1,0,0,0,0.954324," ","integrate((b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \sec\left(d x + c\right)^{3} + A b^{2} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*b^2*sec(d*x + c)^2)*sqrt(b*sec(d*x + c)), x)","F",0
2,0,0,0,0.527676," ","integrate((b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \sec\left(d x + c\right)^{2} + A b \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*b*sec(d*x + c))*sqrt(b*sec(d*x + c)), x)","F",0
3,0,0,0,0.433149," ","integrate((b*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c)), x)","F",0
4,0,0,0,0.459659," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right)}}{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c))/(b*sec(d*x + c)), x)","F",0
5,0,0,0,0.440007," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c))/(b^2*sec(d*x + c)^2), x)","F",0
6,0,0,0,0.445042," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right)}}{b^{3} \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c))/(b^3*sec(d*x + c)^3), x)","F",0
7,0,0,0,0.442545," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)^{2}\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((B*sec(d*x + c)^3 + A*sec(d*x + c)^2)*(b*sec(d*x + c))^(2/3), x)","F",0
8,0,0,0,0.454491," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(d x + c\right)^{2} + A \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((B*sec(d*x + c)^2 + A*sec(d*x + c))*(b*sec(d*x + c))^(2/3), x)","F",0
9,0,0,0,0.441264," ","integrate((b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3), x)","F",0
10,0,0,0,0.466323," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*(b*sec(d*x + c))^(2/3), x)","F",0
11,0,0,0,0.464139," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{2}\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2*sec(d*x + c) + A*cos(d*x + c)^2)*(b*sec(d*x + c))^(2/3), x)","F",0
12,0,0,0,0.453830," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \sec\left(d x + c\right)^{4} + A b \sec\left(d x + c\right)^{3}\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^4 + A*b*sec(d*x + c)^3)*(b*sec(d*x + c))^(1/3), x)","F",0
13,0,0,0,0.441662," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \sec\left(d x + c\right)^{3} + A b \sec\left(d x + c\right)^{2}\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^3 + A*b*sec(d*x + c)^2)*(b*sec(d*x + c))^(1/3), x)","F",0
14,0,0,0,0.464667," ","integrate((b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \sec\left(d x + c\right)^{2} + A b \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*b*sec(d*x + c))*(b*sec(d*x + c))^(1/3), x)","F",0
15,0,0,0,0.443048," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)*sec(d*x + c)^2 + A*b*cos(d*x + c)*sec(d*x + c))*(b*sec(d*x + c))^(1/3), x)","F",0
16,0,0,0,0.464936," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2*sec(d*x + c)^2 + A*b*cos(d*x + c)^2*sec(d*x + c))*(b*sec(d*x + c))^(1/3), x)","F",0
17,0,0,0,0.457351," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{2} + A \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}{b}, x\right)"," ",0,"integral((B*sec(d*x + c)^2 + A*sec(d*x + c))*(b*sec(d*x + c))^(1/3)/b, x)","F",0
18,0,0,0,0.487352," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}{b}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(1/3)/b, x)","F",0
19,0,0,0,0.453636," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(1/3)/(b*sec(d*x + c)), x)","F",0
20,0,0,0,0.449249," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}{b}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(1/3)/b, x)","F",0
21,0,0,0,0.454638," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{2} + A \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}{b}, x\right)"," ",0,"integral((B*sec(d*x + c)^2 + A*sec(d*x + c))*(b*sec(d*x + c))^(1/3)/b, x)","F",0
22,0,0,0,0.437572," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)/b^2, x)","F",0
23,0,0,0,0.493310," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2} \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)/(b^2*sec(d*x + c)), x)","F",0
24,0,0,0,0.468597," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)/(b^2*sec(d*x + c)^2), x)","F",0
25,0,0,0,0.491231," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2} \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)/(b^2*sec(d*x + c)), x)","F",0
26,0,0,0,0.432851," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)/b^2, x)","F",0
27,0,0,0,0.459954," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \sec\left(d x + c\right)^{2} + A b \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*b*sec(d*x + c))*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^m, x)","F",0
28,0,0,0,0.441127," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(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}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^m, x)","F",0
29,0,0,0,0.432727," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(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}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^m, x)","F",0
30,0,0,0,0.458835," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^m/(b*sec(d*x + c)), x)","F",0
31,0,0,0,0.475280," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^m/(b*sec(d*x + c)), x)","F",0
32,0,0,0,0.489464," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}{b^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^m/(b^2*sec(d*x + c)^2), x)","F",0
33,0,0,0,0.432412," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(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}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^m, x)","F",0
34,0,0,0,0.422496," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)^{2}\right)} \left(b \sec\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((B*sec(d*x + c)^3 + A*sec(d*x + c)^2)*(b*sec(d*x + c))^n, x)","F",0
35,0,0,0,0.434882," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(d x + c\right)^{2} + A \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((B*sec(d*x + c)^2 + A*sec(d*x + c))*(b*sec(d*x + c))^n, x)","F",0
36,0,0,0,0.425797," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n, x)","F",0
37,0,0,0,0.413186," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*(b*sec(d*x + c))^n, x)","F",0
38,0,0,0,0.418167," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{2}\right)} \left(b \sec\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((B*cos(d*x + c)^2*sec(d*x + c) + A*cos(d*x + c)^2)*(b*sec(d*x + c))^n, x)","F",0
39,0,0,0,0.428549," ","integrate(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(d x + c\right)^{2} + A \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c)^2 + A*sec(d*x + c))*(b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
40,0,0,0,0.449065," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(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)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
41,0,0,0,0.456660," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sqrt(sec(d*x + c)), x)","F",0
42,0,0,0,0.453971," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(3/2), x)","F",0
43,1,137,0,0.442010," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{45 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 45 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(5 \, A + 4 \, B\right)} a \cos\left(d x + c\right)^{4} + 45 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 4 \, B\right)} a \cos\left(d x + c\right)^{2} + 30 \, {\left(A + B\right)} a \cos\left(d x + c\right) + 24 \, B a\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(45*(A + B)*a*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 45*(A + B)*a*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(5*A + 4*B)*a*cos(d*x + c)^4 + 45*(A + B)*a*cos(d*x + c)^3 + 8*(5*A + 4*B)*a*cos(d*x + c)^2 + 30*(A + B)*a*cos(d*x + c) + 24*B*a)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
44,1,127,0,0.458677," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, A + 3 \, B\right)} a \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, A + 3 \, B\right)} a \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A + 3 \, B\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(A + B\right)} a \cos\left(d x + c\right) + 6 \, B a\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(4*A + 3*B)*a*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*A + 3*B)*a*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*(A + B)*a*cos(d*x + c)^3 + 3*(4*A + 3*B)*a*cos(d*x + c)^2 + 8*(A + B)*a*cos(d*x + c) + 6*B*a)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
45,1,105,0,0.432257," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(3 \, A + 2 \, B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(A + B\right)} a \cos\left(d x + c\right) + 2 \, B a\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(A + B)*a*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(A + B)*a*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(3*A + 2*B)*a*cos(d*x + c)^2 + 3*(A + B)*a*cos(d*x + c) + 2*B*a)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
46,1,89,0,0.424517," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, A + B\right)} a \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, A + B\right)} a \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(A + B\right)} a \cos\left(d x + c\right) + B a\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((2*A + B)*a*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*A + B)*a*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*(A + B)*a*cos(d*x + c) + B*a)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
47,1,79,0,0.436269," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, A a d x \cos\left(d x + c\right) + {\left(A + B\right)} a \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A + B\right)} a \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, B a \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*A*a*d*x*cos(d*x + c) + (A + B)*a*cos(d*x + c)*log(sin(d*x + c) + 1) - (A + B)*a*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*B*a*sin(d*x + c))/(d*cos(d*x + c))","B",0
48,1,51,0,0.441837," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(A + B\right)} a d x + B a \log\left(\sin\left(d x + c\right) + 1\right) - B a \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, A a \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(A + B)*a*d*x + B*a*log(sin(d*x + c) + 1) - B*a*log(-sin(d*x + c) + 1) + 2*A*a*sin(d*x + c))/d","A",0
49,1,38,0,0.416946," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(A + 2 \, B\right)} a d x + {\left(A a \cos\left(d x + c\right) + 2 \, {\left(A + B\right)} a\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((A + 2*B)*a*d*x + (A*a*cos(d*x + c) + 2*(A + B)*a)*sin(d*x + c))/d","A",0
50,1,56,0,0.452103," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(A + B\right)} a d x + {\left(2 \, A a \cos\left(d x + c\right)^{2} + 3 \, {\left(A + B\right)} a \cos\left(d x + c\right) + 2 \, {\left(2 \, A + 3 \, B\right)} a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(A + B)*a*d*x + (2*A*a*cos(d*x + c)^2 + 3*(A + B)*a*cos(d*x + c) + 2*(2*A + 3*B)*a)*sin(d*x + c))/d","A",0
51,1,74,0,0.502159," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A + 4 \, B\right)} a d x + {\left(6 \, A a \cos\left(d x + c\right)^{3} + 8 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 4 \, B\right)} a \cos\left(d x + c\right) + 16 \, {\left(A + B\right)} a\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(3*A + 4*B)*a*d*x + (6*A*a*cos(d*x + c)^3 + 8*(A + B)*a*cos(d*x + c)^2 + 3*(3*A + 4*B)*a*cos(d*x + c) + 16*(A + B)*a)*sin(d*x + c))/d","A",0
52,1,88,0,0.426870," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{45 \, {\left(A + B\right)} a d x + {\left(24 \, A a \cos\left(d x + c\right)^{4} + 30 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(4 \, A + 5 \, B\right)} a \cos\left(d x + c\right)^{2} + 45 \, {\left(A + B\right)} a \cos\left(d x + c\right) + 16 \, {\left(4 \, A + 5 \, B\right)} a\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(45*(A + B)*a*d*x + (24*A*a*cos(d*x + c)^4 + 30*(A + B)*a*cos(d*x + c)^3 + 8*(4*A + 5*B)*a*cos(d*x + c)^2 + 45*(A + B)*a*cos(d*x + c) + 16*(4*A + 5*B)*a)*sin(d*x + c))/d","A",0
53,1,165,0,0.470869," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(7 \, A + 6 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(7 \, A + 6 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(10 \, A + 9 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 15 \, {\left(7 \, A + 6 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(10 \, A + 9 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 30 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right) + 24 \, B a^{2}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(7*A + 6*B)*a^2*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(7*A + 6*B)*a^2*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(10*A + 9*B)*a^2*cos(d*x + c)^4 + 15*(7*A + 6*B)*a^2*cos(d*x + c)^3 + 8*(10*A + 9*B)*a^2*cos(d*x + c)^2 + 30*(A + 2*B)*a^2*cos(d*x + c) + 24*B*a^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
54,1,145,0,0.455945," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, A + 7 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, A + 7 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(5 \, A + 4 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, A + 7 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right) + 6 \, B a^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(8*A + 7*B)*a^2*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(8*A + 7*B)*a^2*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(5*A + 4*B)*a^2*cos(d*x + c)^3 + 3*(8*A + 7*B)*a^2*cos(d*x + c)^2 + 8*(A + 2*B)*a^2*cos(d*x + c) + 6*B*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
55,1,125,0,0.580346," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(6 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right) + 2 \, B a^{2}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(3*A + 2*B)*a^2*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(3*A + 2*B)*a^2*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(6*A + 5*B)*a^2*cos(d*x + c)^2 + 3*(A + 2*B)*a^2*cos(d*x + c) + 2*B*a^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
56,1,119,0,0.467437," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, A a^{2} d x \cos\left(d x + c\right)^{2} + {\left(4 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(4 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right) + B a^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*A*a^2*d*x*cos(d*x + c)^2 + (4*A + 3*B)*a^2*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (4*A + 3*B)*a^2*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*(A + 2*B)*a^2*cos(d*x + c) + B*a^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
57,1,108,0,0.480214," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, A + B\right)} a^{2} d x \cos\left(d x + c\right) + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{2} \cos\left(d x + c\right) + B a^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*(2*A + B)*a^2*d*x*cos(d*x + c) + (A + 2*B)*a^2*cos(d*x + c)*log(sin(d*x + c) + 1) - (A + 2*B)*a^2*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(A*a^2*cos(d*x + c) + B*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
58,1,79,0,0.463968," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 \, A + 4 \, B\right)} a^{2} d x + B a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - B a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(A a^{2} \cos\left(d x + c\right) + 2 \, {\left(2 \, A + B\right)} a^{2}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((3*A + 4*B)*a^2*d*x + B*a^2*log(sin(d*x + c) + 1) - B*a^2*log(-sin(d*x + c) + 1) + (A*a^2*cos(d*x + c) + 2*(2*A + B)*a^2)*sin(d*x + c))/d","A",0
59,1,70,0,0.435343," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A + 3 \, B\right)} a^{2} d x + {\left(2 \, A a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(5 \, A + 6 \, B\right)} a^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(2*A + 3*B)*a^2*d*x + (2*A*a^2*cos(d*x + c)^2 + 3*(2*A + B)*a^2*cos(d*x + c) + 2*(5*A + 6*B)*a^2)*sin(d*x + c))/d","A",0
60,1,90,0,0.461875," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, A + 8 \, B\right)} a^{2} d x + {\left(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, A + 8 \, B\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(4 \, A + 5 \, B\right)} a^{2}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(7*A + 8*B)*a^2*d*x + (6*A*a^2*cos(d*x + c)^3 + 8*(2*A + B)*a^2*cos(d*x + c)^2 + 3*(7*A + 8*B)*a^2*cos(d*x + c) + 8*(4*A + 5*B)*a^2)*sin(d*x + c))/d","A",0
61,1,110,0,0.448501," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(6 \, A + 7 \, B\right)} a^{2} d x + {\left(24 \, A a^{2} \cos\left(d x + c\right)^{4} + 30 \, {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(9 \, A + 10 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(6 \, A + 7 \, B\right)} a^{2} \cos\left(d x + c\right) + 16 \, {\left(9 \, A + 10 \, B\right)} a^{2}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(6*A + 7*B)*a^2*d*x + (24*A*a^2*cos(d*x + c)^4 + 30*(2*A + B)*a^2*cos(d*x + c)^3 + 8*(9*A + 10*B)*a^2*cos(d*x + c)^2 + 15*(6*A + 7*B)*a^2*cos(d*x + c) + 16*(9*A + 10*B)*a^2)*sin(d*x + c))/d","A",0
62,1,185,0,0.450025," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(26 \, A + 23 \, B\right)} a^{3} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(26 \, A + 23 \, B\right)} a^{3} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(32 \, {\left(19 \, A + 17 \, B\right)} a^{3} \cos\left(d x + c\right)^{5} + 15 \, {\left(26 \, A + 23 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} + 16 \, {\left(19 \, A + 17 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 10 \, {\left(18 \, A + 23 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 48 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right) + 40 \, B a^{3}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(26*A + 23*B)*a^3*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(26*A + 23*B)*a^3*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(32*(19*A + 17*B)*a^3*cos(d*x + c)^5 + 15*(26*A + 23*B)*a^3*cos(d*x + c)^4 + 16*(19*A + 17*B)*a^3*cos(d*x + c)^3 + 10*(18*A + 23*B)*a^3*cos(d*x + c)^2 + 48*(A + 3*B)*a^3*cos(d*x + c) + 40*B*a^3)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
63,1,165,0,0.472180," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(15 \, A + 13 \, B\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(15 \, A + 13 \, B\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(45 \, A + 38 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} + 15 \, {\left(15 \, A + 13 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(15 \, A + 19 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 30 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right) + 24 \, B a^{3}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(15*A + 13*B)*a^3*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(15*A + 13*B)*a^3*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(45*A + 38*B)*a^3*cos(d*x + c)^4 + 15*(15*A + 13*B)*a^3*cos(d*x + c)^3 + 8*(15*A + 19*B)*a^3*cos(d*x + c)^2 + 30*(A + 3*B)*a^3*cos(d*x + c) + 24*B*a^3)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
64,1,145,0,0.459781," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(11 \, A + 9 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 9 \, {\left(4 \, A + 5 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 8 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right) + 6 \, B a^{3}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(15*(4*A + 3*B)*a^3*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 15*(4*A + 3*B)*a^3*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(11*A + 9*B)*a^3*cos(d*x + c)^3 + 9*(4*A + 5*B)*a^3*cos(d*x + c)^2 + 8*(A + 3*B)*a^3*cos(d*x + c) + 6*B*a^3)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
65,1,141,0,0.466711," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{12 \, A a^{3} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, A + 5 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(7 \, A + 5 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(9 \, A + 11 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right) + 2 \, B a^{3}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(12*A*a^3*d*x*cos(d*x + c)^3 + 3*(7*A + 5*B)*a^3*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(7*A + 5*B)*a^3*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(9*A + 11*B)*a^3*cos(d*x + c)^2 + 3*(A + 3*B)*a^3*cos(d*x + c) + 2*B*a^3)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
66,1,137,0,0.466437," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, A + B\right)} a^{3} d x \cos\left(d x + c\right)^{2} + {\left(6 \, A + 7 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(6 \, A + 7 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right) + B a^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*(3*A + B)*a^3*d*x*cos(d*x + c)^2 + (6*A + 7*B)*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (6*A + 7*B)*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*A*a^3*cos(d*x + c)^2 + 2*(A + 3*B)*a^3*cos(d*x + c) + B*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
67,1,127,0,0.479327," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(7 \, A + 6 \, B\right)} a^{3} d x \cos\left(d x + c\right) + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(A a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + 2 \, B a^{3}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*((7*A + 6*B)*a^3*d*x*cos(d*x + c) + (A + 3*B)*a^3*cos(d*x + c)*log(sin(d*x + c) + 1) - (A + 3*B)*a^3*cos(d*x + c)*log(-sin(d*x + c) + 1) + (A*a^3*cos(d*x + c)^2 + 2*(3*A + B)*a^3*cos(d*x + c) + 2*B*a^3)*sin(d*x + c))/(d*cos(d*x + c))","A",0
