3}}}{d}"," ",0,"((6*C*a^6 - 15*C*a^4*b^2 + A*a^2*b^4 + 12*C*a^2*b^4 + 2*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4*b^4 - 2*a^2*b^6 + b^8)*sqrt(-a^2 + b^2)) - 3*C*a*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 + 3*C*a*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - (4*C*a^6*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 7*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - A*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*A*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*A*a*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^6*tan(1/2*d*x + 1/2*c) - 5*C*a^5*b*tan(1/2*d*x + 1/2*c) + 7*C*a^4*b^2*tan(1/2*d*x + 1/2*c) - A*a^3*b^3*tan(1/2*d*x + 1/2*c) + 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c) + 3*A*a^2*b^4*tan(1/2*d*x + 1/2*c) + 4*A*a*b^5*tan(1/2*d*x + 1/2*c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) - 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b^3))/d","B",0
693,1,509,0,0.400187," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, C a^{5} - 5 \, C a^{3} b^{2} + 3 \, A a b^{4} + 6 \, C a b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} + \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}} - \frac{2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"-((2*C*a^5 - 5*C*a^3*b^2 + 3*A*a*b^4 + 6*C*a*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4*b^3 - 2*a^2*b^5 + b^7)*sqrt(-a^2 + b^2)) - C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 + C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3 - (2*C*a^5*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 2*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - A*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^5*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^5*tan(1/2*d*x + 1/2*c) - 3*C*a^4*b*tan(1/2*d*x + 1/2*c) + 2*A*a^3*b^2*tan(1/2*d*x + 1/2*c) + 5*C*a^3*b^2*tan(1/2*d*x + 1/2*c) + A*a^2*b^3*tan(1/2*d*x + 1/2*c) + 6*C*a^2*b^3*tan(1/2*d*x + 1/2*c) + A*a*b^4*tan(1/2*d*x + 1/2*c) + 2*A*b^5*tan(1/2*d*x + 1/2*c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
694,1,371,0,0.373527," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, A a^{2} + C a^{2} + A b^{2} + 2 \, C b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"((2*A*a^2 + C*a^2 + A*b^2 + 2*C*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) + (C*a^3*tan(1/2*d*x + 1/2*c)^3 + 4*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 3*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 3*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - A*b^3*tan(1/2*d*x + 1/2*c)^3 + C*a^3*tan(1/2*d*x + 1/2*c) - 4*A*a^2*b*tan(1/2*d*x + 1/2*c) - 3*C*a^2*b*tan(1/2*d*x + 1/2*c) - 3*A*a*b^2*tan(1/2*d*x + 1/2*c) - 4*C*a*b^2*tan(1/2*d*x + 1/2*c) + A*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
695,1,484,0,0.369948," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(6 \, A a^{4} b + 3 \, C a^{4} b - 5 \, A a^{2} b^{3} + 2 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{{\left(d x + c\right)} A}{a^{3}} + \frac{2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"-((6*A*a^4*b + 3*C*a^4*b - 5*A*a^2*b^3 + 2*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(-a^2 + b^2)) - (d*x + c)*A/a^3 + (2*C*a^5*tan(1/2*d*x + 1/2*c)^3 - C*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^5*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^5*tan(1/2*d*x + 1/2*c) - C*a^4*b*tan(1/2*d*x + 1/2*c) - 6*A*a^3*b^2*tan(1/2*d*x + 1/2*c) - C*a^3*b^2*tan(1/2*d*x + 1/2*c) - 5*A*a^2*b^3*tan(1/2*d*x + 1/2*c) - 2*C*a^2*b^3*tan(1/2*d*x + 1/2*c) + 3*A*a*b^4*tan(1/2*d*x + 1/2*c) + 2*A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
696,1,491,0,0.385024," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, C a^{6} + 12 \, A a^{4} b^{2} + C a^{4} b^{2} - 15 \, A a^{2} b^{4} + 6 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{3 \, {\left(d x + c\right)} A b}{a^{4}} + \frac{4 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} + \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}}}{d}"," ",0,"((2*C*a^6 + 12*A*a^4*b^2 + C*a^4*b^2 - 15*A*a^2*b^4 + 6*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^8 - 2*a^6*b^2 + a^4*b^4)*sqrt(-a^2 + b^2)) - 3*(d*x + c)*A*b/a^4 + (4*C*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 + 8*A*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 7*A*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 5*A*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 4*A*b^6*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^5*b*tan(1/2*d*x + 1/2*c) - 3*C*a^4*b^2*tan(1/2*d*x + 1/2*c) - 8*A*a^3*b^3*tan(1/2*d*x + 1/2*c) + C*a^3*b^3*tan(1/2*d*x + 1/2*c) - 7*A*a^2*b^4*tan(1/2*d*x + 1/2*c) + 5*A*a*b^5*tan(1/2*d*x + 1/2*c) + 4*A*b^6*tan(1/2*d*x + 1/2*c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) + 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3))/d","A",0
697,1,2485,0,1.203105," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left({\left(a^{6} - a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} - 23 \, a^{2} b^{4} - 6 \, a b^{5} + 12 \, b^{6}\right)} \sqrt{-a^{2} + b^{2}} A {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} {\left| -a + b \right|} + {\left(2 \, a^{6} + 4 \, a^{5} b - 4 \, a^{4} b^{2} - a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} \sqrt{-a^{2} + b^{2}} C {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} {\left| -a + b \right|} - {\left(a^{15} - a^{14} b + 8 \, a^{13} b^{2} - 28 \, a^{12} b^{3} - 42 \, a^{11} b^{4} + 111 \, a^{10} b^{5} + 68 \, a^{9} b^{6} - 158 \, a^{8} b^{7} - 47 \, a^{7} b^{8} + 100 \, a^{6} b^{9} + 12 \, a^{5} b^{10} - 24 \, a^{4} b^{11}\right)} \sqrt{-a^{2} + b^{2}} A {\left| -a + b \right|} - {\left(2 \, a^{15} - 8 \, a^{14} b - 8 \, a^{13} b^{2} + 25 \, a^{12} b^{3} + 12 \, a^{11} b^{4} - 30 \, a^{10} b^{5} - 8 \, a^{9} b^{6} + 17 \, a^{8} b^{7} + 2 \, a^{7} b^{8} - 4 \, a^{6} b^{9}\right)} \sqrt{-a^{2} + b^{2}} C {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5} + \sqrt{{\left(a^{9} + a^{8} b - 2 \, a^{7} b^{2} - 2 \, a^{6} b^{3} + a^{5} b^{4} + a^{4} b^{5}\right)} {\left(a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}\right)} + {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)}^{2}}}{a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}}}}\right)\right)}}{{\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} + {\left(a^{10} b - 2 \, a^{9} b^{2} - a^{8} b^{3} + 4 \, a^{7} b^{4} - a^{6} b^{5} - 2 \, a^{5} b^{6} + a^{4} b^{7}\right)} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|}} + \frac{{\left(A a^{15} + 2 \, C a^{15} - A a^{14} b - 8 \, C a^{14} b + 8 \, A a^{13} b^{2} - 8 \, C a^{13} b^{2} - 28 \, A a^{12} b^{3} + 25 \, C a^{12} b^{3} - 42 \, A a^{11} b^{4} + 12 \, C a^{11} b^{4} + 111 \, A a^{10} b^{5} - 30 \, C a^{10} b^{5} + 68 \, A a^{9} b^{6} - 8 \, C a^{9} b^{6} - 158 \, A a^{8} b^{7} + 17 \, C a^{8} b^{7} - 47 \, A a^{7} b^{8} + 2 \, C a^{7} b^{8} + 100 \, A a^{6} b^{9} - 4 \, C a^{6} b^{9} + 12 \, A a^{5} b^{10} - 24 \, A a^{4} b^{11} + A a^{6} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 2 \, C a^{6} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - A a^{5} b {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 4 \, C a^{5} b {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 10 \, A a^{4} b^{2} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 4 \, C a^{4} b^{2} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 10 \, A a^{3} b^{3} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - C a^{3} b^{3} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 23 \, A a^{2} b^{4} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 2 \, C a^{2} b^{4} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 6 \, A a b^{5} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 12 \, A b^{6} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5} - \sqrt{{\left(a^{9} + a^{8} b - 2 \, a^{7} b^{2} - 2 \, a^{6} b^{3} + a^{5} b^{4} + a^{4} b^{5}\right)} {\left(a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}\right)} + {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)}^{2}}}{a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}}}}\right)\right)}}{a^{8} b {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 2 \, a^{6} b^{3} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + a^{4} b^{5} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - {\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)}^{2}} + \frac{2 \, {\left(A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 26 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 29 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 67 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 33 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 17 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(((a^6 - a^5*b + 10*a^4*b^2 + 10*a^3*b^3 - 23*a^2*b^4 - 6*a*b^5 + 12*b^6)*sqrt(-a^2 + b^2)*A*abs(a^9 - 2*a^7*b^2 + a^5*b^4)*abs(-a + b) + (2*a^6 + 4*a^5*b - 4*a^4*b^2 - a^3*b^3 + 2*a^2*b^4)*sqrt(-a^2 + b^2)*C*abs(a^9 - 2*a^7*b^2 + a^5*b^4)*abs(-a + b) - (a^15 - a^14*b + 8*a^13*b^2 - 28*a^12*b^3 - 42*a^11*b^4 + 111*a^10*b^5 + 68*a^9*b^6 - 158*a^8*b^7 - 47*a^7*b^8 + 100*a^6*b^9 + 12*a^5*b^10 - 24*a^4*b^11)*sqrt(-a^2 + b^2)*A*abs(-a + b) - (2*a^15 - 8*a^14*b - 8*a^13*b^2 + 25*a^12*b^3 + 12*a^11*b^4 - 30*a^10*b^5 - 8*a^9*b^6 + 17*a^8*b^7 + 2*a^7*b^8 - 4*a^6*b^9)*sqrt(-a^2 + b^2)*C*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^8*b - 2*a^6*b^3 + a^4*b^5 + sqrt((a^9 + a^8*b - 2*a^7*b^2 - 2*a^6*b^3 + a^5*b^4 + a^4*b^5)*(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5) + (a^8*b - 2*a^6*b^3 + a^4*b^5)^2))/(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5))))/((a^9 - 2*a^7*b^2 + a^5*b^4)^2*(a^2 - 2*a*b + b^2) + (a^10*b - 2*a^9*b^2 - a^8*b^3 + 4*a^7*b^4 - a^6*b^5 - 2*a^5*b^6 + a^4*b^7)*abs(a^9 - 2*a^7*b^2 + a^5*b^4)) + (A*a^15 + 2*C*a^15 - A*a^14*b - 8*C*a^14*b + 8*A*a^13*b^2 - 8*C*a^13*b^2 - 28*A*a^12*b^3 + 25*C*a^12*b^3 - 42*A*a^11*b^4 + 12*C*a^11*b^4 + 111*A*a^10*b^5 - 30*C*a^10*b^5 + 68*A*a^9*b^6 - 8*C*a^9*b^6 - 158*A*a^8*b^7 + 17*C*a^8*b^7 - 47*A*a^7*b^8 + 2*C*a^7*b^8 + 100*A*a^6*b^9 - 4*C*a^6*b^9 + 12*A*a^5*b^10 - 24*A*a^4*b^11 + A*a^6*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 2*C*a^6*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - A*a^5*b*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 4*C*a^5*b*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 10*A*a^4*b^2*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 4*C*a^4*b^2*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 10*A*a^3*b^3*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - C*a^3*b^3*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 23*A*a^2*b^4*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 2*C*a^2*b^4*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 6*A*a*b^5*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 12*A*b^6*abs(a^9 - 2*a^7*b^2 + a^5*b^4))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^8*b - 2*a^6*b^3 + a^4*b^5 - sqrt((a^9 + a^8*b - 2*a^7*b^2 - 2*a^6*b^3 + a^5*b^4 + a^4*b^5)*(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5) + (a^8*b - 2*a^6*b^3 + a^4*b^5)^2))/(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5))))/(a^8*b*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 2*a^6*b^3*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + a^4*b^5*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - (a^9 - 2*a^7*b^2 + a^5*b^4)^2) + 2*(A*a^7*tan(1/2*d*x + 1/2*c)^7 + 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 13*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 2*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 5*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 17*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 2*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^7*tan(1/2*d*x + 1/2*c)^7 - 3*A*a^7*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^5 - 5*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 26*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 15*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 29*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 67*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^5 + 36*A*b^7*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^7*tan(1/2*d*x + 1/2*c)^3 - 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 26*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 67*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 36*A*b^7*tan(1/2*d*x + 1/2*c)^3 - A*a^7*tan(1/2*d*x + 1/2*c) + 4*A*a^6*b*tan(1/2*d*x + 1/2*c) + 13*A*a^5*b^2*tan(1/2*d*x + 1/2*c) - 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c) - 2*A*a^4*b^3*tan(1/2*d*x + 1/2*c) - 5*C*a^4*b^3*tan(1/2*d*x + 1/2*c) - 33*A*a^3*b^4*tan(1/2*d*x + 1/2*c) + 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c) - 17*A*a^2*b^5*tan(1/2*d*x + 1/2*c) + 2*C*a^2*b^5*tan(1/2*d*x + 1/2*c) + 18*A*a*b^6*tan(1/2*d*x + 1/2*c) + 12*A*b^7*tan(1/2*d*x + 1/2*c))/((a^8 - 2*a^6*b^2 + a^4*b^4)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
698,1,878,0,0.488009," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(8 \, C a^{8} - 28 \, C a^{6} b^{2} + 35 \, C a^{4} b^{4} - 3 \, A a^{2} b^{6} - 20 \, C a^{2} b^{6} - 2 \, A b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{12 \, C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{5}} + \frac{12 \, C a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{5}} - \frac{18 \, C a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, C a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, C a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 152 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 236 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}} - \frac{6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b^{4}}}{3 \, d}"," ",0,"1/3*(3*(8*C*a^8 - 28*C*a^6*b^2 + 35*C*a^4*b^4 - 3*A*a^2*b^6 - 20*C*a^2*b^6 - 2*A*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*sqrt(-a^2 + b^2)) - 12*C*a*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^5 + 12*C*a*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^5 - (18*C*a^9*tan(1/2*d*x + 1/2*c)^5 - 42*C*a^8*b*tan(1/2*d*x + 1/2*c)^5 - 24*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 + 117*C*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 24*C*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 - 105*C*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 + 60*C*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^8*tan(1/2*d*x + 1/2*c)^5 - 36*C*a^9*tan(1/2*d*x + 1/2*c)^3 + 152*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 - 236*C*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 - 32*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 + 120*C*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 + 36*A*a*b^8*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^9*tan(1/2*d*x + 1/2*c) + 42*C*a^8*b*tan(1/2*d*x + 1/2*c) - 24*C*a^7*b^2*tan(1/2*d*x + 1/2*c) - 117*C*a^6*b^3*tan(1/2*d*x + 1/2*c) + 6*A*a^5*b^4*tan(1/2*d*x + 1/2*c) - 24*C*a^5*b^4*tan(1/2*d*x + 1/2*c) + 3*A*a^4*b^5*tan(1/2*d*x + 1/2*c) + 105*C*a^4*b^5*tan(1/2*d*x + 1/2*c) + 6*A*a^3*b^6*tan(1/2*d*x + 1/2*c) + 60*C*a^3*b^6*tan(1/2*d*x + 1/2*c) + 27*A*a^2*b^7*tan(1/2*d*x + 1/2*c) + 18*A*a*b^8*tan(1/2*d*x + 1/2*c))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) - 6*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b^4))/d","B",0
699,1,876,0,0.507039," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, C a^{7} - 7 \, C a^{5} b^{2} - A a^{3} b^{4} + 8 \, C a^{3} b^{4} - 4 \, A a b^{6} - 8 \, C a b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{3 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} + \frac{3 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, C a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, C a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(2*C*a^7 - 7*C*a^5*b^2 - A*a^3*b^4 + 8*C*a^3*b^4 - 4*A*a*b^6 - 8*C*a*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*sqrt(-a^2 + b^2)) - 3*C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 + 3*C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - (6*C*a^8*tan(1/2*d*x + 1/2*c)^5 - 15*C*a^7*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 45*C*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 60*C*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 6*A*a*b^7*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^8*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^8*tan(1/2*d*x + 1/2*c)^3 + 56*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 - 28*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 - 116*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 + 16*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 + 72*C*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^8*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^8*tan(1/2*d*x + 1/2*c) + 15*C*a^7*b*tan(1/2*d*x + 1/2*c) - 6*C*a^6*b^2*tan(1/2*d*x + 1/2*c) - 3*A*a^5*b^3*tan(1/2*d*x + 1/2*c) - 45*C*a^5*b^3*tan(1/2*d*x + 1/2*c) + 12*A*a^4*b^4*tan(1/2*d*x + 1/2*c) - 6*C*a^4*b^4*tan(1/2*d*x + 1/2*c) + 27*A*a^3*b^5*tan(1/2*d*x + 1/2*c) + 60*C*a^3*b^5*tan(1/2*d*x + 1/2*c) + 12*A*a^2*b^6*tan(1/2*d*x + 1/2*c) + 36*C*a^2*b^6*tan(1/2*d*x + 1/2*c) + 6*A*a*b^7*tan(1/2*d*x + 1/2*c) + 6*A*b^8*tan(1/2*d*x + 1/2*c))/((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
700,1,693,0,0.415609," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(4 \, A a^{2} b + 3 \, C a^{2} b + A b^{3} + 2 \, C b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{6 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(4*A*a^2*b + 3*C*a^2*b + A*b^3 + 2*C*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) + (6*A*a^5*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^5*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 18*C*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*A*b^5*tan(1/2*d*x + 1/2*c)^5 - 12*A*a^5*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^5*tan(1/2*d*x + 1/2*c)^3 - 16*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 32*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 28*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 36*C*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^5*tan(1/2*d*x + 1/2*c) + 6*C*a^5*tan(1/2*d*x + 1/2*c) + 6*A*a^4*b*tan(1/2*d*x + 1/2*c) + 3*C*a^4*b*tan(1/2*d*x + 1/2*c) + 12*A*a^3*b^2*tan(1/2*d*x + 1/2*c) + 6*C*a^3*b^2*tan(1/2*d*x + 1/2*c) + 27*A*a^2*b^3*tan(1/2*d*x + 1/2*c) + 27*C*a^2*b^3*tan(1/2*d*x + 1/2*c) + 12*A*a*b^4*tan(1/2*d*x + 1/2*c) + 18*C*a*b^4*tan(1/2*d*x + 1/2*c) - 3*A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
701,1,693,0,0.436009," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, A a^{3} + C a^{3} + 3 \, A a b^{2} + 4 \, C a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{3 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(2*A*a^3 + C*a^3 + 3*A*a*b^2 + 4*C*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) - (3*C*a^5*tan(1/2*d*x + 1/2*c)^5 + 18*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 3*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*C*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^5*tan(1/2*d*x + 1/2*c)^5 - 36*A*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 28*C*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 32*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 16*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*A*b^5*tan(1/2*d*x + 1/2*c)^3 + 12*C*b^5*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^5*tan(1/2*d*x + 1/2*c) + 18*A*a^4*b*tan(1/2*d*x + 1/2*c) + 12*C*a^4*b*tan(1/2*d*x + 1/2*c) + 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c) + 27*C*a^3*b^2*tan(1/2*d*x + 1/2*c) + 6*A*a^2*b^3*tan(1/2*d*x + 1/2*c) + 12*C*a^2*b^3*tan(1/2*d*x + 1/2*c) + 3*A*a*b^4*tan(1/2*d*x + 1/2*c) + 6*C*a*b^4*tan(1/2*d*x + 1/2*c) + 6*A*b^5*tan(1/2*d*x + 1/2*c) + 6*C*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
702,1,845,0,0.448178," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(8 \, A a^{6} b + 4 \, C a^{6} b - 8 \, A a^{4} b^{3} + C a^{4} b^{3} + 7 \, A a^{2} b^{5} - 2 \, A b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{3 \, {\left(d x + c\right)} A}{a^{4}} + \frac{6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(8*A*a^6*b + 4*C*a^6*b - 8*A*a^4*b^3 + C*a^4*b^3 + 7*A*a^2*b^5 - 2*A*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*sqrt(-a^2 + b^2)) - 3*(d*x + c)*A/a^4 + (6*C*a^8*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^7*b*tan(1/2*d*x + 1/2*c)^5 + 36*A*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 - 60*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 45*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 15*A*a*b^7*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^8*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^8*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 - 16*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 116*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 + 28*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 - 56*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^8*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^8*tan(1/2*d*x + 1/2*c) + 6*C*a^7*b*tan(1/2*d*x + 1/2*c) + 36*A*a^6*b^2*tan(1/2*d*x + 1/2*c) + 12*C*a^6*b^2*tan(1/2*d*x + 1/2*c) + 60*A*a^5*b^3*tan(1/2*d*x + 1/2*c) + 27*C*a^5*b^3*tan(1/2*d*x + 1/2*c) - 6*A*a^4*b^4*tan(1/2*d*x + 1/2*c) + 12*C*a^4*b^4*tan(1/2*d*x + 1/2*c) - 45*A*a^3*b^5*tan(1/2*d*x + 1/2*c) - 3*C*a^3*b^5*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b^6*tan(1/2*d*x + 1/2*c) + 15*A*a*b^7*tan(1/2*d*x + 1/2*c) + 6*A*b^8*tan(1/2*d*x + 1/2*c))/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
703,1,847,0,0.445815," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, C a^{8} + 20 \, A a^{6} b^{2} + 3 \, C a^{6} b^{2} - 35 \, A a^{4} b^{4} + 28 \, A a^{2} b^{6} - 8 \, A b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{12 \, {\left(d x + c\right)} A b}{a^{5}} + \frac{18 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 236 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 152 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}} + \frac{6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{4}}}{3 \, d}"," ",0,"1/3*(3*(2*C*a^8 + 20*A*a^6*b^2 + 3*C*a^6*b^2 - 35*A*a^4*b^4 + 28*A*a^2*b^6 - 8*A*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*sqrt(-a^2 + b^2)) - 12*(d*x + c)*A*b/a^5 + (18*C*a^8*b*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 + 60*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 - 105*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 24*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 117*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 24*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 - 42*A*a*b^8*tan(1/2*d*x + 1/2*c)^5 + 18*A*b^9*tan(1/2*d*x + 1/2*c)^5 - 36*C*a^8*b*tan(1/2*d*x + 1/2*c)^3 - 120*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 + 32*C*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 + 236*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 + 4*C*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 - 152*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^3 + 36*A*b^9*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^8*b*tan(1/2*d*x + 1/2*c) + 27*C*a^7*b^2*tan(1/2*d*x + 1/2*c) + 60*A*a^6*b^3*tan(1/2*d*x + 1/2*c) + 6*C*a^6*b^3*tan(1/2*d*x + 1/2*c) + 105*A*a^5*b^4*tan(1/2*d*x + 1/2*c) + 3*C*a^5*b^4*tan(1/2*d*x + 1/2*c) - 24*A*a^4*b^5*tan(1/2*d*x + 1/2*c) + 6*C*a^4*b^5*tan(1/2*d*x + 1/2*c) - 117*A*a^3*b^6*tan(1/2*d*x + 1/2*c) - 24*A*a^2*b^7*tan(1/2*d*x + 1/2*c) + 42*A*a*b^8*tan(1/2*d*x + 1/2*c) + 18*A*b^9*tan(1/2*d*x + 1/2*c))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) + 6*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^4))/d","B",0
704,1,1031,0,0.481133," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(8 \, C a^{8} b + 40 \, A a^{6} b^{3} - 8 \, C a^{6} b^{3} - 84 \, A a^{4} b^{5} + 7 \, C a^{4} b^{5} + 69 \, A a^{2} b^{7} - 2 \, C a^{2} b^{7} - 20 \, A b^{9}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{2 \, {\left(36 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 90 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 162 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, C a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 213 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 81 \, A a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 180 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 392 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 284 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 90 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 162 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, C a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 213 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 81 \, A a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}} - \frac{3 \, {\left(A a^{2} + 2 \, C a^{2} + 20 \, A b^{2}\right)} {\left(d x + c\right)}}{a^{6}} + \frac{6 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{5}}}{6 \, d}"," ",0,"-1/6*(6*(8*C*a^8*b + 40*A*a^6*b^3 - 8*C*a^6*b^3 - 84*A*a^4*b^5 + 7*C*a^4*b^5 + 69*A*a^2*b^7 - 2*C*a^2*b^7 - 20*A*b^9)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*sqrt(-a^2 + b^2)) + 2*(36*C*a^8*b^2*tan(1/2*d*x + 1/2*c)^5 - 60*C*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 + 90*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 162*A*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 + 45*C*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 - 48*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 + 213*A*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 - 15*C*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 - 48*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 - 81*A*a*b^9*tan(1/2*d*x + 1/2*c)^5 + 36*A*b^10*tan(1/2*d*x + 1/2*c)^5 - 72*C*a^8*b^2*tan(1/2*d*x + 1/2*c)^3 - 180*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 + 116*C*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 + 392*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 - 56*C*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 - 284*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 + 72*A*b^10*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^8*b^2*tan(1/2*d*x + 1/2*c) + 60*C*a^7*b^3*tan(1/2*d*x + 1/2*c) + 90*A*a^6*b^4*tan(1/2*d*x + 1/2*c) - 6*C*a^6*b^4*tan(1/2*d*x + 1/2*c) + 162*A*a^5*b^5*tan(1/2*d*x + 1/2*c) - 45*C*a^5*b^5*tan(1/2*d*x + 1/2*c) - 48*A*a^4*b^6*tan(1/2*d*x + 1/2*c) - 6*C*a^4*b^6*tan(1/2*d*x + 1/2*c) - 213*A*a^3*b^7*tan(1/2*d*x + 1/2*c) + 15*C*a^3*b^7*tan(1/2*d*x + 1/2*c) - 48*A*a^2*b^8*tan(1/2*d*x + 1/2*c) + 6*C*a^2*b^8*tan(1/2*d*x + 1/2*c) + 81*A*a*b^9*tan(1/2*d*x + 1/2*c) + 36*A*b^10*tan(1/2*d*x + 1/2*c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) - 3*(A*a^2 + 2*C*a^2 + 20*A*b^2)*(d*x + c)/a^6 + 6*(A*a*tan(1/2*d*x + 1/2*c)^3 + 8*A*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) + 8*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^5))/d","B",0
705,1,43,0,0.244148," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} a - b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{d}"," ",0,"((d*x + c)*a - b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + b*log(abs(tan(1/2*d*x + 1/2*c) - 1)))/d","B",0
706,1,235,0,0.238397," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{{\left(\sqrt{-a^{2} + b^{2}} {\left(a + b\right)} {\left| a \right|} {\left| -a + b \right|} - {\left(a^{2} - 3 \, a b\right)} \sqrt{-a^{2} + b^{2}} {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{b + \sqrt{{\left(a + b\right)} {\left(a - b\right)} + b^{2}}}{a - b}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} a^{2} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} {\left| a \right|}} - \frac{{\left(a^{2} - 3 \, a b + a {\left| a \right|} + b {\left| a \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{b - \sqrt{{\left(a + b\right)} {\left(a - b\right)} + b^{2}}}{a - b}}}\right)\right)}}{a^{2} - b {\left| a \right|}}}{d}"," ",0,"-((sqrt(-a^2 + b^2)*(a + b)*abs(a)*abs(-a + b) - (a^2 - 3*a*b)*sqrt(-a^2 + b^2)*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(b + sqrt((a + b)*(a - b) + b^2))/(a - b))))/((a^2 - 2*a*b + b^2)*a^2 + (a^2*b - 2*a*b^2 + b^3)*abs(a)) - (a^2 - 3*a*b + a*abs(a) + b*abs(a))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(b - sqrt((a + b)*(a - b) + b^2))/(a - b))))/(a^2 - b*abs(a)))/d","B",0
707,1,175,0,0.386837," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} {\left(a^{2} - b^{2}\right)}} - \frac{2 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{3} - a b^{2}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{d x + c}{a}}{d}"," ",0,"-(4*b^2*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)*(a^2 - b^2)) - 2*(3*a^2*b - b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^3 - a*b^2)*sqrt(-a^2 + b^2)) - (d*x + c)/a)/d","A",0
708,1,317,0,0.379558," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(4 \, a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{d x + c}{a^{2}} - \frac{2 \, {\left(5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"(2*(4*a^4*b - 2*a^2*b^3 + b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - 2*a^4*b^2 + a^2*b^4)*sqrt(-a^2 + b^2)) + (d*x + c)/a^2 - 2*(5*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*a*b^4*tan(1/2*d*x + 1/2*c)^3 + b^5*tan(1/2*d*x + 1/2*c)^3 - 5*a^3*b^2*tan(1/2*d*x + 1/2*c) - 4*a^2*b^3*tan(1/2*d*x + 1/2*c) + 2*a*b^4*tan(1/2*d*x + 1/2*c) + b^5*tan(1/2*d*x + 1/2*c))/((a^5 - 2*a^3*b^2 + a*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
709,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
710,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
711,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c), x)","F",0
712,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a), x)","F",0
713,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c), x)","F",0
714,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
715,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^3, x)","F",0
716,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^4, x)","F",0
717,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
718,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
719,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
720,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2), x)","F",0
721,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
722,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
723,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^3, x)","F",0
724,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^4, x)","F",0
725,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^3, x)","F",0
726,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
727,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
728,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(5/2), x)","F",0
729,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
730,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
731,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^3, x)","F",0
732,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^4, x)","F",0
733,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(a^2-b^2*sec(d*x+c)^2),x, algorithm=""giac"")","\int -{\left(b^{2} \sec\left(d x + c\right)^{2} - a^{2}\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(-(b^2*sec(d*x + c)^2 - a^2)*(b*sec(d*x + c) + a)^(3/2), x)","F",0
734,0,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int -{\left(b^{2} \sec\left(d x + c\right)^{2} - a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(-(b^2*sec(d*x + c)^2 - a^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
735,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^3/sqrt(b*sec(d*x + c) + a), x)","F",0
736,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
737,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
738,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/sqrt(b*sec(d*x + c) + a), x)","F",0
739,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
740,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
741,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^3/sqrt(b*sec(d*x + c) + a), x)","F",0
742,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^3/(b*sec(d*x + c) + a)^(3/2), x)","F",0
743,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
744,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
745,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
746,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
747,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
748,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^3/(b*sec(d*x + c) + a)^(5/2), x)","F",0
749,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^2/(b*sec(d*x + c) + a)^(5/2), x)","F",0
750,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
751,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
752,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
753,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^2/(b*sec(d*x + c) + a)^(5/2), x)","F",0
754,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(b*sec(d*x + c) + a)^(7/2), x)","F",0
755,0,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int -\frac{b^{2} \sec\left(d x + c\right)^{2} - a^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(-(b^2*sec(d*x + c)^2 - a^2)/sqrt(b*sec(d*x + c) + a), x)","F",0
756,0,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int -\frac{b^{2} \sec\left(d x + c\right)^{2} - a^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(b^2*sec(d*x + c)^2 - a^2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
757,0,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int -\frac{b^{2} \sec\left(d x + c\right)^{2} - a^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(b^2*sec(d*x + c)^2 - a^2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
758,0,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(7/2),x, algorithm=""giac"")","\int -\frac{b^{2} \sec\left(d x + c\right)^{2} - a^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-(b^2*sec(d*x + c)^2 - a^2)/(b*sec(d*x + c) + a)^(7/2), x)","F",0
759,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
760,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
761,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(2/3), x)","F",0
762,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(1/3), x)","F",0
763,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(b*sec(d*x + c) + a)^(1/3), x)","F",0
764,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(b*sec(d*x + c) + a)^(2/3), x)","F",0
765,1,330,0,0.265981," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{45 \, {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 45 \, {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 320 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 160 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 400 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 464 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 320 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(45*(C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 45*(C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*B*a*tan(1/2*d*x + 1/2*c)^9 - 75*C*a*tan(1/2*d*x + 1/2*c)^9 - 75*B*b*tan(1/2*d*x + 1/2*c)^9 + 120*C*b*tan(1/2*d*x + 1/2*c)^9 - 320*B*a*tan(1/2*d*x + 1/2*c)^7 + 30*C*a*tan(1/2*d*x + 1/2*c)^7 + 30*B*b*tan(1/2*d*x + 1/2*c)^7 - 160*C*b*tan(1/2*d*x + 1/2*c)^7 + 400*B*a*tan(1/2*d*x + 1/2*c)^5 + 464*C*b*tan(1/2*d*x + 1/2*c)^5 - 320*B*a*tan(1/2*d*x + 1/2*c)^3 - 30*C*a*tan(1/2*d*x + 1/2*c)^3 - 30*B*b*tan(1/2*d*x + 1/2*c)^3 - 160*C*b*tan(1/2*d*x + 1/2*c)^3 + 120*B*a*tan(1/2*d*x + 1/2*c) + 75*C*a*tan(1/2*d*x + 1/2*c) + 75*B*b*tan(1/2*d*x + 1/2*c) + 120*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
766,1,304,0,0.269693," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(4 \, B a + 3 \, C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, B a + 3 \, C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(4*B*a + 3*C*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*B*a + 3*C*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(12*B*a*tan(1/2*d*x + 1/2*c)^7 - 24*C*a*tan(1/2*d*x + 1/2*c)^7 - 24*B*b*tan(1/2*d*x + 1/2*c)^7 + 15*C*b*tan(1/2*d*x + 1/2*c)^7 - 12*B*a*tan(1/2*d*x + 1/2*c)^5 + 40*C*a*tan(1/2*d*x + 1/2*c)^5 + 40*B*b*tan(1/2*d*x + 1/2*c)^5 + 9*C*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*a*tan(1/2*d*x + 1/2*c)^3 - 40*C*a*tan(1/2*d*x + 1/2*c)^3 - 40*B*b*tan(1/2*d*x + 1/2*c)^3 + 9*C*b*tan(1/2*d*x + 1/2*c)^3 + 12*B*a*tan(1/2*d*x + 1/2*c) + 24*C*a*tan(1/2*d*x + 1/2*c) + 24*B*b*tan(1/2*d*x + 1/2*c) + 15*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
767,1,210,0,0.248148," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*B*a*tan(1/2*d*x + 1/2*c)^5 - 3*C*a*tan(1/2*d*x + 1/2*c)^5 - 3*B*b*tan(1/2*d*x + 1/2*c)^5 + 6*C*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*a*tan(1/2*d*x + 1/2*c)^3 - 4*C*b*tan(1/2*d*x + 1/2*c)^3 + 6*B*a*tan(1/2*d*x + 1/2*c) + 3*C*a*tan(1/2*d*x + 1/2*c) + 3*B*b*tan(1/2*d*x + 1/2*c) + 6*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