68,1,102,0,0.489979," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(5 \, A + 7 \, B\right)} a^{3} d x + 3 \, B a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, B a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, A a^{3} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + 2 \, {\left(11 \, A + 9 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(5*A + 7*B)*a^3*d*x + 3*B*a^3*log(sin(d*x + c) + 1) - 3*B*a^3*log(-sin(d*x + c) + 1) + (2*A*a^3*cos(d*x + c)^2 + 3*(3*A + B)*a^3*cos(d*x + c) + 2*(11*A + 9*B)*a^3)*sin(d*x + c))/d","A",0
69,1,90,0,0.453034," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, A + 4 \, B\right)} a^{3} d x + {\left(6 \, A a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + 9 \, {\left(5 \, A + 4 \, B\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(9 \, A + 11 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(15*(3*A + 4*B)*a^3*d*x + (6*A*a^3*cos(d*x + c)^3 + 8*(3*A + B)*a^3*cos(d*x + c)^2 + 9*(5*A + 4*B)*a^3*cos(d*x + c) + 8*(9*A + 11*B)*a^3)*sin(d*x + c))/d","A",0
70,1,110,0,0.449774," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(13 \, A + 15 \, B\right)} a^{3} d x + {\left(24 \, A a^{3} \cos\left(d x + c\right)^{4} + 30 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(19 \, A + 15 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(13 \, A + 15 \, B\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(38 \, A + 45 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(13*A + 15*B)*a^3*d*x + (24*A*a^3*cos(d*x + c)^4 + 30*(3*A + B)*a^3*cos(d*x + c)^3 + 8*(19*A + 15*B)*a^3*cos(d*x + c)^2 + 15*(13*A + 15*B)*a^3*cos(d*x + c) + 8*(38*A + 45*B)*a^3)*sin(d*x + c))/d","A",0
71,1,130,0,0.437241," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(23 \, A + 26 \, B\right)} a^{3} d x + {\left(40 \, A a^{3} \cos\left(d x + c\right)^{5} + 48 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right)^{4} + 10 \, {\left(23 \, A + 18 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 16 \, {\left(17 \, A + 19 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(23 \, A + 26 \, B\right)} a^{3} \cos\left(d x + c\right) + 32 \, {\left(17 \, A + 19 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(23*A + 26*B)*a^3*d*x + (40*A*a^3*cos(d*x + c)^5 + 48*(3*A + B)*a^3*cos(d*x + c)^4 + 10*(23*A + 18*B)*a^3*cos(d*x + c)^3 + 16*(17*A + 19*B)*a^3*cos(d*x + c)^2 + 15*(23*A + 26*B)*a^3*cos(d*x + c) + 32*(17*A + 19*B)*a^3)*sin(d*x + c))/d","A",0
72,1,185,0,0.436202," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, {\left(8 \, A + 7 \, B\right)} a^{4} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(8 \, A + 7 \, B\right)} a^{4} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(83 \, A + 72 \, B\right)} a^{4} \cos\left(d x + c\right)^{5} + 105 \, {\left(8 \, A + 7 \, B\right)} a^{4} \cos\left(d x + c\right)^{4} + 32 \, {\left(17 \, A + 18 \, B\right)} a^{4} \cos\left(d x + c\right)^{3} + 10 \, {\left(24 \, A + 41 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 48 \, {\left(A + 4 \, B\right)} a^{4} \cos\left(d x + c\right) + 40 \, B a^{4}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(105*(8*A + 7*B)*a^4*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 105*(8*A + 7*B)*a^4*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(83*A + 72*B)*a^4*cos(d*x + c)^5 + 105*(8*A + 7*B)*a^4*cos(d*x + c)^4 + 32*(17*A + 18*B)*a^4*cos(d*x + c)^3 + 10*(24*A + 41*B)*a^4*cos(d*x + c)^2 + 48*(A + 4*B)*a^4*cos(d*x + c) + 40*B*a^4)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
73,1,165,0,0.460181," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, {\left(5 \, A + 4 \, B\right)} a^{4} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(5 \, A + 4 \, B\right)} a^{4} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(100 \, A + 83 \, B\right)} a^{4} \cos\left(d x + c\right)^{4} + 15 \, {\left(27 \, A + 28 \, B\right)} a^{4} \cos\left(d x + c\right)^{3} + 16 \, {\left(10 \, A + 17 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 30 \, {\left(A + 4 \, B\right)} a^{4} \cos\left(d x + c\right) + 24 \, B a^{4}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(105*(5*A + 4*B)*a^4*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 105*(5*A + 4*B)*a^4*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(100*A + 83*B)*a^4*cos(d*x + c)^4 + 15*(27*A + 28*B)*a^4*cos(d*x + c)^3 + 16*(10*A + 17*B)*a^4*cos(d*x + c)^2 + 30*(A + 4*B)*a^4*cos(d*x + c) + 24*B*a^4)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
74,1,157,0,0.448120," ","integrate((a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{48 \, A a^{4} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(48 \, A + 35 \, B\right)} a^{4} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(48 \, A + 35 \, B\right)} a^{4} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(160 \, {\left(A + B\right)} a^{4} \cos\left(d x + c\right)^{3} + 3 \, {\left(16 \, A + 27 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 8 \, {\left(A + 4 \, B\right)} a^{4} \cos\left(d x + c\right) + 6 \, B a^{4}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(48*A*a^4*d*x*cos(d*x + c)^4 + 3*(48*A + 35*B)*a^4*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(48*A + 35*B)*a^4*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(160*(A + B)*a^4*cos(d*x + c)^3 + 3*(16*A + 27*B)*a^4*cos(d*x + c)^2 + 8*(A + 4*B)*a^4*cos(d*x + c) + 6*B*a^4)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
75,1,159,0,0.460426," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{12 \, {\left(4 \, A + B\right)} a^{4} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(13 \, A + 12 \, B\right)} a^{4} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(13 \, A + 12 \, B\right)} a^{4} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, A a^{4} \cos\left(d x + c\right)^{3} + 8 \, {\left(3 \, A + 5 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 3 \, {\left(A + 4 \, B\right)} a^{4} \cos\left(d x + c\right) + 2 \, B a^{4}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(12*(4*A + B)*a^4*d*x*cos(d*x + c)^3 + 3*(13*A + 12*B)*a^4*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(13*A + 12*B)*a^4*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(6*A*a^4*cos(d*x + c)^3 + 8*(3*A + 5*B)*a^4*cos(d*x + c)^2 + 3*(A + 4*B)*a^4*cos(d*x + c) + 2*B*a^4)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
76,1,156,0,0.447613," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(13 \, A + 8 \, B\right)} a^{4} d x \cos\left(d x + c\right)^{2} + {\left(8 \, A + 13 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(8 \, A + 13 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 4 \, B\right)} a^{4} \cos\left(d x + c\right) + B a^{4}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(2*(13*A + 8*B)*a^4*d*x*cos(d*x + c)^2 + (8*A + 13*B)*a^4*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (8*A + 13*B)*a^4*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(A*a^4*cos(d*x + c)^3 + 2*(4*A + B)*a^4*cos(d*x + c)^2 + 2*(A + 4*B)*a^4*cos(d*x + c) + B*a^4)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
77,1,150,0,0.437146," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(12 \, A + 13 \, B\right)} a^{4} d x \cos\left(d x + c\right) + 3 \, {\left(A + 4 \, B\right)} a^{4} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(A + 4 \, B\right)} a^{4} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, A a^{4} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{2} + 8 \, {\left(5 \, A + 3 \, B\right)} a^{4} \cos\left(d x + c\right) + 6 \, B a^{4}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}"," ",0,"1/6*(3*(12*A + 13*B)*a^4*d*x*cos(d*x + c) + 3*(A + 4*B)*a^4*cos(d*x + c)*log(sin(d*x + c) + 1) - 3*(A + 4*B)*a^4*cos(d*x + c)*log(-sin(d*x + c) + 1) + (2*A*a^4*cos(d*x + c)^3 + 3*(4*A + B)*a^4*cos(d*x + c)^2 + 8*(5*A + 3*B)*a^4*cos(d*x + c) + 6*B*a^4)*sin(d*x + c))/(d*cos(d*x + c))","A",0
78,1,118,0,0.447222," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(35 \, A + 48 \, B\right)} a^{4} d x + 12 \, B a^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, B a^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, A a^{4} \cos\left(d x + c\right)^{3} + 8 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{2} + 3 \, {\left(27 \, A + 16 \, B\right)} a^{4} \cos\left(d x + c\right) + 160 \, {\left(A + B\right)} a^{4}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(35*A + 48*B)*a^4*d*x + 12*B*a^4*log(sin(d*x + c) + 1) - 12*B*a^4*log(-sin(d*x + c) + 1) + (6*A*a^4*cos(d*x + c)^3 + 8*(4*A + B)*a^4*cos(d*x + c)^2 + 3*(27*A + 16*B)*a^4*cos(d*x + c) + 160*(A + B)*a^4)*sin(d*x + c))/d","A",0
79,1,110,0,0.489840," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, {\left(4 \, A + 5 \, B\right)} a^{4} d x + {\left(24 \, A a^{4} \cos\left(d x + c\right)^{4} + 30 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{3} + 16 \, {\left(17 \, A + 10 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 15 \, {\left(28 \, A + 27 \, B\right)} a^{4} \cos\left(d x + c\right) + 8 \, {\left(83 \, A + 100 \, B\right)} a^{4}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(105*(4*A + 5*B)*a^4*d*x + (24*A*a^4*cos(d*x + c)^4 + 30*(4*A + B)*a^4*cos(d*x + c)^3 + 16*(17*A + 10*B)*a^4*cos(d*x + c)^2 + 15*(28*A + 27*B)*a^4*cos(d*x + c) + 8*(83*A + 100*B)*a^4)*sin(d*x + c))/d","A",0
80,1,130,0,0.449734," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, {\left(7 \, A + 8 \, B\right)} a^{4} d x + {\left(40 \, A a^{4} \cos\left(d x + c\right)^{5} + 48 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{4} + 10 \, {\left(41 \, A + 24 \, B\right)} a^{4} \cos\left(d x + c\right)^{3} + 32 \, {\left(18 \, A + 17 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 105 \, {\left(7 \, A + 8 \, B\right)} a^{4} \cos\left(d x + c\right) + 16 \, {\left(72 \, A + 83 \, B\right)} a^{4}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(105*(7*A + 8*B)*a^4*d*x + (40*A*a^4*cos(d*x + c)^5 + 48*(4*A + B)*a^4*cos(d*x + c)^4 + 10*(41*A + 24*B)*a^4*cos(d*x + c)^3 + 32*(18*A + 17*B)*a^4*cos(d*x + c)^2 + 105*(7*A + 8*B)*a^4*cos(d*x + c) + 16*(72*A + 83*B)*a^4)*sin(d*x + c))/d","A",0
81,1,150,0,0.439886," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, {\left(44 \, A + 49 \, B\right)} a^{4} d x + {\left(240 \, A a^{4} \cos\left(d x + c\right)^{6} + 280 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{5} + 192 \, {\left(12 \, A + 7 \, B\right)} a^{4} \cos\left(d x + c\right)^{4} + 70 \, {\left(44 \, A + 41 \, B\right)} a^{4} \cos\left(d x + c\right)^{3} + 16 \, {\left(227 \, A + 252 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 105 \, {\left(44 \, A + 49 \, B\right)} a^{4} \cos\left(d x + c\right) + 32 \, {\left(227 \, A + 252 \, B\right)} a^{4}\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(105*(44*A + 49*B)*a^4*d*x + (240*A*a^4*cos(d*x + c)^6 + 280*(4*A + B)*a^4*cos(d*x + c)^5 + 192*(12*A + 7*B)*a^4*cos(d*x + c)^4 + 70*(44*A + 41*B)*a^4*cos(d*x + c)^3 + 16*(227*A + 252*B)*a^4*cos(d*x + c)^2 + 105*(44*A + 49*B)*a^4*cos(d*x + c) + 32*(227*A + 252*B)*a^4)*sin(d*x + c))/d","A",0
82,1,170,0,0.449734," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, {\left({\left(A - B\right)} \cos\left(d x + c\right)^{4} + {\left(A - B\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, {\left({\left(A - B\right)} \cos\left(d x + c\right)^{4} + {\left(A - B\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(3 \, A - 4 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, A - B\right)} \cos\left(d x + c\right) - 2 \, B\right)} \sin\left(d x + c\right)}{12 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/12*(9*((A - B)*cos(d*x + c)^4 + (A - B)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 9*((A - B)*cos(d*x + c)^4 + (A - B)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(4*(3*A - 4*B)*cos(d*x + c)^3 + (3*A - 7*B)*cos(d*x + c)^2 - (3*A - B)*cos(d*x + c) - 2*B)*sin(d*x + c))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)","A",0
83,1,156,0,0.475825," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left({\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(A - B\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, A - B\right)} \cos\left(d x + c\right) + B\right)} \sin\left(d x + c\right)}{4 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/4*(((2*A - 3*B)*cos(d*x + c)^3 + (2*A - 3*B)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((2*A - 3*B)*cos(d*x + c)^3 + (2*A - 3*B)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(A - B)*cos(d*x + c)^2 + (2*A - B)*cos(d*x + c) + B)*sin(d*x + c))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)","A",0
84,1,127,0,0.434714," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(A - B\right)} \cos\left(d x + c\right)^{2} + {\left(A - B\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A - B\right)} \cos\left(d x + c\right)^{2} + {\left(A - B\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(A - 2 \, B\right)} \cos\left(d x + c\right) - B\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}"," ",0,"1/2*(((A - B)*cos(d*x + c)^2 + (A - B)*cos(d*x + c))*log(sin(d*x + c) + 1) - ((A - B)*cos(d*x + c)^2 + (A - B)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*((A - 2*B)*cos(d*x + c) - B)*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","B",0
85,1,74,0,0.427708," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(B \cos\left(d x + c\right) + B\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B \cos\left(d x + c\right) + B\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A - B\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*((B*cos(d*x + c) + B)*log(sin(d*x + c) + 1) - (B*cos(d*x + c) + B)*log(-sin(d*x + c) + 1) + 2*(A - B)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
86,1,44,0,0.412753," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{A d x \cos\left(d x + c\right) + A d x - {\left(A - B\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"(A*d*x*cos(d*x + c) + A*d*x - (A - B)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
87,1,63,0,0.435165," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(A - B\right)} d x \cos\left(d x + c\right) + {\left(A - B\right)} d x - {\left(A \cos\left(d x + c\right) + 2 \, A - B\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"-((A - B)*d*x*cos(d*x + c) + (A - B)*d*x - (A*cos(d*x + c) + 2*A - B)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
88,1,81,0,0.445353," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 \, A - 2 \, B\right)} d x \cos\left(d x + c\right) + {\left(3 \, A - 2 \, B\right)} d x + {\left(A \cos\left(d x + c\right)^{2} - {\left(A - 2 \, B\right)} \cos\left(d x + c\right) - 4 \, A + 4 \, B\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*((3*A - 2*B)*d*x*cos(d*x + c) + (3*A - 2*B)*d*x + (A*cos(d*x + c)^2 - (A - 2*B)*cos(d*x + c) - 4*A + 4*B)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
89,1,97,0,0.445271," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{9 \, {\left(A - B\right)} d x \cos\left(d x + c\right) + 9 \, {\left(A - B\right)} d x - {\left(2 \, A \cos\left(d x + c\right)^{3} - {\left(A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 16 \, A - 12 \, B\right)} \sin\left(d x + c\right)}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"-1/6*(9*(A - B)*d*x*cos(d*x + c) + 9*(A - B)*d*x - (2*A*cos(d*x + c)^3 - (A - 3*B)*cos(d*x + c)^2 + (7*A - 3*B)*cos(d*x + c) + 16*A - 12*B)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
90,1,245,0,0.449244," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(7 \, A - 10 \, B\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(7 \, A - 10 \, B\right)} \cos\left(d x + c\right)^{4} + {\left(7 \, A - 10 \, B\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(7 \, A - 10 \, B\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(7 \, A - 10 \, B\right)} \cos\left(d x + c\right)^{4} + {\left(7 \, A - 10 \, B\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{4} + {\left(43 \, A - 66 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(A - 2 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right) - 2 \, B\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} + 2 \, a^{2} d \cos\left(d x + c\right)^{4} + a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/12*(3*((7*A - 10*B)*cos(d*x + c)^5 + 2*(7*A - 10*B)*cos(d*x + c)^4 + (7*A - 10*B)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((7*A - 10*B)*cos(d*x + c)^5 + 2*(7*A - 10*B)*cos(d*x + c)^4 + (7*A - 10*B)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(16*(2*A - 3*B)*cos(d*x + c)^4 + (43*A - 66*B)*cos(d*x + c)^3 + 6*(A - 2*B)*cos(d*x + c)^2 - (3*A - 2*B)*cos(d*x + c) - 2*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^5 + 2*a^2*d*cos(d*x + c)^4 + a^2*d*cos(d*x + c)^3)","A",0
91,1,228,0,0.450183," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(5 \, A - 8 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(28 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(A - B\right)} \cos\left(d x + c\right) + 3 \, B\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/12*(3*((4*A - 7*B)*cos(d*x + c)^4 + 2*(4*A - 7*B)*cos(d*x + c)^3 + (4*A - 7*B)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 3*((4*A - 7*B)*cos(d*x + c)^4 + 2*(4*A - 7*B)*cos(d*x + c)^3 + (4*A - 7*B)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(5*A - 8*B)*cos(d*x + c)^3 + (28*A - 43*B)*cos(d*x + c)^2 + 6*(A - B)*cos(d*x + c) + 3*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2)","A",0
92,1,195,0,0.472640," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(A - 2 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(A - 2 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(A - 2 \, B\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(A - 2 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(A - 2 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(A - 2 \, B\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A - 14 \, B\right)} \cos\left(d x + c\right) - 3 \, B\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"1/6*(3*((A - 2*B)*cos(d*x + c)^3 + 2*(A - 2*B)*cos(d*x + c)^2 + (A - 2*B)*cos(d*x + c))*log(sin(d*x + c) + 1) - 3*((A - 2*B)*cos(d*x + c)^3 + 2*(A - 2*B)*cos(d*x + c)^2 + (A - 2*B)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*(2*A - 5*B)*cos(d*x + c)^2 + (5*A - 14*B)*cos(d*x + c) - 3*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))","A",0
93,1,129,0,0.438335," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(B \cos\left(d x + c\right)^{2} + 2 \, B \cos\left(d x + c\right) + B\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B \cos\left(d x + c\right)^{2} + 2 \, B \cos\left(d x + c\right) + B\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(A - 4 \, B\right)} \cos\left(d x + c\right) + 2 \, A - 5 \, B\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(3*(B*cos(d*x + c)^2 + 2*B*cos(d*x + c) + B)*log(sin(d*x + c) + 1) - 3*(B*cos(d*x + c)^2 + 2*B*cos(d*x + c) + B)*log(-sin(d*x + c) + 1) + 2*((A - 4*B)*cos(d*x + c) + 2*A - 5*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
94,1,58,0,0.409069," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, A + B\right)} \cos\left(d x + c\right) + A + 2 \, B\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*((2*A + B)*cos(d*x + c) + A + 2*B)*sin(d*x + c)/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
95,1,94,0,0.437042," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, A d x \cos\left(d x + c\right)^{2} + 6 \, A d x \cos\left(d x + c\right) + 3 \, A d x - {\left({\left(5 \, A - 2 \, B\right)} \cos\left(d x + c\right) + 4 \, A - B\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*(3*A*d*x*cos(d*x + c)^2 + 6*A*d*x*cos(d*x + c) + 3*A*d*x - ((5*A - 2*B)*cos(d*x + c) + 4*A - B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
96,1,123,0,0.442776," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(2 \, A - B\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(2 \, A - B\right)} d x \cos\left(d x + c\right) + 3 \, {\left(2 \, A - B\right)} d x - {\left(3 \, A \cos\left(d x + c\right)^{2} + {\left(14 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 10 \, A - 4 \, B\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/3*(3*(2*A - B)*d*x*cos(d*x + c)^2 + 6*(2*A - B)*d*x*cos(d*x + c) + 3*(2*A - B)*d*x - (3*A*cos(d*x + c)^2 + (14*A - 5*B)*cos(d*x + c) + 10*A - 4*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
97,1,138,0,0.430898," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, A - 4 \, B\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(7 \, A - 4 \, B\right)} d x \cos\left(d x + c\right) + 3 \, {\left(7 \, A - 4 \, B\right)} d x + {\left(3 \, A \cos\left(d x + c\right)^{3} - 6 \, {\left(A - B\right)} \cos\left(d x + c\right)^{2} - {\left(43 \, A - 28 \, B\right)} \cos\left(d x + c\right) - 32 \, A + 20 \, B\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(3*(7*A - 4*B)*d*x*cos(d*x + c)^2 + 6*(7*A - 4*B)*d*x*cos(d*x + c) + 3*(7*A - 4*B)*d*x + (3*A*cos(d*x + c)^3 - 6*(A - B)*cos(d*x + c)^2 - (43*A - 28*B)*cos(d*x + c) - 32*A + 20*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
98,1,157,0,0.445994," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(10 \, A - 7 \, B\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(10 \, A - 7 \, B\right)} d x \cos\left(d x + c\right) + 3 \, {\left(10 \, A - 7 \, B\right)} d x - {\left(2 \, A \cos\left(d x + c\right)^{4} - {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(2 \, A - B\right)} \cos\left(d x + c\right)^{2} + {\left(66 \, A - 43 \, B\right)} \cos\left(d x + c\right) + 48 \, A - 32 \, B\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/6*(3*(10*A - 7*B)*d*x*cos(d*x + c)^2 + 6*(10*A - 7*B)*d*x*cos(d*x + c) + 3*(10*A - 7*B)*d*x - (2*A*cos(d*x + c)^4 - (2*A - 3*B)*cos(d*x + c)^3 + 6*(2*A - B)*cos(d*x + c)^2 + (66*A - 43*B)*cos(d*x + c) + 48*A - 32*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
99,1,295,0,0.449072," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(6 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(6 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(6 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(6 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(6 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(6 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(9 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(114 \, A - 239 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(234 \, A - 479 \, B\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 15 \, B\right)} \sin\left(d x + c\right)}{60 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/60*(15*((6*A - 13*B)*cos(d*x + c)^5 + 3*(6*A - 13*B)*cos(d*x + c)^4 + 3*(6*A - 13*B)*cos(d*x + c)^3 + (6*A - 13*B)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 15*((6*A - 13*B)*cos(d*x + c)^5 + 3*(6*A - 13*B)*cos(d*x + c)^4 + 3*(6*A - 13*B)*cos(d*x + c)^3 + (6*A - 13*B)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(16*(9*A - 19*B)*cos(d*x + c)^4 + 3*(114*A - 239*B)*cos(d*x + c)^3 + (234*A - 479*B)*cos(d*x + c)^2 + 15*(2*A - 3*B)*cos(d*x + c) + 15*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2)","A",0
100,1,256,0,0.442934," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(A - 3 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(A - 3 \, B\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(A - 3 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(A - 3 \, B\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(11 \, A - 36 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(17 \, A - 57 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(32 \, A - 117 \, B\right)} \cos\left(d x + c\right) - 15 \, B\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}"," ",0,"1/30*(15*((A - 3*B)*cos(d*x + c)^4 + 3*(A - 3*B)*cos(d*x + c)^3 + 3*(A - 3*B)*cos(d*x + c)^2 + (A - 3*B)*cos(d*x + c))*log(sin(d*x + c) + 1) - 15*((A - 3*B)*cos(d*x + c)^4 + 3*(A - 3*B)*cos(d*x + c)^3 + 3*(A - 3*B)*cos(d*x + c)^2 + (A - 3*B)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*(11*A - 36*B)*cos(d*x + c)^3 + 3*(17*A - 57*B)*cos(d*x + c)^2 + (32*A - 117*B)*cos(d*x + c) - 15*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c))","A",0
101,1,183,0,0.459479," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(B \cos\left(d x + c\right)^{3} + 3 \, B \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + B\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(B \cos\left(d x + c\right)^{3} + 3 \, B \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + B\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(A - 11 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A - 17 \, B\right)} \cos\left(d x + c\right) + 7 \, A - 32 \, B\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/30*(15*(B*cos(d*x + c)^3 + 3*B*cos(d*x + c)^2 + 3*B*cos(d*x + c) + B)*log(sin(d*x + c) + 1) - 15*(B*cos(d*x + c)^3 + 3*B*cos(d*x + c)^2 + 3*B*cos(d*x + c) + B)*log(-sin(d*x + c) + 1) + 2*(2*(A - 11*B)*cos(d*x + c)^2 + 3*(2*A - 17*B)*cos(d*x + c) + 7*A - 32*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
102,1,93,0,0.397452," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(3 \, A + 2 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 2 \, B\right)} \cos\left(d x + c\right) + 3 \, A + 7 \, B\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*((3*A + 2*B)*cos(d*x + c)^2 + 3*(3*A + 2*B)*cos(d*x + c) + 3*A + 7*B)*sin(d*x + c)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
103,1,93,0,0.426841," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(7 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 2 \, A + 3 \, B\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*((7*A + 3*B)*cos(d*x + c)^2 + 3*(2*A + 3*B)*cos(d*x + c) + 2*A + 3*B)*sin(d*x + c)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
104,1,138,0,0.430951," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, A d x \cos\left(d x + c\right)^{3} + 45 \, A d x \cos\left(d x + c\right)^{2} + 45 \, A d x \cos\left(d x + c\right) + 15 \, A d x - {\left({\left(32 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(17 \, A - 2 \, B\right)} \cos\left(d x + c\right) + 22 \, A - 2 \, B\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*(15*A*d*x*cos(d*x + c)^3 + 45*A*d*x*cos(d*x + c)^2 + 45*A*d*x*cos(d*x + c) + 15*A*d*x - ((32*A - 7*B)*cos(d*x + c)^2 + 3*(17*A - 2*B)*cos(d*x + c) + 22*A - 2*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
105,1,173,0,0.424409," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left(3 \, A - B\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(3 \, A - B\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(3 \, A - B\right)} d x \cos\left(d x + c\right) + 15 \, {\left(3 \, A - B\right)} d x - {\left(15 \, A \cos\left(d x + c\right)^{3} + {\left(117 \, A - 32 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(57 \, A - 17 \, B\right)} \cos\left(d x + c\right) + 72 \, A - 22 \, B\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/15*(15*(3*A - B)*d*x*cos(d*x + c)^3 + 45*(3*A - B)*d*x*cos(d*x + c)^2 + 45*(3*A - B)*d*x*cos(d*x + c) + 15*(3*A - B)*d*x - (15*A*cos(d*x + c)^3 + (117*A - 32*B)*cos(d*x + c)^2 + 3*(57*A - 17*B)*cos(d*x + c) + 72*A - 22*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
106,1,190,0,0.464809," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(13 \, A - 6 \, B\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(13 \, A - 6 \, B\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(13 \, A - 6 \, B\right)} d x \cos\left(d x + c\right) + 15 \, {\left(13 \, A - 6 \, B\right)} d x + {\left(15 \, A \cos\left(d x + c\right)^{4} - 15 \, {\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{3} - {\left(479 \, A - 234 \, B\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(239 \, A - 114 \, B\right)} \cos\left(d x + c\right) - 304 \, A + 144 \, B\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/30*(15*(13*A - 6*B)*d*x*cos(d*x + c)^3 + 45*(13*A - 6*B)*d*x*cos(d*x + c)^2 + 45*(13*A - 6*B)*d*x*cos(d*x + c) + 15*(13*A - 6*B)*d*x + (15*A*cos(d*x + c)^4 - 15*(3*A - 2*B)*cos(d*x + c)^3 - (479*A - 234*B)*cos(d*x + c)^2 - 3*(239*A - 114*B)*cos(d*x + c) - 304*A + 144*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
107,1,205,0,0.499787," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left(23 \, A - 13 \, B\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(23 \, A - 13 \, B\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(23 \, A - 13 \, B\right)} d x \cos\left(d x + c\right) + 15 \, {\left(23 \, A - 13 \, B\right)} d x - {\left(10 \, A \cos\left(d x + c\right)^{5} - 15 \, {\left(A - B\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(19 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(869 \, A - 479 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(429 \, A - 239 \, B\right)} \cos\left(d x + c\right) + 544 \, A - 304 \, B\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/30*(15*(23*A - 13*B)*d*x*cos(d*x + c)^3 + 45*(23*A - 13*B)*d*x*cos(d*x + c)^2 + 45*(23*A - 13*B)*d*x*cos(d*x + c) + 15*(23*A - 13*B)*d*x - (10*A*cos(d*x + c)^5 - 15*(A - B)*cos(d*x + c)^4 + 5*(19*A - 9*B)*cos(d*x + c)^3 + (869*A - 479*B)*cos(d*x + c)^2 + 3*(429*A - 239*B)*cos(d*x + c) + 544*A - 304*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
108,1,358,0,0.493434," ","integrate(sec(d*x+c)^6*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","-\frac{105 \, {\left({\left(8 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(8 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(8 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(8 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left({\left(8 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(8 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(8 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(8 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(83 \, A - 216 \, B\right)} \cos\left(d x + c\right)^{5} + {\left(4472 \, A - 11619 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(1318 \, A - 3411 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(592 \, A - 1509 \, B\right)} \cos\left(d x + c\right)^{2} + 210 \, {\left(A - 2 \, B\right)} \cos\left(d x + c\right) + 105 \, B\right)} \sin\left(d x + c\right)}{420 \, {\left(a^{4} d \cos\left(d x + c\right)^{6} + 4 \, a^{4} d \cos\left(d x + c\right)^{5} + 6 \, a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + a^{4} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/420*(105*((8*A - 21*B)*cos(d*x + c)^6 + 4*(8*A - 21*B)*cos(d*x + c)^5 + 6*(8*A - 21*B)*cos(d*x + c)^4 + 4*(8*A - 21*B)*cos(d*x + c)^3 + (8*A - 21*B)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 105*((8*A - 21*B)*cos(d*x + c)^6 + 4*(8*A - 21*B)*cos(d*x + c)^5 + 6*(8*A - 21*B)*cos(d*x + c)^4 + 4*(8*A - 21*B)*cos(d*x + c)^3 + (8*A - 21*B)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(16*(83*A - 216*B)*cos(d*x + c)^5 + (4472*A - 11619*B)*cos(d*x + c)^4 + 4*(1318*A - 3411*B)*cos(d*x + c)^3 + 4*(592*A - 1509*B)*cos(d*x + c)^2 + 210*(A - 2*B)*cos(d*x + c) + 105*B)*sin(d*x + c))/(a^4*d*cos(d*x + c)^6 + 4*a^4*d*cos(d*x + c)^5 + 6*a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + a^4*d*cos(d*x + c)^2)","A",0
109,1,317,0,0.441010," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left({\left(A - 4 \, B\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(A - 4 \, B\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(A - 4 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(A - 4 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(A - 4 \, B\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left({\left(A - 4 \, B\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(A - 4 \, B\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(A - 4 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(A - 4 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(A - 4 \, B\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(8 \, {\left(20 \, A - 83 \, B\right)} \cos\left(d x + c\right)^{4} + {\left(535 \, A - 2236 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(155 \, A - 659 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(65 \, A - 296 \, B\right)} \cos\left(d x + c\right) - 105 \, B\right)} \sin\left(d x + c\right)}{210 \, {\left(a^{4} d \cos\left(d x + c\right)^{5} + 4 \, a^{4} d \cos\left(d x + c\right)^{4} + 6 \, a^{4} d \cos\left(d x + c\right)^{3} + 4 \, a^{4} d \cos\left(d x + c\right)^{2} + a^{4} d \cos\left(d x + c\right)\right)}}"," ",0,"1/210*(105*((A - 4*B)*cos(d*x + c)^5 + 4*(A - 4*B)*cos(d*x + c)^4 + 6*(A - 4*B)*cos(d*x + c)^3 + 4*(A - 4*B)*cos(d*x + c)^2 + (A - 4*B)*cos(d*x + c))*log(sin(d*x + c) + 1) - 105*((A - 4*B)*cos(d*x + c)^5 + 4*(A - 4*B)*cos(d*x + c)^4 + 6*(A - 4*B)*cos(d*x + c)^3 + 4*(A - 4*B)*cos(d*x + c)^2 + (A - 4*B)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(8*(20*A - 83*B)*cos(d*x + c)^4 + (535*A - 2236*B)*cos(d*x + c)^3 + 4*(155*A - 659*B)*cos(d*x + c)^2 + 4*(65*A - 296*B)*cos(d*x + c) - 105*B)*sin(d*x + c))/(a^4*d*cos(d*x + c)^5 + 4*a^4*d*cos(d*x + c)^4 + 6*a^4*d*cos(d*x + c)^3 + 4*a^4*d*cos(d*x + c)^2 + a^4*d*cos(d*x + c))","A",0
110,1,236,0,0.452844," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(B \cos\left(d x + c\right)^{4} + 4 \, B \cos\left(d x + c\right)^{3} + 6 \, B \cos\left(d x + c\right)^{2} + 4 \, B \cos\left(d x + c\right) + B\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(B \cos\left(d x + c\right)^{4} + 4 \, B \cos\left(d x + c\right)^{3} + 6 \, B \cos\left(d x + c\right)^{2} + 4 \, B \cos\left(d x + c\right) + B\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(3 \, A - 80 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(24 \, A - 535 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(39 \, A - 620 \, B\right)} \cos\left(d x + c\right) + 36 \, A - 260 \, B\right)} \sin\left(d x + c\right)}{210 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/210*(105*(B*cos(d*x + c)^4 + 4*B*cos(d*x + c)^3 + 6*B*cos(d*x + c)^2 + 4*B*cos(d*x + c) + B)*log(sin(d*x + c) + 1) - 105*(B*cos(d*x + c)^4 + 4*B*cos(d*x + c)^3 + 6*B*cos(d*x + c)^2 + 4*B*cos(d*x + c) + B)*log(-sin(d*x + c) + 1) + 2*(2*(3*A - 80*B)*cos(d*x + c)^3 + (24*A - 535*B)*cos(d*x + c)^2 + (39*A - 620*B)*cos(d*x + c) + 36*A - 260*B)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
111,1,125,0,0.420813," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + 13 \, {\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 13 \, A + 36 \, B\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*(2*(4*A + 3*B)*cos(d*x + c)^3 + 8*(4*A + 3*B)*cos(d*x + c)^2 + 13*(4*A + 3*B)*cos(d*x + c) + 13*A + 36*B)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
112,1,124,0,0.428233," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left({\left(13 \, A + 8 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(13 \, A + 8 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(8 \, A + 13 \, B\right)} \cos\left(d x + c\right) + 8 \, A + 13 \, B\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*((13*A + 8*B)*cos(d*x + c)^3 + 4*(13*A + 8*B)*cos(d*x + c)^2 + 4*(8*A + 13*B)*cos(d*x + c) + 8*A + 13*B)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
113,1,124,0,0.407314," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left({\left(36 \, A + 13 \, B\right)} \cos\left(d x + c\right)^{3} + 13 \, {\left(3 \, A + 4 \, B\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, A + 4 \, B\right)} \cos\left(d x + c\right) + 6 \, A + 8 \, B\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*((36*A + 13*B)*cos(d*x + c)^3 + 13*(3*A + 4*B)*cos(d*x + c)^2 + 8*(3*A + 4*B)*cos(d*x + c) + 6*A + 8*B)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
114,1,181,0,0.436412," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, A d x \cos\left(d x + c\right)^{4} + 420 \, A d x \cos\left(d x + c\right)^{3} + 630 \, A d x \cos\left(d x + c\right)^{2} + 420 \, A d x \cos\left(d x + c\right) + 105 \, A d x - {\left(4 \, {\left(65 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(620 \, A - 39 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(535 \, A - 24 \, B\right)} \cos\left(d x + c\right) + 160 \, A - 6 \, B\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*(105*A*d*x*cos(d*x + c)^4 + 420*A*d*x*cos(d*x + c)^3 + 630*A*d*x*cos(d*x + c)^2 + 420*A*d*x*cos(d*x + c) + 105*A*d*x - (4*(65*A - 9*B)*cos(d*x + c)^3 + (620*A - 39*B)*cos(d*x + c)^2 + (535*A - 24*B)*cos(d*x + c) + 160*A - 6*B)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
115,1,223,0,0.448096," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","-\frac{105 \, {\left(4 \, A - B\right)} d x \cos\left(d x + c\right)^{4} + 420 \, {\left(4 \, A - B\right)} d x \cos\left(d x + c\right)^{3} + 630 \, {\left(4 \, A - B\right)} d x \cos\left(d x + c\right)^{2} + 420 \, {\left(4 \, A - B\right)} d x \cos\left(d x + c\right) + 105 \, {\left(4 \, A - B\right)} d x - {\left(105 \, A \cos\left(d x + c\right)^{4} + 4 \, {\left(296 \, A - 65 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(659 \, A - 155 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(2236 \, A - 535 \, B\right)} \cos\left(d x + c\right) + 664 \, A - 160 \, B\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/105*(105*(4*A - B)*d*x*cos(d*x + c)^4 + 420*(4*A - B)*d*x*cos(d*x + c)^3 + 630*(4*A - B)*d*x*cos(d*x + c)^2 + 420*(4*A - B)*d*x*cos(d*x + c) + 105*(4*A - B)*d*x - (105*A*cos(d*x + c)^4 + 4*(296*A - 65*B)*cos(d*x + c)^3 + 4*(659*A - 155*B)*cos(d*x + c)^2 + (2236*A - 535*B)*cos(d*x + c) + 664*A - 160*B)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
116,1,240,0,0.445444," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(21 \, A - 8 \, B\right)} d x \cos\left(d x + c\right)^{4} + 420 \, {\left(21 \, A - 8 \, B\right)} d x \cos\left(d x + c\right)^{3} + 630 \, {\left(21 \, A - 8 \, B\right)} d x \cos\left(d x + c\right)^{2} + 420 \, {\left(21 \, A - 8 \, B\right)} d x \cos\left(d x + c\right) + 105 \, {\left(21 \, A - 8 \, B\right)} d x + {\left(105 \, A \cos\left(d x + c\right)^{5} - 210 \, {\left(2 \, A - B\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(1509 \, A - 592 \, B\right)} \cos\left(d x + c\right)^{3} - 4 \, {\left(3411 \, A - 1318 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(11619 \, A - 4472 \, B\right)} \cos\left(d x + c\right) - 3456 \, A + 1328 \, B\right)} \sin\left(d x + c\right)}{210 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/210*(105*(21*A - 8*B)*d*x*cos(d*x + c)^4 + 420*(21*A - 8*B)*d*x*cos(d*x + c)^3 + 630*(21*A - 8*B)*d*x*cos(d*x + c)^2 + 420*(21*A - 8*B)*d*x*cos(d*x + c) + 105*(21*A - 8*B)*d*x + (105*A*cos(d*x + c)^5 - 210*(2*A - B)*cos(d*x + c)^4 - 4*(1509*A - 592*B)*cos(d*x + c)^3 - 4*(3411*A - 1318*B)*cos(d*x + c)^2 - (11619*A - 4472*B)*cos(d*x + c) - 3456*A + 1328*B)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
117,1,257,0,0.456555," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","-\frac{105 \, {\left(44 \, A - 21 \, B\right)} d x \cos\left(d x + c\right)^{4} + 420 \, {\left(44 \, A - 21 \, B\right)} d x \cos\left(d x + c\right)^{3} + 630 \, {\left(44 \, A - 21 \, B\right)} d x \cos\left(d x + c\right)^{2} + 420 \, {\left(44 \, A - 21 \, B\right)} d x \cos\left(d x + c\right) + 105 \, {\left(44 \, A - 21 \, B\right)} d x - {\left(70 \, A \cos\left(d x + c\right)^{6} - 35 \, {\left(4 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{5} + 140 \, {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(3196 \, A - 1509 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(7184 \, A - 3411 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(24436 \, A - 11619 \, B\right)} \cos\left(d x + c\right) + 7264 \, A - 3456 \, B\right)} \sin\left(d x + c\right)}{210 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/210*(105*(44*A - 21*B)*d*x*cos(d*x + c)^4 + 420*(44*A - 21*B)*d*x*cos(d*x + c)^3 + 630*(44*A - 21*B)*d*x*cos(d*x + c)^2 + 420*(44*A - 21*B)*d*x*cos(d*x + c) + 105*(44*A - 21*B)*d*x - (70*A*cos(d*x + c)^6 - 35*(4*A - 3*B)*cos(d*x + c)^5 + 140*(7*A - 3*B)*cos(d*x + c)^4 + 4*(3196*A - 1509*B)*cos(d*x + c)^3 + 4*(7184*A - 3411*B)*cos(d*x + c)^2 + (24436*A - 11619*B)*cos(d*x + c) + 7264*A - 3456*B)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
118,1,122,0,0.419881," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, {\left(9 \, A + 8 \, B\right)} \cos\left(d x + c\right)^{4} + 8 \, {\left(9 \, A + 8 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(9 \, A + 8 \, B\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(9 \, A + 8 \, B\right)} \cos\left(d x + c\right) + 35 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"2/315*(16*(9*A + 8*B)*cos(d*x + c)^4 + 8*(9*A + 8*B)*cos(d*x + c)^3 + 6*(9*A + 8*B)*cos(d*x + c)^2 + 5*(9*A + 8*B)*cos(d*x + c) + 35*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
119,1,105,0,0.436830," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(7 \, A + 6 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(7 \, A + 6 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, A + 6 \, B\right)} \cos\left(d x + c\right) + 15 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"2/105*(8*(7*A + 6*B)*cos(d*x + c)^3 + 4*(7*A + 6*B)*cos(d*x + c)^2 + 3*(7*A + 6*B)*cos(d*x + c) + 15*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
120,1,87,0,0.488245," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(5 \, A + 4 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A + 4 \, B\right)} \cos\left(d x + c\right) + 3 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"2/15*(2*(5*A + 4*B)*cos(d*x + c)^2 + (5*A + 4*B)*cos(d*x + c) + 3*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
121,1,66,0,0.437103," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(3 \, A + 2 \, B\right)} \cos\left(d x + c\right) + B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"2/3*((3*A + 2*B)*cos(d*x + c) + B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
122,1,235,0,0.453346," ","integrate((a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(A \cos\left(d x + c\right) + A\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, B \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}, -\frac{2 \, {\left({\left(A \cos\left(d x + c\right) + A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - B \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)\right)}}{d \cos\left(d x + c\right) + d}\right]"," ",0,"[((A*cos(d*x + c) + A)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -2*((A*cos(d*x + c) + A)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
123,1,261,0,0.539860," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, A \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left({\left(A + 2 \, B\right)} \cos\left(d x + c\right) + A + 2 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right)}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{A \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left({\left(A + 2 \, B\right)} \cos\left(d x + c\right) + A + 2 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{d \cos\left(d x + c\right) + d}\right]"," ",0,"[1/2*(2*A*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + ((A + 2*B)*cos(d*x + c) + A + 2*B)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)))/(d*cos(d*x + c) + d), (A*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - ((A + 2*B)*cos(d*x + c) + A + 2*B)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)]","A",0
124,1,308,0,0.538887," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left({\left(3 \, A + 4 \, B\right)} \cos\left(d x + c\right) + 3 \, A + 4 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(2 \, A \cos\left(d x + c\right)^{2} + {\left(3 \, A + 4 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{8 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{{\left({\left(3 \, A + 4 \, B\right)} \cos\left(d x + c\right) + 3 \, A + 4 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(2 \, A \cos\left(d x + c\right)^{2} + {\left(3 \, A + 4 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/8*(((3*A + 4*B)*cos(d*x + c) + 3*A + 4*B)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(2*A*cos(d*x + c)^2 + (3*A + 4*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/4*(((3*A + 4*B)*cos(d*x + c) + 3*A + 4*B)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (2*A*cos(d*x + c)^2 + (3*A + 4*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