768,1,153,0,0.210537," ","integrate((a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(2 \, B a + C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, B a + C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((2*B*a + C*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*B*a + C*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*C*a*tan(1/2*d*x + 1/2*c)^3 + 2*B*b*tan(1/2*d*x + 1/2*c)^3 - C*b*tan(1/2*d*x + 1/2*c)^3 - 2*C*a*tan(1/2*d*x + 1/2*c) - 2*B*b*tan(1/2*d*x + 1/2*c) - C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
769,1,84,0,0.233417," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} B a + {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"((d*x + c)*B*a + (C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*C*b*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
770,1,79,0,0.233288," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{C b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - C b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(C a + B b\right)} {\left(d x + c\right)} + \frac{2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"(C*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - C*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (C*a + B*b)*(d*x + c) + 2*B*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
771,1,121,0,0.212806," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(B a + 2 \, C b\right)} {\left(d x + c\right)} - \frac{2 \, {\left(B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((B*a + 2*C*b)*(d*x + c) - 2*(B*a*tan(1/2*d*x + 1/2*c)^3 - 2*C*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*b*tan(1/2*d*x + 1/2*c)^3 - B*a*tan(1/2*d*x + 1/2*c) - 2*C*a*tan(1/2*d*x + 1/2*c) - 2*B*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
772,1,180,0,0.203988," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(C a + B b\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(C*a + B*b)*(d*x + c) + 2*(6*B*a*tan(1/2*d*x + 1/2*c)^5 - 3*C*a*tan(1/2*d*x + 1/2*c)^5 - 3*B*b*tan(1/2*d*x + 1/2*c)^5 + 6*C*b*tan(1/2*d*x + 1/2*c)^5 + 4*B*a*tan(1/2*d*x + 1/2*c)^3 + 12*C*b*tan(1/2*d*x + 1/2*c)^3 + 6*B*a*tan(1/2*d*x + 1/2*c) + 3*C*a*tan(1/2*d*x + 1/2*c) + 3*B*b*tan(1/2*d*x + 1/2*c) + 6*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
773,1,272,0,0.231007," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, B a + 4 \, C b\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*B*a + 4*C*b)*(d*x + c) - 2*(15*B*a*tan(1/2*d*x + 1/2*c)^7 - 24*C*a*tan(1/2*d*x + 1/2*c)^7 - 24*B*b*tan(1/2*d*x + 1/2*c)^7 + 12*C*b*tan(1/2*d*x + 1/2*c)^7 - 9*B*a*tan(1/2*d*x + 1/2*c)^5 - 40*C*a*tan(1/2*d*x + 1/2*c)^5 - 40*B*b*tan(1/2*d*x + 1/2*c)^5 + 12*C*b*tan(1/2*d*x + 1/2*c)^5 + 9*B*a*tan(1/2*d*x + 1/2*c)^3 - 40*C*a*tan(1/2*d*x + 1/2*c)^3 - 40*B*b*tan(1/2*d*x + 1/2*c)^3 - 12*C*b*tan(1/2*d*x + 1/2*c)^3 - 15*B*a*tan(1/2*d*x + 1/2*c) - 24*C*a*tan(1/2*d*x + 1/2*c) - 24*B*b*tan(1/2*d*x + 1/2*c) - 12*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
774,1,300,0,0.303475," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{45 \, {\left(C a + B b\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(45*(C*a + B*b)*(d*x + c) + 2*(120*B*a*tan(1/2*d*x + 1/2*c)^9 - 75*C*a*tan(1/2*d*x + 1/2*c)^9 - 75*B*b*tan(1/2*d*x + 1/2*c)^9 + 120*C*b*tan(1/2*d*x + 1/2*c)^9 + 160*B*a*tan(1/2*d*x + 1/2*c)^7 - 30*C*a*tan(1/2*d*x + 1/2*c)^7 - 30*B*b*tan(1/2*d*x + 1/2*c)^7 + 320*C*b*tan(1/2*d*x + 1/2*c)^7 + 464*B*a*tan(1/2*d*x + 1/2*c)^5 + 400*C*b*tan(1/2*d*x + 1/2*c)^5 + 160*B*a*tan(1/2*d*x + 1/2*c)^3 + 30*C*a*tan(1/2*d*x + 1/2*c)^3 + 30*B*b*tan(1/2*d*x + 1/2*c)^3 + 320*C*b*tan(1/2*d*x + 1/2*c)^3 + 120*B*a*tan(1/2*d*x + 1/2*c) + 75*C*a*tan(1/2*d*x + 1/2*c) + 75*B*b*tan(1/2*d*x + 1/2*c) + 120*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
775,1,528,0,0.328988," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, B a^{2} + 6 \, C a b + 3 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, B a^{2} + 6 \, C a b + 3 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(60 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 150 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 75 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 640 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 160 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 400 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 800 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 464 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 640 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 150 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 75 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(4*B*a^2 + 6*C*a*b + 3*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*B*a^2 + 6*C*a*b + 3*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(60*B*a^2*tan(1/2*d*x + 1/2*c)^9 - 120*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 240*B*a*b*tan(1/2*d*x + 1/2*c)^9 + 150*C*a*b*tan(1/2*d*x + 1/2*c)^9 + 75*B*b^2*tan(1/2*d*x + 1/2*c)^9 - 120*C*b^2*tan(1/2*d*x + 1/2*c)^9 - 120*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 320*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 640*B*a*b*tan(1/2*d*x + 1/2*c)^7 - 60*C*a*b*tan(1/2*d*x + 1/2*c)^7 - 30*B*b^2*tan(1/2*d*x + 1/2*c)^7 + 160*C*b^2*tan(1/2*d*x + 1/2*c)^7 - 400*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 800*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 464*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 120*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 320*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 640*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 60*C*a*b*tan(1/2*d*x + 1/2*c)^3 + 30*B*b^2*tan(1/2*d*x + 1/2*c)^3 + 160*C*b^2*tan(1/2*d*x + 1/2*c)^3 - 60*B*a^2*tan(1/2*d*x + 1/2*c) - 120*C*a^2*tan(1/2*d*x + 1/2*c) - 240*B*a*b*tan(1/2*d*x + 1/2*c) - 150*C*a*b*tan(1/2*d*x + 1/2*c) - 75*B*b^2*tan(1/2*d*x + 1/2*c) - 120*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
776,1,478,0,0.325580," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(4 \, C a^{2} + 8 \, B a b + 3 \, C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, C a^{2} + 8 \, B a b + 3 \, C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 80 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(4*C*a^2 + 8*B*a*b + 3*C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*C*a^2 + 8*B*a*b + 3*C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(24*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^7 + 48*C*a*b*tan(1/2*d*x + 1/2*c)^7 + 24*B*b^2*tan(1/2*d*x + 1/2*c)^7 - 15*C*b^2*tan(1/2*d*x + 1/2*c)^7 - 72*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 80*C*a*b*tan(1/2*d*x + 1/2*c)^5 - 40*B*b^2*tan(1/2*d*x + 1/2*c)^5 - 9*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 80*C*a*b*tan(1/2*d*x + 1/2*c)^3 + 40*B*b^2*tan(1/2*d*x + 1/2*c)^3 - 9*C*b^2*tan(1/2*d*x + 1/2*c)^3 - 24*B*a^2*tan(1/2*d*x + 1/2*c) - 12*C*a^2*tan(1/2*d*x + 1/2*c) - 24*B*a*b*tan(1/2*d*x + 1/2*c) - 48*C*a*b*tan(1/2*d*x + 1/2*c) - 24*B*b^2*tan(1/2*d*x + 1/2*c) - 15*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
777,1,294,0,0.333990," ","integrate((a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(2 \, B a^{2} + 2 \, C a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, B a^{2} + 2 \, C a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*B*a^2 + 2*C*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*B*a^2 + 2*C*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 12*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*a*b*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^2*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 4*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*tan(1/2*d*x + 1/2*c) + 12*B*a*b*tan(1/2*d*x + 1/2*c) + 6*C*a*b*tan(1/2*d*x + 1/2*c) + 3*B*b^2*tan(1/2*d*x + 1/2*c) + 6*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
778,1,192,0,0.280905," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} B a^{2} + {\left(2 \, C a^{2} + 4 \, B a b + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, C a^{2} + 4 \, B a b + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(4 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*B*a^2 + (2*C*a^2 + 4*B*a*b + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*C*a^2 + 4*B*a*b + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(4*C*a*b*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^2*tan(1/2*d*x + 1/2*c)^3 - C*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*b*tan(1/2*d*x + 1/2*c) - 2*B*b^2*tan(1/2*d*x + 1/2*c) - C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
779,1,154,0,0.268315," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(C a^{2} + 2 \, B a b\right)} {\left(d x + c\right)} + {\left(2 \, C a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, C a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((C*a^2 + 2*B*a*b)*(d*x + c) + (2*C*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*C*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(B*a^2*tan(1/2*d*x + 1/2*c)^3 - C*b^2*tan(1/2*d*x + 1/2*c)^3 - B*a^2*tan(1/2*d*x + 1/2*c) - C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
780,1,178,0,0.253320," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, C b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, C b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(B a^{2} + 4 \, C a b + 2 \, B b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*C*b^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*C*b^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (B*a^2 + 4*C*a*b + 2*B*b^2)*(d*x + c) - 2*(B*a^2*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*b*tan(1/2*d*x + 1/2*c)^3 - B*a^2*tan(1/2*d*x + 1/2*c) - 2*C*a^2*tan(1/2*d*x + 1/2*c) - 4*B*a*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
781,1,254,0,0.240238," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(C a^{2} + 2 \, B a b + 2 \, C b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(C*a^2 + 2*B*a*b + 2*C*b^2)*(d*x + c) + 2*(6*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 12*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*C*a*b*tan(1/2*d*x + 1/2*c)^3 + 12*B*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^2*tan(1/2*d*x + 1/2*c) + 3*C*a^2*tan(1/2*d*x + 1/2*c) + 6*B*a*b*tan(1/2*d*x + 1/2*c) + 12*C*a*b*tan(1/2*d*x + 1/2*c) + 6*B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
782,1,437,0,0.264446," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, B a^{2} + 8 \, C a b + 4 \, B b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 80 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*B*a^2 + 8*C*a*b + 4*B*b^2)*(d*x + c) - 2*(15*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 24*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 48*B*a*b*tan(1/2*d*x + 1/2*c)^7 + 24*C*a*b*tan(1/2*d*x + 1/2*c)^7 + 12*B*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*C*b^2*tan(1/2*d*x + 1/2*c)^7 - 9*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 40*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 80*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 24*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 12*B*b^2*tan(1/2*d*x + 1/2*c)^5 - 72*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 40*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 80*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 24*C*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*B*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*C*b^2*tan(1/2*d*x + 1/2*c)^3 - 15*B*a^2*tan(1/2*d*x + 1/2*c) - 24*C*a^2*tan(1/2*d*x + 1/2*c) - 48*B*a*b*tan(1/2*d*x + 1/2*c) - 24*C*a*b*tan(1/2*d*x + 1/2*c) - 12*B*b^2*tan(1/2*d*x + 1/2*c) - 24*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
783,1,487,0,0.259521," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, C a^{2} + 6 \, B a b + 4 \, C b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 150 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 240 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 640 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 800 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 640 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 150 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*C*a^2 + 6*B*a*b + 4*C*b^2)*(d*x + c) + 2*(120*B*a^2*tan(1/2*d*x + 1/2*c)^9 - 75*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 150*B*a*b*tan(1/2*d*x + 1/2*c)^9 + 240*C*a*b*tan(1/2*d*x + 1/2*c)^9 + 120*B*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*C*b^2*tan(1/2*d*x + 1/2*c)^9 + 160*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 30*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 60*B*a*b*tan(1/2*d*x + 1/2*c)^7 + 640*C*a*b*tan(1/2*d*x + 1/2*c)^7 + 320*B*b^2*tan(1/2*d*x + 1/2*c)^7 - 120*C*b^2*tan(1/2*d*x + 1/2*c)^7 + 464*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 800*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 400*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 160*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 30*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 60*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 640*C*a*b*tan(1/2*d*x + 1/2*c)^3 + 320*B*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*B*a^2*tan(1/2*d*x + 1/2*c) + 75*C*a^2*tan(1/2*d*x + 1/2*c) + 150*B*a*b*tan(1/2*d*x + 1/2*c) + 240*C*a*b*tan(1/2*d*x + 1/2*c) + 120*B*b^2*tan(1/2*d*x + 1/2*c) + 60*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
784,1,932,0,0.378857," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(8 \, B a^{3} + 18 \, C a^{2} b + 18 \, B a b^{2} + 5 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(8 \, B a^{3} + 18 \, C a^{2} b + 18 \, B a b^{2} + 5 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 165 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 360 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 880 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2640 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 630 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 630 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1680 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 560 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 25 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 240 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1440 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4320 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 180 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3744 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1248 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 450 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1440 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4320 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 180 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3744 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1248 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 450 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 360 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 880 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2640 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 630 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 630 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1680 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 560 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 25 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 450 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 450 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 165 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(8*B*a^3 + 18*C*a^2*b + 18*B*a*b^2 + 5*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(8*B*a^3 + 18*C*a^2*b + 18*B*a*b^2 + 5*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(120*B*a^3*tan(1/2*d*x + 1/2*c)^11 - 240*C*a^3*tan(1/2*d*x + 1/2*c)^11 - 720*B*a^2*b*tan(1/2*d*x + 1/2*c)^11 + 450*C*a^2*b*tan(1/2*d*x + 1/2*c)^11 + 450*B*a*b^2*tan(1/2*d*x + 1/2*c)^11 - 720*C*a*b^2*tan(1/2*d*x + 1/2*c)^11 - 240*B*b^3*tan(1/2*d*x + 1/2*c)^11 + 165*C*b^3*tan(1/2*d*x + 1/2*c)^11 - 360*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 880*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 2640*B*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 630*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 630*B*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 1680*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 560*B*b^3*tan(1/2*d*x + 1/2*c)^9 + 25*C*b^3*tan(1/2*d*x + 1/2*c)^9 + 240*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 1440*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 4320*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 180*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 180*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 3744*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 1248*B*b^3*tan(1/2*d*x + 1/2*c)^7 + 450*C*b^3*tan(1/2*d*x + 1/2*c)^7 + 240*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 1440*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 4320*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 180*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 180*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 3744*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 1248*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 450*C*b^3*tan(1/2*d*x + 1/2*c)^5 - 360*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 880*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 2640*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 630*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 630*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 1680*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 560*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 25*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*B*a^3*tan(1/2*d*x + 1/2*c) + 240*C*a^3*tan(1/2*d*x + 1/2*c) + 720*B*a^2*b*tan(1/2*d*x + 1/2*c) + 450*C*a^2*b*tan(1/2*d*x + 1/2*c) + 450*B*a*b^2*tan(1/2*d*x + 1/2*c) + 720*C*a*b^2*tan(1/2*d*x + 1/2*c) + 240*B*b^3*tan(1/2*d*x + 1/2*c) + 165*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
785,1,722,0,0.358542," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, C a^{3} + 12 \, B a^{2} b + 9 \, C a b^{2} + 3 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, C a^{3} + 12 \, B a^{2} b + 9 \, C a b^{2} + 3 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 225 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 480 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 90 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 160 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 464 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 480 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 90 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 225 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(4*C*a^3 + 12*B*a^2*b + 9*C*a*b^2 + 3*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*C*a^3 + 12*B*a^2*b + 9*C*a*b^2 + 3*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*B*a^3*tan(1/2*d*x + 1/2*c)^9 - 60*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 180*B*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*B*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 225*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 75*B*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*C*b^3*tan(1/2*d*x + 1/2*c)^9 - 480*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 120*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 360*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 960*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 960*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 90*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 30*B*b^3*tan(1/2*d*x + 1/2*c)^7 - 160*C*b^3*tan(1/2*d*x + 1/2*c)^7 + 720*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 1200*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 1200*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 464*C*b^3*tan(1/2*d*x + 1/2*c)^5 - 480*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 120*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 360*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 960*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 960*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 90*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 30*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 160*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*B*a^3*tan(1/2*d*x + 1/2*c) + 60*C*a^3*tan(1/2*d*x + 1/2*c) + 180*B*a^2*b*tan(1/2*d*x + 1/2*c) + 360*C*a^2*b*tan(1/2*d*x + 1/2*c) + 360*B*a*b^2*tan(1/2*d*x + 1/2*c) + 225*C*a*b^2*tan(1/2*d*x + 1/2*c) + 75*B*b^3*tan(1/2*d*x + 1/2*c) + 120*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
786,1,586,0,0.309142," ","integrate((a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(8 \, B a^{3} + 12 \, C a^{2} b + 12 \, B a b^{2} + 3 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, B a^{3} + 12 \, C a^{2} b + 12 \, B a b^{2} + 3 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 216 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 120 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 216 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(8*B*a^3 + 12*C*a^2*b + 12*B*a*b^2 + 3*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*B*a^3 + 12*C*a^2*b + 12*B*a*b^2 + 3*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(24*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 72*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 72*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 24*B*b^3*tan(1/2*d*x + 1/2*c)^7 - 15*C*b^3*tan(1/2*d*x + 1/2*c)^7 - 72*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 216*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 120*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 40*B*b^3*tan(1/2*d*x + 1/2*c)^5 - 9*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 216*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 40*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 9*C*b^3*tan(1/2*d*x + 1/2*c)^3 - 24*C*a^3*tan(1/2*d*x + 1/2*c) - 72*B*a^2*b*tan(1/2*d*x + 1/2*c) - 36*C*a^2*b*tan(1/2*d*x + 1/2*c) - 36*B*a*b^2*tan(1/2*d*x + 1/2*c) - 72*C*a*b^2*tan(1/2*d*x + 1/2*c) - 24*B*b^3*tan(1/2*d*x + 1/2*c) - 15*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
787,1,336,0,0.350410," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} B a^{3} + 3 \, {\left(2 \, C a^{3} + 6 \, B a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, C a^{3} + 6 \, B a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*B*a^3 + 3*(2*C*a^3 + 6*B*a^2*b + 3*C*a*b^2 + B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*C*a^3 + 6*B*a^2*b + 3*C*a*b^2 + B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(18*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 9*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^3*tan(1/2*d*x + 1/2*c)^5 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^2*b*tan(1/2*d*x + 1/2*c) + 18*B*a*b^2*tan(1/2*d*x + 1/2*c) + 9*C*a*b^2*tan(1/2*d*x + 1/2*c) + 3*B*b^3*tan(1/2*d*x + 1/2*c) + 6*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
788,1,241,0,0.343165," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{4 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 2 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} {\left(d x + c\right)} + {\left(6 \, C a^{2} b + 6 \, B a b^{2} + C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(6 \, C a^{2} b + 6 \, B a b^{2} + C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*B*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(C*a^3 + 3*B*a^2*b)*(d*x + c) + (6*C*a^2*b + 6*B*a*b^2 + C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (6*C*a^2*b + 6*B*a*b^2 + C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^3*tan(1/2*d*x + 1/2*c)^3 - C*b^3*tan(1/2*d*x + 1/2*c)^3 - 6*C*a*b^2*tan(1/2*d*x + 1/2*c) - 2*B*b^3*tan(1/2*d*x + 1/2*c) - C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
789,1,234,0,0.337898," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{4 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - {\left(B a^{3} + 6 \, C a^{2} b + 6 \, B a b^{2}\right)} {\left(d x + c\right)} - 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(4*C*b^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (B*a^3 + 6*C*a^2*b + 6*B*a*b^2)*(d*x + c) - 2*(3*C*a*b^2 + B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 2*(3*C*a*b^2 + B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(B*a^3*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 6*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - B*a^3*tan(1/2*d*x + 1/2*c) - 2*C*a^3*tan(1/2*d*x + 1/2*c) - 6*B*a^2*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
790,1,314,0,0.412979," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{6 \, C b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6 \, C b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(C a^{3} + 3 \, B a^{2} b + 6 \, C a b^{2} + 2 \, B b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*C*b^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6*C*b^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(C*a^3 + 3*B*a^2*b + 6*C*a*b^2 + 2*B*b^3)*(d*x + c) + 2*(6*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^3*tan(1/2*d*x + 1/2*c) + 3*C*a^3*tan(1/2*d*x + 1/2*c) + 9*B*a^2*b*tan(1/2*d*x + 1/2*c) + 18*C*a^2*b*tan(1/2*d*x + 1/2*c) + 18*B*a*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
791,1,536,0,0.544936," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, B a^{3} + 12 \, C a^{2} b + 12 \, B a b^{2} + 8 \, C b^{3}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 120 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 216 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 216 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*B*a^3 + 12*C*a^2*b + 12*B*a*b^2 + 8*C*b^3)*(d*x + c) - 2*(15*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 72*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 72*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*b^3*tan(1/2*d*x + 1/2*c)^7 - 9*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 40*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 120*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 216*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 72*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 120*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 216*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*B*a^3*tan(1/2*d*x + 1/2*c) - 24*C*a^3*tan(1/2*d*x + 1/2*c) - 72*B*a^2*b*tan(1/2*d*x + 1/2*c) - 36*C*a^2*b*tan(1/2*d*x + 1/2*c) - 36*B*a*b^2*tan(1/2*d*x + 1/2*c) - 72*C*a*b^2*tan(1/2*d*x + 1/2*c) - 24*B*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
792,1,672,0,0.362859," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, C a^{3} + 9 \, B a^{2} b + 12 \, C a b^{2} + 4 \, B b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 225 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 90 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 90 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 960 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 960 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 225 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*C*a^3 + 9*B*a^2*b + 12*C*a*b^2 + 4*B*b^3)*(d*x + c) + 2*(120*B*a^3*tan(1/2*d*x + 1/2*c)^9 - 75*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 225*B*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*B*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 180*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*B*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*C*b^3*tan(1/2*d*x + 1/2*c)^9 + 160*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 30*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 90*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 960*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 960*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 120*B*b^3*tan(1/2*d*x + 1/2*c)^7 + 480*C*b^3*tan(1/2*d*x + 1/2*c)^7 + 464*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 1200*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 1200*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 720*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 160*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 30*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 90*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 960*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 960*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 480*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*B*a^3*tan(1/2*d*x + 1/2*c) + 75*C*a^3*tan(1/2*d*x + 1/2*c) + 225*B*a^2*b*tan(1/2*d*x + 1/2*c) + 360*C*a^2*b*tan(1/2*d*x + 1/2*c) + 360*B*a*b^2*tan(1/2*d*x + 1/2*c) + 180*C*a*b^2*tan(1/2*d*x + 1/2*c) + 60*B*b^3*tan(1/2*d*x + 1/2*c) + 120*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
793,1,412,0,0.635363," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, C a^{3} - 2 \, B a^{2} b + C a b^{2} - B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} - \frac{3 \, {\left(2 \, C a^{3} - 2 \, B a^{2} b + C a b^{2} - B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{12 \, {\left(C a^{4} - B a^{3} b\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} b^{4}} + \frac{2 \, {\left(6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"-1/6*(3*(2*C*a^3 - 2*B*a^2*b + C*a*b^2 - B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - 3*(2*C*a^3 - 2*B*a^2*b + C*a*b^2 - B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - 12*(C*a^4 - B*a^3*b)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*b^4) + 2*(6*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 3*C*a*b*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^2*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 4*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*tan(1/2*d*x + 1/2*c) - 6*B*a*b*tan(1/2*d*x + 1/2*c) - 3*C*a*b*tan(1/2*d*x + 1/2*c) + 3*B*b^2*tan(1/2*d*x + 1/2*c) + 6*C*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*b^3))/d","B",0
794,1,269,0,0.338273," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, C a^{2} - 2 \, B a b + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} - \frac{{\left(2 \, C a^{2} - 2 \, B a b + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}} - \frac{4 \, {\left(C a^{3} - B a^{2} b\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} b^{3}} + \frac{2 \, {\left(2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} b^{2}}}{2 \, d}"," ",0,"1/2*((2*C*a^2 - 2*B*a*b + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 - (2*C*a^2 - 2*B*a*b + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3 - 4*(C*a^3 - B*a^2*b)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*b^3) + 2*(2*C*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*b*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 - 2*C*a*tan(1/2*d*x + 1/2*c) + 2*B*b*tan(1/2*d*x + 1/2*c) + C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*b^2))/d","B",0
795,1,175,0,0.314751," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{2}} - \frac{{\left(C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{2}} + \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b} + \frac{2 \, {\left(C a^{2} - B a b\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} b^{2}}}{d}"," ",0,"-((C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^2 - (C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^2 + 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b) + 2*(C*a^2 - B*a*b)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*b^2))/d","A",0
796,1,128,0,2.089209," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b} - \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b} - \frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)} {\left(C a - B b\right)}}{\sqrt{-a^{2} + b^{2}} b}}{d}"," ",0,"(C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b - C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b - 2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))*(C*a - B*b)/(sqrt(-a^2 + b^2)*b))/d","A",0
797,1,274,0,3.077163," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(\sqrt{-a^{2} + b^{2}} B {\left(a - 2 \, b\right)} {\left| -a + b \right|} + \sqrt{-a^{2} + b^{2}} C a {\left| -a + b \right|} - \sqrt{-a^{2} + b^{2}} B {\left| a \right|} {\left| -a + b \right|} + \sqrt{-a^{2} + b^{2}} C {\left| a \right|} {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{b + \sqrt{{\left(a + b\right)} {\left(a - b\right)} + b^{2}}}{a - b}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} a^{2} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} {\left| a \right|}} + \frac{{\left(B a + C a - 2 \, B b + B {\left| a \right|} - C {\left| a \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{b - \sqrt{{\left(a + b\right)} {\left(a - b\right)} + b^{2}}}{a - b}}}\right)\right)}}{a^{2} - b {\left| a \right|}}}{d}"," ",0,"((sqrt(-a^2 + b^2)*B*(a - 2*b)*abs(-a + b) + sqrt(-a^2 + b^2)*C*a*abs(-a + b) - sqrt(-a^2 + b^2)*B*abs(a)*abs(-a + b) + sqrt(-a^2 + b^2)*C*abs(a)*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(b + sqrt((a + b)*(a - b) + b^2))/(a - b))))/((a^2 - 2*a*b + b^2)*a^2 + (a^2*b - 2*a*b^2 + b^3)*abs(a)) + (B*a + C*a - 2*B*b + B*abs(a) - C*abs(a))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(b - sqrt((a + b)*(a - b) + b^2))/(a - b))))/(a^2 - b*abs(a)))/d","B",0
798,1,141,0,0.259859," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(C a - B b\right)} {\left(d x + c\right)}}{a^{2}} + \frac{2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a} - \frac{2 \, {\left(C a b - B b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{2}}}{d}"," ",0,"((C*a - B*b)*(d*x + c)/a^2 + 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a) - 2*(C*a*b - B*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^2))/d","A",0
799,1,227,0,0.251265," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(B a^{2} - 2 \, C a b + 2 \, B b^{2}\right)} {\left(d x + c\right)}}{a^{3}} + \frac{4 \, {\left(C a b^{2} - B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{3}} - \frac{2 \, {\left(B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"1/2*((B*a^2 - 2*C*a*b + 2*B*b^2)*(d*x + c)/a^3 + 4*(C*a*b^2 - B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^3) - 2*(B*a*tan(1/2*d*x + 1/2*c)^3 - 2*C*a*tan(1/2*d*x + 1/2*c)^3 + 2*B*b*tan(1/2*d*x + 1/2*c)^3 - B*a*tan(1/2*d*x + 1/2*c) - 2*C*a*tan(1/2*d*x + 1/2*c) + 2*B*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2))/d","A",0
800,1,360,0,0.273145," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(C a^{3} - B a^{2} b + 2 \, C a b^{2} - 2 \, B b^{3}\right)} {\left(d x + c\right)}}{a^{4}} - \frac{12 \, {\left(C a b^{3} - B b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{4}} + \frac{2 \, {\left(6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}}}{6 \, d}"," ",0,"1/6*(3*(C*a^3 - B*a^2*b + 2*C*a*b^2 - 2*B*b^3)*(d*x + c)/a^4 - 12*(C*a*b^3 - B*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^4) + 2*(6*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*C*a*b*tan(1/2*d*x + 1/2*c)^3 + 12*B*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^2*tan(1/2*d*x + 1/2*c) + 3*C*a^2*tan(1/2*d*x + 1/2*c) - 3*B*a*b*tan(1/2*d*x + 1/2*c) - 6*C*a*b*tan(1/2*d*x + 1/2*c) + 6*B*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3))/d","B",0
801,1,384,0,0.357434," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(3 \, C a^{5} - 2 \, B a^{4} b - 4 \, C a^{3} b^{2} + 3 \, B a^{2} b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{4 \, {\left(C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} - \frac{{\left(6 \, C a^{2} - 4 \, B a b + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} + \frac{{\left(6 \, C a^{2} - 4 \, B a b + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{2 \, {\left(4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} b^{3}}}{2 \, d}"," ",0,"-1/2*(4*(3*C*a^5 - 2*B*a^4*b - 4*C*a^3*b^2 + 3*B*a^2*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) - 4*(C*a^4*tan(1/2*d*x + 1/2*c) - B*a^3*b*tan(1/2*d*x + 1/2*c))/((a^2*b^3 - b^5)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) - (6*C*a^2 - 4*B*a*b + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 + (6*C*a^2 - 4*B*a*b + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - 2*(4*C*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*b*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*tan(1/2*d*x + 1/2*c) + 2*B*b*tan(1/2*d*x + 1/2*c) + C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*b^3))/d","A",0