125,1,346,0,0.507553," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(5 \, A + 6 \, B\right)} \cos\left(d x + c\right) + 5 \, A + 6 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(8 \, A \cos\left(d x + c\right)^{3} + 2 \, {\left(5 \, A + 6 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 6 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{3 \, {\left({\left(5 \, A + 6 \, B\right)} \cos\left(d x + c\right) + 5 \, A + 6 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(8 \, A \cos\left(d x + c\right)^{3} + 2 \, {\left(5 \, A + 6 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 6 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/48*(3*((5*A + 6*B)*cos(d*x + c) + 5*A + 6*B)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(8*A*cos(d*x + c)^3 + 2*(5*A + 6*B)*cos(d*x + c)^2 + 3*(5*A + 6*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/24*(3*((5*A + 6*B)*cos(d*x + c) + 5*A + 6*B)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (8*A*cos(d*x + c)^3 + 2*(5*A + 6*B)*cos(d*x + c)^2 + 3*(5*A + 6*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
126,1,380,0,0.533550," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(7 \, A + 8 \, B\right)} \cos\left(d x + c\right) + 7 \, A + 8 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(48 \, A \cos\left(d x + c\right)^{4} + 8 \, {\left(7 \, A + 8 \, B\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left(7 \, A + 8 \, B\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(7 \, A + 8 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{384 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{15 \, {\left({\left(7 \, A + 8 \, B\right)} \cos\left(d x + c\right) + 7 \, A + 8 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(48 \, A \cos\left(d x + c\right)^{4} + 8 \, {\left(7 \, A + 8 \, B\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left(7 \, A + 8 \, B\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(7 \, A + 8 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/384*(15*((7*A + 8*B)*cos(d*x + c) + 7*A + 8*B)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(48*A*cos(d*x + c)^4 + 8*(7*A + 8*B)*cos(d*x + c)^3 + 10*(7*A + 8*B)*cos(d*x + c)^2 + 15*(7*A + 8*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/192*(15*((7*A + 8*B)*cos(d*x + c) + 7*A + 8*B)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (48*A*cos(d*x + c)^4 + 8*(7*A + 8*B)*cos(d*x + c)^3 + 10*(7*A + 8*B)*cos(d*x + c)^2 + 15*(7*A + 8*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
127,1,127,0,0.421993," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(39 \, A + 34 \, B\right)} a \cos\left(d x + c\right)^{4} + 4 \, {\left(39 \, A + 34 \, B\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(39 \, A + 34 \, B\right)} a \cos\left(d x + c\right)^{2} + 5 \, {\left(9 \, A + 17 \, B\right)} a \cos\left(d x + c\right) + 35 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"2/315*(8*(39*A + 34*B)*a*cos(d*x + c)^4 + 4*(39*A + 34*B)*a*cos(d*x + c)^3 + 3*(39*A + 34*B)*a*cos(d*x + c)^2 + 5*(9*A + 17*B)*a*cos(d*x + c) + 35*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
128,1,108,0,0.418064," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(63 \, A + 52 \, B\right)} a \cos\left(d x + c\right)^{3} + {\left(63 \, A + 52 \, B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, A + 13 \, B\right)} a \cos\left(d x + c\right) + 15 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"2/105*(2*(63*A + 52*B)*a*cos(d*x + c)^3 + (63*A + 52*B)*a*cos(d*x + c)^2 + 3*(7*A + 13*B)*a*cos(d*x + c) + 15*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
129,1,89,0,0.417098," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(25 \, A + 18 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(5 \, A + 9 \, B\right)} a \cos\left(d x + c\right) + 3 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"2/15*((25*A + 18*B)*a*cos(d*x + c)^2 + (5*A + 9*B)*a*cos(d*x + c) + 3*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
130,1,314,0,0.459019," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left({\left(3 \, A + 5 \, B\right)} a \cos\left(d x + c\right) + B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, -\frac{2 \, {\left(3 \, {\left(A a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left({\left(3 \, A + 5 \, B\right)} a \cos\left(d x + c\right) + B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)\right)}}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/3*(3*(A*a*cos(d*x + c)^2 + A*a*cos(d*x + c))*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*((3*A + 5*B)*a*cos(d*x + c) + B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), -2/3*(3*(A*a*cos(d*x + c)^2 + A*a*cos(d*x + c))*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - ((3*A + 5*B)*a*cos(d*x + c) + B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
131,1,292,0,0.513800," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left({\left(3 \, A + 2 \, B\right)} a \cos\left(d x + c\right) + {\left(3 \, A + 2 \, B\right)} a\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(A a \cos\left(d x + c\right) + 2 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{{\left({\left(3 \, A + 2 \, B\right)} a \cos\left(d x + c\right) + {\left(3 \, A + 2 \, B\right)} a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(A a \cos\left(d x + c\right) + 2 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}\right]"," ",0,"[1/2*(((3*A + 2*B)*a*cos(d*x + c) + (3*A + 2*B)*a)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(A*a*cos(d*x + c) + 2*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -(((3*A + 2*B)*a*cos(d*x + c) + (3*A + 2*B)*a)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (A*a*cos(d*x + c) + 2*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
132,1,320,0,0.497688," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left({\left(7 \, A + 12 \, B\right)} a \cos\left(d x + c\right) + {\left(7 \, A + 12 \, B\right)} a\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(2 \, A a \cos\left(d x + c\right)^{2} + {\left(7 \, A + 4 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{8 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{{\left({\left(7 \, A + 12 \, B\right)} a \cos\left(d x + c\right) + {\left(7 \, A + 12 \, B\right)} a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(2 \, A a \cos\left(d x + c\right)^{2} + {\left(7 \, A + 4 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/8*(((7*A + 12*B)*a*cos(d*x + c) + (7*A + 12*B)*a)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(2*A*a*cos(d*x + c)^2 + (7*A + 4*B)*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/4*(((7*A + 12*B)*a*cos(d*x + c) + (7*A + 12*B)*a)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (2*A*a*cos(d*x + c)^2 + (7*A + 4*B)*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
133,1,360,0,0.515286," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(11 \, A + 14 \, B\right)} a \cos\left(d x + c\right) + {\left(11 \, A + 14 \, B\right)} a\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(8 \, A a \cos\left(d x + c\right)^{3} + 2 \, {\left(11 \, A + 6 \, B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(11 \, A + 14 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{3 \, {\left({\left(11 \, A + 14 \, B\right)} a \cos\left(d x + c\right) + {\left(11 \, A + 14 \, B\right)} a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(8 \, A a \cos\left(d x + c\right)^{3} + 2 \, {\left(11 \, A + 6 \, B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(11 \, A + 14 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/48*(3*((11*A + 14*B)*a*cos(d*x + c) + (11*A + 14*B)*a)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(8*A*a*cos(d*x + c)^3 + 2*(11*A + 6*B)*a*cos(d*x + c)^2 + 3*(11*A + 14*B)*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/24*(3*((11*A + 14*B)*a*cos(d*x + c) + (11*A + 14*B)*a)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (8*A*a*cos(d*x + c)^3 + 2*(11*A + 6*B)*a*cos(d*x + c)^2 + 3*(11*A + 14*B)*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
134,1,396,0,0.557780," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(75 \, A + 88 \, B\right)} a \cos\left(d x + c\right) + {\left(75 \, A + 88 \, B\right)} a\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(48 \, A a \cos\left(d x + c\right)^{4} + 8 \, {\left(15 \, A + 8 \, B\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(75 \, A + 88 \, B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A + 88 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{384 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{3 \, {\left({\left(75 \, A + 88 \, B\right)} a \cos\left(d x + c\right) + {\left(75 \, A + 88 \, B\right)} a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(48 \, A a \cos\left(d x + c\right)^{4} + 8 \, {\left(15 \, A + 8 \, B\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(75 \, A + 88 \, B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A + 88 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/384*(3*((75*A + 88*B)*a*cos(d*x + c) + (75*A + 88*B)*a)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(48*A*a*cos(d*x + c)^4 + 8*(15*A + 8*B)*a*cos(d*x + c)^3 + 2*(75*A + 88*B)*a*cos(d*x + c)^2 + 3*(75*A + 88*B)*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/192*(3*((75*A + 88*B)*a*cos(d*x + c) + (75*A + 88*B)*a)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (48*A*a*cos(d*x + c)^4 + 8*(15*A + 8*B)*a*cos(d*x + c)^3 + 2*(75*A + 88*B)*a*cos(d*x + c)^2 + 3*(75*A + 88*B)*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
135,1,157,0,0.434751," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(803 \, A + 710 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} + 4 \, {\left(803 \, A + 710 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(803 \, A + 710 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 5 \, {\left(286 \, A + 355 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 35 \, {\left(11 \, A + 32 \, B\right)} a^{2} \cos\left(d x + c\right) + 315 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{3465 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"2/3465*(8*(803*A + 710*B)*a^2*cos(d*x + c)^5 + 4*(803*A + 710*B)*a^2*cos(d*x + c)^4 + 3*(803*A + 710*B)*a^2*cos(d*x + c)^3 + 5*(286*A + 355*B)*a^2*cos(d*x + c)^2 + 35*(11*A + 32*B)*a^2*cos(d*x + c) + 315*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^6 + d*cos(d*x + c)^5)","A",0
136,1,136,0,0.431728," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(345 \, A + 292 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(345 \, A + 292 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(60 \, A + 73 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 5 \, {\left(9 \, A + 26 \, B\right)} a^{2} \cos\left(d x + c\right) + 35 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"2/315*(2*(345*A + 292*B)*a^2*cos(d*x + c)^4 + (345*A + 292*B)*a^2*cos(d*x + c)^3 + 3*(60*A + 73*B)*a^2*cos(d*x + c)^2 + 5*(9*A + 26*B)*a^2*cos(d*x + c) + 35*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
137,1,115,0,0.430730," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(301 \, A + 230 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(98 \, A + 115 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, A + 20 \, B\right)} a^{2} \cos\left(d x + c\right) + 15 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"2/105*((301*A + 230*B)*a^2*cos(d*x + c)^3 + (98*A + 115*B)*a^2*cos(d*x + c)^2 + 3*(7*A + 20*B)*a^2*cos(d*x + c) + 15*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
138,1,378,0,0.490986," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(A a^{2} \cos\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left({\left(40 \, A + 43 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(5 \, A + 14 \, B\right)} a^{2} \cos\left(d x + c\right) + 3 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, -\frac{2 \, {\left(15 \, {\left(A a^{2} \cos\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left({\left(40 \, A + 43 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(5 \, A + 14 \, B\right)} a^{2} \cos\left(d x + c\right) + 3 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)\right)}}{15 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/15*(15*(A*a^2*cos(d*x + c)^3 + A*a^2*cos(d*x + c)^2)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*((40*A + 43*B)*a^2*cos(d*x + c)^2 + (5*A + 14*B)*a^2*cos(d*x + c) + 3*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2), -2/15*(15*(A*a^2*cos(d*x + c)^3 + A*a^2*cos(d*x + c)^2)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - ((40*A + 43*B)*a^2*cos(d*x + c)^2 + (5*A + 14*B)*a^2*cos(d*x + c) + 3*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)]","A",0
139,1,386,0,0.513011," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(5 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(5 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(3 \, A a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + 8 \, B\right)} a^{2} \cos\left(d x + c\right) + 2 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, -\frac{3 \, {\left({\left(5 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(5 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(3 \, A a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + 8 \, B\right)} a^{2} \cos\left(d x + c\right) + 2 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/6*(3*((5*A + 2*B)*a^2*cos(d*x + c)^2 + (5*A + 2*B)*a^2*cos(d*x + c))*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(3*A*a^2*cos(d*x + c)^2 + 2*(3*A + 8*B)*a^2*cos(d*x + c) + 2*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), -1/3*(3*((5*A + 2*B)*a^2*cos(d*x + c)^2 + (5*A + 2*B)*a^2*cos(d*x + c))*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (3*A*a^2*cos(d*x + c)^2 + 2*(3*A + 8*B)*a^2*cos(d*x + c) + 2*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
140,1,348,0,0.537826," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left({\left(19 \, A + 20 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(19 \, A + 20 \, B\right)} a^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(2 \, A a^{2} \cos\left(d x + c\right)^{2} + {\left(11 \, A + 4 \, B\right)} a^{2} \cos\left(d x + c\right) + 8 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{8 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{{\left({\left(19 \, A + 20 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(19 \, A + 20 \, B\right)} a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(2 \, A a^{2} \cos\left(d x + c\right)^{2} + {\left(11 \, A + 4 \, B\right)} a^{2} \cos\left(d x + c\right) + 8 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/8*(((19*A + 20*B)*a^2*cos(d*x + c) + (19*A + 20*B)*a^2)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(2*A*a^2*cos(d*x + c)^2 + (11*A + 4*B)*a^2*cos(d*x + c) + 8*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/4*(((19*A + 20*B)*a^2*cos(d*x + c) + (19*A + 20*B)*a^2)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (2*A*a^2*cos(d*x + c)^2 + (11*A + 4*B)*a^2*cos(d*x + c) + 8*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
141,1,380,0,0.522019," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(25 \, A + 38 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(25 \, A + 38 \, B\right)} a^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(8 \, A a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(17 \, A + 6 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(25 \, A + 22 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{3 \, {\left({\left(25 \, A + 38 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(25 \, A + 38 \, B\right)} a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(8 \, A a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(17 \, A + 6 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(25 \, A + 22 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/48*(3*((25*A + 38*B)*a^2*cos(d*x + c) + (25*A + 38*B)*a^2)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(8*A*a^2*cos(d*x + c)^3 + 2*(17*A + 6*B)*a^2*cos(d*x + c)^2 + 3*(25*A + 22*B)*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/24*(3*((25*A + 38*B)*a^2*cos(d*x + c) + (25*A + 38*B)*a^2)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (8*A*a^2*cos(d*x + c)^3 + 2*(17*A + 6*B)*a^2*cos(d*x + c)^2 + 3*(25*A + 22*B)*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
142,1,420,0,0.560897," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(163 \, A + 200 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(163 \, A + 200 \, B\right)} a^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(48 \, A a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(23 \, A + 8 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(163 \, A + 136 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A + 200 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{384 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{3 \, {\left({\left(163 \, A + 200 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(163 \, A + 200 \, B\right)} a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(48 \, A a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(23 \, A + 8 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(163 \, A + 136 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A + 200 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/384*(3*((163*A + 200*B)*a^2*cos(d*x + c) + (163*A + 200*B)*a^2)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(48*A*a^2*cos(d*x + c)^4 + 8*(23*A + 8*B)*a^2*cos(d*x + c)^3 + 2*(163*A + 136*B)*a^2*cos(d*x + c)^2 + 3*(163*A + 200*B)*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/192*(3*((163*A + 200*B)*a^2*cos(d*x + c) + (163*A + 200*B)*a^2)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (48*A*a^2*cos(d*x + c)^4 + 8*(23*A + 8*B)*a^2*cos(d*x + c)^3 + 2*(163*A + 136*B)*a^2*cos(d*x + c)^2 + 3*(163*A + 200*B)*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
143,1,460,0,0.741076," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(283 \, A + 326 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(283 \, A + 326 \, B\right)} a^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(384 \, A a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(29 \, A + 10 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(283 \, A + 230 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(283 \, A + 326 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(283 \, A + 326 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{3840 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{15 \, {\left({\left(283 \, A + 326 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(283 \, A + 326 \, B\right)} a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(384 \, A a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(29 \, A + 10 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(283 \, A + 230 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(283 \, A + 326 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(283 \, A + 326 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{1920 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/3840*(15*((283*A + 326*B)*a^2*cos(d*x + c) + (283*A + 326*B)*a^2)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(384*A*a^2*cos(d*x + c)^5 + 48*(29*A + 10*B)*a^2*cos(d*x + c)^4 + 8*(283*A + 230*B)*a^2*cos(d*x + c)^3 + 10*(283*A + 326*B)*a^2*cos(d*x + c)^2 + 15*(283*A + 326*B)*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/1920*(15*((283*A + 326*B)*a^2*cos(d*x + c) + (283*A + 326*B)*a^2)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (384*A*a^2*cos(d*x + c)^5 + 48*(29*A + 10*B)*a^2*cos(d*x + c)^4 + 8*(283*A + 230*B)*a^2*cos(d*x + c)^3 + 10*(283*A + 326*B)*a^2*cos(d*x + c)^2 + 15*(283*A + 326*B)*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
144,1,432,0,0.512906," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{4} + {\left(A - B\right)} a \cos\left(d x + c\right)^{3}\right)} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left({\left(91 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{3} - {\left(7 \, A - 31 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, A - B\right)} \cos\left(d x + c\right) + 15 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{210 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}, \frac{2 \, {\left({\left(91 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{3} - {\left(7 \, A - 31 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, A - B\right)} \cos\left(d x + c\right) + 15 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right) + \frac{105 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{4} + {\left(A - B\right)} a \cos\left(d x + c\right)^{3}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{105 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[-1/210*(105*sqrt(2)*((A - B)*a*cos(d*x + c)^4 + (A - B)*a*cos(d*x + c)^3)*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*cos(d*x + c)*sin(d*x + c) - 3*cos(d*x + c)^2 - 2*cos(d*x + c) + 1)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*((91*A - 43*B)*cos(d*x + c)^3 - (7*A - 31*B)*cos(d*x + c)^2 + 3*(7*A - B)*cos(d*x + c) + 15*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3), 1/105*(2*((91*A - 43*B)*cos(d*x + c)^3 - (7*A - 31*B)*cos(d*x + c)^2 + 3*(7*A - B)*cos(d*x + c) + 15*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 105*sqrt(2)*((A - B)*a*cos(d*x + c)^4 + (A - B)*a*cos(d*x + c)^3)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)]","A",0