802,1,404,0,0.284530," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(2 \, C a^{4} - B a^{3} b - 3 \, C a^{2} b^{2} + 2 \, B a b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, {\left(2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} {\left(a^{2} b^{2} - b^{4}\right)}} - \frac{{\left(2 \, C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} + \frac{{\left(2 \, C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}}}{d}"," ",0,"(2*(2*C*a^4 - B*a^3*b - 3*C*a^2*b^2 + 2*B*a*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^2*b^3 - b^5)*sqrt(-a^2 + b^2)) - 2*(2*C*a^3*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + C*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^3*tan(1/2*d*x + 1/2*c) + B*a^2*b*tan(1/2*d*x + 1/2*c) - C*a^2*b*tan(1/2*d*x + 1/2*c) + C*a*b^2*tan(1/2*d*x + 1/2*c) + C*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)*(a^2*b^2 - b^4)) - (2*C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 + (2*C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3)/d","B",0
803,1,229,0,0.300683," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(C a^{3} - 2 \, C a b^{2} + B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{2} b^{2} - b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{2}} - \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{2}} + \frac{2 \, {\left(C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b - b^{3}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}}}{d}"," ",0,"(2*(C*a^3 - 2*C*a*b^2 + B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^2*b^2 - b^4)*sqrt(-a^2 + b^2)) + C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^2 - C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^2 + 2*(C*a^2*tan(1/2*d*x + 1/2*c) - B*a*b*tan(1/2*d*x + 1/2*c))/((a^2*b - b^3)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)))/d","A",0
804,1,174,0,0.230554," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)} {\left(B a - C b\right)}}{{\left(a^{2} - b^{2}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} {\left(a^{2} - b^{2}\right)}}\right)}}{d}"," ",0,"2*((pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))*(B*a - C*b)/((a^2 - b^2)*sqrt(-a^2 + b^2)) - (C*a*tan(1/2*d*x + 1/2*c) - B*b*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)*(a^2 - b^2)))/d","A",0
805,1,201,0,0.278240," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(C a^{3} - 2 \, B a^{2} b + B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - a^{2} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{{\left(d x + c\right)} B}{a^{2}} + \frac{2 \, {\left(C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{3} - a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}}}{d}"," ",0,"(2*(C*a^3 - 2*B*a^2*b + B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - a^2*b^2)*sqrt(-a^2 + b^2)) + (d*x + c)*B/a^2 + 2*(C*a*b*tan(1/2*d*x + 1/2*c) - B*b^2*tan(1/2*d*x + 1/2*c))/((a^3 - a*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)))/d","A",0
806,1,1107,0,0.494555," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(C a^{8} - 2 \, B a^{7} b - 3 \, C a^{7} b + 5 \, B a^{6} b^{2} - 2 \, C a^{6} b^{2} + 4 \, B a^{5} b^{3} + 5 \, C a^{5} b^{3} - 9 \, B a^{4} b^{4} + C a^{4} b^{4} - 2 \, B a^{3} b^{5} - 2 \, C a^{3} b^{5} + 4 \, B a^{2} b^{6} - C a^{3} {\left| -a^{5} + a^{3} b^{2} \right|} + 2 \, B a^{2} b {\left| -a^{5} + a^{3} b^{2} \right|} - C a^{2} b {\left| -a^{5} + a^{3} b^{2} \right|} + B a b^{2} {\left| -a^{5} + a^{3} b^{2} \right|} + C a b^{2} {\left| -a^{5} + a^{3} b^{2} \right|} - 2 \, B b^{3} {\left| -a^{5} + a^{3} b^{2} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{4} b - a^{2} b^{3} + \sqrt{{\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} {\left(a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}\right)} + {\left(a^{4} b - a^{2} b^{3}\right)}^{2}}}{a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}}}}\right)\right)}}{a^{4} b {\left| -a^{5} + a^{3} b^{2} \right|} - a^{2} b^{3} {\left| -a^{5} + a^{3} b^{2} \right|} + {\left(a^{5} - a^{3} b^{2}\right)}^{2}} - \frac{{\left({\left(2 \, a^{2} b + a b^{2} - 2 \, b^{3}\right)} \sqrt{-a^{2} + b^{2}} B {\left| -a^{5} + a^{3} b^{2} \right|} {\left| -a + b \right|} - {\left(a^{3} + a^{2} b - a b^{2}\right)} \sqrt{-a^{2} + b^{2}} C {\left| -a^{5} + a^{3} b^{2} \right|} {\left| -a + b \right|} + {\left(2 \, a^{7} b - 5 \, a^{6} b^{2} - 4 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 2 \, a^{3} b^{5} - 4 \, a^{2} b^{6}\right)} \sqrt{-a^{2} + b^{2}} B {\left| -a + b \right|} - {\left(a^{8} - 3 \, a^{7} b - 2 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + a^{4} b^{4} - 2 \, a^{3} b^{5}\right)} \sqrt{-a^{2} + b^{2}} C {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{4} b - a^{2} b^{3} - \sqrt{{\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} {\left(a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}\right)} + {\left(a^{4} b - a^{2} b^{3}\right)}^{2}}}{a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}}}}\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} - {\left(a^{6} b - 2 \, a^{5} b^{2} + 2 \, a^{3} b^{4} - a^{2} b^{5}\right)} {\left| -a^{5} + a^{3} b^{2} \right|}} + \frac{2 \, {\left(B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} {\left(a^{4} - a^{2} b^{2}\right)}}}{d}"," ",0,"((C*a^8 - 2*B*a^7*b - 3*C*a^7*b + 5*B*a^6*b^2 - 2*C*a^6*b^2 + 4*B*a^5*b^3 + 5*C*a^5*b^3 - 9*B*a^4*b^4 + C*a^4*b^4 - 2*B*a^3*b^5 - 2*C*a^3*b^5 + 4*B*a^2*b^6 - C*a^3*abs(-a^5 + a^3*b^2) + 2*B*a^2*b*abs(-a^5 + a^3*b^2) - C*a^2*b*abs(-a^5 + a^3*b^2) + B*a*b^2*abs(-a^5 + a^3*b^2) + C*a*b^2*abs(-a^5 + a^3*b^2) - 2*B*b^3*abs(-a^5 + a^3*b^2))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^4*b - a^2*b^3 + sqrt((a^5 + a^4*b - a^3*b^2 - a^2*b^3)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3) + (a^4*b - a^2*b^3)^2))/(a^5 - a^4*b - a^3*b^2 + a^2*b^3))))/(a^4*b*abs(-a^5 + a^3*b^2) - a^2*b^3*abs(-a^5 + a^3*b^2) + (a^5 - a^3*b^2)^2) - ((2*a^2*b + a*b^2 - 2*b^3)*sqrt(-a^2 + b^2)*B*abs(-a^5 + a^3*b^2)*abs(-a + b) - (a^3 + a^2*b - a*b^2)*sqrt(-a^2 + b^2)*C*abs(-a^5 + a^3*b^2)*abs(-a + b) + (2*a^7*b - 5*a^6*b^2 - 4*a^5*b^3 + 9*a^4*b^4 + 2*a^3*b^5 - 4*a^2*b^6)*sqrt(-a^2 + b^2)*B*abs(-a + b) - (a^8 - 3*a^7*b - 2*a^6*b^2 + 5*a^5*b^3 + a^4*b^4 - 2*a^3*b^5)*sqrt(-a^2 + b^2)*C*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^4*b - a^2*b^3 - sqrt((a^5 + a^4*b - a^3*b^2 - a^2*b^3)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3) + (a^4*b - a^2*b^3)^2))/(a^5 - a^4*b - a^3*b^2 + a^2*b^3))))/((a^5 - a^3*b^2)^2*(a^2 - 2*a*b + b^2) - (a^6*b - 2*a^5*b^2 + 2*a^3*b^4 - a^2*b^5)*abs(-a^5 + a^3*b^2)) + 2*(B*a^3*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^3*tan(1/2*d*x + 1/2*c)^3 - B*a^3*tan(1/2*d*x + 1/2*c) - B*a^2*b*tan(1/2*d*x + 1/2*c) + B*a*b^2*tan(1/2*d*x + 1/2*c) - C*a*b^2*tan(1/2*d*x + 1/2*c) + 2*B*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)*(a^4 - a^2*b^2)))/d","B",0
807,1,340,0,0.254548," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(3 \, C a^{3} b^{2} - 4 \, B a^{2} b^{3} - 2 \, C a b^{4} + 3 \, B b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{4 \, {\left(C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} + \frac{{\left(B a^{2} - 4 \, C a b + 6 \, B b^{2}\right)} {\left(d x + c\right)}}{a^{4}} - \frac{2 \, {\left(B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}}}{2 \, d}"," ",0,"1/2*(4*(3*C*a^3*b^2 - 4*B*a^2*b^3 - 2*C*a*b^4 + 3*B*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - a^4*b^2)*sqrt(-a^2 + b^2)) + 4*(C*a*b^3*tan(1/2*d*x + 1/2*c) - B*b^4*tan(1/2*d*x + 1/2*c))/((a^5 - a^3*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) + (B*a^2 - 4*C*a*b + 6*B*b^2)*(d*x + c)/a^4 - 2*(B*a*tan(1/2*d*x + 1/2*c)^3 - 2*C*a*tan(1/2*d*x + 1/2*c)^3 + 4*B*b*tan(1/2*d*x + 1/2*c)^3 - B*a*tan(1/2*d*x + 1/2*c) - 2*C*a*tan(1/2*d*x + 1/2*c) + 4*B*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3))/d","A",0
808,1,581,0,0.460289," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(6 \, C a^{6} - 2 \, B a^{5} b - 15 \, C a^{4} b^{2} + 5 \, B a^{3} b^{3} + 12 \, C a^{2} b^{4} - 6 \, B a b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{4 \, C a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} - \frac{{\left(3 \, C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} + \frac{{\left(3 \, C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b^{3}}}{d}"," ",0,"((6*C*a^6 - 2*B*a^5*b - 15*C*a^4*b^2 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 6*B*a*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4*b^4 - 2*a^2*b^6 + b^8)*sqrt(-a^2 + b^2)) - (4*C*a^6*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 7*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 6*B*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^6*tan(1/2*d*x + 1/2*c) + 2*B*a^5*b*tan(1/2*d*x + 1/2*c) - 5*C*a^5*b*tan(1/2*d*x + 1/2*c) + 3*B*a^4*b^2*tan(1/2*d*x + 1/2*c) + 7*C*a^4*b^2*tan(1/2*d*x + 1/2*c) - 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c) + 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c) - 6*B*a^2*b^4*tan(1/2*d*x + 1/2*c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) - (3*C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 + (3*C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b^3))/d","B",0
809,1,486,0,0.402116," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, C a^{5} - 5 \, C a^{3} b^{2} - B a^{2} b^{3} + 6 \, C a b^{4} - 2 \, B b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} + \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}} - \frac{2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"-((2*C*a^5 - 5*C*a^3*b^2 - B*a^2*b^3 + 6*C*a*b^4 - 2*B*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4*b^3 - 2*a^2*b^5 + b^7)*sqrt(-a^2 + b^2)) - C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 + C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3 - (2*C*a^5*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^4*b*tan(1/2*d*x + 1/2*c)^3 + B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^5*tan(1/2*d*x + 1/2*c) - 3*C*a^4*b*tan(1/2*d*x + 1/2*c) + B*a^3*b^2*tan(1/2*d*x + 1/2*c) + 5*C*a^3*b^2*tan(1/2*d*x + 1/2*c) - 3*B*a^2*b^3*tan(1/2*d*x + 1/2*c) + 6*C*a^2*b^3*tan(1/2*d*x + 1/2*c) - 4*B*a*b^4*tan(1/2*d*x + 1/2*c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
810,1,400,0,0.386722," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(C a^{2} - 3 \, B a b + 2 \, C b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"((C*a^2 - 3*B*a*b + 2*C*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) - (2*B*a^3*tan(1/2*d*x + 1/2*c)^3 - C*a^3*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 2*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^3*tan(1/2*d*x + 1/2*c) - C*a^3*tan(1/2*d*x + 1/2*c) - B*a^2*b*tan(1/2*d*x + 1/2*c) + 3*C*a^2*b*tan(1/2*d*x + 1/2*c) - B*a*b^2*tan(1/2*d*x + 1/2*c) + 4*C*a*b^2*tan(1/2*d*x + 1/2*c) - 2*B*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
811,1,399,0,0.363832," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, B a^{2} - 3 \, C a b + B b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"((2*B*a^2 - 3*C*a*b + B*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) - (2*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 3*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + B*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*C*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^3*tan(1/2*d*x + 1/2*c) + 4*B*a^2*b*tan(1/2*d*x + 1/2*c) - C*a^2*b*tan(1/2*d*x + 1/2*c) + 3*B*a*b^2*tan(1/2*d*x + 1/2*c) - C*a*b^2*tan(1/2*d*x + 1/2*c) - B*b^3*tan(1/2*d*x + 1/2*c) - 2*C*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
812,1,457,0,0.385324," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, C a^{5} - 6 \, B a^{4} b + C a^{3} b^{2} + 5 \, B a^{2} b^{3} - 2 \, B b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{{\left(d x + c\right)} B}{a^{3}} + \frac{4 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"((2*C*a^5 - 6*B*a^4*b + C*a^3*b^2 + 5*B*a^2*b^3 - 2*B*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(-a^2 + b^2)) + (d*x + c)*B/a^3 + (4*C*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 6*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 3*B*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 2*B*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^4*b*tan(1/2*d*x + 1/2*c) + 6*B*a^3*b^2*tan(1/2*d*x + 1/2*c) - 3*C*a^3*b^2*tan(1/2*d*x + 1/2*c) + 5*B*a^2*b^3*tan(1/2*d*x + 1/2*c) + C*a^2*b^3*tan(1/2*d*x + 1/2*c) - 3*B*a*b^4*tan(1/2*d*x + 1/2*c) - 2*B*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
813,1,546,0,0.410748," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(6 \, C a^{5} b - 12 \, B a^{4} b^{2} - 5 \, C a^{3} b^{3} + 15 \, B a^{2} b^{4} + 2 \, C a b^{5} - 6 \, B b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{6 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} - \frac{{\left(C a - 3 \, B b\right)} {\left(d x + c\right)}}{a^{4}} - \frac{2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}}}{d}"," ",0,"-((6*C*a^5*b - 12*B*a^4*b^2 - 5*C*a^3*b^3 + 15*B*a^2*b^4 + 2*C*a*b^5 - 6*B*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^8 - 2*a^6*b^2 + a^4*b^4)*sqrt(-a^2 + b^2)) + (6*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 8*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 7*B*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 5*B*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 2*C*a*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*B*b^6*tan(1/2*d*x + 1/2*c)^3 - 6*C*a^4*b^2*tan(1/2*d*x + 1/2*c) + 8*B*a^3*b^3*tan(1/2*d*x + 1/2*c) - 5*C*a^3*b^3*tan(1/2*d*x + 1/2*c) + 7*B*a^2*b^4*tan(1/2*d*x + 1/2*c) + 3*C*a^2*b^4*tan(1/2*d*x + 1/2*c) - 5*B*a*b^5*tan(1/2*d*x + 1/2*c) + 2*C*a*b^5*tan(1/2*d*x + 1/2*c) - 4*B*b^6*tan(1/2*d*x + 1/2*c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) - (C*a - 3*B*b)*(d*x + c)/a^4 - 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3))/d","A",0
814,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
815,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
816,0,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sec(d*x + c), x)","F",0
817,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
818,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*cos(d*x + c), x)","F",0
819,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
820,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^3, x)","F",0
821,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
822,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
823,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
824,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2), x)","F",0
825,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
826,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
827,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^3, x)","F",0
828,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^4, x)","F",0
829,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
830,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
831,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(5/2), x)","F",0
832,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
833,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
834,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^3, x)","F",0
835,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^4, x)","F",0
836,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^5, x)","F",0
837,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)^3/sqrt(b*sec(d*x + c) + a), x)","F",0
838,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
839,0,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
840,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
841,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
842,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
843,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)^3/(b*sec(d*x + c) + a)^(3/2), x)","F",0
844,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
845,0,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
846,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/(b*sec(d*x + c) + a)^(3/2), x)","F",0
847,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
848,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
849,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)^3/(b*sec(d*x + c) + a)^(5/2), x)","F",0
850,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)^2/(b*sec(d*x + c) + a)^(5/2), x)","F",0
851,0,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
852,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/(b*sec(d*x + c) + a)^(5/2), x)","F",0
853,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
854,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/(b*sec(d*x + c) + a)^(7/2), x)","F",0
855,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/((b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
856,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
857,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(2/3), x)","F",0
858,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(1/3), x)","F",0
859,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/(b*sec(d*x + c) + a)^(1/3), x)","F",0
860,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/(b*sec(d*x + c) + a)^(2/3), x)","F",0
861,1,473,0,0.315849," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, A a + 3 \, C a + 3 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, A a + 3 \, C a + 3 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(60 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 75 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 75 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 160 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 400 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 400 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 464 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 75 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 75 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(4*A*a + 3*C*a + 3*B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*A*a + 3*C*a + 3*B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(60*A*a*tan(1/2*d*x + 1/2*c)^9 - 120*B*a*tan(1/2*d*x + 1/2*c)^9 + 75*C*a*tan(1/2*d*x + 1/2*c)^9 - 120*A*b*tan(1/2*d*x + 1/2*c)^9 + 75*B*b*tan(1/2*d*x + 1/2*c)^9 - 120*C*b*tan(1/2*d*x + 1/2*c)^9 - 120*A*a*tan(1/2*d*x + 1/2*c)^7 + 320*B*a*tan(1/2*d*x + 1/2*c)^7 - 30*C*a*tan(1/2*d*x + 1/2*c)^7 + 320*A*b*tan(1/2*d*x + 1/2*c)^7 - 30*B*b*tan(1/2*d*x + 1/2*c)^7 + 160*C*b*tan(1/2*d*x + 1/2*c)^7 - 400*B*a*tan(1/2*d*x + 1/2*c)^5 - 400*A*b*tan(1/2*d*x + 1/2*c)^5 - 464*C*b*tan(1/2*d*x + 1/2*c)^5 + 120*A*a*tan(1/2*d*x + 1/2*c)^3 + 320*B*a*tan(1/2*d*x + 1/2*c)^3 + 30*C*a*tan(1/2*d*x + 1/2*c)^3 + 320*A*b*tan(1/2*d*x + 1/2*c)^3 + 30*B*b*tan(1/2*d*x + 1/2*c)^3 + 160*C*b*tan(1/2*d*x + 1/2*c)^3 - 60*A*a*tan(1/2*d*x + 1/2*c) - 120*B*a*tan(1/2*d*x + 1/2*c) - 75*C*a*tan(1/2*d*x + 1/2*c) - 120*A*b*tan(1/2*d*x + 1/2*c) - 75*B*b*tan(1/2*d*x + 1/2*c) - 120*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
862,1,428,0,0.257511," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(4 \, B a + 4 \, A b + 3 \, C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, B a + 4 \, A b + 3 \, C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(24 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(4*B*a + 4*A*b + 3*C*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*B*a + 4*A*b + 3*C*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(24*A*a*tan(1/2*d*x + 1/2*c)^7 - 12*B*a*tan(1/2*d*x + 1/2*c)^7 + 24*C*a*tan(1/2*d*x + 1/2*c)^7 - 12*A*b*tan(1/2*d*x + 1/2*c)^7 + 24*B*b*tan(1/2*d*x + 1/2*c)^7 - 15*C*b*tan(1/2*d*x + 1/2*c)^7 - 72*A*a*tan(1/2*d*x + 1/2*c)^5 + 12*B*a*tan(1/2*d*x + 1/2*c)^5 - 40*C*a*tan(1/2*d*x + 1/2*c)^5 + 12*A*b*tan(1/2*d*x + 1/2*c)^5 - 40*B*b*tan(1/2*d*x + 1/2*c)^5 - 9*C*b*tan(1/2*d*x + 1/2*c)^5 + 72*A*a*tan(1/2*d*x + 1/2*c)^3 + 12*B*a*tan(1/2*d*x + 1/2*c)^3 + 40*C*a*tan(1/2*d*x + 1/2*c)^3 + 12*A*b*tan(1/2*d*x + 1/2*c)^3 + 40*B*b*tan(1/2*d*x + 1/2*c)^3 - 9*C*b*tan(1/2*d*x + 1/2*c)^3 - 24*A*a*tan(1/2*d*x + 1/2*c) - 12*B*a*tan(1/2*d*x + 1/2*c) - 24*C*a*tan(1/2*d*x + 1/2*c) - 12*A*b*tan(1/2*d*x + 1/2*c) - 24*B*b*tan(1/2*d*x + 1/2*c) - 15*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
863,1,261,0,0.272884," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(2 \, A a + C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, A a + C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*A*a + C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*A*a + C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*B*a*tan(1/2*d*x + 1/2*c)^5 - 3*C*a*tan(1/2*d*x + 1/2*c)^5 + 6*A*b*tan(1/2*d*x + 1/2*c)^5 - 3*B*b*tan(1/2*d*x + 1/2*c)^5 + 6*C*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*a*tan(1/2*d*x + 1/2*c)^3 - 12*A*b*tan(1/2*d*x + 1/2*c)^3 - 4*C*b*tan(1/2*d*x + 1/2*c)^3 + 6*B*a*tan(1/2*d*x + 1/2*c) + 3*C*a*tan(1/2*d*x + 1/2*c) + 6*A*b*tan(1/2*d*x + 1/2*c) + 3*B*b*tan(1/2*d*x + 1/2*c) + 6*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
864,1,170,0,0.257142," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} A a + {\left(2 \, B a + 2 \, A b + C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, B a + 2 \, A b + C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*A*a + (2*B*a + 2*A*b + C*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*B*a + 2*A*b + C*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*C*a*tan(1/2*d*x + 1/2*c)^3 + 2*B*b*tan(1/2*d*x + 1/2*c)^3 - C*b*tan(1/2*d*x + 1/2*c)^3 - 2*C*a*tan(1/2*d*x + 1/2*c) - 2*B*b*tan(1/2*d*x + 1/2*c) - C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
865,1,134,0,0.265348," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(B a + A b\right)} {\left(d x + c\right)} + {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((B*a + A*b)*(d*x + c) + (C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - C*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) - C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
866,1,159,0,0.238786," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, C b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, C b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(A a + 2 \, C a + 2 \, B b\right)} {\left(d x + c\right)} - \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*C*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*C*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (A*a + 2*C*a + 2*B*b)*(d*x + c) - 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c)^3 - 2*A*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) - 2*B*a*tan(1/2*d*x + 1/2*c) - 2*A*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
867,1,227,0,0.227528," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(B a + A b + 2 \, C b\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a + A*b + 2*C*b)*(d*x + c) + 2*(6*A*a*tan(1/2*d*x + 1/2*c)^5 - 3*B*a*tan(1/2*d*x + 1/2*c)^5 + 6*C*a*tan(1/2*d*x + 1/2*c)^5 - 3*A*b*tan(1/2*d*x + 1/2*c)^5 + 6*B*b*tan(1/2*d*x + 1/2*c)^5 + 4*A*a*tan(1/2*d*x + 1/2*c)^3 + 12*C*a*tan(1/2*d*x + 1/2*c)^3 + 12*B*b*tan(1/2*d*x + 1/2*c)^3 + 6*A*a*tan(1/2*d*x + 1/2*c) + 3*B*a*tan(1/2*d*x + 1/2*c) + 6*C*a*tan(1/2*d*x + 1/2*c) + 3*A*b*tan(1/2*d*x + 1/2*c) + 6*B*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
868,1,392,0,0.215455," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a + 4 \, C a + 4 \, B b\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a + 4*C*a + 4*B*b)*(d*x + c) - 2*(15*A*a*tan(1/2*d*x + 1/2*c)^7 - 24*B*a*tan(1/2*d*x + 1/2*c)^7 + 12*C*a*tan(1/2*d*x + 1/2*c)^7 - 24*A*b*tan(1/2*d*x + 1/2*c)^7 + 12*B*b*tan(1/2*d*x + 1/2*c)^7 - 24*C*b*tan(1/2*d*x + 1/2*c)^7 - 9*A*a*tan(1/2*d*x + 1/2*c)^5 - 40*B*a*tan(1/2*d*x + 1/2*c)^5 + 12*C*a*tan(1/2*d*x + 1/2*c)^5 - 40*A*b*tan(1/2*d*x + 1/2*c)^5 + 12*B*b*tan(1/2*d*x + 1/2*c)^5 - 72*C*b*tan(1/2*d*x + 1/2*c)^5 + 9*A*a*tan(1/2*d*x + 1/2*c)^3 - 40*B*a*tan(1/2*d*x + 1/2*c)^3 - 12*C*a*tan(1/2*d*x + 1/2*c)^3 - 40*A*b*tan(1/2*d*x + 1/2*c)^3 - 12*B*b*tan(1/2*d*x + 1/2*c)^3 - 72*C*b*tan(1/2*d*x + 1/2*c)^3 - 15*A*a*tan(1/2*d*x + 1/2*c) - 24*B*a*tan(1/2*d*x + 1/2*c) - 12*C*a*tan(1/2*d*x + 1/2*c) - 24*A*b*tan(1/2*d*x + 1/2*c) - 12*B*b*tan(1/2*d*x + 1/2*c) - 24*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
869,1,437,0,0.243295," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, B a + 3 \, A b + 4 \, C b\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*B*a + 3*A*b + 4*C*b)*(d*x + c) + 2*(120*A*a*tan(1/2*d*x + 1/2*c)^9 - 75*B*a*tan(1/2*d*x + 1/2*c)^9 + 120*C*a*tan(1/2*d*x + 1/2*c)^9 - 75*A*b*tan(1/2*d*x + 1/2*c)^9 + 120*B*b*tan(1/2*d*x + 1/2*c)^9 - 60*C*b*tan(1/2*d*x + 1/2*c)^9 + 160*A*a*tan(1/2*d*x + 1/2*c)^7 - 30*B*a*tan(1/2*d*x + 1/2*c)^7 + 320*C*a*tan(1/2*d*x + 1/2*c)^7 - 30*A*b*tan(1/2*d*x + 1/2*c)^7 + 320*B*b*tan(1/2*d*x + 1/2*c)^7 - 120*C*b*tan(1/2*d*x + 1/2*c)^7 + 464*A*a*tan(1/2*d*x + 1/2*c)^5 + 400*C*a*tan(1/2*d*x + 1/2*c)^5 + 400*B*b*tan(1/2*d*x + 1/2*c)^5 + 160*A*a*tan(1/2*d*x + 1/2*c)^3 + 30*B*a*tan(1/2*d*x + 1/2*c)^3 + 320*C*a*tan(1/2*d*x + 1/2*c)^3 + 30*A*b*tan(1/2*d*x + 1/2*c)^3 + 320*B*b*tan(1/2*d*x + 1/2*c)^3 + 120*C*b*tan(1/2*d*x + 1/2*c)^3 + 120*A*a*tan(1/2*d*x + 1/2*c) + 75*B*a*tan(1/2*d*x + 1/2*c) + 120*C*a*tan(1/2*d*x + 1/2*c) + 75*A*b*tan(1/2*d*x + 1/2*c) + 120*B*b*tan(1/2*d*x + 1/2*c) + 60*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
870,1,766,0,0.317033," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, B a^{2} + 8 \, A a b + 6 \, C a b + 3 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, B a^{2} + 8 \, A a b + 6 \, C a b + 3 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 240 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 150 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 480 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 320 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 640 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 320 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 160 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 800 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 464 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 480 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 640 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 150 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(4*B*a^2 + 8*A*a*b + 6*C*a*b + 3*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*B*a^2 + 8*A*a*b + 6*C*a*b + 3*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*A*a^2*tan(1/2*d*x + 1/2*c)^9 - 60*B*a^2*tan(1/2*d*x + 1/2*c)^9 + 120*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 120*A*a*b*tan(1/2*d*x + 1/2*c)^9 + 240*B*a*b*tan(1/2*d*x + 1/2*c)^9 - 150*C*a*b*tan(1/2*d*x + 1/2*c)^9 + 120*A*b^2*tan(1/2*d*x + 1/2*c)^9 - 75*B*b^2*tan(1/2*d*x + 1/2*c)^9 + 120*C*b^2*tan(1/2*d*x + 1/2*c)^9 - 480*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 120*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 320*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 240*A*a*b*tan(1/2*d*x + 1/2*c)^7 - 640*B*a*b*tan(1/2*d*x + 1/2*c)^7 + 60*C*a*b*tan(1/2*d*x + 1/2*c)^7 - 320*A*b^2*tan(1/2*d*x + 1/2*c)^7 + 30*B*b^2*tan(1/2*d*x + 1/2*c)^7 - 160*C*b^2*tan(1/2*d*x + 1/2*c)^7 + 720*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 400*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 800*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 400*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 464*C*b^2*tan(1/2*d*x + 1/2*c)^5 - 480*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 120*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 320*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 240*A*a*b*tan(1/2*d*x + 1/2*c)^3 - 640*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 60*C*a*b*tan(1/2*d*x + 1/2*c)^3 - 320*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 30*B*b^2*tan(1/2*d*x + 1/2*c)^3 - 160*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^2*tan(1/2*d*x + 1/2*c) + 60*B*a^2*tan(1/2*d*x + 1/2*c) + 120*C*a^2*tan(1/2*d*x + 1/2*c) + 120*A*a*b*tan(1/2*d*x + 1/2*c) + 240*B*a*b*tan(1/2*d*x + 1/2*c) + 150*C*a*b*tan(1/2*d*x + 1/2*c) + 120*A*b^2*tan(1/2*d*x + 1/2*c) + 75*B*b^2*tan(1/2*d*x + 1/2*c) + 120*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
871,1,630,0,0.323712," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(8 \, A a^{2} + 4 \, C a^{2} + 8 \, B a b + 4 \, A b^{2} + 3 \, C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, A a^{2} + 4 \, C a^{2} + 8 \, B a b + 4 \, A b^{2} + 3 \, C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 144 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 80 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 144 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(8*A*a^2 + 4*C*a^2 + 8*B*a*b + 4*A*b^2 + 3*C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*A*a^2 + 4*C*a^2 + 8*B*a*b + 4*A*b^2 + 3*C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(24*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 48*A*a*b*tan(1/2*d*x + 1/2*c)^7 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^7 + 48*C*a*b*tan(1/2*d*x + 1/2*c)^7 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^7 + 24*B*b^2*tan(1/2*d*x + 1/2*c)^7 - 15*C*b^2*tan(1/2*d*x + 1/2*c)^7 - 72*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 144*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 80*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 40*B*b^2*tan(1/2*d*x + 1/2*c)^5 - 9*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 144*A*a*b*tan(1/2*d*x + 1/2*c)^3 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 80*C*a*b*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 40*B*b^2*tan(1/2*d*x + 1/2*c)^3 - 9*C*b^2*tan(1/2*d*x + 1/2*c)^3 - 24*B*a^2*tan(1/2*d*x + 1/2*c) - 12*C*a^2*tan(1/2*d*x + 1/2*c) - 48*A*a*b*tan(1/2*d*x + 1/2*c) - 24*B*a*b*tan(1/2*d*x + 1/2*c) - 48*C*a*b*tan(1/2*d*x + 1/2*c) - 12*A*b^2*tan(1/2*d*x + 1/2*c) - 24*B*b^2*tan(1/2*d*x + 1/2*c) - 15*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
872,1,364,0,0.291718," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} A a^{2} + 3 \, {\left(2 \, B a^{2} + 4 \, A a b + 2 \, C a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, B a^{2} + 4 \, A a b + 2 \, C a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*A*a^2 + 3*(2*B*a^2 + 4*A*a*b + 2*C*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*B*a^2 + 4*A*a*b + 2*C*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 12*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^2*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*tan(1/2*d*x + 1/2*c) + 12*B*a*b*tan(1/2*d*x + 1/2*c) + 6*C*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c) + 3*B*b^2*tan(1/2*d*x + 1/2*c) + 6*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
873,1,241,0,0.297374," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} {\left(d x + c\right)} + {\left(2 \, C a^{2} + 4 \, B a b + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, C a^{2} + 4 \, B a b + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(4 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*A*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(B*a^2 + 2*A*a*b)*(d*x + c) + (2*C*a^2 + 4*B*a*b + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*C*a^2 + 4*B*a*b + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(4*C*a*b*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^2*tan(1/2*d*x + 1/2*c)^3 - C*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*b*tan(1/2*d*x + 1/2*c) - 2*B*b^2*tan(1/2*d*x + 1/2*c) - C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
874,1,229,0,0.271198," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - {\left(A a^{2} + 2 \, C a^{2} + 4 \, B a b + 2 \, A b^{2}\right)} {\left(d x + c\right)} - 2 \, {\left(2 \, C a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 2 \, {\left(2 \, C a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(4*C*b^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (A*a^2 + 2*C*a^2 + 4*B*a*b + 2*A*b^2)*(d*x + c) - 2*(2*C*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 2*(2*C*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a^2*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 4*A*a*b*tan(1/2*d*x + 1/2*c)^3 - A*a^2*tan(1/2*d*x + 1/2*c) - 2*B*a^2*tan(1/2*d*x + 1/2*c) - 4*A*a*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
875,1,346,0,0.299035," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{6 \, C b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6 \, C b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(B a^{2} + 2 \, A a b + 4 \, C a b + 2 \, B b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*C*b^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6*C*b^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(B*a^2 + 2*A*a*b + 4*C*a*b + 2*B*b^2)*(d*x + c) + 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 12*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2*tan(1/2*d*x + 1/2*c) + 6*C*a^2*tan(1/2*d*x + 1/2*c) + 6*A*a*b*tan(1/2*d*x + 1/2*c) + 12*B*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
876,1,577,0,0.285652," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a^{2} + 4 \, C a^{2} + 8 \, B a b + 4 \, A b^{2} + 8 \, C b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 80 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 144 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 144 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a^2 + 4*C*a^2 + 8*B*a*b + 4*A*b^2 + 8*C*b^2)*(d*x + c) - 2*(15*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 48*A*a*b*tan(1/2*d*x + 1/2*c)^7 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^7 - 48*C*a*b*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*b^2*tan(1/2*d*x + 1/2*c)^7 - 9*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 40*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 80*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 144*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 72*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 80*A*a*b*tan(1/2*d*x + 1/2*c)^3 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 144*C*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*B*b^2*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^2*tan(1/2*d*x + 1/2*c) - 24*B*a^2*tan(1/2*d*x + 1/2*c) - 12*C*a^2*tan(1/2*d*x + 1/2*c) - 48*A*a*b*tan(1/2*d*x + 1/2*c) - 24*B*a*b*tan(1/2*d*x + 1/2*c) - 48*C*a*b*tan(1/2*d*x + 1/2*c) - 12*A*b^2*tan(1/2*d*x + 1/2*c) - 24*B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
877,1,720,0,0.310654," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, B a^{2} + 6 \, A a b + 8 \, C a b + 4 \, B b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 150 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 240 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 640 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 240 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 800 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 640 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 150 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*B*a^2 + 6*A*a*b + 8*C*a*b + 4*B*b^2)*(d*x + c) + 2*(120*A*a^2*tan(1/2*d*x + 1/2*c)^9 - 75*B*a^2*tan(1/2*d*x + 1/2*c)^9 + 120*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 150*A*a*b*tan(1/2*d*x + 1/2*c)^9 + 240*B*a*b*tan(1/2*d*x + 1/2*c)^9 - 120*C*a*b*tan(1/2*d*x + 1/2*c)^9 + 120*A*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*B*b^2*tan(1/2*d*x + 1/2*c)^9 + 120*C*b^2*tan(1/2*d*x + 1/2*c)^9 + 160*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 30*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 320*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 60*A*a*b*tan(1/2*d*x + 1/2*c)^7 + 640*B*a*b*tan(1/2*d*x + 1/2*c)^7 - 240*C*a*b*tan(1/2*d*x + 1/2*c)^7 + 320*A*b^2*tan(1/2*d*x + 1/2*c)^7 - 120*B*b^2*tan(1/2*d*x + 1/2*c)^7 + 480*C*b^2*tan(1/2*d*x + 1/2*c)^7 + 464*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 400*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 800*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 400*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 720*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 160*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 30*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 320*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 60*A*a*b*tan(1/2*d*x + 1/2*c)^3 + 640*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 240*C*a*b*tan(1/2*d*x + 1/2*c)^3 + 320*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*B*b^2*tan(1/2*d*x + 1/2*c)^3 + 480*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^2*tan(1/2*d*x + 1/2*c) + 75*B*a^2*tan(1/2*d*x + 1/2*c) + 120*C*a^2*tan(1/2*d*x + 1/2*c) + 150*A*a*b*tan(1/2*d*x + 1/2*c) + 240*B*a*b*tan(1/2*d*x + 1/2*c) + 120*C*a*b*tan(1/2*d*x + 1/2*c) + 120*A*b^2*tan(1/2*d*x + 1/2*c) + 60*B*b^2*tan(1/2*d*x + 1/2*c) + 120*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