145,1,397,0,0.494361," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B\right)} a \cos\left(d x + c\right)^{2}\right)} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) - 1}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left({\left(5 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(5 \, A - B\right)} \cos\left(d x + c\right) - 3 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{30 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}, -\frac{2 \, {\left({\left(5 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(5 \, A - B\right)} \cos\left(d x + c\right) - 3 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right) + \frac{15 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B\right)} a \cos\left(d x + c\right)^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{15 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[-1/30*(15*sqrt(2)*((A - B)*a*cos(d*x + c)^3 + (A - B)*a*cos(d*x + c)^2)*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*cos(d*x + c)*sin(d*x + c) + 3*cos(d*x + c)^2 + 2*cos(d*x + c) - 1)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*((5*A - 13*B)*cos(d*x + c)^2 - (5*A - B)*cos(d*x + c) - 3*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2), -1/15*(2*((5*A - 13*B)*cos(d*x + c)^2 - (5*A - B)*cos(d*x + c) - 3*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 15*sqrt(2)*((A - B)*a*cos(d*x + c)^3 + (A - B)*a*cos(d*x + c)^2)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)]","A",0
146,1,352,0,0.513793," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B\right)} a \cos\left(d x + c\right)\right)} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left({\left(3 \, A - B\right)} \cos\left(d x + c\right) + B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{6 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}, \frac{2 \, {\left({\left(3 \, A - B\right)} \cos\left(d x + c\right) + B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right) + \frac{3 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B\right)} a \cos\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{3 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/6*(3*sqrt(2)*((A - B)*a*cos(d*x + c)^2 + (A - B)*a*cos(d*x + c))*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*cos(d*x + c)*sin(d*x + c) - 3*cos(d*x + c)^2 - 2*cos(d*x + c) + 1)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*((3*A - B)*cos(d*x + c) + B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c)), 1/3*(2*((3*A - B)*cos(d*x + c) + B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 3*sqrt(2)*((A - B)*a*cos(d*x + c)^2 + (A - B)*a*cos(d*x + c))*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))]","A",0
147,1,287,0,0.482883," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) - 1}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, B \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{2 \, B \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right) - \frac{\sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{a d \cos\left(d x + c\right) + a d}\right]"," ",0,"[-1/2*(sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*cos(d*x + c)*sin(d*x + c) + 3*cos(d*x + c)^2 + 2*cos(d*x + c) - 1)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d), (2*B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c) + a*d)]","A",0
148,1,307,0,1.209678," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left(A - B\right)} a \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 2 \, A \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right)}{2 \, a d}, \frac{\sqrt{2} {\left(A - B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, A \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{a d}\right]"," ",0,"[-1/2*(sqrt(2)*(A - B)*a*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*cos(d*x + c)*sin(d*x + c) - 3*cos(d*x + c)^2 - 2*cos(d*x + c) + 1)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 2*A*sqrt(-a)*log((2*a*cos(d*x + c)^2 + 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)))/(a*d), (sqrt(2)*(A - B)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*A*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))))/(a*d)]","A",0
149,1,458,0,1.478086," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, A \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) - 1}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + {\left({\left(A - 2 \, B\right)} \cos\left(d x + c\right) + A - 2 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{A \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left({\left(A - 2 \, B\right)} \cos\left(d x + c\right) + A - 2 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{\sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{a d \cos\left(d x + c\right) + a d}\right]"," ",0,"[1/2*(2*A*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*cos(d*x + c)*sin(d*x + c) + 3*cos(d*x + c)^2 + 2*cos(d*x + c) - 1)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + ((A - 2*B)*cos(d*x + c) + A - 2*B)*sqrt(-a)*log((2*a*cos(d*x + c)^2 + 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)))/(a*d*cos(d*x + c) + a*d), (A*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + ((A - 2*B)*cos(d*x + c) + A - 2*B)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c) + a*d)]","A",0
150,1,506,0,2.449682," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - {\left({\left(7 \, A - 4 \, B\right)} \cos\left(d x + c\right) + 7 \, A - 4 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) - 2 \, {\left(2 \, A \cos\left(d x + c\right)^{2} - {\left(A - 4 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{8 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, -\frac{{\left({\left(7 \, A - 4 \, B\right)} \cos\left(d x + c\right) + 7 \, A - 4 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(2 \, A \cos\left(d x + c\right)^{2} - {\left(A - 4 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right) - \frac{4 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{4 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[-1/8*(4*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*cos(d*x + c)*sin(d*x + c) - 3*cos(d*x + c)^2 - 2*cos(d*x + c) + 1)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - ((7*A - 4*B)*cos(d*x + c) + 7*A - 4*B)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) - 2*(2*A*cos(d*x + c)^2 - (A - 4*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d), -1/4*(((7*A - 4*B)*cos(d*x + c) + 7*A - 4*B)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (2*A*cos(d*x + c)^2 - (A - 4*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - 4*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c) + a*d)]","A",0
151,1,539,0,2.444953," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{24 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) - 1}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 3 \, {\left({\left(9 \, A - 14 \, B\right)} \cos\left(d x + c\right) + 9 \, A - 14 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) - 2 \, {\left(8 \, A \cos\left(d x + c\right)^{3} - 2 \, {\left(A - 6 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, A - 2 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{48 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{3 \, {\left({\left(9 \, A - 14 \, B\right)} \cos\left(d x + c\right) + 9 \, A - 14 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + {\left(8 \, A \cos\left(d x + c\right)^{3} - 2 \, {\left(A - 6 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, A - 2 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right) - \frac{24 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{24 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[-1/48*(24*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*cos(d*x + c)*sin(d*x + c) + 3*cos(d*x + c)^2 + 2*cos(d*x + c) - 1)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 3*((9*A - 14*B)*cos(d*x + c) + 9*A - 14*B)*sqrt(-a)*log((2*a*cos(d*x + c)^2 + 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) - 2*(8*A*cos(d*x + c)^3 - 2*(A - 6*B)*cos(d*x + c)^2 + 3*(7*A - 2*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d), 1/24*(3*((9*A - 14*B)*cos(d*x + c) + 9*A - 14*B)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + (8*A*cos(d*x + c)^3 - 2*(A - 6*B)*cos(d*x + c)^2 + 3*(7*A - 2*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - 24*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c) + a*d)]","A",0
152,1,504,0,0.497998," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left({\left(11 \, A - 15 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(11 \, A - 15 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(11 \, A - 15 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left({\left(95 \, A - 147 \, B\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(5 \, A - 3 \, B\right)} \cos\left(d x + c\right) - 12 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{120 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}, -\frac{15 \, \sqrt{2} {\left({\left(11 \, A - 15 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(11 \, A - 15 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(11 \, A - 15 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, {\left({\left(95 \, A - 147 \, B\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(5 \, A - 3 \, B\right)} \cos\left(d x + c\right) - 12 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{60 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/120*(15*sqrt(2)*((11*A - 15*B)*cos(d*x + c)^4 + 2*(11*A - 15*B)*cos(d*x + c)^3 + (11*A - 15*B)*cos(d*x + c)^2)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - 3*a*cos(d*x + c)^2 - 2*a*cos(d*x + c) + a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*((95*A - 147*B)*cos(d*x + c)^3 + 12*(5*A - 9*B)*cos(d*x + c)^2 - 4*(5*A - 3*B)*cos(d*x + c) - 12*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2), -1/60*(15*sqrt(2)*((11*A - 15*B)*cos(d*x + c)^4 + 2*(11*A - 15*B)*cos(d*x + c)^3 + (11*A - 15*B)*cos(d*x + c)^2)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + 2*((95*A - 147*B)*cos(d*x + c)^3 + 12*(5*A - 9*B)*cos(d*x + c)^2 - 4*(5*A - 3*B)*cos(d*x + c) - 12*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2)]","A",0
153,1,459,0,0.515157," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left({\left(7 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(7 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A - 11 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left({\left(15 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(A - B\right)} \cos\left(d x + c\right) + 4 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{24 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}, \frac{3 \, \sqrt{2} {\left({\left(7 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(7 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A - 11 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, {\left({\left(15 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(A - B\right)} \cos\left(d x + c\right) + 4 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/24*(3*sqrt(2)*((7*A - 11*B)*cos(d*x + c)^3 + 2*(7*A - 11*B)*cos(d*x + c)^2 + (7*A - 11*B)*cos(d*x + c))*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*((15*A - 19*B)*cos(d*x + c)^2 + 12*(A - B)*cos(d*x + c) + 4*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c)), 1/12*(3*sqrt(2)*((7*A - 11*B)*cos(d*x + c)^3 + 2*(7*A - 11*B)*cos(d*x + c)^2 + (7*A - 11*B)*cos(d*x + c))*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + 2*((15*A - 19*B)*cos(d*x + c)^2 + 12*(A - B)*cos(d*x + c) + 4*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))]","A",0
154,1,386,0,0.499693," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(3 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A - 7 \, B\right)} \cos\left(d x + c\right) + 3 \, A - 7 \, B\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left({\left(A - 5 \, B\right)} \cos\left(d x + c\right) - 4 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, -\frac{\sqrt{2} {\left({\left(3 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A - 7 \, B\right)} \cos\left(d x + c\right) + 3 \, A - 7 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, {\left({\left(A - 5 \, B\right)} \cos\left(d x + c\right) - 4 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[1/8*(sqrt(2)*((3*A - 7*B)*cos(d*x + c)^2 + 2*(3*A - 7*B)*cos(d*x + c) + 3*A - 7*B)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - 3*a*cos(d*x + c)^2 - 2*a*cos(d*x + c) + a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*((A - 5*B)*cos(d*x + c) - 4*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/4*(sqrt(2)*((3*A - 7*B)*cos(d*x + c)^2 + 2*(3*A - 7*B)*cos(d*x + c) + 3*A - 7*B)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + 2*((A - 5*B)*cos(d*x + c) - 4*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
155,1,367,0,0.513921," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - \sqrt{2} {\left({\left(A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 3 \, B\right)} \cos\left(d x + c\right) + A + 3 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, \frac{2 \, {\left(A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - \sqrt{2} {\left({\left(A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 3 \, B\right)} \cos\left(d x + c\right) + A + 3 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[1/8*(4*(A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((A + 3*B)*cos(d*x + c)^2 + 2*(A + 3*B)*cos(d*x + c) + A + 3*B)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), 1/4*(2*(A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((A + 3*B)*cos(d*x + c)^2 + 2*(A + 3*B)*cos(d*x + c) + A + 3*B)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","B",0
156,1,548,0,3.221369," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - \sqrt{2} {\left({\left(5 \, A - B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - B\right)} \cos\left(d x + c\right) + 5 \, A - B\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 8 \, {\left(A \cos\left(d x + c\right)^{2} + 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, -\frac{2 \, {\left(A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - \sqrt{2} {\left({\left(5 \, A - B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - B\right)} \cos\left(d x + c\right) + 5 \, A - B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + 8 \, {\left(A \cos\left(d x + c\right)^{2} + 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[-1/8*(4*(A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((5*A - B)*cos(d*x + c)^2 + 2*(5*A - B)*cos(d*x + c) + 5*A - B)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 8*(A*cos(d*x + c)^2 + 2*A*cos(d*x + c) + A)*sqrt(-a)*log((2*a*cos(d*x + c)^2 + 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/4*(2*(A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((5*A - B)*cos(d*x + c)^2 + 2*(5*A - B)*cos(d*x + c) + 5*A - B)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + 8*(A*cos(d*x + c)^2 + 2*A*cos(d*x + c) + A)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","B",0
157,1,609,0,4.047471," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 9 \, A - 5 \, B\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left({\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right) + 3 \, A - 2 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 4 \, {\left(2 \, A \cos\left(d x + c\right)^{2} + {\left(3 \, A - B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, -\frac{\sqrt{2} {\left({\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 9 \, A - 5 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 4 \, {\left({\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right) + 3 \, A - 2 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, {\left(2 \, A \cos\left(d x + c\right)^{2} + {\left(3 \, A - B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[1/8*(sqrt(2)*((9*A - 5*B)*cos(d*x + c)^2 + 2*(9*A - 5*B)*cos(d*x + c) + 9*A - 5*B)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - 3*a*cos(d*x + c)^2 - 2*a*cos(d*x + c) + a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*((3*A - 2*B)*cos(d*x + c)^2 + 2*(3*A - 2*B)*cos(d*x + c) + 3*A - 2*B)*sqrt(-a)*log((2*a*cos(d*x + c)^2 + 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 4*(2*A*cos(d*x + c)^2 + (3*A - B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/4*(sqrt(2)*((9*A - 5*B)*cos(d*x + c)^2 + 2*(9*A - 5*B)*cos(d*x + c) + 9*A - 5*B)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 4*((3*A - 2*B)*cos(d*x + c)^2 + 2*(3*A - 2*B)*cos(d*x + c) + 3*A - 2*B)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*(2*A*cos(d*x + c)^2 + (3*A - B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
158,1,644,0,5.839477," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(13 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(13 \, A - 9 \, B\right)} \cos\left(d x + c\right) + 13 \, A - 9 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + {\left({\left(19 \, A - 12 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(19 \, A - 12 \, B\right)} \cos\left(d x + c\right) + 19 \, A - 12 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(2 \, A \cos\left(d x + c\right)^{3} - {\left(3 \, A - 4 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(7 \, A - 6 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, \frac{\sqrt{2} {\left({\left(13 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(13 \, A - 9 \, B\right)} \cos\left(d x + c\right) + 13 \, A - 9 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left({\left(19 \, A - 12 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(19 \, A - 12 \, B\right)} \cos\left(d x + c\right) + 19 \, A - 12 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + {\left(2 \, A \cos\left(d x + c\right)^{3} - {\left(3 \, A - 4 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(7 \, A - 6 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[1/8*(sqrt(2)*((13*A - 9*B)*cos(d*x + c)^2 + 2*(13*A - 9*B)*cos(d*x + c) + 13*A - 9*B)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + ((19*A - 12*B)*cos(d*x + c)^2 + 2*(19*A - 12*B)*cos(d*x + c) + 19*A - 12*B)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(2*A*cos(d*x + c)^3 - (3*A - 4*B)*cos(d*x + c)^2 - (7*A - 6*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), 1/4*(sqrt(2)*((13*A - 9*B)*cos(d*x + c)^2 + 2*(13*A - 9*B)*cos(d*x + c) + 13*A - 9*B)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - ((19*A - 12*B)*cos(d*x + c)^2 + 2*(19*A - 12*B)*cos(d*x + c) + 19*A - 12*B)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + (2*A*cos(d*x + c)^3 - (3*A - 4*B)*cos(d*x + c)^2 - (7*A - 6*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
159,1,675,0,5.776245," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{2} {\left({\left(17 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(17 \, A - 13 \, B\right)} \cos\left(d x + c\right) + 17 \, A - 13 \, B\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 3 \, {\left({\left(47 \, A - 38 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(47 \, A - 38 \, B\right)} \cos\left(d x + c\right) + 47 \, A - 38 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 2 \, {\left(8 \, A \cos\left(d x + c\right)^{4} - 6 \, {\left(A - 2 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(37 \, A - 18 \, B\right)} \cos\left(d x + c\right)^{2} + 21 \, {\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{48 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, -\frac{6 \, \sqrt{2} {\left({\left(17 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(17 \, A - 13 \, B\right)} \cos\left(d x + c\right) + 17 \, A - 13 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 3 \, {\left({\left(47 \, A - 38 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(47 \, A - 38 \, B\right)} \cos\left(d x + c\right) + 47 \, A - 38 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(8 \, A \cos\left(d x + c\right)^{4} - 6 \, {\left(A - 2 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(37 \, A - 18 \, B\right)} \cos\left(d x + c\right)^{2} + 21 \, {\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{24 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[1/48*(6*sqrt(2)*((17*A - 13*B)*cos(d*x + c)^2 + 2*(17*A - 13*B)*cos(d*x + c) + 17*A - 13*B)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - 3*a*cos(d*x + c)^2 - 2*a*cos(d*x + c) + a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 3*((47*A - 38*B)*cos(d*x + c)^2 + 2*(47*A - 38*B)*cos(d*x + c) + 47*A - 38*B)*sqrt(-a)*log((2*a*cos(d*x + c)^2 + 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(8*A*cos(d*x + c)^4 - 6*(A - 2*B)*cos(d*x + c)^3 + (37*A - 18*B)*cos(d*x + c)^2 + 21*(3*A - 2*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/24*(6*sqrt(2)*((17*A - 13*B)*cos(d*x + c)^2 + 2*(17*A - 13*B)*cos(d*x + c) + 17*A - 13*B)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 3*((47*A - 38*B)*cos(d*x + c)^2 + 2*(47*A - 38*B)*cos(d*x + c) + 47*A - 38*B)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (8*A*cos(d*x + c)^4 - 6*(A - 2*B)*cos(d*x + c)^3 + (37*A - 18*B)*cos(d*x + c)^2 + 21*(3*A - 2*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