878,1,1370,0,0.430533," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(8 \, B a^{3} + 24 \, A a^{2} b + 18 \, C a^{2} b + 18 \, B a b^{2} + 6 \, A b^{3} + 5 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(8 \, B a^{3} + 24 \, A a^{2} b + 18 \, C a^{2} b + 18 \, B a b^{2} + 6 \, A b^{3} + 5 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(240 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 240 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 360 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 720 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 450 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 720 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 450 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 150 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 240 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 165 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1200 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 880 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1080 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2640 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 630 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2640 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 630 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1680 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 210 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 560 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 25 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2400 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 240 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1440 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 720 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4320 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4320 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 180 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3744 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1248 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 450 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2400 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1440 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 720 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4320 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4320 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 180 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3744 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1248 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 450 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 360 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 880 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1080 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2640 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 630 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2640 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 630 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1680 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 210 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 560 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 360 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 450 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 450 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 150 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 165 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(8*B*a^3 + 24*A*a^2*b + 18*C*a^2*b + 18*B*a*b^2 + 6*A*b^3 + 5*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(8*B*a^3 + 24*A*a^2*b + 18*C*a^2*b + 18*B*a*b^2 + 6*A*b^3 + 5*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(240*A*a^3*tan(1/2*d*x + 1/2*c)^11 - 120*B*a^3*tan(1/2*d*x + 1/2*c)^11 + 240*C*a^3*tan(1/2*d*x + 1/2*c)^11 - 360*A*a^2*b*tan(1/2*d*x + 1/2*c)^11 + 720*B*a^2*b*tan(1/2*d*x + 1/2*c)^11 - 450*C*a^2*b*tan(1/2*d*x + 1/2*c)^11 + 720*A*a*b^2*tan(1/2*d*x + 1/2*c)^11 - 450*B*a*b^2*tan(1/2*d*x + 1/2*c)^11 + 720*C*a*b^2*tan(1/2*d*x + 1/2*c)^11 - 150*A*b^3*tan(1/2*d*x + 1/2*c)^11 + 240*B*b^3*tan(1/2*d*x + 1/2*c)^11 - 165*C*b^3*tan(1/2*d*x + 1/2*c)^11 - 1200*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 360*B*a^3*tan(1/2*d*x + 1/2*c)^9 - 880*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 1080*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 2640*B*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 630*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 2640*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 630*B*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 1680*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 210*A*b^3*tan(1/2*d*x + 1/2*c)^9 - 560*B*b^3*tan(1/2*d*x + 1/2*c)^9 - 25*C*b^3*tan(1/2*d*x + 1/2*c)^9 + 2400*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 240*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 1440*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 720*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 4320*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 180*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 4320*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 180*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 3744*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 60*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 1248*B*b^3*tan(1/2*d*x + 1/2*c)^7 - 450*C*b^3*tan(1/2*d*x + 1/2*c)^7 - 2400*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 240*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 1440*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 720*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 4320*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 180*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 4320*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 180*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 3744*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 60*A*b^3*tan(1/2*d*x + 1/2*c)^5 - 1248*B*b^3*tan(1/2*d*x + 1/2*c)^5 - 450*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 1200*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 360*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 880*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 1080*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 2640*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 630*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 2640*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 630*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 1680*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 210*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 560*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 25*C*b^3*tan(1/2*d*x + 1/2*c)^3 - 240*A*a^3*tan(1/2*d*x + 1/2*c) - 120*B*a^3*tan(1/2*d*x + 1/2*c) - 240*C*a^3*tan(1/2*d*x + 1/2*c) - 360*A*a^2*b*tan(1/2*d*x + 1/2*c) - 720*B*a^2*b*tan(1/2*d*x + 1/2*c) - 450*C*a^2*b*tan(1/2*d*x + 1/2*c) - 720*A*a*b^2*tan(1/2*d*x + 1/2*c) - 450*B*a*b^2*tan(1/2*d*x + 1/2*c) - 720*C*a*b^2*tan(1/2*d*x + 1/2*c) - 150*A*b^3*tan(1/2*d*x + 1/2*c) - 240*B*b^3*tan(1/2*d*x + 1/2*c) - 165*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
879,1,989,0,0.403416," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(8 \, A a^{3} + 4 \, C a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 9 \, C a b^{2} + 3 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(8 \, A a^{3} + 4 \, C a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 9 \, C a b^{2} + 3 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 225 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 480 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1440 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 90 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 320 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 160 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2160 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 464 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 480 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1440 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 90 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 225 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(8*A*a^3 + 4*C*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 9*C*a*b^2 + 3*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(8*A*a^3 + 4*C*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 9*C*a*b^2 + 3*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*B*a^3*tan(1/2*d*x + 1/2*c)^9 - 60*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 360*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 180*B*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 180*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 360*B*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 225*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 120*A*b^3*tan(1/2*d*x + 1/2*c)^9 - 75*B*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*C*b^3*tan(1/2*d*x + 1/2*c)^9 - 480*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 120*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 1440*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 360*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 960*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 360*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 960*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 90*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 320*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 30*B*b^3*tan(1/2*d*x + 1/2*c)^7 - 160*C*b^3*tan(1/2*d*x + 1/2*c)^7 + 720*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 2160*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 1200*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 1200*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 400*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 464*C*b^3*tan(1/2*d*x + 1/2*c)^5 - 480*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 120*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 1440*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 360*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 960*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 360*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 960*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 90*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 320*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 30*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 160*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*B*a^3*tan(1/2*d*x + 1/2*c) + 60*C*a^3*tan(1/2*d*x + 1/2*c) + 360*A*a^2*b*tan(1/2*d*x + 1/2*c) + 180*B*a^2*b*tan(1/2*d*x + 1/2*c) + 360*C*a^2*b*tan(1/2*d*x + 1/2*c) + 180*A*a*b^2*tan(1/2*d*x + 1/2*c) + 360*B*a*b^2*tan(1/2*d*x + 1/2*c) + 225*C*a*b^2*tan(1/2*d*x + 1/2*c) + 120*A*b^3*tan(1/2*d*x + 1/2*c) + 75*B*b^3*tan(1/2*d*x + 1/2*c) + 120*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
880,1,759,0,0.376141," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{24 \, {\left(d x + c\right)} A a^{3} + 3 \, {\left(8 \, B a^{3} + 24 \, A a^{2} b + 12 \, C a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3} + 3 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, B a^{3} + 24 \, A a^{2} b + 12 \, C a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3} + 3 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 216 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 216 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 120 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 216 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 216 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*(d*x + c)*A*a^3 + 3*(8*B*a^3 + 24*A*a^2*b + 12*C*a^2*b + 12*B*a*b^2 + 4*A*b^3 + 3*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*B*a^3 + 24*A*a^2*b + 12*C*a^2*b + 12*B*a*b^2 + 4*A*b^3 + 3*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(24*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 72*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 72*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 72*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 12*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 24*B*b^3*tan(1/2*d*x + 1/2*c)^7 - 15*C*b^3*tan(1/2*d*x + 1/2*c)^7 - 72*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 216*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 216*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 120*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*A*b^3*tan(1/2*d*x + 1/2*c)^5 - 40*B*b^3*tan(1/2*d*x + 1/2*c)^5 - 9*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 216*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 216*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 40*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 9*C*b^3*tan(1/2*d*x + 1/2*c)^3 - 24*C*a^3*tan(1/2*d*x + 1/2*c) - 72*B*a^2*b*tan(1/2*d*x + 1/2*c) - 36*C*a^2*b*tan(1/2*d*x + 1/2*c) - 72*A*a*b^2*tan(1/2*d*x + 1/2*c) - 36*B*a*b^2*tan(1/2*d*x + 1/2*c) - 72*C*a*b^2*tan(1/2*d*x + 1/2*c) - 12*A*b^3*tan(1/2*d*x + 1/2*c) - 24*B*b^3*tan(1/2*d*x + 1/2*c) - 15*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
881,1,438,0,0.369778," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{12 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 6 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} {\left(d x + c\right)} + 3 \, {\left(2 \, C a^{3} + 6 \, B a^{2} b + 6 \, A a b^{2} + 3 \, C a b^{2} + B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, C a^{3} + 6 \, B a^{2} b + 6 \, A a b^{2} + 3 \, C a b^{2} + B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*A*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 6*(B*a^3 + 3*A*a^2*b)*(d*x + c) + 3*(2*C*a^3 + 6*B*a^2*b + 6*A*a*b^2 + 3*C*a*b^2 + B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*C*a^3 + 6*B*a^2*b + 6*A*a*b^2 + 3*C*a*b^2 + B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(18*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 9*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^3*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^3*tan(1/2*d*x + 1/2*c)^5 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 4*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^2*b*tan(1/2*d*x + 1/2*c) + 18*B*a*b^2*tan(1/2*d*x + 1/2*c) + 9*C*a*b^2*tan(1/2*d*x + 1/2*c) + 6*A*b^3*tan(1/2*d*x + 1/2*c) + 3*B*b^3*tan(1/2*d*x + 1/2*c) + 6*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
882,1,540,0,0.355986," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(A a^{3} + 2 \, C a^{3} + 6 \, B a^{2} b + 6 \, A a b^{2}\right)} {\left(d x + c\right)} + {\left(6 \, C a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3} + C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(6 \, C a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3} + C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((A*a^3 + 2*C*a^3 + 6*B*a^2*b + 6*A*a*b^2)*(d*x + c) + (6*C*a^2*b + 6*B*a*b^2 + 2*A*b^3 + C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (6*C*a^2*b + 6*B*a*b^2 + 2*A*b^3 + C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(A*a^3*tan(1/2*d*x + 1/2*c)^7 - 2*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 6*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 2*B*b^3*tan(1/2*d*x + 1/2*c)^7 - C*b^3*tan(1/2*d*x + 1/2*c)^7 - 3*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 2*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 6*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 2*B*b^3*tan(1/2*d*x + 1/2*c)^5 - 3*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 6*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 2*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*C*b^3*tan(1/2*d*x + 1/2*c)^3 - A*a^3*tan(1/2*d*x + 1/2*c) - 2*B*a^3*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b*tan(1/2*d*x + 1/2*c) - 6*C*a*b^2*tan(1/2*d*x + 1/2*c) - 2*B*b^3*tan(1/2*d*x + 1/2*c) - C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","B",0
883,1,418,0,0.344997," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{12 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, {\left(B a^{3} + 3 \, A a^{2} b + 6 \, C a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3}\right)} {\left(d x + c\right)} - 6 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 6 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(12*C*b^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*(B*a^3 + 3*A*a^2*b + 6*C*a^2*b + 6*B*a*b^2 + 2*A*b^3)*(d*x + c) - 6*(3*C*a*b^2 + B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 6*(3*C*a*b^2 + B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*tan(1/2*d*x + 1/2*c) + 3*B*a^3*tan(1/2*d*x + 1/2*c) + 6*C*a^3*tan(1/2*d*x + 1/2*c) + 9*A*a^2*b*tan(1/2*d*x + 1/2*c) + 18*B*a^2*b*tan(1/2*d*x + 1/2*c) + 18*A*a*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
884,1,723,0,0.350318," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{24 \, C b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 24 \, C b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(3 \, A a^{3} + 4 \, C a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 24 \, C a b^{2} + 8 \, B b^{3}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 120 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 216 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 216 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 216 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 216 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*C*b^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 24*C*b^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(3*A*a^3 + 4*C*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 24*C*a*b^2 + 8*B*b^3)*(d*x + c) - 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 72*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 72*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 9*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 40*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 120*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 216*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 216*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 72*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 120*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 216*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 216*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^3*tan(1/2*d*x + 1/2*c) - 24*B*a^3*tan(1/2*d*x + 1/2*c) - 12*C*a^3*tan(1/2*d*x + 1/2*c) - 72*A*a^2*b*tan(1/2*d*x + 1/2*c) - 36*B*a^2*b*tan(1/2*d*x + 1/2*c) - 72*C*a^2*b*tan(1/2*d*x + 1/2*c) - 36*A*a*b^2*tan(1/2*d*x + 1/2*c) - 72*B*a*b^2*tan(1/2*d*x + 1/2*c) - 24*A*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
885,1,926,0,0.321089," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, B a^{3} + 9 \, A a^{2} b + 12 \, C a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3} + 8 \, C b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 225 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 90 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1440 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2160 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 90 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 960 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1440 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 225 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*B*a^3 + 9*A*a^2*b + 12*C*a^2*b + 12*B*a*b^2 + 4*A*b^3 + 8*C*b^3)*(d*x + c) + 2*(120*A*a^3*tan(1/2*d*x + 1/2*c)^9 - 75*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 120*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 225*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*B*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 180*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 180*B*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*A*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*B*b^3*tan(1/2*d*x + 1/2*c)^9 + 160*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 30*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 320*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 90*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 960*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 360*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 360*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 1440*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 120*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 480*B*b^3*tan(1/2*d*x + 1/2*c)^7 + 464*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 400*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 1200*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 1200*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 2160*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 720*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 160*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 30*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 320*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 90*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 960*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 360*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 360*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 1440*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 480*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^3*tan(1/2*d*x + 1/2*c) + 75*B*a^3*tan(1/2*d*x + 1/2*c) + 120*C*a^3*tan(1/2*d*x + 1/2*c) + 225*A*a^2*b*tan(1/2*d*x + 1/2*c) + 360*B*a^2*b*tan(1/2*d*x + 1/2*c) + 180*C*a^2*b*tan(1/2*d*x + 1/2*c) + 360*A*a*b^2*tan(1/2*d*x + 1/2*c) + 180*B*a*b^2*tan(1/2*d*x + 1/2*c) + 360*C*a*b^2*tan(1/2*d*x + 1/2*c) + 60*A*b^3*tan(1/2*d*x + 1/2*c) + 120*B*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
886,1,1307,0,0.355800," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(5 \, A a^{3} + 6 \, C a^{3} + 18 \, B a^{2} b + 18 \, A a b^{2} + 24 \, C a b^{2} + 8 \, B b^{3}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 150 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 25 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 560 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 210 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1680 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 630 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2640 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 630 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2640 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1080 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 880 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1200 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 450 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1248 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3744 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 180 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4320 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 180 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4320 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1440 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2400 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 450 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1248 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3744 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 180 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4320 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 180 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4320 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1440 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2400 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 560 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1680 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 630 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2640 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 630 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2640 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1080 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 880 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1200 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 150 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 450 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 450 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(5*A*a^3 + 6*C*a^3 + 18*B*a^2*b + 18*A*a*b^2 + 24*C*a*b^2 + 8*B*b^3)*(d*x + c) - 2*(165*A*a^3*tan(1/2*d*x + 1/2*c)^11 - 240*B*a^3*tan(1/2*d*x + 1/2*c)^11 + 150*C*a^3*tan(1/2*d*x + 1/2*c)^11 - 720*A*a^2*b*tan(1/2*d*x + 1/2*c)^11 + 450*B*a^2*b*tan(1/2*d*x + 1/2*c)^11 - 720*C*a^2*b*tan(1/2*d*x + 1/2*c)^11 + 450*A*a*b^2*tan(1/2*d*x + 1/2*c)^11 - 720*B*a*b^2*tan(1/2*d*x + 1/2*c)^11 + 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^11 - 240*A*b^3*tan(1/2*d*x + 1/2*c)^11 + 120*B*b^3*tan(1/2*d*x + 1/2*c)^11 - 240*C*b^3*tan(1/2*d*x + 1/2*c)^11 - 25*A*a^3*tan(1/2*d*x + 1/2*c)^9 - 560*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 210*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 1680*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 630*B*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 2640*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 630*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 2640*B*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 1080*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 880*A*b^3*tan(1/2*d*x + 1/2*c)^9 + 360*B*b^3*tan(1/2*d*x + 1/2*c)^9 - 1200*C*b^3*tan(1/2*d*x + 1/2*c)^9 + 450*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 1248*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 3744*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 180*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 4320*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 180*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 4320*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 720*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 1440*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 240*B*b^3*tan(1/2*d*x + 1/2*c)^7 - 2400*C*b^3*tan(1/2*d*x + 1/2*c)^7 - 450*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 1248*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 60*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 3744*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 180*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 4320*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 180*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 4320*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 720*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 1440*A*b^3*tan(1/2*d*x + 1/2*c)^5 - 240*B*b^3*tan(1/2*d*x + 1/2*c)^5 - 2400*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 25*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 560*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 210*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 1680*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 630*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 2640*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 630*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 2640*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 1080*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 880*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 360*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 1200*C*b^3*tan(1/2*d*x + 1/2*c)^3 - 165*A*a^3*tan(1/2*d*x + 1/2*c) - 240*B*a^3*tan(1/2*d*x + 1/2*c) - 150*C*a^3*tan(1/2*d*x + 1/2*c) - 720*A*a^2*b*tan(1/2*d*x + 1/2*c) - 450*B*a^2*b*tan(1/2*d*x + 1/2*c) - 720*C*a^2*b*tan(1/2*d*x + 1/2*c) - 450*A*a*b^2*tan(1/2*d*x + 1/2*c) - 720*B*a*b^2*tan(1/2*d*x + 1/2*c) - 360*C*a*b^2*tan(1/2*d*x + 1/2*c) - 240*A*b^3*tan(1/2*d*x + 1/2*c) - 120*B*b^3*tan(1/2*d*x + 1/2*c) - 240*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","B",0
887,1,1888,0,0.462904," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 24 \, C a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 20 \, C a b^{3} + 5 \, B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 24 \, C a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 20 \, C a b^{3} + 5 \, B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(1680 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 840 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1680 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 3360 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 6720 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 4200 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 10080 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 6300 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 10080 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 4200 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 6720 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 4620 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1680 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1155 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1680 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 10080 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3360 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 7840 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 13440 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 31360 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 10080 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 47040 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 15120 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 33600 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 10080 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 22400 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3920 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 5600 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 980 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 3360 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 25200 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4200 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 16240 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 16800 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 64960 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 7560 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 97440 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 11340 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 75936 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 7560 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 50624 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 11900 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 12656 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2975 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 14448 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 33600 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 20160 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 80640 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120960 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 104832 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 69888 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17472 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 10176 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 25200 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4200 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16240 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16800 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 64960 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7560 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 97440 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 11340 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 75936 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7560 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 50624 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 11900 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12656 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2975 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 14448 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10080 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3360 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7840 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 13440 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 31360 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10080 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 47040 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15120 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 33600 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10080 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 22400 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3920 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5600 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 980 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3360 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1680 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 840 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3360 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6720 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4200 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10080 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6300 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10080 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4200 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6720 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4620 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1155 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{1680 \, d}"," ",0,"1/1680*(105*(8*B*a^4 + 32*A*a^3*b + 24*C*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 20*C*a*b^3 + 5*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(8*B*a^4 + 32*A*a^3*b + 24*C*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 20*C*a*b^3 + 5*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(1680*A*a^4*tan(1/2*d*x + 1/2*c)^13 - 840*B*a^4*tan(1/2*d*x + 1/2*c)^13 + 1680*C*a^4*tan(1/2*d*x + 1/2*c)^13 - 3360*A*a^3*b*tan(1/2*d*x + 1/2*c)^13 + 6720*B*a^3*b*tan(1/2*d*x + 1/2*c)^13 - 4200*C*a^3*b*tan(1/2*d*x + 1/2*c)^13 + 10080*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 - 6300*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 + 10080*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 - 4200*A*a*b^3*tan(1/2*d*x + 1/2*c)^13 + 6720*B*a*b^3*tan(1/2*d*x + 1/2*c)^13 - 4620*C*a*b^3*tan(1/2*d*x + 1/2*c)^13 + 1680*A*b^4*tan(1/2*d*x + 1/2*c)^13 - 1155*B*b^4*tan(1/2*d*x + 1/2*c)^13 + 1680*C*b^4*tan(1/2*d*x + 1/2*c)^13 - 10080*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 3360*B*a^4*tan(1/2*d*x + 1/2*c)^11 - 7840*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 13440*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 31360*B*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 10080*C*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 47040*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 15120*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 33600*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 10080*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 22400*B*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 3920*C*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 5600*A*b^4*tan(1/2*d*x + 1/2*c)^11 + 980*B*b^4*tan(1/2*d*x + 1/2*c)^11 - 3360*C*b^4*tan(1/2*d*x + 1/2*c)^11 + 25200*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 4200*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 16240*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 16800*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 64960*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 7560*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 97440*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 11340*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 75936*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 7560*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 50624*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 11900*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 12656*A*b^4*tan(1/2*d*x + 1/2*c)^9 - 2975*B*b^4*tan(1/2*d*x + 1/2*c)^9 + 14448*C*b^4*tan(1/2*d*x + 1/2*c)^9 - 33600*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 20160*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 80640*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 120960*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 104832*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 69888*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 17472*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 10176*C*b^4*tan(1/2*d*x + 1/2*c)^7 + 25200*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 4200*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 16240*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 16800*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 64960*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 7560*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 97440*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 11340*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 75936*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 7560*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 50624*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 11900*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 12656*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 2975*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 14448*C*b^4*tan(1/2*d*x + 1/2*c)^5 - 10080*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 3360*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 7840*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 13440*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 31360*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 10080*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 47040*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 15120*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 33600*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 10080*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 22400*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 3920*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 5600*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 980*B*b^4*tan(1/2*d*x + 1/2*c)^3 - 3360*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 1680*A*a^4*tan(1/2*d*x + 1/2*c) + 840*B*a^4*tan(1/2*d*x + 1/2*c) + 1680*C*a^4*tan(1/2*d*x + 1/2*c) + 3360*A*a^3*b*tan(1/2*d*x + 1/2*c) + 6720*B*a^3*b*tan(1/2*d*x + 1/2*c) + 4200*C*a^3*b*tan(1/2*d*x + 1/2*c) + 10080*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 6300*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 10080*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 4200*A*a*b^3*tan(1/2*d*x + 1/2*c) + 6720*B*a*b^3*tan(1/2*d*x + 1/2*c) + 4620*C*a*b^3*tan(1/2*d*x + 1/2*c) + 1680*A*b^4*tan(1/2*d*x + 1/2*c) + 1155*B*b^4*tan(1/2*d*x + 1/2*c) + 1680*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","B",0
888,1,1658,0,0.468434," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(16 \, A a^{4} + 8 \, C a^{4} + 32 \, B a^{3} b + 48 \, A a^{2} b^{2} + 36 \, C a^{2} b^{2} + 24 \, B a b^{3} + 6 \, A b^{4} + 5 \, C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(16 \, A a^{4} + 8 \, C a^{4} + 32 \, B a^{3} b + 48 \, A a^{2} b^{2} + 36 \, C a^{2} b^{2} + 24 \, B a b^{3} + 6 \, A b^{4} + 5 \, C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(240 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 960 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1440 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 900 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 600 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 960 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 150 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 240 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 165 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1200 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4800 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1440 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2160 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 5280 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1260 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 840 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2240 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 210 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 560 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 25 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2400 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 240 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9600 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5760 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1440 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 8640 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 360 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 240 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4992 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1248 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 450 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2400 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9600 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 960 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5760 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1440 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8640 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 360 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4992 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1248 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 450 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 360 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4800 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1440 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2160 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5280 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1260 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 840 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2240 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 210 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 560 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1440 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 900 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 600 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 150 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 165 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(16*A*a^4 + 8*C*a^4 + 32*B*a^3*b + 48*A*a^2*b^2 + 36*C*a^2*b^2 + 24*B*a*b^3 + 6*A*b^4 + 5*C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(16*A*a^4 + 8*C*a^4 + 32*B*a^3*b + 48*A*a^2*b^2 + 36*C*a^2*b^2 + 24*B*a*b^3 + 6*A*b^4 + 5*C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(240*B*a^4*tan(1/2*d*x + 1/2*c)^11 - 120*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 960*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 480*B*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 960*C*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 1440*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 900*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 960*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 600*B*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 960*C*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 150*A*b^4*tan(1/2*d*x + 1/2*c)^11 + 240*B*b^4*tan(1/2*d*x + 1/2*c)^11 - 165*C*b^4*tan(1/2*d*x + 1/2*c)^11 - 1200*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 360*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 4800*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 1440*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 3520*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 2160*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 5280*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 1260*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 840*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 2240*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 210*A*b^4*tan(1/2*d*x + 1/2*c)^9 - 560*B*b^4*tan(1/2*d*x + 1/2*c)^9 - 25*C*b^4*tan(1/2*d*x + 1/2*c)^9 + 2400*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 240*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 9600*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 960*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 5760*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 1440*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 8640*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 360*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 240*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 4992*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 60*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 1248*B*b^4*tan(1/2*d*x + 1/2*c)^7 - 450*C*b^4*tan(1/2*d*x + 1/2*c)^7 - 2400*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 240*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 9600*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 960*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 5760*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 1440*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 8640*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 360*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 240*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 4992*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 60*A*b^4*tan(1/2*d*x + 1/2*c)^5 - 1248*B*b^4*tan(1/2*d*x + 1/2*c)^5 - 450*C*b^4*tan(1/2*d*x + 1/2*c)^5 + 1200*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 360*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 4800*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 1440*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 3520*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 2160*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 5280*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 1260*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 840*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 2240*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 210*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 560*B*b^4*tan(1/2*d*x + 1/2*c)^3 - 25*C*b^4*tan(1/2*d*x + 1/2*c)^3 - 240*B*a^4*tan(1/2*d*x + 1/2*c) - 120*C*a^4*tan(1/2*d*x + 1/2*c) - 960*A*a^3*b*tan(1/2*d*x + 1/2*c) - 480*B*a^3*b*tan(1/2*d*x + 1/2*c) - 960*C*a^3*b*tan(1/2*d*x + 1/2*c) - 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c) - 1440*B*a^2*b^2*tan(1/2*d*x + 1/2*c) - 900*C*a^2*b^2*tan(1/2*d*x + 1/2*c) - 960*A*a*b^3*tan(1/2*d*x + 1/2*c) - 600*B*a*b^3*tan(1/2*d*x + 1/2*c) - 960*C*a*b^3*tan(1/2*d*x + 1/2*c) - 150*A*b^4*tan(1/2*d*x + 1/2*c) - 240*B*b^4*tan(1/2*d*x + 1/2*c) - 165*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
889,1,1140,0,0.404987," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{120 \, {\left(d x + c\right)} A a^{4} + 15 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 16 \, C a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 12 \, C a b^{3} + 3 \, B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 16 \, C a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 12 \, C a b^{3} + 3 \, B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 300 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 480 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1920 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2880 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1920 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1280 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 320 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 160 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2880 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4320 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1600 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 464 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 480 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1920 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2880 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1920 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1280 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 300 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(120*(d*x + c)*A*a^4 + 15*(8*B*a^4 + 32*A*a^3*b + 16*C*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 12*C*a*b^3 + 3*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(8*B*a^4 + 32*A*a^3*b + 16*C*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 12*C*a*b^3 + 3*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 480*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 240*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 240*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 480*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 300*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^9 - 75*B*b^4*tan(1/2*d*x + 1/2*c)^9 + 120*C*b^4*tan(1/2*d*x + 1/2*c)^9 - 480*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 1920*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 480*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 2880*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 1920*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 480*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 1280*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 120*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 320*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 30*B*b^4*tan(1/2*d*x + 1/2*c)^7 - 160*C*b^4*tan(1/2*d*x + 1/2*c)^7 + 720*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 2880*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 4320*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 2400*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 1600*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 400*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 464*C*b^4*tan(1/2*d*x + 1/2*c)^5 - 480*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 1920*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 480*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 2880*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 1920*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 480*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 1280*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 120*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 320*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 30*B*b^4*tan(1/2*d*x + 1/2*c)^3 - 160*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 120*C*a^4*tan(1/2*d*x + 1/2*c) + 480*B*a^3*b*tan(1/2*d*x + 1/2*c) + 240*C*a^3*b*tan(1/2*d*x + 1/2*c) + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 240*A*a*b^3*tan(1/2*d*x + 1/2*c) + 480*B*a*b^3*tan(1/2*d*x + 1/2*c) + 300*C*a*b^3*tan(1/2*d*x + 1/2*c) + 120*A*b^4*tan(1/2*d*x + 1/2*c) + 75*B*b^4*tan(1/2*d*x + 1/2*c) + 120*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
890,1,840,0,0.417605," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{48 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 24 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} {\left(d x + c\right)} + 3 \, {\left(8 \, C a^{4} + 32 \, B a^{3} b + 48 \, A a^{2} b^{2} + 24 \, C a^{2} b^{2} + 16 \, B a b^{3} + 4 \, A b^{4} + 3 \, C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, C a^{4} + 32 \, B a^{3} b + 48 \, A a^{2} b^{2} + 24 \, C a^{2} b^{2} + 16 \, B a b^{3} + 4 \, A b^{4} + 3 \, C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 144 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 432 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 432 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 144 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(48*A*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 24*(B*a^4 + 4*A*a^3*b)*(d*x + c) + 3*(8*C*a^4 + 32*B*a^3*b + 48*A*a^2*b^2 + 24*C*a^2*b^2 + 16*B*a*b^3 + 4*A*b^4 + 3*C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*C*a^4 + 32*B*a^3*b + 48*A*a^2*b^2 + 24*C*a^2*b^2 + 16*B*a*b^3 + 4*A*b^4 + 3*C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(96*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 144*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 96*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 48*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 96*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 12*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 24*B*b^4*tan(1/2*d*x + 1/2*c)^7 - 15*C*b^4*tan(1/2*d*x + 1/2*c)^7 - 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 432*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 48*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 160*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*b^4*tan(1/2*d*x + 1/2*c)^5 - 40*B*b^4*tan(1/2*d*x + 1/2*c)^5 - 9*C*b^4*tan(1/2*d*x + 1/2*c)^5 + 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 432*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 48*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 160*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 40*B*b^4*tan(1/2*d*x + 1/2*c)^3 - 9*C*b^4*tan(1/2*d*x + 1/2*c)^3 - 96*C*a^3*b*tan(1/2*d*x + 1/2*c) - 144*B*a^2*b^2*tan(1/2*d*x + 1/2*c) - 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c) - 96*A*a*b^3*tan(1/2*d*x + 1/2*c) - 48*B*a*b^3*tan(1/2*d*x + 1/2*c) - 96*C*a*b^3*tan(1/2*d*x + 1/2*c) - 12*A*b^4*tan(1/2*d*x + 1/2*c) - 24*B*b^4*tan(1/2*d*x + 1/2*c) - 15*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
891,1,550,0,0.399837," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(A a^{4} + 2 \, C a^{4} + 8 \, B a^{3} b + 12 \, A a^{2} b^{2}\right)} {\left(d x + c\right)} + 3 \, {\left(8 \, C a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3} + 4 \, C a b^{3} + B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, C a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3} + 4 \, C a b^{3} + B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{6 \, {\left(A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{2 \, {\left(36 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(A*a^4 + 2*C*a^4 + 8*B*a^3*b + 12*A*a^2*b^2)*(d*x + c) + 3*(8*C*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3 + 4*C*a*b^3 + B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*C*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3 + 4*C*a*b^3 + B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 6*(A*a^4*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 8*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - A*a^4*tan(1/2*d*x + 1/2*c) - 2*B*a^4*tan(1/2*d*x + 1/2*c) - 8*A*a^3*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - 2*(36*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 24*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 12*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^4*tan(1/2*d*x + 1/2*c)^5 - 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 48*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 4*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 24*B*a*b^3*tan(1/2*d*x + 1/2*c) + 12*C*a*b^3*tan(1/2*d*x + 1/2*c) + 6*A*b^4*tan(1/2*d*x + 1/2*c) + 3*B*b^4*tan(1/2*d*x + 1/2*c) + 6*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
892,1,543,0,0.395409," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(B a^{4} + 4 \, A a^{3} b + 8 \, C a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3}\right)} {\left(d x + c\right)} + 3 \, {\left(12 \, C a^{2} b^{2} + 8 \, B a b^{3} + 2 \, A b^{4} + C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(12 \, C a^{2} b^{2} + 8 \, B a b^{3} + 2 \, A b^{4} + C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{6 \, {\left(8 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{2 \, {\left(6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a^4 + 4*A*a^3*b + 8*C*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3)*(d*x + c) + 3*(12*C*a^2*b^2 + 8*B*a*b^3 + 2*A*b^4 + C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(12*C*a^2*b^2 + 8*B*a*b^3 + 2*A*b^4 + C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 6*(8*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^4*tan(1/2*d*x + 1/2*c)^3 - C*b^4*tan(1/2*d*x + 1/2*c)^3 - 8*C*a*b^3*tan(1/2*d*x + 1/2*c) - 2*B*b^4*tan(1/2*d*x + 1/2*c) - C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + 2*(6*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 12*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 24*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 36*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^4*tan(1/2*d*x + 1/2*c) + 3*B*a^4*tan(1/2*d*x + 1/2*c) + 6*C*a^4*tan(1/2*d*x + 1/2*c) + 12*A*a^3*b*tan(1/2*d*x + 1/2*c) + 24*B*a^3*b*tan(1/2*d*x + 1/2*c) + 36*A*a^2*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
893,1,802,0,0.387777," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{48 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, {\left(3 \, A a^{4} + 4 \, C a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 48 \, C a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} {\left(d x + c\right)} - 24 \, {\left(4 \, C a b^{3} + B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 24 \, {\left(4 \, C a b^{3} + B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 144 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 432 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 432 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 144 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"-1/24*(48*C*b^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*(3*A*a^4 + 4*C*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 48*C*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*(d*x + c) - 24*(4*C*a*b^3 + B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 24*(4*C*a*b^3 + B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 96*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 96*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 144*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 96*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 9*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 40*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 160*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 432*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 160*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 432*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^4*tan(1/2*d*x + 1/2*c) - 24*B*a^4*tan(1/2*d*x + 1/2*c) - 12*C*a^4*tan(1/2*d*x + 1/2*c) - 96*A*a^3*b*tan(1/2*d*x + 1/2*c) - 48*B*a^3*b*tan(1/2*d*x + 1/2*c) - 96*C*a^3*b*tan(1/2*d*x + 1/2*c) - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c) - 144*B*a^2*b^2*tan(1/2*d*x + 1/2*c) - 96*A*a*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
894,1,1094,0,0.377224," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{120 \, C b^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 120 \, C b^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 15 \, {\left(3 \, B a^{4} + 12 \, A a^{3} b + 16 \, C a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 32 \, C a b^{3} + 8 \, B b^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 300 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1280 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1920 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2880 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1920 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1600 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4320 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2880 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1280 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1920 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2880 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1920 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 300 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(120*C*b^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 120*C*b^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 15*(3*B*a^4 + 12*A*a^3*b + 16*C*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 32*C*a*b^3 + 8*B*b^4)*(d*x + c) + 2*(120*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 75*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 120*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 300*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 480*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 240*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 240*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 480*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 160*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 30*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 320*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 120*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 1280*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 480*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 1920*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 2880*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 480*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 1920*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 480*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 464*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 400*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 1600*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 2400*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 4320*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 2880*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 720*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 160*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 30*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 320*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 1280*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 480*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 1920*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 2880*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 480*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 1920*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 480*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^4*tan(1/2*d*x + 1/2*c) + 75*B*a^4*tan(1/2*d*x + 1/2*c) + 120*C*a^4*tan(1/2*d*x + 1/2*c) + 300*A*a^3*b*tan(1/2*d*x + 1/2*c) + 480*B*a^3*b*tan(1/2*d*x + 1/2*c) + 240*C*a^3*b*tan(1/2*d*x + 1/2*c) + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 240*A*a*b^3*tan(1/2*d*x + 1/2*c) + 480*B*a*b^3*tan(1/2*d*x + 1/2*c) + 120*A*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
895,1,1578,0,0.372476," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(5 \, A a^{4} + 6 \, C a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 48 \, C a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4} + 16 \, C b^{4}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 150 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 600 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 900 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1440 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 25 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 560 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 210 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2240 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 840 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1260 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 5280 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2160 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1440 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4800 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1200 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 450 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1248 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4992 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8640 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1440 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9600 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2400 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 450 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1248 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4992 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5760 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8640 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1440 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9600 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2400 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 560 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 840 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1260 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5280 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2160 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1440 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4800 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1200 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 150 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 600 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 900 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1440 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(5*A*a^4 + 6*C*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 48*C*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4 + 16*C*b^4)*(d*x + c) - 2*(165*A*a^4*tan(1/2*d*x + 1/2*c)^11 - 240*B*a^4*tan(1/2*d*x + 1/2*c)^11 + 150*C*a^4*tan(1/2*d*x + 1/2*c)^11 - 960*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 600*B*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 960*C*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 900*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 1440*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 960*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 480*B*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 960*C*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^11 - 240*B*b^4*tan(1/2*d*x + 1/2*c)^11 - 25*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 560*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 210*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 2240*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 840*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 3520*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 1260*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 5280*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 2160*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 1440*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 4800*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 360*A*b^4*tan(1/2*d*x + 1/2*c)^9 - 1200*B*b^4*tan(1/2*d*x + 1/2*c)^9 + 450*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 1248*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 60*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 4992*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 240*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 5760*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 8640*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 1440*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 960*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 9600*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 240*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 2400*B*b^4*tan(1/2*d*x + 1/2*c)^7 - 450*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 1248*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 60*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 4992*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 240*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 5760*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 8640*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 1440*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 960*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 9600*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 240*A*b^4*tan(1/2*d*x + 1/2*c)^5 - 2400*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 25*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 560*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 210*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 2240*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 840*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 3520*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 1260*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 5280*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 2160*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 1440*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 4800*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 360*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 1200*B*b^4*tan(1/2*d*x + 1/2*c)^3 - 165*A*a^4*tan(1/2*d*x + 1/2*c) - 240*B*a^4*tan(1/2*d*x + 1/2*c) - 150*C*a^4*tan(1/2*d*x + 1/2*c) - 960*A*a^3*b*tan(1/2*d*x + 1/2*c) - 600*B*a^3*b*tan(1/2*d*x + 1/2*c) - 960*C*a^3*b*tan(1/2*d*x + 1/2*c) - 900*A*a^2*b^2*tan(1/2*d*x + 1/2*c) - 1440*B*a^2*b^2*tan(1/2*d*x + 1/2*c) - 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c) - 960*A*a*b^3*tan(1/2*d*x + 1/2*c) - 480*B*a*b^3*tan(1/2*d*x + 1/2*c) - 960*C*a*b^3*tan(1/2*d*x + 1/2*c) - 120*A*b^4*tan(1/2*d*x + 1/2*c) - 240*B*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","B",0