160,1,557,0,0.494883," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left({\left(75 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(75 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(75 \, A - 163 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left({\left(147 \, A - 299 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(255 \, A - 503 \, B\right)} \cos\left(d x + c\right)^{2} + 32 \, {\left(3 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 32 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{192 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}, \frac{3 \, \sqrt{2} {\left({\left(75 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(75 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(75 \, A - 163 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, {\left({\left(147 \, A - 299 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(255 \, A - 503 \, B\right)} \cos\left(d x + c\right)^{2} + 32 \, {\left(3 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 32 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{96 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/192*(3*sqrt(2)*((75*A - 163*B)*cos(d*x + c)^4 + 3*(75*A - 163*B)*cos(d*x + c)^3 + 3*(75*A - 163*B)*cos(d*x + c)^2 + (75*A - 163*B)*cos(d*x + c))*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*((147*A - 299*B)*cos(d*x + c)^3 + (255*A - 503*B)*cos(d*x + c)^2 + 32*(3*A - 5*B)*cos(d*x + c) + 32*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c)), 1/96*(3*sqrt(2)*((75*A - 163*B)*cos(d*x + c)^4 + 3*(75*A - 163*B)*cos(d*x + c)^3 + 3*(75*A - 163*B)*cos(d*x + c)^2 + (75*A - 163*B)*cos(d*x + c))*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + 2*((147*A - 299*B)*cos(d*x + c)^3 + (255*A - 503*B)*cos(d*x + c)^2 + 32*(3*A - 5*B)*cos(d*x + c) + 32*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c))]","A",0
161,1,484,0,0.477426," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(19 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A - 75 \, B\right)} \cos\left(d x + c\right) + 19 \, A - 75 \, B\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left({\left(9 \, A - 49 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(13 \, A - 85 \, B\right)} \cos\left(d x + c\right) - 32 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, -\frac{\sqrt{2} {\left({\left(19 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A - 75 \, B\right)} \cos\left(d x + c\right) + 19 \, A - 75 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, {\left({\left(9 \, A - 49 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(13 \, A - 85 \, B\right)} \cos\left(d x + c\right) - 32 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[1/64*(sqrt(2)*((19*A - 75*B)*cos(d*x + c)^3 + 3*(19*A - 75*B)*cos(d*x + c)^2 + 3*(19*A - 75*B)*cos(d*x + c) + 19*A - 75*B)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - 3*a*cos(d*x + c)^2 - 2*a*cos(d*x + c) + a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*((9*A - 49*B)*cos(d*x + c)^2 + (13*A - 85*B)*cos(d*x + c) - 32*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), -1/32*(sqrt(2)*((19*A - 75*B)*cos(d*x + c)^3 + 3*(19*A - 75*B)*cos(d*x + c)^2 + 3*(19*A - 75*B)*cos(d*x + c) + 19*A - 75*B)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + 2*((9*A - 49*B)*cos(d*x + c)^2 + (13*A - 85*B)*cos(d*x + c) - 32*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
162,1,475,0,0.478433," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(5 \, A + 19 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 19 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 19 \, B\right)} \cos\left(d x + c\right) + 5 \, A + 19 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left({\left(A - 9 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A - 13 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, -\frac{\sqrt{2} {\left({\left(5 \, A + 19 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 19 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 19 \, B\right)} \cos\left(d x + c\right) + 5 \, A + 19 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, {\left({\left(A - 9 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A - 13 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[-1/64*(sqrt(2)*((5*A + 19*B)*cos(d*x + c)^3 + 3*(5*A + 19*B)*cos(d*x + c)^2 + 3*(5*A + 19*B)*cos(d*x + c) + 5*A + 19*B)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*((A - 9*B)*cos(d*x + c)^2 + (5*A - 13*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), -1/32*(sqrt(2)*((5*A + 19*B)*cos(d*x + c)^3 + 3*(5*A + 19*B)*cos(d*x + c)^2 + 3*(5*A + 19*B)*cos(d*x + c) + 5*A + 19*B)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*((A - 9*B)*cos(d*x + c)^2 + (5*A - 13*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
163,1,475,0,0.522385," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(3 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 3 \, A + 5 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left({\left(7 \, A + B\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A + 5 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, -\frac{\sqrt{2} {\left({\left(3 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 3 \, A + 5 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, {\left({\left(7 \, A + B\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A + 5 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[-1/64*(sqrt(2)*((3*A + 5*B)*cos(d*x + c)^3 + 3*(3*A + 5*B)*cos(d*x + c)^2 + 3*(3*A + 5*B)*cos(d*x + c) + 3*A + 5*B)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*((7*A + B)*cos(d*x + c)^2 + (3*A + 5*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), -1/32*(sqrt(2)*((3*A + 5*B)*cos(d*x + c)^3 + 3*(3*A + 5*B)*cos(d*x + c)^2 + 3*(3*A + 5*B)*cos(d*x + c) + 3*A + 5*B)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*((7*A + B)*cos(d*x + c)^2 + (3*A + 5*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
164,1,670,0,6.312006," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(43 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 43 \, A - 3 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 64 \, {\left(A \cos\left(d x + c\right)^{3} + 3 \, A \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + A\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) - 4 \, {\left({\left(15 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(11 \, A - 3 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, \frac{\sqrt{2} {\left({\left(43 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 43 \, A - 3 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 64 \, {\left(A \cos\left(d x + c\right)^{3} + 3 \, A \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, {\left({\left(15 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(11 \, A - 3 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[1/64*(sqrt(2)*((43*A - 3*B)*cos(d*x + c)^3 + 3*(43*A - 3*B)*cos(d*x + c)^2 + 3*(43*A - 3*B)*cos(d*x + c) + 43*A - 3*B)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 64*(A*cos(d*x + c)^3 + 3*A*cos(d*x + c)^2 + 3*A*cos(d*x + c) + A)*sqrt(-a)*log((2*a*cos(d*x + c)^2 + 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) - 4*((15*A - 7*B)*cos(d*x + c)^2 + (11*A - 3*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), 1/32*(sqrt(2)*((43*A - 3*B)*cos(d*x + c)^3 + 3*(43*A - 3*B)*cos(d*x + c)^2 + 3*(43*A - 3*B)*cos(d*x + c) + 43*A - 3*B)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 64*(A*cos(d*x + c)^3 + 3*A*cos(d*x + c)^2 + 3*A*cos(d*x + c) + A)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*((15*A - 7*B)*cos(d*x + c)^2 + (11*A - 3*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","B",0
165,1,739,0,8.200264," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(115 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(115 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(115 \, A - 43 \, B\right)} \cos\left(d x + c\right) + 115 \, A - 43 \, B\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 32 \, {\left({\left(5 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A - 2 \, B\right)} \cos\left(d x + c\right) + 5 \, A - 2 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 4 \, {\left(16 \, A \cos\left(d x + c\right)^{3} + 5 \, {\left(11 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(35 \, A - 11 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, -\frac{\sqrt{2} {\left({\left(115 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(115 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(115 \, A - 43 \, B\right)} \cos\left(d x + c\right) + 115 \, A - 43 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 32 \, {\left({\left(5 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A - 2 \, B\right)} \cos\left(d x + c\right) + 5 \, A - 2 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, {\left(16 \, A \cos\left(d x + c\right)^{3} + 5 \, {\left(11 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(35 \, A - 11 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[1/64*(sqrt(2)*((115*A - 43*B)*cos(d*x + c)^3 + 3*(115*A - 43*B)*cos(d*x + c)^2 + 3*(115*A - 43*B)*cos(d*x + c) + 115*A - 43*B)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - 3*a*cos(d*x + c)^2 - 2*a*cos(d*x + c) + a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 32*((5*A - 2*B)*cos(d*x + c)^3 + 3*(5*A - 2*B)*cos(d*x + c)^2 + 3*(5*A - 2*B)*cos(d*x + c) + 5*A - 2*B)*sqrt(-a)*log((2*a*cos(d*x + c)^2 + 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 4*(16*A*cos(d*x + c)^3 + 5*(11*A - 3*B)*cos(d*x + c)^2 + (35*A - 11*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), -1/32*(sqrt(2)*((115*A - 43*B)*cos(d*x + c)^3 + 3*(115*A - 43*B)*cos(d*x + c)^2 + 3*(115*A - 43*B)*cos(d*x + c) + 115*A - 43*B)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 32*((5*A - 2*B)*cos(d*x + c)^3 + 3*(5*A - 2*B)*cos(d*x + c)^2 + 3*(5*A - 2*B)*cos(d*x + c) + 5*A - 2*B)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*(16*A*cos(d*x + c)^3 + 5*(11*A - 3*B)*cos(d*x + c)^2 + (35*A - 11*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
166,1,776,0,10.814424," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(219 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(219 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(219 \, A - 115 \, B\right)} \cos\left(d x + c\right) + 219 \, A - 115 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 8 \, {\left({\left(39 \, A - 20 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(39 \, A - 20 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(39 \, A - 20 \, B\right)} \cos\left(d x + c\right) + 39 \, A - 20 \, B\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right) + 4 \, {\left(8 \, A \cos\left(d x + c\right)^{4} - 4 \, {\left(5 \, A - 4 \, B\right)} \cos\left(d x + c\right)^{3} - 5 \, {\left(19 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} - 7 \, {\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, \frac{\sqrt{2} {\left({\left(219 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(219 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(219 \, A - 115 \, B\right)} \cos\left(d x + c\right) + 219 \, A - 115 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 8 \, {\left({\left(39 \, A - 20 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(39 \, A - 20 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(39 \, A - 20 \, B\right)} \cos\left(d x + c\right) + 39 \, A - 20 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, {\left(8 \, A \cos\left(d x + c\right)^{4} - 4 \, {\left(5 \, A - 4 \, B\right)} \cos\left(d x + c\right)^{3} - 5 \, {\left(19 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} - 7 \, {\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[1/64*(sqrt(2)*((219*A - 115*B)*cos(d*x + c)^3 + 3*(219*A - 115*B)*cos(d*x + c)^2 + 3*(219*A - 115*B)*cos(d*x + c) + 219*A - 115*B)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 8*((39*A - 20*B)*cos(d*x + c)^3 + 3*(39*A - 20*B)*cos(d*x + c)^2 + 3*(39*A - 20*B)*cos(d*x + c) + 39*A - 20*B)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 4*(8*A*cos(d*x + c)^4 - 4*(5*A - 4*B)*cos(d*x + c)^3 - 5*(19*A - 11*B)*cos(d*x + c)^2 - 7*(9*A - 5*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), 1/32*(sqrt(2)*((219*A - 115*B)*cos(d*x + c)^3 + 3*(219*A - 115*B)*cos(d*x + c)^2 + 3*(219*A - 115*B)*cos(d*x + c) + 219*A - 115*B)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 8*((39*A - 20*B)*cos(d*x + c)^3 + 3*(39*A - 20*B)*cos(d*x + c)^2 + 3*(39*A - 20*B)*cos(d*x + c) + 39*A - 20*B)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + 2*(8*A*cos(d*x + c)^4 - 4*(5*A - 4*B)*cos(d*x + c)^3 - 5*(19*A - 11*B)*cos(d*x + c)^2 - 7*(9*A - 5*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
167,1,305,0,0.466091," ","integrate((A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} A a \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) - A \sqrt{-a} \log\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} - {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right)}{a d}, \frac{2 \, {\left(\sqrt{2} A \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - A \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)\right)}}{a d}\right]"," ",0,"[(sqrt(2)*A*a*sqrt(-1/a)*log(-(2*sqrt(2)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*sqrt(-1/a) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c))) - A*sqrt(-a)*log((2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) - (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c)))/(a*d), 2*(sqrt(2)*A*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - A*sqrt(a)*arctan(sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))))/(a*d)]","A",0
168,1,435,0,0.454983," ","integrate(cos(d*x+c)*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{2} A a \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 3 \, A \sqrt{-a} \log\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} - {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 2 \, {\left(A \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{2 \, a d \sin\left(d x + c\right)}, \frac{2 \, \sqrt{2} A \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 3 \, A \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - {\left(A \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{a d \sin\left(d x + c\right)}\right]"," ",0,"[1/2*(2*sqrt(2)*A*a*sqrt(-1/a)*log(-(2*sqrt(2)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*sqrt(-1/a) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) - 3*A*sqrt(-a)*log((2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) - (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) - 2*(A*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/(a*d*sin(d*x + c)), (2*sqrt(2)*A*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 3*A*sqrt(a)*arctan(sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - (A*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/(a*d*sin(d*x + c))]","A",0
169,1,462,0,0.463467," ","integrate(cos(d*x+c)^2*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{8 \, \sqrt{2} A a \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 11 \, A \sqrt{-a} \log\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} - {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 2 \, {\left(2 \, A \cos\left(d x + c\right)^{3} + 7 \, A \cos\left(d x + c\right)^{2} + 5 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{8 \, a d \sin\left(d x + c\right)}, \frac{8 \, \sqrt{2} A \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 11 \, A \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - {\left(2 \, A \cos\left(d x + c\right)^{3} + 7 \, A \cos\left(d x + c\right)^{2} + 5 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{4 \, a d \sin\left(d x + c\right)}\right]"," ",0,"[1/8*(8*sqrt(2)*A*a*sqrt(-1/a)*log(-(2*sqrt(2)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*sqrt(-1/a) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) - 11*A*sqrt(-a)*log((2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) - (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) - 2*(2*A*cos(d*x + c)^3 + 7*A*cos(d*x + c)^2 + 5*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/(a*d*sin(d*x + c)), 1/4*(8*sqrt(2)*A*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 11*A*sqrt(a)*arctan(sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - (2*A*cos(d*x + c)^3 + 7*A*cos(d*x + c)^2 + 5*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/(a*d*sin(d*x + c))]","A",0
170,1,484,0,0.466004," ","integrate(cos(d*x+c)^3*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{48 \, \sqrt{2} A a \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 69 \, A \sqrt{-a} \log\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} - {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 2 \, {\left(8 \, A \cos\left(d x + c\right)^{4} + 22 \, A \cos\left(d x + c\right)^{3} + 41 \, A \cos\left(d x + c\right)^{2} + 27 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{48 \, a d \sin\left(d x + c\right)}, \frac{48 \, \sqrt{2} A \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 69 \, A \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - {\left(8 \, A \cos\left(d x + c\right)^{4} + 22 \, A \cos\left(d x + c\right)^{3} + 41 \, A \cos\left(d x + c\right)^{2} + 27 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{24 \, a d \sin\left(d x + c\right)}\right]"," ",0,"[1/48*(48*sqrt(2)*A*a*sqrt(-1/a)*log(-(2*sqrt(2)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*sqrt(-1/a) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) - 69*A*sqrt(-a)*log((2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) - (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) - 2*(8*A*cos(d*x + c)^4 + 22*A*cos(d*x + c)^3 + 41*A*cos(d*x + c)^2 + 27*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/(a*d*sin(d*x + c)), 1/24*(48*sqrt(2)*A*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 69*A*sqrt(a)*arctan(sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - (8*A*cos(d*x + c)^4 + 22*A*cos(d*x + c)^3 + 41*A*cos(d*x + c)^2 + 27*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/(a*d*sin(d*x + c))]","A",0
171,1,502,0,0.488109," ","integrate((A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} + {\left(3 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 4 \, {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{-a} \log\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} - {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 4 \, {\left(A \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{4 \, {\left(a^{2} d \cos\left(d x + c\right) - a^{2} d\right)} \sin\left(d x + c\right)}, \frac{3 \, \sqrt{2} {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 4 \, {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 2 \, {\left(A \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{2 \, {\left(a^{2} d \cos\left(d x + c\right) - a^{2} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/4*(3*sqrt(2)*(A*cos(d*x + c) - A)*sqrt(-a)*log((2*sqrt(2)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) + (3*a*cos(d*x + c) + a)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 4*(A*cos(d*x + c) - A)*sqrt(-a)*log((2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) - (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) - 4*(A*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^2*d*cos(d*x + c) - a^2*d)*sin(d*x + c)), 1/2*(3*sqrt(2)*(A*cos(d*x + c) - A)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 4*(A*cos(d*x + c) - A)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) + 2*(A*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^2*d*cos(d*x + c) - a^2*d)*sin(d*x + c))]","B",0
172,1,526,0,0.475454," ","integrate(cos(d*x+c)*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{7 \, \sqrt{2} {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} + {\left(3 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 10 \, {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{-a} \log\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} - {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 4 \, {\left(A \cos\left(d x + c\right)^{3} - A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{4 \, {\left(a^{2} d \cos\left(d x + c\right) - a^{2} d\right)} \sin\left(d x + c\right)}, \frac{7 \, \sqrt{2} {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 10 \, {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 2 \, {\left(A \cos\left(d x + c\right)^{3} - A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{2 \, {\left(a^{2} d \cos\left(d x + c\right) - a^{2} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/4*(7*sqrt(2)*(A*cos(d*x + c) - A)*sqrt(-a)*log((2*sqrt(2)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) + (3*a*cos(d*x + c) + a)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 10*(A*cos(d*x + c) - A)*sqrt(-a)*log((2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) - (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) + 4*(A*cos(d*x + c)^3 - A*cos(d*x + c)^2 - 2*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^2*d*cos(d*x + c) - a^2*d)*sin(d*x + c)), 1/2*(7*sqrt(2)*(A*cos(d*x + c) - A)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 10*(A*cos(d*x + c) - A)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 2*(A*cos(d*x + c)^3 - A*cos(d*x + c)^2 - 2*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^2*d*cos(d*x + c) - a^2*d)*sin(d*x + c))]","A",0
173,1,550,0,0.466801," ","integrate(cos(d*x+c)^2*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{22 \, \sqrt{2} {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} + {\left(3 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 31 \, {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{-a} \log\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} - {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 2 \, {\left(2 \, A \cos\left(d x + c\right)^{4} + 9 \, A \cos\left(d x + c\right)^{3} - 6 \, A \cos\left(d x + c\right)^{2} - 13 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{8 \, {\left(a^{2} d \cos\left(d x + c\right) - a^{2} d\right)} \sin\left(d x + c\right)}, \frac{22 \, \sqrt{2} {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 31 \, {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - {\left(2 \, A \cos\left(d x + c\right)^{4} + 9 \, A \cos\left(d x + c\right)^{3} - 6 \, A \cos\left(d x + c\right)^{2} - 13 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{4 \, {\left(a^{2} d \cos\left(d x + c\right) - a^{2} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/8*(22*sqrt(2)*(A*cos(d*x + c) - A)*sqrt(-a)*log((2*sqrt(2)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) + (3*a*cos(d*x + c) + a)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 31*(A*cos(d*x + c) - A)*sqrt(-a)*log((2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) - (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) + 2*(2*A*cos(d*x + c)^4 + 9*A*cos(d*x + c)^3 - 6*A*cos(d*x + c)^2 - 13*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^2*d*cos(d*x + c) - a^2*d)*sin(d*x + c)), 1/4*(22*sqrt(2)*(A*cos(d*x + c) - A)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 31*(A*cos(d*x + c) - A)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - (2*A*cos(d*x + c)^4 + 9*A*cos(d*x + c)^3 - 6*A*cos(d*x + c)^2 - 13*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^2*d*cos(d*x + c) - a^2*d)*sin(d*x + c))]","A",0