896,1,1815,0,0.415940," ","integrate(cos(d*x+c)^7*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\frac{105 \, {\left(5 \, B a^{4} + 20 \, A a^{3} b + 24 \, C a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 32 \, C a b^{3} + 8 \, B b^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(1680 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1155 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1680 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 4620 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 6720 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 4200 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 10080 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 6300 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 10080 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 4200 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 6720 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 3360 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1680 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 840 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1680 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 3360 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 980 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 5600 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 3920 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 22400 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 10080 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 33600 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 15120 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 47040 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 10080 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 31360 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 13440 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 7840 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 3360 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 10080 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 14448 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2975 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 12656 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 11900 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 50624 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 7560 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 75936 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 11340 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 97440 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 7560 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 64960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 16800 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 16240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4200 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 25200 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 10176 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 17472 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 69888 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 104832 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120960 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 80640 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 20160 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33600 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 14448 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2975 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12656 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 11900 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 50624 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7560 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 75936 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 11340 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 97440 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7560 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 64960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16800 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4200 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25200 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3360 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 980 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5600 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3920 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 22400 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10080 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33600 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15120 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 47040 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10080 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 31360 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 13440 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7840 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3360 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10080 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1680 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1155 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4620 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6720 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4200 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10080 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6300 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10080 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4200 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6720 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3360 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 840 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7}}}{1680 \, d}"," ",0,"1/1680*(105*(5*B*a^4 + 20*A*a^3*b + 24*C*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 32*C*a*b^3 + 8*B*b^4)*(d*x + c) + 2*(1680*A*a^4*tan(1/2*d*x + 1/2*c)^13 - 1155*B*a^4*tan(1/2*d*x + 1/2*c)^13 + 1680*C*a^4*tan(1/2*d*x + 1/2*c)^13 - 4620*A*a^3*b*tan(1/2*d*x + 1/2*c)^13 + 6720*B*a^3*b*tan(1/2*d*x + 1/2*c)^13 - 4200*C*a^3*b*tan(1/2*d*x + 1/2*c)^13 + 10080*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 - 6300*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 + 10080*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 - 4200*A*a*b^3*tan(1/2*d*x + 1/2*c)^13 + 6720*B*a*b^3*tan(1/2*d*x + 1/2*c)^13 - 3360*C*a*b^3*tan(1/2*d*x + 1/2*c)^13 + 1680*A*b^4*tan(1/2*d*x + 1/2*c)^13 - 840*B*b^4*tan(1/2*d*x + 1/2*c)^13 + 1680*C*b^4*tan(1/2*d*x + 1/2*c)^13 + 3360*A*a^4*tan(1/2*d*x + 1/2*c)^11 - 980*B*a^4*tan(1/2*d*x + 1/2*c)^11 + 5600*C*a^4*tan(1/2*d*x + 1/2*c)^11 - 3920*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 22400*B*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 10080*C*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 33600*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 15120*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 47040*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 10080*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 31360*B*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 13440*C*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 7840*A*b^4*tan(1/2*d*x + 1/2*c)^11 - 3360*B*b^4*tan(1/2*d*x + 1/2*c)^11 + 10080*C*b^4*tan(1/2*d*x + 1/2*c)^11 + 14448*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 2975*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 12656*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 11900*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 50624*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 7560*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 75936*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 11340*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 97440*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 7560*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 64960*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 16800*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 16240*A*b^4*tan(1/2*d*x + 1/2*c)^9 - 4200*B*b^4*tan(1/2*d*x + 1/2*c)^9 + 25200*C*b^4*tan(1/2*d*x + 1/2*c)^9 + 10176*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 17472*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 69888*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 104832*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 120960*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 80640*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 20160*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 33600*C*b^4*tan(1/2*d*x + 1/2*c)^7 + 14448*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 2975*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 12656*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 11900*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 50624*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 7560*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 75936*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 11340*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 97440*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 7560*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 64960*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 16800*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 16240*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 4200*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 25200*C*b^4*tan(1/2*d*x + 1/2*c)^5 + 3360*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 980*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 5600*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 3920*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 22400*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 10080*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 33600*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 15120*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 47040*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 10080*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 31360*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 13440*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 7840*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 3360*B*b^4*tan(1/2*d*x + 1/2*c)^3 + 10080*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 1680*A*a^4*tan(1/2*d*x + 1/2*c) + 1155*B*a^4*tan(1/2*d*x + 1/2*c) + 1680*C*a^4*tan(1/2*d*x + 1/2*c) + 4620*A*a^3*b*tan(1/2*d*x + 1/2*c) + 6720*B*a^3*b*tan(1/2*d*x + 1/2*c) + 4200*C*a^3*b*tan(1/2*d*x + 1/2*c) + 10080*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 6300*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 10080*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 4200*A*a*b^3*tan(1/2*d*x + 1/2*c) + 6720*B*a*b^3*tan(1/2*d*x + 1/2*c) + 3360*C*a*b^3*tan(1/2*d*x + 1/2*c) + 1680*A*b^4*tan(1/2*d*x + 1/2*c) + 840*B*b^4*tan(1/2*d*x + 1/2*c) + 1680*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^7)/d","B",0
897,1,658,0,0.391801," ","integrate((a+b*sec(d*x+c))^3*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{24 \, {\left(C a^{5} - B a^{4} b\right)} {\left(d x + c\right)} + 3 \, {\left(24 \, C a^{4} b - 32 \, B a^{3} b^{2} - 8 \, C a^{2} b^{3} - 16 \, B a b^{4} - 3 \, C b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(24 \, C a^{4} b - 32 \, B a^{3} b^{2} - 8 \, C a^{2} b^{3} - 16 \, B a b^{4} - 3 \, C b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(48 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 144 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 144 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 432 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 144 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 432 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 144 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"-1/24*(24*(C*a^5 - B*a^4*b)*(d*x + c) + 3*(24*C*a^4*b - 32*B*a^3*b^2 - 8*C*a^2*b^3 - 16*B*a*b^4 - 3*C*b^5)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(24*C*a^4*b - 32*B*a^3*b^2 - 8*C*a^2*b^3 - 16*B*a*b^4 - 3*C*b^5)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(48*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^7 - 144*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 24*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 48*B*a*b^4*tan(1/2*d*x + 1/2*c)^7 - 72*C*a*b^4*tan(1/2*d*x + 1/2*c)^7 - 24*B*b^5*tan(1/2*d*x + 1/2*c)^7 + 15*C*b^5*tan(1/2*d*x + 1/2*c)^7 - 144*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 432*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 24*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 48*B*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 120*C*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 40*B*b^5*tan(1/2*d*x + 1/2*c)^5 + 9*C*b^5*tan(1/2*d*x + 1/2*c)^5 + 144*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 432*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 24*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 48*B*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 120*C*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 40*B*b^5*tan(1/2*d*x + 1/2*c)^3 + 9*C*b^5*tan(1/2*d*x + 1/2*c)^3 - 48*C*a^3*b^2*tan(1/2*d*x + 1/2*c) + 144*B*a^2*b^3*tan(1/2*d*x + 1/2*c) + 24*C*a^2*b^3*tan(1/2*d*x + 1/2*c) + 48*B*a*b^4*tan(1/2*d*x + 1/2*c) + 72*C*a*b^4*tan(1/2*d*x + 1/2*c) + 24*B*b^5*tan(1/2*d*x + 1/2*c) + 15*C*b^5*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
898,1,301,0,0.295839," ","integrate((a+b*sec(d*x+c))^2*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{6 \, {\left(C a^{4} - B a^{3} b\right)} {\left(d x + c\right)} + 3 \, {\left(4 \, C a^{3} b - 6 \, B a^{2} b^{2} - 2 \, C a b^{3} - B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, C a^{3} b - 6 \, B a^{2} b^{2} - 2 \, C a b^{3} - B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(18 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(6*(C*a^4 - B*a^3*b)*(d*x + c) + 3*(4*C*a^3*b - 6*B*a^2*b^2 - 2*C*a*b^3 - B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*C*a^3*b - 6*B*a^2*b^2 - 2*C*a*b^3 - B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(18*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^4*tan(1/2*d*x + 1/2*c)^5 - 36*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 4*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 18*B*a*b^3*tan(1/2*d*x + 1/2*c) + 6*C*a*b^3*tan(1/2*d*x + 1/2*c) + 3*B*b^4*tan(1/2*d*x + 1/2*c) + 6*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
899,1,213,0,0.314644," ","integrate((a+b*sec(d*x+c))*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""giac"")","-\frac{2 \, {\left(C a^{3} - B a^{2} b\right)} {\left(d x + c\right)} + {\left(2 \, C a^{2} b - 4 \, B a b^{2} - C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, C a^{2} b - 4 \, B a b^{2} - C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(2 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(2*(C*a^3 - B*a^2*b)*(d*x + c) + (2*C*a^2*b - 4*B*a*b^2 - C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*C*a^2*b - 4*B*a*b^2 - C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(2*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^3*tan(1/2*d*x + 1/2*c)^3 - C*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*C*a*b^2*tan(1/2*d*x + 1/2*c) - 2*B*b^3*tan(1/2*d*x + 1/2*c) - C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
900,1,483,0,0.339890," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, C a^{3} - 2 \, B a^{2} b + 2 \, A a b^{2} + C a b^{2} - B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} - \frac{3 \, {\left(2 \, C a^{3} - 2 \, B a^{2} b + 2 \, A a b^{2} + C a b^{2} - B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{12 \, {\left(C a^{4} - B a^{3} b + A a^{2} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} b^{4}} + \frac{2 \, {\left(6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"-1/6*(3*(2*C*a^3 - 2*B*a^2*b + 2*A*a*b^2 + C*a*b^2 - B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - 3*(2*C*a^3 - 2*B*a^2*b + 2*A*a*b^2 + C*a*b^2 - B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - 12*(C*a^4 - B*a^3*b + A*a^2*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*b^4) + 2*(6*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 3*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^2*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*tan(1/2*d*x + 1/2*c) - 6*B*a*b*tan(1/2*d*x + 1/2*c) - 3*C*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c) + 3*B*b^2*tan(1/2*d*x + 1/2*c) + 6*C*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*b^3))/d","B",0
901,1,287,0,0.311657," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, C a^{2} - 2 \, B a b + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} - \frac{{\left(2 \, C a^{2} - 2 \, B a b + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}} - \frac{4 \, {\left(C a^{3} - B a^{2} b + A a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} b^{3}} + \frac{2 \, {\left(2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} b^{2}}}{2 \, d}"," ",0,"1/2*((2*C*a^2 - 2*B*a*b + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 - (2*C*a^2 - 2*B*a*b + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3 - 4*(C*a^3 - B*a^2*b + A*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*b^3) + 2*(2*C*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*b*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 - 2*C*a*tan(1/2*d*x + 1/2*c) + 2*B*b*tan(1/2*d*x + 1/2*c) + C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*b^2))/d","B",0
902,1,180,0,0.304847," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{2}} - \frac{{\left(C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{2}} + \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b} + \frac{2 \, {\left(C a^{2} - B a b + A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} b^{2}}}{d}"," ",0,"-((C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^2 - (C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^2 + 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b) + 2*(C*a^2 - B*a*b + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*b^2))/d","A",0
903,1,149,0,0.287481," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} A}{a} + \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b} - \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b} - \frac{2 \, {\left(C a^{2} - B a b + A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a b}}{d}"," ",0,"((d*x + c)*A/a + C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b - C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b - 2*(C*a^2 - B*a*b + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a*b))/d","A",0
904,1,146,0,0.276745," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(B a - A b\right)} {\left(d x + c\right)}}{a^{2}} + \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a} + \frac{2 \, {\left(C a^{2} - B a b + A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{2}}}{d}"," ",0,"((B*a - A*b)*(d*x + c)/a^2 + 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a) + 2*(C*a^2 - B*a*b + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^2))/d","A",0
905,1,239,0,0.273467," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(A a^{2} + 2 \, C a^{2} - 2 \, B a b + 2 \, A b^{2}\right)} {\left(d x + c\right)}}{a^{3}} - \frac{4 \, {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{3}} - \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"1/2*((A*a^2 + 2*C*a^2 - 2*B*a*b + 2*A*b^2)*(d*x + c)/a^3 - 4*(C*a^2*b - B*a*b^2 + A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^3) - 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c)^3 + 2*A*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) - 2*B*a*tan(1/2*d*x + 1/2*c) + 2*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2))/d","A",0
906,1,424,0,0.256017," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(B a^{3} - A a^{2} b - 2 \, C a^{2} b + 2 \, B a b^{2} - 2 \, A b^{3}\right)} {\left(d x + c\right)}}{a^{4}} + \frac{12 \, {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{4}} + \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a^3 - A*a^2*b - 2*C*a^2*b + 2*B*a*b^2 - 2*A*b^3)*(d*x + c)/a^4 + 12*(C*a^2*b^2 - B*a*b^3 + A*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^4) + 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a*b*tan(1/2*d*x + 1/2*c)^5 - 6*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2*tan(1/2*d*x + 1/2*c) + 6*C*a^2*tan(1/2*d*x + 1/2*c) - 3*A*a*b*tan(1/2*d*x + 1/2*c) - 6*B*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3))/d","B",0
907,1,801,0,0.301124," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(3 \, A a^{4} + 4 \, C a^{4} - 4 \, B a^{3} b + 4 \, A a^{2} b^{2} + 8 \, C a^{2} b^{2} - 8 \, B a b^{3} + 8 \, A b^{4}\right)} {\left(d x + c\right)}}{a^{5}} - \frac{48 \, {\left(C a^{2} b^{3} - B a b^{4} + A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{5}} - \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a^4 + 4*C*a^4 - 4*B*a^3*b + 4*A*a^2*b^2 + 8*C*a^2*b^2 - 8*B*a*b^3 + 8*A*b^4)*(d*x + c)/a^5 - 48*(C*a^2*b^3 - B*a*b^4 + A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^5) - 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 24*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 12*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 24*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 24*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 9*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 40*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 72*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 40*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 12*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 72*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^3*tan(1/2*d*x + 1/2*c) - 24*B*a^3*tan(1/2*d*x + 1/2*c) - 12*C*a^3*tan(1/2*d*x + 1/2*c) + 24*A*a^2*b*tan(1/2*d*x + 1/2*c) + 12*B*a^2*b*tan(1/2*d*x + 1/2*c) + 24*C*a^2*b*tan(1/2*d*x + 1/2*c) - 12*A*a*b^2*tan(1/2*d*x + 1/2*c) - 24*B*a*b^2*tan(1/2*d*x + 1/2*c) + 24*A*b^3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^4))/d","B",0
908,1,627,0,0.335119," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(4 \, C a^{6} - 3 \, B a^{5} b + 2 \, A a^{4} b^{2} - 5 \, C a^{4} b^{2} + 4 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{2} b^{5} - b^{7}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{12 \, {\left(C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} - \frac{3 \, {\left(8 \, C a^{3} - 6 \, B a^{2} b + 4 \, A a b^{2} + 2 \, C a b^{2} - B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{5}} + \frac{3 \, {\left(8 \, C a^{3} - 6 \, B a^{2} b + 4 \, A a b^{2} + 2 \, C a b^{2} - B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{5}} - \frac{2 \, {\left(18 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} b^{4}}}{6 \, d}"," ",0,"1/6*(12*(4*C*a^6 - 3*B*a^5*b + 2*A*a^4*b^2 - 5*C*a^4*b^2 + 4*B*a^3*b^3 - 3*A*a^2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^2*b^5 - b^7)*sqrt(-a^2 + b^2)) - 12*(C*a^5*tan(1/2*d*x + 1/2*c) - B*a^4*b*tan(1/2*d*x + 1/2*c) + A*a^3*b^2*tan(1/2*d*x + 1/2*c))/((a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) - 3*(8*C*a^3 - 6*B*a^2*b + 4*A*a*b^2 + 2*C*a*b^2 - B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^5 + 3*(8*C*a^3 - 6*B*a^2*b + 4*A*a*b^2 + 2*C*a*b^2 - B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^5 - 2*(18*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 12*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^2*tan(1/2*d*x + 1/2*c)^5 - 36*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^2*tan(1/2*d*x + 1/2*c) - 12*B*a*b*tan(1/2*d*x + 1/2*c) - 6*C*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c) + 3*B*b^2*tan(1/2*d*x + 1/2*c) + 6*C*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*b^4))/d","A",0
909,1,428,0,0.350436," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(3 \, C a^{5} - 2 \, B a^{4} b + A a^{3} b^{2} - 4 \, C a^{3} b^{2} + 3 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{4 \, {\left(C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} - \frac{{\left(6 \, C a^{2} - 4 \, B a b + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} + \frac{{\left(6 \, C a^{2} - 4 \, B a b + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{2 \, {\left(4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} b^{3}}}{2 \, d}"," ",0,"-1/2*(4*(3*C*a^5 - 2*B*a^4*b + A*a^3*b^2 - 4*C*a^3*b^2 + 3*B*a^2*b^3 - 2*A*a*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) - 4*(C*a^4*tan(1/2*d*x + 1/2*c) - B*a^3*b*tan(1/2*d*x + 1/2*c) + A*a^2*b^2*tan(1/2*d*x + 1/2*c))/((a^2*b^3 - b^5)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) - (6*C*a^2 - 4*B*a*b + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 + (6*C*a^2 - 4*B*a*b + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - 2*(4*C*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*b*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*tan(1/2*d*x + 1/2*c) + 2*B*b*tan(1/2*d*x + 1/2*c) + C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*b^3))/d","A",0
910,1,443,0,0.309656," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(2 \, C a^{4} - B a^{3} b - 3 \, C a^{2} b^{2} + 2 \, B a b^{3} - A b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, {\left(2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} {\left(a^{2} b^{2} - b^{4}\right)}} - \frac{{\left(2 \, C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} + \frac{{\left(2 \, C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}}}{d}"," ",0,"(2*(2*C*a^4 - B*a^3*b - 3*C*a^2*b^2 + 2*B*a*b^3 - A*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^2*b^3 - b^5)*sqrt(-a^2 + b^2)) - 2*(2*C*a^3*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + C*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^3*tan(1/2*d*x + 1/2*c) + B*a^2*b*tan(1/2*d*x + 1/2*c) - C*a^2*b*tan(1/2*d*x + 1/2*c) - A*a*b^2*tan(1/2*d*x + 1/2*c) + C*a*b^2*tan(1/2*d*x + 1/2*c) + C*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)*(a^2*b^2 - b^4)) - (2*C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 + (2*C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3)/d","B",0
911,1,250,0,0.289162," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(C a^{3} - A a b^{2} - 2 \, C a b^{2} + B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{2} b^{2} - b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{2}} - \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{2}} + \frac{2 \, {\left(C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b - b^{3}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}}}{d}"," ",0,"(2*(C*a^3 - A*a*b^2 - 2*C*a*b^2 + B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^2*b^2 - b^4)*sqrt(-a^2 + b^2)) + C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^2 - C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^2 + 2*(C*a^2*tan(1/2*d*x + 1/2*c) - B*a*b*tan(1/2*d*x + 1/2*c) + A*b^2*tan(1/2*d*x + 1/2*c))/((a^2*b - b^3)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)))/d","A",0
912,1,222,0,0.249975," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(B a^{3} - 2 \, A a^{2} b - C a^{2} b + A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - a^{2} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{{\left(d x + c\right)} A}{a^{2}} - \frac{2 \, {\left(C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{3} - a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}}}{d}"," ",0,"(2*(B*a^3 - 2*A*a^2*b - C*a^2*b + A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - a^2*b^2)*sqrt(-a^2 + b^2)) + (d*x + c)*A/a^2 - 2*(C*a^2*tan(1/2*d*x + 1/2*c) - B*a*b*tan(1/2*d*x + 1/2*c) + A*b^2*tan(1/2*d*x + 1/2*c))/((a^3 - a*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)))/d","A",0
913,1,1240,0,0.629299," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(B a^{8} + C a^{8} - 2 \, A a^{7} b - 3 \, B a^{7} b + 5 \, A a^{6} b^{2} - 2 \, B a^{6} b^{2} - C a^{6} b^{2} + 4 \, A a^{5} b^{3} + 5 \, B a^{5} b^{3} - 9 \, A a^{4} b^{4} + B a^{4} b^{4} - 2 \, A a^{3} b^{5} - 2 \, B a^{3} b^{5} + 4 \, A a^{2} b^{6} - B a^{3} {\left| -a^{5} + a^{3} b^{2} \right|} + C a^{3} {\left| -a^{5} + a^{3} b^{2} \right|} + 2 \, A a^{2} b {\left| -a^{5} + a^{3} b^{2} \right|} - B a^{2} b {\left| -a^{5} + a^{3} b^{2} \right|} + A a b^{2} {\left| -a^{5} + a^{3} b^{2} \right|} + B a b^{2} {\left| -a^{5} + a^{3} b^{2} \right|} - 2 \, A b^{3} {\left| -a^{5} + a^{3} b^{2} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{4} b - a^{2} b^{3} + \sqrt{{\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} {\left(a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}\right)} + {\left(a^{4} b - a^{2} b^{3}\right)}^{2}}}{a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}}}}\right)\right)}}{a^{4} b {\left| -a^{5} + a^{3} b^{2} \right|} - a^{2} b^{3} {\left| -a^{5} + a^{3} b^{2} \right|} + {\left(a^{5} - a^{3} b^{2}\right)}^{2}} - \frac{{\left(\sqrt{-a^{2} + b^{2}} C a^{3} {\left| -a^{5} + a^{3} b^{2} \right|} {\left| -a + b \right|} + {\left(2 \, a^{2} b + a b^{2} - 2 \, b^{3}\right)} \sqrt{-a^{2} + b^{2}} A {\left| -a^{5} + a^{3} b^{2} \right|} {\left| -a + b \right|} - {\left(a^{3} + a^{2} b - a b^{2}\right)} \sqrt{-a^{2} + b^{2}} B {\left| -a^{5} + a^{3} b^{2} \right|} {\left| -a + b \right|} + {\left(2 \, a^{7} b - 5 \, a^{6} b^{2} - 4 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 2 \, a^{3} b^{5} - 4 \, a^{2} b^{6}\right)} \sqrt{-a^{2} + b^{2}} A {\left| -a + b \right|} - {\left(a^{8} - 3 \, a^{7} b - 2 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + a^{4} b^{4} - 2 \, a^{3} b^{5}\right)} \sqrt{-a^{2} + b^{2}} B {\left| -a + b \right|} - {\left(a^{8} - a^{6} b^{2}\right)} \sqrt{-a^{2} + b^{2}} C {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{4} b - a^{2} b^{3} - \sqrt{{\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} {\left(a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}\right)} + {\left(a^{4} b - a^{2} b^{3}\right)}^{2}}}{a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}}}}\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} - {\left(a^{6} b - 2 \, a^{5} b^{2} + 2 \, a^{3} b^{4} - a^{2} b^{5}\right)} {\left| -a^{5} + a^{3} b^{2} \right|}} + \frac{2 \, {\left(A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} {\left(a^{4} - a^{2} b^{2}\right)}}}{d}"," ",0,"((B*a^8 + C*a^8 - 2*A*a^7*b - 3*B*a^7*b + 5*A*a^6*b^2 - 2*B*a^6*b^2 - C*a^6*b^2 + 4*A*a^5*b^3 + 5*B*a^5*b^3 - 9*A*a^4*b^4 + B*a^4*b^4 - 2*A*a^3*b^5 - 2*B*a^3*b^5 + 4*A*a^2*b^6 - B*a^3*abs(-a^5 + a^3*b^2) + C*a^3*abs(-a^5 + a^3*b^2) + 2*A*a^2*b*abs(-a^5 + a^3*b^2) - B*a^2*b*abs(-a^5 + a^3*b^2) + A*a*b^2*abs(-a^5 + a^3*b^2) + B*a*b^2*abs(-a^5 + a^3*b^2) - 2*A*b^3*abs(-a^5 + a^3*b^2))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^4*b - a^2*b^3 + sqrt((a^5 + a^4*b - a^3*b^2 - a^2*b^3)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3) + (a^4*b - a^2*b^3)^2))/(a^5 - a^4*b - a^3*b^2 + a^2*b^3))))/(a^4*b*abs(-a^5 + a^3*b^2) - a^2*b^3*abs(-a^5 + a^3*b^2) + (a^5 - a^3*b^2)^2) - (sqrt(-a^2 + b^2)*C*a^3*abs(-a^5 + a^3*b^2)*abs(-a + b) + (2*a^2*b + a*b^2 - 2*b^3)*sqrt(-a^2 + b^2)*A*abs(-a^5 + a^3*b^2)*abs(-a + b) - (a^3 + a^2*b - a*b^2)*sqrt(-a^2 + b^2)*B*abs(-a^5 + a^3*b^2)*abs(-a + b) + (2*a^7*b - 5*a^6*b^2 - 4*a^5*b^3 + 9*a^4*b^4 + 2*a^3*b^5 - 4*a^2*b^6)*sqrt(-a^2 + b^2)*A*abs(-a + b) - (a^8 - 3*a^7*b - 2*a^6*b^2 + 5*a^5*b^3 + a^4*b^4 - 2*a^3*b^5)*sqrt(-a^2 + b^2)*B*abs(-a + b) - (a^8 - a^6*b^2)*sqrt(-a^2 + b^2)*C*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^4*b - a^2*b^3 - sqrt((a^5 + a^4*b - a^3*b^2 - a^2*b^3)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3) + (a^4*b - a^2*b^3)^2))/(a^5 - a^4*b - a^3*b^2 + a^2*b^3))))/((a^5 - a^3*b^2)^2*(a^2 - 2*a*b + b^2) - (a^6*b - 2*a^5*b^2 + 2*a^3*b^4 - a^2*b^5)*abs(-a^5 + a^3*b^2)) + 2*(A*a^3*tan(1/2*d*x + 1/2*c)^3 - A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^3*tan(1/2*d*x + 1/2*c)^3 - A*a^3*tan(1/2*d*x + 1/2*c) - A*a^2*b*tan(1/2*d*x + 1/2*c) + C*a^2*b*tan(1/2*d*x + 1/2*c) + A*a*b^2*tan(1/2*d*x + 1/2*c) - B*a*b^2*tan(1/2*d*x + 1/2*c) + 2*A*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)*(a^4 - a^2*b^2)))/d","B",0
914,1,380,0,0.667309," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(2 \, C a^{4} b - 3 \, B a^{3} b^{2} + 4 \, A a^{2} b^{3} - C a^{2} b^{3} + 2 \, B a b^{4} - 3 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{4 \, {\left(C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} - \frac{{\left(A a^{2} + 2 \, C a^{2} - 4 \, B a b + 6 \, A b^{2}\right)} {\left(d x + c\right)}}{a^{4}} + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}}}{2 \, d}"," ",0,"-1/2*(4*(2*C*a^4*b - 3*B*a^3*b^2 + 4*A*a^2*b^3 - C*a^2*b^3 + 2*B*a*b^4 - 3*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - a^4*b^2)*sqrt(-a^2 + b^2)) + 4*(C*a^2*b^2*tan(1/2*d*x + 1/2*c) - B*a*b^3*tan(1/2*d*x + 1/2*c) + A*b^4*tan(1/2*d*x + 1/2*c))/((a^5 - a^3*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) - (A*a^2 + 2*C*a^2 - 4*B*a*b + 6*A*b^2)*(d*x + c)/a^4 + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c)^3 + 4*A*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) - 2*B*a*tan(1/2*d*x + 1/2*c) + 4*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3))/d","A",0
915,1,564,0,1.526324," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(3 \, C a^{4} b^{2} - 4 \, B a^{3} b^{3} + 5 \, A a^{2} b^{4} - 2 \, C a^{2} b^{4} + 3 \, B a b^{5} - 4 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{7} - a^{5} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{12 \, {\left(C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} + \frac{3 \, {\left(B a^{3} - 2 \, A a^{2} b - 4 \, C a^{2} b + 6 \, B a b^{2} - 8 \, A b^{3}\right)} {\left(d x + c\right)}}{a^{5}} + \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{4}}}{6 \, d}"," ",0,"1/6*(12*(3*C*a^4*b^2 - 4*B*a^3*b^3 + 5*A*a^2*b^4 - 2*C*a^2*b^4 + 3*B*a*b^5 - 4*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^7 - a^5*b^2)*sqrt(-a^2 + b^2)) + 12*(C*a^2*b^3*tan(1/2*d*x + 1/2*c) - B*a*b^4*tan(1/2*d*x + 1/2*c) + A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - a^4*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) + 3*(B*a^3 - 2*A*a^2*b - 4*C*a^2*b + 6*B*a*b^2 - 8*A*b^3)*(d*x + c)/a^5 + 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*A*a*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 18*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 36*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2*tan(1/2*d*x + 1/2*c) + 6*C*a^2*tan(1/2*d*x + 1/2*c) - 6*A*a*b*tan(1/2*d*x + 1/2*c) - 12*B*a*b*tan(1/2*d*x + 1/2*c) + 18*A*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^4))/d","A",0
916,1,1740,0,0.503359," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(12 \, C a^{7} - 6 \, B a^{6} b + 2 \, A a^{5} b^{2} - 29 \, C a^{5} b^{2} + 15 \, B a^{4} b^{3} - 5 \, A a^{3} b^{4} + 20 \, C a^{3} b^{4} - 12 \, B a^{2} b^{5} + 6 \, A a b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, {\left(12 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 67 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 29 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 26 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 16 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 13 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}} - \frac{{\left(12 \, C a^{2} - 6 \, B a b + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{5}} + \frac{{\left(12 \, C a^{2} - 6 \, B a b + 2 \, A b^{2} + C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{5}}}{2 \, d}"," ",0,"-1/2*(2*(12*C*a^7 - 6*B*a^6*b + 2*A*a^5*b^2 - 29*C*a^5*b^2 + 15*B*a^4*b^3 - 5*A*a^3*b^4 + 20*C*a^3*b^4 - 12*B*a^2*b^5 + 6*A*a*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4*b^5 - 2*a^2*b^7 + b^9)*sqrt(-a^2 + b^2)) - 2*(12*C*a^7*tan(1/2*d*x + 1/2*c)^7 - 6*B*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^7 + 2*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 17*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 5*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 16*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 2*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 + 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 2*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 13*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^7 + 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^7 - 2*B*b^7*tan(1/2*d*x + 1/2*c)^7 + C*b^7*tan(1/2*d*x + 1/2*c)^7 - 36*C*a^7*tan(1/2*d*x + 1/2*c)^5 + 18*B*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 9*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 67*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 35*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 29*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 15*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 16*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 26*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 10*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 5*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^5 + 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^5 - 2*B*b^7*tan(1/2*d*x + 1/2*c)^5 + 3*C*b^7*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^7*tan(1/2*d*x + 1/2*c)^3 - 18*B*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 9*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 67*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 35*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 16*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 26*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 10*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 5*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^7*tan(1/2*d*x + 1/2*c)^3 + 3*C*b^7*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^7*tan(1/2*d*x + 1/2*c) + 6*B*a^6*b*tan(1/2*d*x + 1/2*c) - 18*C*a^6*b*tan(1/2*d*x + 1/2*c) - 2*A*a^5*b^2*tan(1/2*d*x + 1/2*c) + 9*B*a^5*b^2*tan(1/2*d*x + 1/2*c) + 17*C*a^5*b^2*tan(1/2*d*x + 1/2*c) - 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c) - 9*B*a^4*b^3*tan(1/2*d*x + 1/2*c) + 33*C*a^4*b^3*tan(1/2*d*x + 1/2*c) + 5*A*a^3*b^4*tan(1/2*d*x + 1/2*c) - 16*B*a^3*b^4*tan(1/2*d*x + 1/2*c) + 2*C*a^3*b^4*tan(1/2*d*x + 1/2*c) + 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c) - 2*B*a^2*b^5*tan(1/2*d*x + 1/2*c) - 13*C*a^2*b^5*tan(1/2*d*x + 1/2*c) + 4*B*a*b^6*tan(1/2*d*x + 1/2*c) - 4*C*a*b^6*tan(1/2*d*x + 1/2*c) + 2*B*b^7*tan(1/2*d*x + 1/2*c) + C*b^7*tan(1/2*d*x + 1/2*c))/((a^4*b^4 - 2*a^2*b^6 + b^8)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)^2) - (12*C*a^2 - 6*B*a*b + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^5 + (12*C*a^2 - 6*B*a*b + 2*A*b^2 + C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^5)/d","B",0
917,1,705,0,1.969702," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(6 \, C a^{6} - 2 \, B a^{5} b - 15 \, C a^{4} b^{2} + 5 \, B a^{3} b^{3} + A a^{2} b^{4} + 12 \, C a^{2} b^{4} - 6 \, B a b^{5} + 2 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{4 \, C a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} - \frac{{\left(3 \, C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} + \frac{{\left(3 \, C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b^{3}}}{d}"," ",0,"((6*C*a^6 - 2*B*a^5*b - 15*C*a^4*b^2 + 5*B*a^3*b^3 + A*a^2*b^4 + 12*C*a^2*b^4 - 6*B*a*b^5 + 2*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4*b^4 - 2*a^2*b^6 + b^8)*sqrt(-a^2 + b^2)) - (4*C*a^6*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 7*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - A*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*A*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 6*B*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*A*a*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^6*tan(1/2*d*x + 1/2*c) + 2*B*a^5*b*tan(1/2*d*x + 1/2*c) - 5*C*a^5*b*tan(1/2*d*x + 1/2*c) + 3*B*a^4*b^2*tan(1/2*d*x + 1/2*c) + 7*C*a^4*b^2*tan(1/2*d*x + 1/2*c) - A*a^3*b^3*tan(1/2*d*x + 1/2*c) - 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c) + 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c) + 3*A*a^2*b^4*tan(1/2*d*x + 1/2*c) - 6*B*a^2*b^4*tan(1/2*d*x + 1/2*c) + 4*A*a*b^5*tan(1/2*d*x + 1/2*c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) - (3*C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 + (3*C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b^3))/d","B",0
918,1,632,0,0.470402," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, C a^{5} - 5 \, C a^{3} b^{2} - B a^{2} b^{3} + 3 \, A a b^{4} + 6 \, C a b^{4} - 2 \, B b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} + \frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}} - \frac{2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"-((2*C*a^5 - 5*C*a^3*b^2 - B*a^2*b^3 + 3*A*a*b^4 + 6*C*a*b^4 - 2*B*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4*b^3 - 2*a^2*b^5 + b^7)*sqrt(-a^2 + b^2)) - C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 + C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3 - (2*C*a^5*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 2*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - A*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^5*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^5*tan(1/2*d*x + 1/2*c) - 3*C*a^4*b*tan(1/2*d*x + 1/2*c) + 2*A*a^3*b^2*tan(1/2*d*x + 1/2*c) + B*a^3*b^2*tan(1/2*d*x + 1/2*c) + 5*C*a^3*b^2*tan(1/2*d*x + 1/2*c) + A*a^2*b^3*tan(1/2*d*x + 1/2*c) - 3*B*a^2*b^3*tan(1/2*d*x + 1/2*c) + 6*C*a^2*b^3*tan(1/2*d*x + 1/2*c) + A*a*b^4*tan(1/2*d*x + 1/2*c) - 4*B*a*b^4*tan(1/2*d*x + 1/2*c) + 2*A*b^5*tan(1/2*d*x + 1/2*c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
919,1,510,0,0.408180," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, A a^{2} + C a^{2} - 3 \, B a b + A b^{2} + 2 \, C b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"((2*A*a^2 + C*a^2 - 3*B*a*b + A*b^2 + 2*C*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) - (2*B*a^3*tan(1/2*d*x + 1/2*c)^3 - C*a^3*tan(1/2*d*x + 1/2*c)^3 - 4*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 3*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + A*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^3*tan(1/2*d*x + 1/2*c) - C*a^3*tan(1/2*d*x + 1/2*c) + 4*A*a^2*b*tan(1/2*d*x + 1/2*c) - B*a^2*b*tan(1/2*d*x + 1/2*c) + 3*C*a^2*b*tan(1/2*d*x + 1/2*c) + 3*A*a*b^2*tan(1/2*d*x + 1/2*c) - B*a*b^2*tan(1/2*d*x + 1/2*c) + 4*C*a*b^2*tan(1/2*d*x + 1/2*c) - A*b^3*tan(1/2*d*x + 1/2*c) - 2*B*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
920,1,606,0,0.380426," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, B a^{5} - 6 \, A a^{4} b - 3 \, C a^{4} b + B a^{3} b^{2} + 5 \, A a^{2} b^{3} - 2 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{{\left(d x + c\right)} A}{a^{3}} - \frac{2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"((2*B*a^5 - 6*A*a^4*b - 3*C*a^4*b + B*a^3*b^2 + 5*A*a^2*b^3 - 2*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(-a^2 + b^2)) + (d*x + c)*A/a^3 - (2*C*a^5*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^4*b*tan(1/2*d*x + 1/2*c)^3 - C*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^5*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^5*tan(1/2*d*x + 1/2*c) + 4*B*a^4*b*tan(1/2*d*x + 1/2*c) - C*a^4*b*tan(1/2*d*x + 1/2*c) - 6*A*a^3*b^2*tan(1/2*d*x + 1/2*c) + 3*B*a^3*b^2*tan(1/2*d*x + 1/2*c) - C*a^3*b^2*tan(1/2*d*x + 1/2*c) - 5*A*a^2*b^3*tan(1/2*d*x + 1/2*c) - B*a^2*b^3*tan(1/2*d*x + 1/2*c) - 2*C*a^2*b^3*tan(1/2*d*x + 1/2*c) + 3*A*a*b^4*tan(1/2*d*x + 1/2*c) + 2*A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
921,1,667,0,1.568130," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, C a^{6} - 6 \, B a^{5} b + 12 \, A a^{4} b^{2} + C a^{4} b^{2} + 5 \, B a^{3} b^{3} - 15 \, A a^{2} b^{4} - 2 \, B a b^{5} + 6 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{4 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} + \frac{{\left(B a - 3 \, A b\right)} {\left(d x + c\right)}}{a^{4}} + \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}}}{d}"," ",0,"((2*C*a^6 - 6*B*a^5*b + 12*A*a^4*b^2 + C*a^4*b^2 + 5*B*a^3*b^3 - 15*A*a^2*b^4 - 2*B*a*b^5 + 6*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^8 - 2*a^6*b^2 + a^4*b^4)*sqrt(-a^2 + b^2)) + (4*C*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 6*B*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 + 8*A*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 7*A*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 5*A*a*b^5*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 4*A*b^6*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^5*b*tan(1/2*d*x + 1/2*c) + 6*B*a^4*b^2*tan(1/2*d*x + 1/2*c) - 3*C*a^4*b^2*tan(1/2*d*x + 1/2*c) - 8*A*a^3*b^3*tan(1/2*d*x + 1/2*c) + 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c) + C*a^3*b^3*tan(1/2*d*x + 1/2*c) - 7*A*a^2*b^4*tan(1/2*d*x + 1/2*c) - 3*B*a^2*b^4*tan(1/2*d*x + 1/2*c) + 5*A*a*b^5*tan(1/2*d*x + 1/2*c) - 2*B*a*b^5*tan(1/2*d*x + 1/2*c) + 4*A*b^6*tan(1/2*d*x + 1/2*c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) + (B*a - 3*A*b)*(d*x + c)/a^4 + 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3))/d","B",0
922,1,3408,0,10.007056," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left({\left(a^{6} - a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} - 23 \, a^{2} b^{4} - 6 \, a b^{5} + 12 \, b^{6}\right)} \sqrt{-a^{2} + b^{2}} A {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} {\left| -a + b \right|} - 3 \, {\left(2 \, a^{5} b + 2 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - a^{2} b^{4} + 2 \, a b^{5}\right)} \sqrt{-a^{2} + b^{2}} B {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} {\left| -a + b \right|} + {\left(2 \, a^{6} + 4 \, a^{5} b - 4 \, a^{4} b^{2} - a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} \sqrt{-a^{2} + b^{2}} C {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} {\left| -a + b \right|} - {\left(a^{15} - a^{14} b + 8 \, a^{13} b^{2} - 28 \, a^{12} b^{3} - 42 \, a^{11} b^{4} + 111 \, a^{10} b^{5} + 68 \, a^{9} b^{6} - 158 \, a^{8} b^{7} - 47 \, a^{7} b^{8} + 100 \, a^{6} b^{9} + 12 \, a^{5} b^{10} - 24 \, a^{4} b^{11}\right)} \sqrt{-a^{2} + b^{2}} A {\left| -a + b \right|} + 3 \, {\left(2 \, a^{14} b - 6 \, a^{13} b^{2} - 8 \, a^{12} b^{3} + 21 \, a^{11} b^{4} + 12 \, a^{10} b^{5} - 28 \, a^{9} b^{6} - 8 \, a^{8} b^{7} + 17 \, a^{7} b^{8} + 2 \, a^{6} b^{9} - 4 \, a^{5} b^{10}\right)} \sqrt{-a^{2} + b^{2}} B {\left| -a + b \right|} - {\left(2 \, a^{15} - 8 \, a^{14} b - 8 \, a^{13} b^{2} + 25 \, a^{12} b^{3} + 12 \, a^{11} b^{4} - 30 \, a^{10} b^{5} - 8 \, a^{9} b^{6} + 17 \, a^{8} b^{7} + 2 \, a^{7} b^{8} - 4 \, a^{6} b^{9}\right)} \sqrt{-a^{2} + b^{2}} C {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5} + \sqrt{{\left(a^{9} + a^{8} b - 2 \, a^{7} b^{2} - 2 \, a^{6} b^{3} + a^{5} b^{4} + a^{4} b^{5}\right)} {\left(a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}\right)} + {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)}^{2}}}{a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}}}}\right)\right)}}{{\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} + {\left(a^{10} b - 2 \, a^{9} b^{2} - a^{8} b^{3} + 4 \, a^{7} b^{4} - a^{6} b^{5} - 2 \, a^{5} b^{6} + a^{4} b^{7}\right)} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|}} + \frac{{\left(A a^{15} + 2 \, C a^{15} - A a^{14} b - 6 \, B a^{14} b - 8 \, C a^{14} b + 8 \, A a^{13} b^{2} + 18 \, B a^{13} b^{2} - 8 \, C a^{13} b^{2} - 28 \, A a^{12} b^{3} + 24 \, B a^{12} b^{3} + 25 \, C a^{12} b^{3} - 42 \, A a^{11} b^{4} - 63 \, B a^{11} b^{4} + 12 \, C a^{11} b^{4} + 111 \, A a^{10} b^{5} - 36 \, B a^{10} b^{5} - 30 \, C a^{10} b^{5} + 68 \, A a^{9} b^{6} + 84 \, B a^{9} b^{6} - 8 \, C a^{9} b^{6} - 158 \, A a^{8} b^{7} + 24 \, B a^{8} b^{7} + 17 \, C a^{8} b^{7} - 47 \, A a^{7} b^{8} - 51 \, B a^{7} b^{8} + 2 \, C a^{7} b^{8} + 100 \, A a^{6} b^{9} - 6 \, B a^{6} b^{9} - 4 \, C a^{6} b^{9} + 12 \, A a^{5} b^{10} + 12 \, B a^{5} b^{10} - 24 \, A a^{4} b^{11} + A a^{6} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 2 \, C a^{6} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - A a^{5} b {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 6 \, B a^{5} b {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 4 \, C a^{5} b {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 10 \, A a^{4} b^{2} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 6 \, B a^{4} b^{2} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 4 \, C a^{4} b^{2} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 10 \, A a^{3} b^{3} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 12 \, B a^{3} b^{3} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - C a^{3} b^{3} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 23 \, A a^{2} b^{4} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 3 \, B a^{2} b^{4} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 2 \, C a^{2} b^{4} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 6 \, A a b^{5} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 6 \, B a b^{5} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 12 \, A b^{6} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5} - \sqrt{{\left(a^{9} + a^{8} b - 2 \, a^{7} b^{2} - 2 \, a^{6} b^{3} + a^{5} b^{4} + a^{4} b^{5}\right)} {\left(a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}\right)} + {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)}^{2}}}{a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}}}}\right)\right)}}{a^{8} b {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 2 \, a^{6} b^{3} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + a^{4} b^{5} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - {\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)}^{2}} + \frac{2 \, {\left(A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 26 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 29 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 35 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 67 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 33 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 17 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(((a^6 - a^5*b + 10*a^4*b^2 + 10*a^3*b^3 - 23*a^2*b^4 - 6*a*b^5 + 12*b^6)*sqrt(-a^2 + b^2)*A*abs(a^9 - 2*a^7*b^2 + a^5*b^4)*abs(-a + b) - 3*(2*a^5*b + 2*a^4*b^2 - 4*a^3*b^3 - a^2*b^4 + 2*a*b^5)*sqrt(-a^2 + b^2)*B*abs(a^9 - 2*a^7*b^2 + a^5*b^4)*abs(-a + b) + (2*a^6 + 4*a^5*b - 4*a^4*b^2 - a^3*b^3 + 2*a^2*b^4)*sqrt(-a^2 + b^2)*C*abs(a^9 - 2*a^7*b^2 + a^5*b^4)*abs(-a + b) - (a^15 - a^14*b + 8*a^13*b^2 - 28*a^12*b^3 - 42*a^11*b^4 + 111*a^10*b^5 + 68*a^9*b^6 - 158*a^8*b^7 - 47*a^7*b^8 + 100*a^6*b^9 + 12*a^5*b^10 - 24*a^4*b^11)*sqrt(-a^2 + b^2)*A*abs(-a + b) + 3*(2*a^14*b - 6*a^13*b^2 - 8*a^12*b^3 + 21*a^11*b^4 + 12*a^10*b^5 - 28*a^9*b^6 - 8*a^8*b^7 + 17*a^7*b^8 + 2*a^6*b^9 - 4*a^5*b^10)*sqrt(-a^2 + b^2)*B*abs(-a + b) - (2*a^15 - 8*a^14*b - 8*a^13*b^2 + 25*a^12*b^3 + 12*a^11*b^4 - 30*a^10*b^5 - 8*a^9*b^6 + 17*a^8*b^7 + 2*a^7*b^8 - 4*a^6*b^9)*sqrt(-a^2 + b^2)*C*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^8*b - 2*a^6*b^3 + a^4*b^5 + sqrt((a^9 + a^8*b - 2*a^7*b^2 - 2*a^6*b^3 + a^5*b^4 + a^4*b^5)*(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5) + (a^8*b - 2*a^6*b^3 + a^4*b^5)^2))/(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5))))/((a^9 - 2*a^7*b^2 + a^5*b^4)^2*(a^2 - 2*a*b + b^2) + (a^10*b - 2*a^9*b^2 - a^8*b^3 + 4*a^7*b^4 - a^6*b^5 - 2*a^5*b^6 + a^4*b^7)*abs(a^9 - 2*a^7*b^2 + a^5*b^4)) + (A*a^15 + 2*C*a^15 - A*a^14*b - 6*B*a^14*b - 8*C*a^14*b + 8*A*a^13*b^2 + 18*B*a^13*b^2 - 8*C*a^13*b^2 - 28*A*a^12*b^3 + 24*B*a^12*b^3 + 25*C*a^12*b^3 - 42*A*a^11*b^4 - 63*B*a^11*b^4 + 12*C*a^11*b^4 + 111*A*a^10*b^5 - 36*B*a^10*b^5 - 30*C*a^10*b^5 + 68*A*a^9*b^6 + 84*B*a^9*b^6 - 8*C*a^9*b^6 - 158*A*a^8*b^7 + 24*B*a^8*b^7 + 17*C*a^8*b^7 - 47*A*a^7*b^8 - 51*B*a^7*b^8 + 2*C*a^7*b^8 + 100*A*a^6*b^9 - 6*B*a^6*b^9 - 4*C*a^6*b^9 + 12*A*a^5*b^10 + 12*B*a^5*b^10 - 24*A*a^4*b^11 + A*a^6*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 2*C*a^6*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - A*a^5*b*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 6*B*a^5*b*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 4*C*a^5*b*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 10*A*a^4*b^2*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 6*B*a^4*b^2*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 4*C*a^4*b^2*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 10*A*a^3*b^3*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 12*B*a^3*b^3*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - C*a^3*b^3*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 23*A*a^2*b^4*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 3*B*a^2*b^4*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 2*C*a^2*b^4*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 6*A*a*b^5*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 6*B*a*b^5*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 12*A*b^6*abs(a^9 - 2*a^7*b^2 + a^5*b^4))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^8*b - 2*a^6*b^3 + a^4*b^5 - sqrt((a^9 + a^8*b - 2*a^7*b^2 - 2*a^6*b^3 + a^5*b^4 + a^4*b^5)*(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5) + (a^8*b - 2*a^6*b^3 + a^4*b^5)^2))/(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5))))/(a^8*b*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 2*a^6*b^3*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + a^4*b^5*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - (a^9 - 2*a^7*b^2 + a^5*b^4)^2) + 2*(A*a^7*tan(1/2*d*x + 1/2*c)^7 - 2*B*a^7*tan(1/2*d*x + 1/2*c)^7 + 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^7 + 4*B*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 13*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 2*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 2*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 5*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 17*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 2*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^7 - 6*B*a*b^6*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^7*tan(1/2*d*x + 1/2*c)^7 - 3*A*a^7*tan(1/2*d*x + 1/2*c)^5 + 2*B*a^7*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 4*B*a^6*b*tan(1/2*d*x + 1/2*c)^5 - 5*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 10*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 26*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 15*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 29*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 35*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 67*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^5 - 18*B*a*b^6*tan(1/2*d*x + 1/2*c)^5 + 36*A*b^7*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^7*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^7*tan(1/2*d*x + 1/2*c)^3 - 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 10*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 26*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 35*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 67*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^3 - 18*B*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 36*A*b^7*tan(1/2*d*x + 1/2*c)^3 - A*a^7*tan(1/2*d*x + 1/2*c) - 2*B*a^7*tan(1/2*d*x + 1/2*c) + 4*A*a^6*b*tan(1/2*d*x + 1/2*c) - 4*B*a^6*b*tan(1/2*d*x + 1/2*c) + 13*A*a^5*b^2*tan(1/2*d*x + 1/2*c) + 2*B*a^5*b^2*tan(1/2*d*x + 1/2*c) - 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c) - 2*A*a^4*b^3*tan(1/2*d*x + 1/2*c) + 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c) - 5*C*a^4*b^3*tan(1/2*d*x + 1/2*c) - 33*A*a^3*b^4*tan(1/2*d*x + 1/2*c) + 9*B*a^3*b^4*tan(1/2*d*x + 1/2*c) + 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c) - 17*A*a^2*b^5*tan(1/2*d*x + 1/2*c) - 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c) + 2*C*a^2*b^5*tan(1/2*d*x + 1/2*c) + 18*A*a*b^6*tan(1/2*d*x + 1/2*c) - 6*B*a*b^6*tan(1/2*d*x + 1/2*c) + 12*A*b^7*tan(1/2*d*x + 1/2*c))/((a^8 - 2*a^6*b^2 + a^4*b^4)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
923,1,1264,0,0.495072," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(8 \, C a^{8} - 2 \, B a^{7} b - 28 \, C a^{6} b^{2} + 7 \, B a^{5} b^{3} + 35 \, C a^{4} b^{4} - 8 \, B a^{3} b^{5} - 3 \, A a^{2} b^{6} - 20 \, C a^{2} b^{6} + 8 \, B a b^{7} - 2 \, A b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{18 \, C a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, C a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, C a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 152 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 236 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}} - \frac{3 \, {\left(4 \, C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{5}} + \frac{3 \, {\left(4 \, C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{5}} - \frac{6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b^{4}}}{3 \, d}"," ",0,"1/3*(3*(8*C*a^8 - 2*B*a^7*b - 28*C*a^6*b^2 + 7*B*a^5*b^3 + 35*C*a^4*b^4 - 8*B*a^3*b^5 - 3*A*a^2*b^6 - 20*C*a^2*b^6 + 8*B*a*b^7 - 2*A*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*sqrt(-a^2 + b^2)) - (18*C*a^9*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^8*b*tan(1/2*d*x + 1/2*c)^5 - 42*C*a^8*b*tan(1/2*d*x + 1/2*c)^5 + 15*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 - 24*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 117*C*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 45*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 24*C*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 - 105*C*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 + 60*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 + 60*C*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 - 36*B*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^8*tan(1/2*d*x + 1/2*c)^5 - 36*C*a^9*tan(1/2*d*x + 1/2*c)^3 + 12*B*a^8*b*tan(1/2*d*x + 1/2*c)^3 + 152*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^3 - 56*B*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 - 4*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 - 236*C*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 + 116*B*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 - 32*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 + 120*C*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 - 72*B*a^2*b^7*tan(1/2*d*x + 1/2*c)^3 + 36*A*a*b^8*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^9*tan(1/2*d*x + 1/2*c) - 6*B*a^8*b*tan(1/2*d*x + 1/2*c) + 42*C*a^8*b*tan(1/2*d*x + 1/2*c) - 15*B*a^7*b^2*tan(1/2*d*x + 1/2*c) - 24*C*a^7*b^2*tan(1/2*d*x + 1/2*c) + 6*B*a^6*b^3*tan(1/2*d*x + 1/2*c) - 117*C*a^6*b^3*tan(1/2*d*x + 1/2*c) + 6*A*a^5*b^4*tan(1/2*d*x + 1/2*c) + 45*B*a^5*b^4*tan(1/2*d*x + 1/2*c) - 24*C*a^5*b^4*tan(1/2*d*x + 1/2*c) + 3*A*a^4*b^5*tan(1/2*d*x + 1/2*c) + 6*B*a^4*b^5*tan(1/2*d*x + 1/2*c) + 105*C*a^4*b^5*tan(1/2*d*x + 1/2*c) + 6*A*a^3*b^6*tan(1/2*d*x + 1/2*c) - 60*B*a^3*b^6*tan(1/2*d*x + 1/2*c) + 60*C*a^3*b^6*tan(1/2*d*x + 1/2*c) + 27*A*a^2*b^7*tan(1/2*d*x + 1/2*c) - 36*B*a^2*b^7*tan(1/2*d*x + 1/2*c) + 18*A*a*b^8*tan(1/2*d*x + 1/2*c))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) - 3*(4*C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^5 + 3*(4*C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^5 - 6*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b^4))/d","B",0
924,1,1135,0,0.503054," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, C a^{7} - 7 \, C a^{5} b^{2} - A a^{3} b^{4} + 8 \, C a^{3} b^{4} + 3 \, B a^{2} b^{5} - 4 \, A a b^{6} - 8 \, C a b^{6} + 2 \, B b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{3 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} + \frac{3 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, B a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, C a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, B a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, C a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, B a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(2*C*a^7 - 7*C*a^5*b^2 - A*a^3*b^4 + 8*C*a^3*b^4 + 3*B*a^2*b^5 - 4*A*a*b^6 - 8*C*a*b^6 + 2*B*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*sqrt(-a^2 + b^2)) - 3*C*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 + 3*C*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - (6*C*a^8*tan(1/2*d*x + 1/2*c)^5 - 15*C*a^7*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 45*C*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*B*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 60*C*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 27*B*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 6*A*a*b^7*tan(1/2*d*x + 1/2*c)^5 - 18*B*a*b^7*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^8*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^8*tan(1/2*d*x + 1/2*c)^3 + 56*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^3 - 28*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 - 116*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 + 32*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^3 + 16*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 + 72*C*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 - 36*B*a*b^7*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^8*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^8*tan(1/2*d*x + 1/2*c) + 15*C*a^7*b*tan(1/2*d*x + 1/2*c) - 6*C*a^6*b^2*tan(1/2*d*x + 1/2*c) - 3*A*a^5*b^3*tan(1/2*d*x + 1/2*c) - 6*B*a^5*b^3*tan(1/2*d*x + 1/2*c) - 45*C*a^5*b^3*tan(1/2*d*x + 1/2*c) + 12*A*a^4*b^4*tan(1/2*d*x + 1/2*c) - 3*B*a^4*b^4*tan(1/2*d*x + 1/2*c) - 6*C*a^4*b^4*tan(1/2*d*x + 1/2*c) + 27*A*a^3*b^5*tan(1/2*d*x + 1/2*c) - 6*B*a^3*b^5*tan(1/2*d*x + 1/2*c) + 60*C*a^3*b^5*tan(1/2*d*x + 1/2*c) + 12*A*a^2*b^6*tan(1/2*d*x + 1/2*c) - 27*B*a^2*b^6*tan(1/2*d*x + 1/2*c) + 36*C*a^2*b^6*tan(1/2*d*x + 1/2*c) + 6*A*a*b^7*tan(1/2*d*x + 1/2*c) - 18*B*a*b^7*tan(1/2*d*x + 1/2*c) + 6*A*b^8*tan(1/2*d*x + 1/2*c))/((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
925,1,970,0,0.418446," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(B a^{3} - 4 \, A a^{2} b - 3 \, C a^{2} b + 4 \, B a b^{2} - A b^{3} - 2 \, C b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{6 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(B*a^3 - 4*A*a^2*b - 3*C*a^2*b + 4*B*a*b^2 - A*b^3 - 2*C*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) - (6*A*a^5*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^5*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^5*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 27*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*B*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 18*C*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*A*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*B*b^5*tan(1/2*d*x + 1/2*c)^5 - 12*A*a^5*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^5*tan(1/2*d*x + 1/2*c)^3 + 28*B*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 16*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 32*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 16*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 28*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 36*C*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 12*B*b^5*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^5*tan(1/2*d*x + 1/2*c) + 3*B*a^5*tan(1/2*d*x + 1/2*c) + 6*C*a^5*tan(1/2*d*x + 1/2*c) + 6*A*a^4*b*tan(1/2*d*x + 1/2*c) - 12*B*a^4*b*tan(1/2*d*x + 1/2*c) + 3*C*a^4*b*tan(1/2*d*x + 1/2*c) + 12*A*a^3*b^2*tan(1/2*d*x + 1/2*c) - 27*B*a^3*b^2*tan(1/2*d*x + 1/2*c) + 6*C*a^3*b^2*tan(1/2*d*x + 1/2*c) + 27*A*a^2*b^3*tan(1/2*d*x + 1/2*c) - 12*B*a^2*b^3*tan(1/2*d*x + 1/2*c) + 27*C*a^2*b^3*tan(1/2*d*x + 1/2*c) + 12*A*a*b^4*tan(1/2*d*x + 1/2*c) - 6*B*a*b^4*tan(1/2*d*x + 1/2*c) + 18*C*a*b^4*tan(1/2*d*x + 1/2*c) - 3*A*b^5*tan(1/2*d*x + 1/2*c) - 6*B*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
926,1,968,0,0.429430," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, A a^{3} + C a^{3} - 4 \, B a^{2} b + 3 \, A a b^{2} + 4 \, C a b^{2} - B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{6 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(2*A*a^3 + C*a^3 - 4*B*a^2*b + 3*A*a*b^2 + 4*C*a*b^2 - B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) + (6*B*a^5*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^5*tan(1/2*d*x + 1/2*c)^5 - 18*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 27*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 27*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 12*B*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*C*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*A*b^5*tan(1/2*d*x + 1/2*c)^5 + 3*B*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*C*b^5*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^5*tan(1/2*d*x + 1/2*c)^3 + 36*A*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 28*C*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 16*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 32*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 16*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 28*B*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 4*A*b^5*tan(1/2*d*x + 1/2*c)^3 - 12*C*b^5*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^5*tan(1/2*d*x + 1/2*c) + 3*C*a^5*tan(1/2*d*x + 1/2*c) - 18*A*a^4*b*tan(1/2*d*x + 1/2*c) + 6*B*a^4*b*tan(1/2*d*x + 1/2*c) - 12*C*a^4*b*tan(1/2*d*x + 1/2*c) - 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c) + 12*B*a^3*b^2*tan(1/2*d*x + 1/2*c) - 27*C*a^3*b^2*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b^3*tan(1/2*d*x + 1/2*c) + 27*B*a^2*b^3*tan(1/2*d*x + 1/2*c) - 12*C*a^2*b^3*tan(1/2*d*x + 1/2*c) - 3*A*a*b^4*tan(1/2*d*x + 1/2*c) + 12*B*a*b^4*tan(1/2*d*x + 1/2*c) - 6*C*a*b^4*tan(1/2*d*x + 1/2*c) - 6*A*b^5*tan(1/2*d*x + 1/2*c) - 3*B*b^5*tan(1/2*d*x + 1/2*c) - 6*C*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
927,1,1106,0,0.421068," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, B a^{7} - 8 \, A a^{6} b - 4 \, C a^{6} b + 3 \, B a^{5} b^{2} + 8 \, A a^{4} b^{3} - C a^{4} b^{3} - 7 \, A a^{2} b^{5} + 2 \, A b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{3 \, {\left(d x + c\right)} A}{a^{4}} - \frac{6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(2*B*a^7 - 8*A*a^6*b - 4*C*a^6*b + 3*B*a^5*b^2 + 8*A*a^4*b^3 - C*a^4*b^3 - 7*A*a^2*b^5 + 2*A*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*sqrt(-a^2 + b^2)) + 3*(d*x + c)*A/a^4 - (6*C*a^8*tan(1/2*d*x + 1/2*c)^5 - 18*B*a^7*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^7*b*tan(1/2*d*x + 1/2*c)^5 + 36*A*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 27*B*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 - 60*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*B*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 45*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 15*A*a*b^7*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^8*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^8*tan(1/2*d*x + 1/2*c)^3 + 36*B*a^7*b*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 - 16*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 - 32*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^3 + 116*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 + 28*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^3 - 56*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^8*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^8*tan(1/2*d*x + 1/2*c) - 18*B*a^7*b*tan(1/2*d*x + 1/2*c) + 6*C*a^7*b*tan(1/2*d*x + 1/2*c) + 36*A*a^6*b^2*tan(1/2*d*x + 1/2*c) - 27*B*a^6*b^2*tan(1/2*d*x + 1/2*c) + 12*C*a^6*b^2*tan(1/2*d*x + 1/2*c) + 60*A*a^5*b^3*tan(1/2*d*x + 1/2*c) - 6*B*a^5*b^3*tan(1/2*d*x + 1/2*c) + 27*C*a^5*b^3*tan(1/2*d*x + 1/2*c) - 6*A*a^4*b^4*tan(1/2*d*x + 1/2*c) - 3*B*a^4*b^4*tan(1/2*d*x + 1/2*c) + 12*C*a^4*b^4*tan(1/2*d*x + 1/2*c) - 45*A*a^3*b^5*tan(1/2*d*x + 1/2*c) - 6*B*a^3*b^5*tan(1/2*d*x + 1/2*c) - 3*C*a^3*b^5*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b^6*tan(1/2*d*x + 1/2*c) + 15*A*a*b^7*tan(1/2*d*x + 1/2*c) + 6*A*b^8*tan(1/2*d*x + 1/2*c))/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
928,1,1225,0,2.407437," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, C a^{8} - 8 \, B a^{7} b + 20 \, A a^{6} b^{2} + 3 \, C a^{6} b^{2} + 8 \, B a^{5} b^{3} - 35 \, A a^{4} b^{4} - 7 \, B a^{3} b^{5} + 28 \, A a^{2} b^{6} + 2 \, B a b^{7} - 8 \, A b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{18 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 236 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 152 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}} + \frac{3 \, {\left(B a - 4 \, A b\right)} {\left(d x + c\right)}}{a^{5}} + \frac{6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{4}}}{3 \, d}"," ",0,"1/3*(3*(2*C*a^8 - 8*B*a^7*b + 20*A*a^6*b^2 + 3*C*a^6*b^2 + 8*B*a^5*b^3 - 35*A*a^4*b^4 - 7*B*a^3*b^5 + 28*A*a^2*b^6 + 2*B*a*b^7 - 8*A*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*sqrt(-a^2 + b^2)) + (18*C*a^8*b*tan(1/2*d*x + 1/2*c)^5 - 36*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 + 60*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 60*B*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 - 105*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 24*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 - 45*B*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 117*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 24*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 + 15*B*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 - 42*A*a*b^8*tan(1/2*d*x + 1/2*c)^5 - 6*B*a*b^8*tan(1/2*d*x + 1/2*c)^5 + 18*A*b^9*tan(1/2*d*x + 1/2*c)^5 - 36*C*a^8*b*tan(1/2*d*x + 1/2*c)^3 + 72*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 + 32*C*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 - 116*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 + 236*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 + 4*C*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 + 56*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 - 152*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^3 - 12*B*a*b^8*tan(1/2*d*x + 1/2*c)^3 + 36*A*b^9*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^8*b*tan(1/2*d*x + 1/2*c) - 36*B*a^7*b^2*tan(1/2*d*x + 1/2*c) + 27*C*a^7*b^2*tan(1/2*d*x + 1/2*c) + 60*A*a^6*b^3*tan(1/2*d*x + 1/2*c) - 60*B*a^6*b^3*tan(1/2*d*x + 1/2*c) + 6*C*a^6*b^3*tan(1/2*d*x + 1/2*c) + 105*A*a^5*b^4*tan(1/2*d*x + 1/2*c) + 6*B*a^5*b^4*tan(1/2*d*x + 1/2*c) + 3*C*a^5*b^4*tan(1/2*d*x + 1/2*c) - 24*A*a^4*b^5*tan(1/2*d*x + 1/2*c) + 45*B*a^4*b^5*tan(1/2*d*x + 1/2*c) + 6*C*a^4*b^5*tan(1/2*d*x + 1/2*c) - 117*A*a^3*b^6*tan(1/2*d*x + 1/2*c) + 6*B*a^3*b^6*tan(1/2*d*x + 1/2*c) - 24*A*a^2*b^7*tan(1/2*d*x + 1/2*c) - 15*B*a^2*b^7*tan(1/2*d*x + 1/2*c) + 42*A*a*b^8*tan(1/2*d*x + 1/2*c) - 6*B*a*b^8*tan(1/2*d*x + 1/2*c) + 18*A*b^9*tan(1/2*d*x + 1/2*c))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) + 3*(B*a - 4*A*b)*(d*x + c)/a^5 + 6*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^4))/d","B",0
929,1,1438,0,0.483322," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(8 \, C a^{8} b - 20 \, B a^{7} b^{2} + 40 \, A a^{6} b^{3} - 8 \, C a^{6} b^{3} + 35 \, B a^{5} b^{4} - 84 \, A a^{4} b^{5} + 7 \, C a^{4} b^{5} - 28 \, B a^{3} b^{6} + 69 \, A a^{2} b^{7} - 2 \, C a^{2} b^{7} + 8 \, B a b^{8} - 20 \, A b^{9}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{2 \, {\left(36 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 90 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, B a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 162 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, C a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 117 \, B a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 213 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 42 \, B a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 81 \, A a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 180 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 236 \, B a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 392 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 152 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 284 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 90 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 162 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, C a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 117 \, B a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 213 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 42 \, B a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 81 \, A a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, B a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}} - \frac{3 \, {\left(A a^{2} + 2 \, C a^{2} - 8 \, B a b + 20 \, A b^{2}\right)} {\left(d x + c\right)}}{a^{6}} + \frac{6 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{5}}}{6 \, d}"," ",0,"-1/6*(6*(8*C*a^8*b - 20*B*a^7*b^2 + 40*A*a^6*b^3 - 8*C*a^6*b^3 + 35*B*a^5*b^4 - 84*A*a^4*b^5 + 7*C*a^4*b^5 - 28*B*a^3*b^6 + 69*A*a^2*b^7 - 2*C*a^2*b^7 + 8*B*a*b^8 - 20*A*b^9)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*sqrt(-a^2 + b^2)) + 2*(36*C*a^8*b^2*tan(1/2*d*x + 1/2*c)^5 - 60*B*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 - 60*C*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 + 90*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 + 105*B*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 162*A*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 + 24*B*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 + 45*C*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 - 48*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 - 117*B*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 + 213*A*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 + 24*B*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 - 15*C*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 - 48*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 + 42*B*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 - 81*A*a*b^9*tan(1/2*d*x + 1/2*c)^5 - 18*B*a*b^9*tan(1/2*d*x + 1/2*c)^5 + 36*A*b^10*tan(1/2*d*x + 1/2*c)^5 - 72*C*a^8*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*B*a^7*b^3*tan(1/2*d*x + 1/2*c)^3 - 180*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 + 116*C*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 - 236*B*a^5*b^5*tan(1/2*d*x + 1/2*c)^3 + 392*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 - 56*C*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 + 152*B*a^3*b^7*tan(1/2*d*x + 1/2*c)^3 - 284*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 - 36*B*a*b^9*tan(1/2*d*x + 1/2*c)^3 + 72*A*b^10*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^8*b^2*tan(1/2*d*x + 1/2*c) - 60*B*a^7*b^3*tan(1/2*d*x + 1/2*c) + 60*C*a^7*b^3*tan(1/2*d*x + 1/2*c) + 90*A*a^6*b^4*tan(1/2*d*x + 1/2*c) - 105*B*a^6*b^4*tan(1/2*d*x + 1/2*c) - 6*C*a^6*b^4*tan(1/2*d*x + 1/2*c) + 162*A*a^5*b^5*tan(1/2*d*x + 1/2*c) + 24*B*a^5*b^5*tan(1/2*d*x + 1/2*c) - 45*C*a^5*b^5*tan(1/2*d*x + 1/2*c) - 48*A*a^4*b^6*tan(1/2*d*x + 1/2*c) + 117*B*a^4*b^6*tan(1/2*d*x + 1/2*c) - 6*C*a^4*b^6*tan(1/2*d*x + 1/2*c) - 213*A*a^3*b^7*tan(1/2*d*x + 1/2*c) + 24*B*a^3*b^7*tan(1/2*d*x + 1/2*c) + 15*C*a^3*b^7*tan(1/2*d*x + 1/2*c) - 48*A*a^2*b^8*tan(1/2*d*x + 1/2*c) - 42*B*a^2*b^8*tan(1/2*d*x + 1/2*c) + 6*C*a^2*b^8*tan(1/2*d*x + 1/2*c) + 81*A*a*b^9*tan(1/2*d*x + 1/2*c) - 18*B*a*b^9*tan(1/2*d*x + 1/2*c) + 36*A*b^10*tan(1/2*d*x + 1/2*c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) - 3*(A*a^2 + 2*C*a^2 - 8*B*a*b + 20*A*b^2)*(d*x + c)/a^6 + 6*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c)^3 + 8*A*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) - 2*B*a*tan(1/2*d*x + 1/2*c) + 8*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^5))/d","B",0
930,1,53,0,0.264788," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{C b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - C b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - {\left(C a - B b\right)} {\left(d x + c\right)}}{d}"," ",0,"(C*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - C*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - (C*a - B*b)*(d*x + c))/d","B",0
931,1,309,0,0.252342," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(\sqrt{-a^{2} + b^{2}} C {\left(a + b\right)} {\left| a \right|} {\left| -a + b \right|} - \sqrt{-a^{2} + b^{2}} B b {\left| a \right|} {\left| -a + b \right|} + \sqrt{-a^{2} + b^{2}} {\left(a b - 2 \, b^{2}\right)} B {\left| -a + b \right|} - {\left(a^{2} - 3 \, a b\right)} \sqrt{-a^{2} + b^{2}} C {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{b + \sqrt{{\left(a + b\right)} {\left(a - b\right)} + b^{2}}}{a - b}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} a^{2} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} {\left| a \right|}} - \frac{{\left(C a^{2} - B a b - 3 \, C a b + 2 \, B b^{2} + C a {\left| a \right|} - B b {\left| a \right|} + C b {\left| a \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{b - \sqrt{{\left(a + b\right)} {\left(a - b\right)} + b^{2}}}{a - b}}}\right)\right)}}{a^{2} - b {\left| a \right|}}}{d}"," ",0,"((sqrt(-a^2 + b^2)*C*(a + b)*abs(a)*abs(-a + b) - sqrt(-a^2 + b^2)*B*b*abs(a)*abs(-a + b) + sqrt(-a^2 + b^2)*(a*b - 2*b^2)*B*abs(-a + b) - (a^2 - 3*a*b)*sqrt(-a^2 + b^2)*C*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(b + sqrt((a + b)*(a - b) + b^2))/(a - b))))/((a^2 - 2*a*b + b^2)*a^2 + (a^2*b - 2*a*b^2 + b^3)*abs(a)) - (C*a^2 - B*a*b - 3*C*a*b + 2*B*b^2 + C*a*abs(a) - B*b*abs(a) + C*b*abs(a))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(b - sqrt((a + b)*(a - b) + b^2))/(a - b))))/(a^2 - b*abs(a)))/d","B",0