174,1,572,0,0.492074," ","integrate(cos(d*x+c)^3*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{180 \, \sqrt{2} {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} + {\left(3 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 255 \, {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{-a} \log\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} - {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 2 \, {\left(8 \, A \cos\left(d x + c\right)^{5} + 26 \, A \cos\left(d x + c\right)^{4} + 73 \, A \cos\left(d x + c\right)^{3} - 50 \, A \cos\left(d x + c\right)^{2} - 105 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{48 \, {\left(a^{2} d \cos\left(d x + c\right) - a^{2} d\right)} \sin\left(d x + c\right)}, \frac{180 \, \sqrt{2} {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 255 \, {\left(A \cos\left(d x + c\right) - A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - {\left(8 \, A \cos\left(d x + c\right)^{5} + 26 \, A \cos\left(d x + c\right)^{4} + 73 \, A \cos\left(d x + c\right)^{3} - 50 \, A \cos\left(d x + c\right)^{2} - 105 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{24 \, {\left(a^{2} d \cos\left(d x + c\right) - a^{2} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/48*(180*sqrt(2)*(A*cos(d*x + c) - A)*sqrt(-a)*log((2*sqrt(2)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) + (3*a*cos(d*x + c) + a)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 255*(A*cos(d*x + c) - A)*sqrt(-a)*log((2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) - (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) + 2*(8*A*cos(d*x + c)^5 + 26*A*cos(d*x + c)^4 + 73*A*cos(d*x + c)^3 - 50*A*cos(d*x + c)^2 - 105*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^2*d*cos(d*x + c) - a^2*d)*sin(d*x + c)), 1/24*(180*sqrt(2)*(A*cos(d*x + c) - A)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 255*(A*cos(d*x + c) - A)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - (8*A*cos(d*x + c)^5 + 26*A*cos(d*x + c)^4 + 73*A*cos(d*x + c)^3 - 50*A*cos(d*x + c)^2 - 105*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^2*d*cos(d*x + c) - a^2*d)*sin(d*x + c))]","A",0
175,1,590,0,0.468508," ","integrate((A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{23 \, \sqrt{2} {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} + {\left(3 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 32 \, {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{-a} \log\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} - {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 4 \, {\left(11 \, A \cos\left(d x + c\right)^{3} + 4 \, A \cos\left(d x + c\right)^{2} - 7 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)} \sin\left(d x + c\right)}, \frac{23 \, \sqrt{2} {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 32 \, {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 2 \, {\left(11 \, A \cos\left(d x + c\right)^{3} + 4 \, A \cos\left(d x + c\right)^{2} - 7 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{16 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/32*(23*sqrt(2)*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(-a)*log((2*sqrt(2)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) + (3*a*cos(d*x + c) + a)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 32*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(-a)*log((2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) - (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) - 4*(11*A*cos(d*x + c)^3 + 4*A*cos(d*x + c)^2 - 7*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) + a^3*d)*sin(d*x + c)), 1/16*(23*sqrt(2)*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 32*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) + 2*(11*A*cos(d*x + c)^3 + 4*A*cos(d*x + c)^2 - 7*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) + a^3*d)*sin(d*x + c))]","B",0
176,1,612,0,0.476835," ","integrate(cos(d*x+c)*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{79 \, \sqrt{2} {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} + {\left(3 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 112 \, {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{-a} \log\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} - {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 4 \, {\left(8 \, A \cos\left(d x + c\right)^{4} - 27 \, A \cos\left(d x + c\right)^{3} - 12 \, A \cos\left(d x + c\right)^{2} + 23 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)} \sin\left(d x + c\right)}, \frac{79 \, \sqrt{2} {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 112 \, {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 2 \, {\left(8 \, A \cos\left(d x + c\right)^{4} - 27 \, A \cos\left(d x + c\right)^{3} - 12 \, A \cos\left(d x + c\right)^{2} + 23 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{16 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/32*(79*sqrt(2)*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(-a)*log((2*sqrt(2)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) + (3*a*cos(d*x + c) + a)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 112*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(-a)*log((2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) - (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) + 4*(8*A*cos(d*x + c)^4 - 27*A*cos(d*x + c)^3 - 12*A*cos(d*x + c)^2 + 23*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) + a^3*d)*sin(d*x + c)), 1/16*(79*sqrt(2)*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 112*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 2*(8*A*cos(d*x + c)^4 - 27*A*cos(d*x + c)^3 - 12*A*cos(d*x + c)^2 + 23*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) + a^3*d)*sin(d*x + c))]","A",0
177,1,634,0,0.493181," ","integrate(cos(d*x+c)^2*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{167 \, \sqrt{2} {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} + {\left(3 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 236 \, {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{-a} \log\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} - {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 4 \, {\left(4 \, A \cos\left(d x + c\right)^{5} + 22 \, A \cos\left(d x + c\right)^{4} - 57 \, A \cos\left(d x + c\right)^{3} - 26 \, A \cos\left(d x + c\right)^{2} + 49 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)} \sin\left(d x + c\right)}, \frac{167 \, \sqrt{2} {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 236 \, {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 2 \, {\left(4 \, A \cos\left(d x + c\right)^{5} + 22 \, A \cos\left(d x + c\right)^{4} - 57 \, A \cos\left(d x + c\right)^{3} - 26 \, A \cos\left(d x + c\right)^{2} + 49 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{16 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/32*(167*sqrt(2)*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(-a)*log((2*sqrt(2)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) + (3*a*cos(d*x + c) + a)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 236*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(-a)*log((2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) - (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) + 4*(4*A*cos(d*x + c)^5 + 22*A*cos(d*x + c)^4 - 57*A*cos(d*x + c)^3 - 26*A*cos(d*x + c)^2 + 49*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) + a^3*d)*sin(d*x + c)), 1/16*(167*sqrt(2)*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 236*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 2*(4*A*cos(d*x + c)^5 + 22*A*cos(d*x + c)^4 - 57*A*cos(d*x + c)^3 - 26*A*cos(d*x + c)^2 + 49*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) + a^3*d)*sin(d*x + c))]","A",0
178,1,656,0,0.518892," ","integrate(cos(d*x+c)^3*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{861 \, \sqrt{2} {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} + {\left(3 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 1218 \, {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{-a} \log\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} - {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 4 \, {\left(8 \, A \cos\left(d x + c\right)^{6} + 30 \, A \cos\left(d x + c\right)^{5} + 113 \, A \cos\left(d x + c\right)^{4} - 294 \, A \cos\left(d x + c\right)^{3} - 133 \, A \cos\left(d x + c\right)^{2} + 252 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{96 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)} \sin\left(d x + c\right)}, \frac{861 \, \sqrt{2} {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 1218 \, {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 2 \, {\left(8 \, A \cos\left(d x + c\right)^{6} + 30 \, A \cos\left(d x + c\right)^{5} + 113 \, A \cos\left(d x + c\right)^{4} - 294 \, A \cos\left(d x + c\right)^{3} - 133 \, A \cos\left(d x + c\right)^{2} + 252 \, A \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{48 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/96*(861*sqrt(2)*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(-a)*log((2*sqrt(2)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) + (3*a*cos(d*x + c) + a)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 1218*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(-a)*log((2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) - (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) + 4*(8*A*cos(d*x + c)^6 + 30*A*cos(d*x + c)^5 + 113*A*cos(d*x + c)^4 - 294*A*cos(d*x + c)^3 - 133*A*cos(d*x + c)^2 + 252*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) + a^3*d)*sin(d*x + c)), 1/48*(861*sqrt(2)*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 1218*(A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + A)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))*sin(d*x + c) - 2*(8*A*cos(d*x + c)^6 + 30*A*cos(d*x + c)^5 + 113*A*cos(d*x + c)^4 - 294*A*cos(d*x + c)^3 - 133*A*cos(d*x + c)^2 + 252*A*cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/((a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) + a^3*d)*sin(d*x + c))]","A",0
179,0,0,0,0.440905," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \sec\left(d x + c\right)^{4} + {\left(A + B\right)} a \sec\left(d x + c\right)^{3} + A a \sec\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*a*sec(d*x + c)^4 + (A + B)*a*sec(d*x + c)^3 + A*a*sec(d*x + c)^2)*sqrt(sec(d*x + c)), x)","F",0
180,0,0,0,0.416196," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \sec\left(d x + c\right)^{3} + {\left(A + B\right)} a \sec\left(d x + c\right)^{2} + A a \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*a*sec(d*x + c)^3 + (A + B)*a*sec(d*x + c)^2 + A*a*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
181,0,0,0,0.449017," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \sec\left(d x + c\right)^{2} + {\left(A + B\right)} a \sec\left(d x + c\right) + A a\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)*sqrt(sec(d*x + c)), x)","F",0
182,0,0,0,0.423289," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a \sec\left(d x + c\right)^{2} + {\left(A + B\right)} a \sec\left(d x + c\right) + A a}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)/sqrt(sec(d*x + c)), x)","F",0
183,0,0,0,0.449669," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a \sec\left(d x + c\right)^{2} + {\left(A + B\right)} a \sec\left(d x + c\right) + A a}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)/sec(d*x + c)^(3/2), x)","F",0
184,0,0,0,0.458095," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a \sec\left(d x + c\right)^{2} + {\left(A + B\right)} a \sec\left(d x + c\right) + A a}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)/sec(d*x + c)^(5/2), x)","F",0
185,0,0,0,0.464999," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a \sec\left(d x + c\right)^{2} + {\left(A + B\right)} a \sec\left(d x + c\right) + A a}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)/sec(d*x + c)^(7/2), x)","F",0
186,0,0,0,0.437872," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{2} \sec\left(d x + c\right)^{4} + {\left(A + 2 \, B\right)} a^{2} \sec\left(d x + c\right)^{3} + {\left(2 \, A + B\right)} a^{2} \sec\left(d x + c\right)^{2} + A a^{2} \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^2*sec(d*x + c)^4 + (A + 2*B)*a^2*sec(d*x + c)^3 + (2*A + B)*a^2*sec(d*x + c)^2 + A*a^2*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
187,0,0,0,0.421899," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \sec\left(d x + c\right) + A a^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^2*sec(d*x + c)^3 + (A + 2*B)*a^2*sec(d*x + c)^2 + (2*A + B)*a^2*sec(d*x + c) + A*a^2)*sqrt(sec(d*x + c)), x)","F",0
188,0,0,0,0.465089," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \sec\left(d x + c\right) + A a^{2}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*a^2*sec(d*x + c)^3 + (A + 2*B)*a^2*sec(d*x + c)^2 + (2*A + B)*a^2*sec(d*x + c) + A*a^2)/sqrt(sec(d*x + c)), x)","F",0
189,0,0,0,0.444642," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \sec\left(d x + c\right) + A a^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*a^2*sec(d*x + c)^3 + (A + 2*B)*a^2*sec(d*x + c)^2 + (2*A + B)*a^2*sec(d*x + c) + A*a^2)/sec(d*x + c)^(3/2), x)","F",0
190,0,0,0,0.455475," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \sec\left(d x + c\right) + A a^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*a^2*sec(d*x + c)^3 + (A + 2*B)*a^2*sec(d*x + c)^2 + (2*A + B)*a^2*sec(d*x + c) + A*a^2)/sec(d*x + c)^(5/2), x)","F",0
191,0,0,0,0.453353," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \sec\left(d x + c\right) + A a^{2}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*a^2*sec(d*x + c)^3 + (A + 2*B)*a^2*sec(d*x + c)^2 + (2*A + B)*a^2*sec(d*x + c) + A*a^2)/sec(d*x + c)^(7/2), x)","F",0
192,0,0,0,0.468298," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \sec\left(d x + c\right) + A a^{2}}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*a^2*sec(d*x + c)^3 + (A + 2*B)*a^2*sec(d*x + c)^2 + (2*A + B)*a^2*sec(d*x + c) + A*a^2)/sec(d*x + c)^(9/2), x)","F",0
193,0,0,0,0.450078," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{3} \sec\left(d x + c\right)^{5} + {\left(A + 3 \, B\right)} a^{3} \sec\left(d x + c\right)^{4} + 3 \, {\left(A + B\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + B\right)} a^{3} \sec\left(d x + c\right)^{2} + A a^{3} \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^3*sec(d*x + c)^5 + (A + 3*B)*a^3*sec(d*x + c)^4 + 3*(A + B)*a^3*sec(d*x + c)^3 + (3*A + B)*a^3*sec(d*x + c)^2 + A*a^3*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
194,0,0,0,0.424150," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \sec\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \sec\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \sec\left(d x + c\right) + A a^{3}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^3*sec(d*x + c)^4 + (A + 3*B)*a^3*sec(d*x + c)^3 + 3*(A + B)*a^3*sec(d*x + c)^2 + (3*A + B)*a^3*sec(d*x + c) + A*a^3)*sqrt(sec(d*x + c)), x)","F",0
195,0,0,0,0.469827," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \sec\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \sec\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \sec\left(d x + c\right) + A a^{3}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*a^3*sec(d*x + c)^4 + (A + 3*B)*a^3*sec(d*x + c)^3 + 3*(A + B)*a^3*sec(d*x + c)^2 + (3*A + B)*a^3*sec(d*x + c) + A*a^3)/sqrt(sec(d*x + c)), x)","F",0
196,0,0,0,0.486087," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \sec\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \sec\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \sec\left(d x + c\right) + A a^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*a^3*sec(d*x + c)^4 + (A + 3*B)*a^3*sec(d*x + c)^3 + 3*(A + B)*a^3*sec(d*x + c)^2 + (3*A + B)*a^3*sec(d*x + c) + A*a^3)/sec(d*x + c)^(3/2), x)","F",0
197,0,0,0,0.449012," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \sec\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \sec\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \sec\left(d x + c\right) + A a^{3}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*a^3*sec(d*x + c)^4 + (A + 3*B)*a^3*sec(d*x + c)^3 + 3*(A + B)*a^3*sec(d*x + c)^2 + (3*A + B)*a^3*sec(d*x + c) + A*a^3)/sec(d*x + c)^(5/2), x)","F",0
198,0,0,0,0.431546," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \sec\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \sec\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \sec\left(d x + c\right) + A a^{3}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*a^3*sec(d*x + c)^4 + (A + 3*B)*a^3*sec(d*x + c)^3 + 3*(A + B)*a^3*sec(d*x + c)^2 + (3*A + B)*a^3*sec(d*x + c) + A*a^3)/sec(d*x + c)^(7/2), x)","F",0
199,0,0,0,0.458113," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \sec\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \sec\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \sec\left(d x + c\right) + A a^{3}}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*a^3*sec(d*x + c)^4 + (A + 3*B)*a^3*sec(d*x + c)^3 + 3*(A + B)*a^3*sec(d*x + c)^2 + (3*A + B)*a^3*sec(d*x + c) + A*a^3)/sec(d*x + c)^(9/2), x)","F",0
200,0,0,0,0.467986," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \sec\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \sec\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \sec\left(d x + c\right) + A a^{3}}{\sec\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((B*a^3*sec(d*x + c)^4 + (A + 3*B)*a^3*sec(d*x + c)^3 + 3*(A + B)*a^3*sec(d*x + c)^2 + (3*A + B)*a^3*sec(d*x + c) + A*a^3)/sec(d*x + c)^(11/2), x)","F",0
201,0,0,0,0.443706," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{4} + A \sec\left(d x + c\right)^{3}\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*sec(d*x + c)^4 + A*sec(d*x + c)^3)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
202,0,0,0,0.466468," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*sec(d*x + c)^3 + A*sec(d*x + c)^2)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
203,0,0,0,0.458834," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{2} + A \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*sec(d*x + c)^2 + A*sec(d*x + c))*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
204,0,0,0,0.428586," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
205,0,0,0,0.426700," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c)^2 + a*sec(d*x + c)), x)","F",0
206,0,0,0,0.484731," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c)^3 + a*sec(d*x + c)^2), x)","F",0
207,0,0,0,0.454874," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{4} + a \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c)^4 + a*sec(d*x + c)^3), x)","F",0
208,0,0,0,0.473670," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{5} + a \sec\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c)^5 + a*sec(d*x + c)^4), x)","F",0
209,0,0,0,0.446033," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{4} + A \sec\left(d x + c\right)^{3}\right)} \sqrt{\sec\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c)^4 + A*sec(d*x + c)^3)*sqrt(sec(d*x + c))/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
210,0,0,0,0.439065," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c)^3 + A*sec(d*x + c)^2)*sqrt(sec(d*x + c))/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
211,0,0,0,0.448117," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{2} + A \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c)^2 + A*sec(d*x + c))*sqrt(sec(d*x + c))/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
212,0,0,0,0.462019," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
213,0,0,0,0.470592," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{3} + 2 \, a^{2} \sec\left(d x + c\right)^{2} + a^{2} \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a^2*sec(d*x + c)^3 + 2*a^2*sec(d*x + c)^2 + a^2*sec(d*x + c)), x)","F",0
214,0,0,0,0.447924," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{4} + 2 \, a^{2} \sec\left(d x + c\right)^{3} + a^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a^2*sec(d*x + c)^4 + 2*a^2*sec(d*x + c)^3 + a^2*sec(d*x + c)^2), x)","F",0
215,0,0,0,0.489684," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{5} + 2 \, a^{2} \sec\left(d x + c\right)^{4} + a^{2} \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a^2*sec(d*x + c)^5 + 2*a^2*sec(d*x + c)^4 + a^2*sec(d*x + c)^3), x)","F",0
216,0,0,0,0.456423," ","integrate(sec(d*x+c)^(9/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{5} + A \sec\left(d x + c\right)^{4}\right)} \sqrt{\sec\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c)^5 + A*sec(d*x + c)^4)*sqrt(sec(d*x + c))/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
217,0,0,0,0.442799," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{4} + A \sec\left(d x + c\right)^{3}\right)} \sqrt{\sec\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c)^4 + A*sec(d*x + c)^3)*sqrt(sec(d*x + c))/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
218,0,0,0,0.435061," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c)^3 + A*sec(d*x + c)^2)*sqrt(sec(d*x + c))/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