932,1,223,0,0.399718," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(3 \, C a^{3} b - 2 \, B a^{2} b^{2} - C a b^{3} + B b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - a^{2} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{{\left(C a - B b\right)} {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(2 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{3} - a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}}}{d}"," ",0,"(2*(3*C*a^3*b - 2*B*a^2*b^2 - C*a*b^3 + B*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - a^2*b^2)*sqrt(-a^2 + b^2)) - (C*a - B*b)*(d*x + c)/a^2 + 2*(2*C*a*b^2*tan(1/2*d*x + 1/2*c) - B*b^3*tan(1/2*d*x + 1/2*c))/((a^3 - a*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)))/d","A",0
933,1,515,0,0.418867," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{{\left(8 \, C a^{5} b - 6 \, B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 5 \, B a^{2} b^{4} + 2 \, C a b^{5} - 2 \, B b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{{\left(C a - B b\right)} {\left(d x + c\right)}}{a^{3}} + \frac{10 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, C a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"((8*C*a^5*b - 6*B*a^4*b^2 - 4*C*a^3*b^3 + 5*B*a^2*b^4 + 2*C*a*b^5 - 2*B*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(-a^2 + b^2)) - (C*a - B*b)*(d*x + c)/a^3 + (10*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 6*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 3*B*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 2*C*a*b^5*tan(1/2*d*x + 1/2*c)^3 - 2*B*b^6*tan(1/2*d*x + 1/2*c)^3 - 10*C*a^4*b^2*tan(1/2*d*x + 1/2*c) + 6*B*a^3*b^3*tan(1/2*d*x + 1/2*c) - 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c) + 5*B*a^2*b^4*tan(1/2*d*x + 1/2*c) + 4*C*a^2*b^4*tan(1/2*d*x + 1/2*c) - 3*B*a*b^5*tan(1/2*d*x + 1/2*c) + 2*C*a*b^5*tan(1/2*d*x + 1/2*c) - 2*B*b^6*tan(1/2*d*x + 1/2*c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
934,1,860,0,0.672903," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^5,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(10 \, C a^{7} b - 8 \, B a^{6} b^{2} - 5 \, C a^{5} b^{3} + 8 \, B a^{4} b^{4} + 7 \, C a^{3} b^{5} - 7 \, B a^{2} b^{6} - 2 \, C a b^{7} + 2 \, B b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{3 \, {\left(C a - B b\right)} {\left(d x + c\right)}}{a^{4}} + \frac{54 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 87 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 42 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 108 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 148 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 52 \, C a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 54 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 87 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 42 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(10*C*a^7*b - 8*B*a^6*b^2 - 5*C*a^5*b^3 + 8*B*a^4*b^4 + 7*C*a^3*b^5 - 7*B*a^2*b^6 - 2*C*a*b^7 + 2*B*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*sqrt(-a^2 + b^2)) - 3*(C*a - B*b)*(d*x + c)/a^4 + (54*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 - 36*B*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 - 87*C*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 60*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 42*C*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 - 45*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 - 15*C*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 + 15*B*a*b^8*tan(1/2*d*x + 1/2*c)^5 + 6*C*a*b^8*tan(1/2*d*x + 1/2*c)^5 - 6*B*b^9*tan(1/2*d*x + 1/2*c)^5 - 108*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^3 + 72*B*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 + 148*C*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 - 116*B*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 - 52*C*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 + 56*B*a^2*b^7*tan(1/2*d*x + 1/2*c)^3 + 12*C*a*b^8*tan(1/2*d*x + 1/2*c)^3 - 12*B*b^9*tan(1/2*d*x + 1/2*c)^3 + 54*C*a^7*b^2*tan(1/2*d*x + 1/2*c) - 36*B*a^6*b^3*tan(1/2*d*x + 1/2*c) + 87*C*a^6*b^3*tan(1/2*d*x + 1/2*c) - 60*B*a^5*b^4*tan(1/2*d*x + 1/2*c) + 6*B*a^4*b^5*tan(1/2*d*x + 1/2*c) - 42*C*a^4*b^5*tan(1/2*d*x + 1/2*c) + 45*B*a^3*b^6*tan(1/2*d*x + 1/2*c) + 6*B*a^2*b^7*tan(1/2*d*x + 1/2*c) + 15*C*a^2*b^7*tan(1/2*d*x + 1/2*c) - 15*B*a*b^8*tan(1/2*d*x + 1/2*c) + 6*C*a*b^8*tan(1/2*d*x + 1/2*c) - 6*B*b^9*tan(1/2*d*x + 1/2*c))/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
935,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
936,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
937,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c), x)","F",0
938,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a), x)","F",0
939,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c), x)","F",0
940,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
941,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^3, x)","F",0
942,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
943,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
944,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
945,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2), x)","F",0
946,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
947,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
948,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^3, x)","F",0
949,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^4, x)","F",0
950,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
951,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
952,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2), x)","F",0
953,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
954,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
955,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^3, x)","F",0
956,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^4, x)","F",0
957,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^5, x)","F",0
958,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^3/sqrt(b*sec(d*x + c) + a), x)","F",0
959,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
960,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
961,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/sqrt(b*sec(d*x + c) + a), x)","F",0
962,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
963,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
964,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^3/(b*sec(d*x + c) + a)^(3/2), x)","F",0
965,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
966,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
967,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
968,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
969,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
970,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^3/(b*sec(d*x + c) + a)^(5/2), x)","F",0
971,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c) + a)^(5/2), x)","F",0
972,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
973,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
974,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
975,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C b^{2} \sec\left(d x + c\right)^{2} + B b^{2} \sec\left(d x + c\right) - C a^{2} + B a b\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*b^2*sec(d*x + c)^2 + B*b^2*sec(d*x + c) - C*a^2 + B*a*b)*(b*sec(d*x + c) + a)^(3/2), x)","F",0
976,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C b^{2} \sec\left(d x + c\right)^{2} + B b^{2} \sec\left(d x + c\right) - C a^{2} + B a b\right)} \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*b^2*sec(d*x + c)^2 + B*b^2*sec(d*x + c) - C*a^2 + B*a*b)*sqrt(b*sec(d*x + c) + a), x)","F",0
977,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C b^{2} \sec\left(d x + c\right)^{2} + B b^{2} \sec\left(d x + c\right) - C a^{2} + B a b}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*b^2*sec(d*x + c)^2 + B*b^2*sec(d*x + c) - C*a^2 + B*a*b)/sqrt(b*sec(d*x + c) + a), x)","F",0
978,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C b^{2} \sec\left(d x + c\right)^{2} + B b^{2} \sec\left(d x + c\right) - C a^{2} + B a b}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*b^2*sec(d*x + c)^2 + B*b^2*sec(d*x + c) - C*a^2 + B*a*b)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
979,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C b^{2} \sec\left(d x + c\right)^{2} + B b^{2} \sec\left(d x + c\right) - C a^{2} + B a b}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*b^2*sec(d*x + c)^2 + B*b^2*sec(d*x + c) - C*a^2 + B*a*b)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
980,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{C b^{2} \sec\left(d x + c\right)^{2} + B b^{2} \sec\left(d x + c\right) - C a^{2} + B a b}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*b^2*sec(d*x + c)^2 + B*b^2*sec(d*x + c) - C*a^2 + B*a*b)/(b*sec(d*x + c) + a)^(7/2), x)","F",0
981,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
982,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
983,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
984,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
985,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
986,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
987,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
988,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(9/2), x)","F",0
989,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(11/2), x)","F",0
990,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
991,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
992,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
993,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
994,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sec(d*x + c)^(5/2), x)","F",0
995,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sec(d*x + c)^(7/2), x)","F",0
996,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sec(d*x + c)^(9/2), x)","F",0
997,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
998,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
999,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
1000,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sec(d*x + c)^(5/2), x)","F",0
1001,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sec(d*x + c)^(7/2), x)","F",0
1002,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sec(d*x + c)^(9/2), x)","F",0
1003,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sec(d*x + c)^(11/2), x)","F",0
1004,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4*sqrt(sec(d*x + c)), x)","F",0
1005,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4/sqrt(sec(d*x + c)), x)","F",0
1006,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4/sec(d*x + c)^(3/2), x)","F",0
1007,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4/sec(d*x + c)^(5/2), x)","F",0
1008,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4/sec(d*x + c)^(7/2), x)","F",0
1009,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4/sec(d*x + c)^(9/2), x)","F",0
1010,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4/sec(d*x + c)^(11/2), x)","F",0
1011,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4/sec(d*x + c)^(13/2), x)","F",0
1012,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a), x)","F",0
1013,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a), x)","F",0
1014,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
1015,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1016,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1017,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1018,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sec(d*x + c)^(7/2)), x)","F",0
1019,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^2, x)","F",0
1020,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^2, x)","F",0
1021,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^2, x)","F",0
1022,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
1023,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
1024,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
1025,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(7/2)/(b*sec(d*x + c) + a)^3, x)","F",0
1026,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^3, x)","F",0
1027,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^3, x)","F",0
1028,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^3, x)","F",0
1029,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
1030,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
1031,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1032,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1033,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1034,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1035,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
1036,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
1037,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(9/2), x)","F",0
1038,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
1039,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
1040,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
1041,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
1042,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(5/2), x)","F",0
1043,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(7/2), x)","F",0
1044,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(9/2), x)","F",0
1045,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c)), x)","F",0
1046,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
1047,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(3/2), x)","F",0
1048,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(5/2), x)","F",0
1049,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(7/2), x)","F",0
1050,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(9/2), x)","F",0
1051,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(11/2), x)","F",0
1052,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
1053,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
1054,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1055,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1056,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1057,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(7/2)), x)","F",0
1058,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*sec(d*x+c)+b*B*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B b \sec\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sqrt(sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
1059,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
1060,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^(3/2), x)","F",0
1061,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
1062,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
1063,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2)), x)","F",0
1064,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
1065,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
1066,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^(5/2), x)","F",0
1067,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
1068,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
1069,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
1070,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(2/3), x)","F",0
1071,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(1/3), x)","F",0
1072,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(1/3), x)","F",0
1073,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(2/3), x)","F",0
1074,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^m*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C b^{2} \sec\left(d x + c\right)^{2} + B b^{2} \sec\left(d x + c\right) - C a^{2} + B a b\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*b^2*sec(d*x + c)^2 + B*b^2*sec(d*x + c) - C*a^2 + B*a*b)*(b*sec(d*x + c) + a)^m, x)","F",0
1075,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(9/2), x)","F",0
1076,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(7/2), x)","F",0
1077,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(5/2), x)","F",0
1078,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(3/2), x)","F",0
1079,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c)), x)","F",0
1080,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/sqrt(cos(d*x + c)), x)","F",0
1081,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/cos(d*x + c)^(3/2), x)","F",0
1082,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/cos(d*x + c)^(5/2), x)","F",0
1083,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(9/2), x)","F",0
1084,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
1085,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
1086,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
1087,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1088,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1089,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
1090,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(11/2), x)","F",0
1091,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(9/2), x)","F",0
1092,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2), x)","F",0
1093,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
1094,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
1095,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
1096,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
1097,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
1098,0,0,0,0.000000," ","integrate(cos(d*x+c)^(13/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3*cos(d*x + c)^(13/2), x)","F",0
1099,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3*cos(d*x + c)^(11/2), x)","F",0
1100,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3*cos(d*x + c)^(9/2), x)","F",0
1101,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3*cos(d*x + c)^(7/2), x)","F",0
1102,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2), x)","F",0
1103,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
1104,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
1105,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
1106,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
1107,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(7/2)/(a*sec(d*x + c) + a), x)","F",0
1108,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
1109,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
1110,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
1111,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1112,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
1113,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
1114,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
1115,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
1116,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
1117,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
1118,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
1119,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
1120,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^3, x)","F",0
1121,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^3, x)","F",0
1122,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^3, x)","F",0
1123,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
1124,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
1125,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
1126,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(7/2)), x)","F",0
1127,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(9/2), x)","F",0
1128,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
1129,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
1130,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
1131,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1132,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1133,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
1134,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(a*sec(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
1135,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(11/2), x)","F",0
1136,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(9/2), x)","F",0
1137,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2), x)","F",0
1138,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2), x)","F",0
1139,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
1140,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
1141,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
1142,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
1143,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(3/2)/cos(d*x + c)^(5/2), x)","F",0
1144,0,0,0,0.000000," ","integrate(cos(d*x+c)^(13/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(13/2), x)","F",0
1145,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(11/2), x)","F",0
1146,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(9/2), x)","F",0
1147,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2), x)","F",0
1148,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2), x)","F",0
1149,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2), x)","F",0
1150,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
1151,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
1152,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
1153,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(5/2)/cos(d*x + c)^(5/2), x)","F",0
1154,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(7/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
1155,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
1156,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
1157,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c))/sqrt(a*sec(d*x + c) + a), x)","F",0
1158,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{a \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(sqrt(a*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1159,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
1160,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
1161,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
1162,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
1163,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^(3/2), x)","F",0
1164,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
1165,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
1166,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
1167,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
1168,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
1169,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^(5/2), x)","F",0
1170,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
1171,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
1172,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
1173,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^(9/2), x)","F",0
1174,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^(7/2), x)","F",0
1175,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^(5/2), x)","F",0
1176,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^(3/2), x)","F",0
1177,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1178,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
1179,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
1180,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(7/2), x)","F",0
1181,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2), x)","F",0
1182,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2), x)","F",0
1183,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c)), x)","F",0
1184,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/sqrt(cos(d*x + c)), x)","F",0
1185,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/cos(d*x + c)^(3/2), x)","F",0
1186,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/cos(d*x + c)^(5/2), x)","F",0
1187,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(9/2), x)","F",0
1188,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
1189,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
1190,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
1191,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1192,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1193,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
1194,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(11/2), x)","F",0
1195,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(9/2), x)","F",0
1196,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2), x)","F",0
1197,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
1198,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
1199,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
1200,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
1201,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
1202,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3*cos(d*x + c)^(11/2), x)","F",0
1203,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3*cos(d*x + c)^(9/2), x)","F",0
1204,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3*cos(d*x + c)^(7/2), x)","F",0
1205,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2), x)","F",0
1206,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
1207,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
1208,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
1209,0,0,0,0.000000," ","integrate(cos(d*x+c)^(13/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^4*cos(d*x + c)^(13/2), x)","F",0
1210,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^4*cos(d*x + c)^(11/2), x)","F",0
1211,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^4*cos(d*x + c)^(9/2), x)","F",0
1212,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^4*cos(d*x + c)^(7/2), x)","F",0
1213,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^4*cos(d*x + c)^(5/2), x)","F",0
1214,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^4*cos(d*x + c)^(3/2), x)","F",0
1215,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{4} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^4*sqrt(cos(d*x + c)), x)","F",0
1216,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{4}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^4/sqrt(cos(d*x + c)), x)","F",0
1217,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(7/2)/(a*sec(d*x + c) + a), x)","F",0
1218,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
1219,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
1220,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
1221,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1222,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
1223,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
1224,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(7/2)/(a*sec(d*x + c) + a)^2, x)","F",0
1225,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
1226,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
1227,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
1228,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
1229,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
1230,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
1231,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2)), x)","F",0
1232,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^3, x)","F",0
1233,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^3, x)","F",0
1234,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^3, x)","F",0
1235,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
1236,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
1237,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
1238,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(7/2)), x)","F",0
1239,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^4, x)","F",0
1240,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^4, x)","F",0
1241,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{4} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^4*sqrt(cos(d*x + c))), x)","F",0
1242,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^4*cos(d*x + c)^(3/2)), x)","F",0
1243,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^4*cos(d*x + c)^(5/2)), x)","F",0
1244,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^4*cos(d*x + c)^(7/2)), x)","F",0
1245,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(9/2), x)","F",0
1246,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
1247,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
1248,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
1249,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1250,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1251,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
1252,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
1253,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(11/2), x)","F",0
1254,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(9/2), x)","F",0
1255,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2), x)","F",0
1256,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2), x)","F",0
1257,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
1258,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
1259,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
1260,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
1261,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/cos(d*x + c)^(5/2), x)","F",0
1262,0,0,0,0.000000," ","integrate(cos(d*x+c)^(13/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(13/2), x)","F",0
1263,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(11/2), x)","F",0
1264,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(9/2), x)","F",0
1265,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2), x)","F",0
1266,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2), x)","F",0
1267,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2), x)","F",0
1268,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
1269,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
1270,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
1271,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/cos(d*x + c)^(5/2), x)","F",0
1272,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(7/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
1273,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
1274,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
1275,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(a*sec(d*x + c) + a), x)","F",0
1276,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1277,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
1278,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
1279,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*sec(d*x+c)+b*B*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B b \sec\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sqrt(cos(d*x + c))/sqrt(a*sec(d*x + c) + a), x)","F",0
1280,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
1281,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
1282,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^(3/2), x)","F",0
1283,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
1284,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
1285,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
1286,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
1287,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
1288,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^(5/2), x)","F",0
1289,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
1290,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
1291,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
1292,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*cos(d*x + c)^(9/2), x)","F",0
1293,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
1294,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
1295,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
1296,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1297,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1298,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
1299,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*cos(d*x + c)^(9/2), x)","F",0
1300,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2), x)","F",0
1301,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
1302,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
1303,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
1304,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
1305,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3*cos(d*x + c)^(11/2), x)","F",0
1306,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3*cos(d*x + c)^(9/2), x)","F",0
1307,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3*cos(d*x + c)^(7/2), x)","F",0
1308,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2), x)","F",0
1309,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
1310,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
1311,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
1312,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4*cos(d*x + c)^(11/2), x)","F",0
1313,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4*cos(d*x + c)^(9/2), x)","F",0
1314,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4*cos(d*x + c)^(7/2), x)","F",0
1315,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4*cos(d*x + c)^(5/2), x)","F",0
1316,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4*cos(d*x + c)^(3/2), x)","F",0
1317,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4*sqrt(cos(d*x + c)), x)","F",0
1318,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*sec(d*x + c) + a), x)","F",0
1319,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a), x)","F",0
1320,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
1321,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1322,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
1323,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
1324,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^2, x)","F",0
1325,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^2, x)","F",0
1326,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
1327,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
1328,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
1329,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^3, x)","F",0
1330,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^3, x)","F",0
1331,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
1332,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
1333,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
1334,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(9/2), x)","F",0
1335,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
1336,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
1337,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
1338,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1339,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1340,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
1341,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(9/2), x)","F",0
1342,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2), x)","F",0
1343,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2), x)","F",0
1344,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
1345,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
1346,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
1347,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
1348,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(11/2), x)","F",0
1349,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(9/2), x)","F",0
1350,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2), x)","F",0
1351,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2), x)","F",0
1352,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2), x)","F",0
1353,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
1354,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
1355,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
1356,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(7/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
1357,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
1358,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
1359,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
1360,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1361,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
1362,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*sec(d*x+c)+b*B*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B b \sec\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sqrt(cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
1363,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
1364,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
1365,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^(3/2), x)","F",0
1366,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
1367,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
1368,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
1369,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
1370,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^(5/2), x)","F",0
1371,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
1372,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
1373,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