219,0,0,0,0.426111," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{2} + A \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c)^2 + A*sec(d*x + c))*sqrt(sec(d*x + c))/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
220,0,0,0,0.440419," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
221,0,0,0,0.462617," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{4} + 3 \, a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + a^{3} \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a^3*sec(d*x + c)^4 + 3*a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + a^3*sec(d*x + c)), x)","F",0
222,0,0,0,0.465092," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{5} + 3 \, a^{3} \sec\left(d x + c\right)^{4} + 3 \, a^{3} \sec\left(d x + c\right)^{3} + a^{3} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a^3*sec(d*x + c)^5 + 3*a^3*sec(d*x + c)^4 + 3*a^3*sec(d*x + c)^3 + a^3*sec(d*x + c)^2), x)","F",0
223,0,0,0,0.472382," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{6} + 3 \, a^{3} \sec\left(d x + c\right)^{5} + 3 \, a^{3} \sec\left(d x + c\right)^{4} + a^{3} \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a^3*sec(d*x + c)^6 + 3*a^3*sec(d*x + c)^5 + 3*a^3*sec(d*x + c)^4 + a^3*sec(d*x + c)^3), x)","F",0
224,1,448,0,0.563250," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(3 \, {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 8 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{96 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, \frac{3 \, {\left({\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(3 \, {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 8 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{48 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/96*(3*((6*A + 5*B)*cos(d*x + c)^3 + (6*A + 5*B)*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(3*(6*A + 5*B)*cos(d*x + c)^2 + 2*(6*A + 5*B)*cos(d*x + c) + 8*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2), 1/48*(3*((6*A + 5*B)*cos(d*x + c)^3 + (6*A + 5*B)*cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(3*(6*A + 5*B)*cos(d*x + c)^2 + 2*(6*A + 5*B)*cos(d*x + c) + 8*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)]","A",0
225,1,402,0,0.564411," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left({\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{16 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{{\left({\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left({\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{8 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(((4*A + 3*B)*cos(d*x + c)^2 + (4*A + 3*B)*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*((4*A + 3*B)*cos(d*x + c) + 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), 1/8*(((4*A + 3*B)*cos(d*x + c)^2 + (4*A + 3*B)*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*((4*A + 3*B)*cos(d*x + c) + 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
226,1,322,0,0.748739," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, A + B\right)} \cos\left(d x + c\right) + 2 \, A + B\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, B \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{{\left({\left(2 \, A + B\right)} \cos\left(d x + c\right) + 2 \, A + B\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, B \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/4*(((2*A + B)*cos(d*x + c) + 2*A + B)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d), 1/2*(((2*A + B)*cos(d*x + c) + 2*A + B)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)]","B",0
227,1,307,0,0.472445," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, A \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left(B \cos\left(d x + c\right) + B\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{2 \, A \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left(B \cos\left(d x + c\right) + B\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{d \cos\left(d x + c\right) + d}\right]"," ",0,"[1/2*(4*A*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + (B*cos(d*x + c) + B)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c) + d), (2*A*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + (B*cos(d*x + c) + B)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c) + d)]","B",0
228,1,74,0,0.424069," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(A \cos\left(d x + c\right)^{2} + {\left(2 \, A + 3 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/3*(A*cos(d*x + c)^2 + (2*A + 3*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
229,1,92,0,0.406105," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, A \cos\left(d x + c\right)^{3} + {\left(4 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, A + 5 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/15*(3*A*cos(d*x + c)^3 + (4*A + 5*B)*cos(d*x + c)^2 + 2*(4*A + 5*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
230,1,110,0,0.406309," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, A \cos\left(d x + c\right)^{4} + 3 \, {\left(6 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(6 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(6 \, A + 7 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/105*(15*A*cos(d*x + c)^4 + 3*(6*A + 7*B)*cos(d*x + c)^3 + 4*(6*A + 7*B)*cos(d*x + c)^2 + 8*(6*A + 7*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
231,1,494,0,0.684756," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{4} + {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(3 \, {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, A + 15 \, B\right)} a \cos\left(d x + c\right) + 48 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{768 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}, \frac{3 \, {\left({\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{4} + {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{3}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(3 \, {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, A + 15 \, B\right)} a \cos\left(d x + c\right) + 48 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/768*(3*((88*A + 75*B)*a*cos(d*x + c)^4 + (88*A + 75*B)*a*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(3*(88*A + 75*B)*a*cos(d*x + c)^3 + 2*(88*A + 75*B)*a*cos(d*x + c)^2 + 8*(8*A + 15*B)*a*cos(d*x + c) + 48*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3), 1/384*(3*((88*A + 75*B)*a*cos(d*x + c)^4 + (88*A + 75*B)*a*cos(d*x + c)^3)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(3*(88*A + 75*B)*a*cos(d*x + c)^3 + 2*(88*A + 75*B)*a*cos(d*x + c)^2 + 8*(8*A + 15*B)*a*cos(d*x + c) + 48*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)]","A",0
232,1,458,0,0.589351," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{3} + {\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(3 \, {\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 11 \, B\right)} a \cos\left(d x + c\right) + 8 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{96 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, \frac{3 \, {\left({\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{3} + {\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(3 \, {\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 11 \, B\right)} a \cos\left(d x + c\right) + 8 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{48 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/96*(3*((14*A + 11*B)*a*cos(d*x + c)^3 + (14*A + 11*B)*a*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(3*(14*A + 11*B)*a*cos(d*x + c)^2 + 2*(6*A + 11*B)*a*cos(d*x + c) + 8*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2), 1/48*(3*((14*A + 11*B)*a*cos(d*x + c)^3 + (14*A + 11*B)*a*cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(3*(14*A + 11*B)*a*cos(d*x + c)^2 + 2*(6*A + 11*B)*a*cos(d*x + c) + 8*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)]","A",0
233,1,410,0,0.614124," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(12 \, A + 7 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(12 \, A + 7 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left({\left(4 \, A + 7 \, B\right)} a \cos\left(d x + c\right) + 2 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{16 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{{\left({\left(12 \, A + 7 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(12 \, A + 7 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left({\left(4 \, A + 7 \, B\right)} a \cos\left(d x + c\right) + 2 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{8 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(((12*A + 7*B)*a*cos(d*x + c)^2 + (12*A + 7*B)*a*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*((4*A + 7*B)*a*cos(d*x + c) + 2*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), 1/8*(((12*A + 7*B)*a*cos(d*x + c)^2 + (12*A + 7*B)*a*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*((4*A + 7*B)*a*cos(d*x + c) + 2*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
234,1,364,0,0.539706," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, A + 3 \, B\right)} a \cos\left(d x + c\right) + {\left(2 \, A + 3 \, B\right)} a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(2 \, A a \cos\left(d x + c\right) + B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{{\left({\left(2 \, A + 3 \, B\right)} a \cos\left(d x + c\right) + {\left(2 \, A + 3 \, B\right)} a\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(2 \, A a \cos\left(d x + c\right) + B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/4*(((2*A + 3*B)*a*cos(d*x + c) + (2*A + 3*B)*a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(2*A*a*cos(d*x + c) + B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d), 1/2*(((2*A + 3*B)*a*cos(d*x + c) + (2*A + 3*B)*a)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(2*A*a*cos(d*x + c) + B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)]","A",0
235,1,368,0,0.471468," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a \cos\left(d x + c\right) + B a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(A a \cos\left(d x + c\right)^{2} + {\left(5 \, A + 3 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{6 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{3 \, {\left(B a \cos\left(d x + c\right) + B a\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(A a \cos\left(d x + c\right)^{2} + {\left(5 \, A + 3 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{3 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/6*(3*(B*a*cos(d*x + c) + B*a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(A*a*cos(d*x + c)^2 + (5*A + 3*B)*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d), 1/3*(3*(B*a*cos(d*x + c) + B*a)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(A*a*cos(d*x + c)^2 + (5*A + 3*B)*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)]","A",0
236,1,94,0,0.418613," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, A a \cos\left(d x + c\right)^{3} + {\left(9 \, A + 5 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(18 \, A + 25 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/15*(3*A*a*cos(d*x + c)^3 + (9*A + 5*B)*a*cos(d*x + c)^2 + (18*A + 25*B)*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
237,1,113,0,0.420953," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, A a \cos\left(d x + c\right)^{4} + 3 \, {\left(13 \, A + 7 \, B\right)} a \cos\left(d x + c\right)^{3} + {\left(52 \, A + 63 \, B\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(52 \, A + 63 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/105*(15*A*a*cos(d*x + c)^4 + 3*(13*A + 7*B)*a*cos(d*x + c)^3 + (52*A + 63*B)*a*cos(d*x + c)^2 + 2*(52*A + 63*B)*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
238,1,132,0,0.428252," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A a \cos\left(d x + c\right)^{5} + 5 \, {\left(17 \, A + 9 \, B\right)} a \cos\left(d x + c\right)^{4} + 3 \, {\left(34 \, A + 39 \, B\right)} a \cos\left(d x + c\right)^{3} + 4 \, {\left(34 \, A + 39 \, B\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(34 \, A + 39 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/315*(35*A*a*cos(d*x + c)^5 + 5*(17*A + 9*B)*a*cos(d*x + c)^4 + 3*(34*A + 39*B)*a*cos(d*x + c)^3 + 4*(34*A + 39*B)*a*cos(d*x + c)^2 + 8*(34*A + 39*B)*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
239,1,558,0,0.679823," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(15 \, {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(230 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 48 \, {\left(10 \, A + 29 \, B\right)} a^{2} \cos\left(d x + c\right) + 384 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{7680 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}, \frac{15 \, {\left({\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(15 \, {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(230 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 48 \, {\left(10 \, A + 29 \, B\right)} a^{2} \cos\left(d x + c\right) + 384 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{3840 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/7680*(15*((326*A + 283*B)*a^2*cos(d*x + c)^5 + (326*A + 283*B)*a^2*cos(d*x + c)^4)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(15*(326*A + 283*B)*a^2*cos(d*x + c)^4 + 10*(326*A + 283*B)*a^2*cos(d*x + c)^3 + 8*(230*A + 283*B)*a^2*cos(d*x + c)^2 + 48*(10*A + 29*B)*a^2*cos(d*x + c) + 384*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4), 1/3840*(15*((326*A + 283*B)*a^2*cos(d*x + c)^5 + (326*A + 283*B)*a^2*cos(d*x + c)^4)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(15*(326*A + 283*B)*a^2*cos(d*x + c)^4 + 10*(326*A + 283*B)*a^2*cos(d*x + c)^3 + 8*(230*A + 283*B)*a^2*cos(d*x + c)^2 + 48*(10*A + 29*B)*a^2*cos(d*x + c) + 384*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)]","A",0
240,1,518,0,0.695768," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(3 \, {\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(136 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, A + 23 \, B\right)} a^{2} \cos\left(d x + c\right) + 48 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{768 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}, \frac{3 \, {\left({\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(3 \, {\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(136 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, A + 23 \, B\right)} a^{2} \cos\left(d x + c\right) + 48 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/768*(3*((200*A + 163*B)*a^2*cos(d*x + c)^4 + (200*A + 163*B)*a^2*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(3*(200*A + 163*B)*a^2*cos(d*x + c)^3 + 2*(136*A + 163*B)*a^2*cos(d*x + c)^2 + 8*(8*A + 23*B)*a^2*cos(d*x + c) + 48*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3), 1/384*(3*((200*A + 163*B)*a^2*cos(d*x + c)^4 + (200*A + 163*B)*a^2*cos(d*x + c)^3)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(3*(200*A + 163*B)*a^2*cos(d*x + c)^3 + 2*(136*A + 163*B)*a^2*cos(d*x + c)^2 + 8*(8*A + 23*B)*a^2*cos(d*x + c) + 48*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)]","A",0
241,1,478,0,0.592058," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(38 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(38 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(3 \, {\left(22 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 17 \, B\right)} a^{2} \cos\left(d x + c\right) + 8 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{96 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, \frac{3 \, {\left({\left(38 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(38 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(3 \, {\left(22 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 17 \, B\right)} a^{2} \cos\left(d x + c\right) + 8 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{48 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/96*(3*((38*A + 25*B)*a^2*cos(d*x + c)^3 + (38*A + 25*B)*a^2*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(3*(22*A + 25*B)*a^2*cos(d*x + c)^2 + 2*(6*A + 17*B)*a^2*cos(d*x + c) + 8*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2), 1/48*(3*((38*A + 25*B)*a^2*cos(d*x + c)^3 + (38*A + 25*B)*a^2*cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(3*(22*A + 25*B)*a^2*cos(d*x + c)^2 + 2*(6*A + 17*B)*a^2*cos(d*x + c) + 8*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)]","A",0
242,1,454,0,0.557104," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(20 \, A + 19 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(20 \, A + 19 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(8 \, A a^{2} \cos\left(d x + c\right)^{2} + {\left(4 \, A + 11 \, B\right)} a^{2} \cos\left(d x + c\right) + 2 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{16 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{{\left({\left(20 \, A + 19 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(20 \, A + 19 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(8 \, A a^{2} \cos\left(d x + c\right)^{2} + {\left(4 \, A + 11 \, B\right)} a^{2} \cos\left(d x + c\right) + 2 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{8 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(((20*A + 19*B)*a^2*cos(d*x + c)^2 + (20*A + 19*B)*a^2*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(8*A*a^2*cos(d*x + c)^2 + (4*A + 11*B)*a^2*cos(d*x + c) + 2*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), 1/8*(((20*A + 19*B)*a^2*cos(d*x + c)^2 + (20*A + 19*B)*a^2*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(8*A*a^2*cos(d*x + c)^2 + (4*A + 11*B)*a^2*cos(d*x + c) + 2*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
243,1,424,0,0.604578," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(2 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(2 \, A + 5 \, B\right)} a^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(2 \, A a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right) + 3 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{12 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{3 \, {\left({\left(2 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(2 \, A + 5 \, B\right)} a^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(2 \, A a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right) + 3 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{6 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/12*(3*((2*A + 5*B)*a^2*cos(d*x + c) + (2*A + 5*B)*a^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(2*A*a^2*cos(d*x + c)^2 + 2*(8*A + 3*B)*a^2*cos(d*x + c) + 3*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d), 1/6*(3*((2*A + 5*B)*a^2*cos(d*x + c) + (2*A + 5*B)*a^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(2*A*a^2*cos(d*x + c)^2 + 2*(8*A + 3*B)*a^2*cos(d*x + c) + 3*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)]","A",0
244,1,424,0,0.484993," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(B a^{2} \cos\left(d x + c\right) + B a^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(3 \, A a^{2} \cos\left(d x + c\right)^{3} + {\left(14 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(43 \, A + 40 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{30 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{15 \, {\left(B a^{2} \cos\left(d x + c\right) + B a^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(3 \, A a^{2} \cos\left(d x + c\right)^{3} + {\left(14 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(43 \, A + 40 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{15 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/30*(15*(B*a^2*cos(d*x + c) + B*a^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(3*A*a^2*cos(d*x + c)^3 + (14*A + 5*B)*a^2*cos(d*x + c)^2 + (43*A + 40*B)*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d), 1/15*(15*(B*a^2*cos(d*x + c) + B*a^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(3*A*a^2*cos(d*x + c)^3 + (14*A + 5*B)*a^2*cos(d*x + c)^2 + (43*A + 40*B)*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)]","A",0
245,1,120,0,0.440823," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, A a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(20 \, A + 7 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(115 \, A + 98 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(230 \, A + 301 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/105*(15*A*a^2*cos(d*x + c)^4 + 3*(20*A + 7*B)*a^2*cos(d*x + c)^3 + (115*A + 98*B)*a^2*cos(d*x + c)^2 + (230*A + 301*B)*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
246,1,141,0,0.452442," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A a^{2} \cos\left(d x + c\right)^{5} + 5 \, {\left(26 \, A + 9 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(73 \, A + 60 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(292 \, A + 345 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(292 \, A + 345 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/315*(35*A*a^2*cos(d*x + c)^5 + 5*(26*A + 9*B)*a^2*cos(d*x + c)^4 + 3*(73*A + 60*B)*a^2*cos(d*x + c)^3 + (292*A + 345*B)*a^2*cos(d*x + c)^2 + 2*(292*A + 345*B)*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
247,1,162,0,0.477855," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, A a^{2} \cos\left(d x + c\right)^{6} + 35 \, {\left(32 \, A + 11 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} + 5 \, {\left(355 \, A + 286 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(710 \, A + 803 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 4 \, {\left(710 \, A + 803 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(710 \, A + 803 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{3465 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/3465*(315*A*a^2*cos(d*x + c)^6 + 35*(32*A + 11*B)*a^2*cos(d*x + c)^5 + 5*(355*A + 286*B)*a^2*cos(d*x + c)^4 + 3*(710*A + 803*B)*a^2*cos(d*x + c)^3 + 4*(710*A + 803*B)*a^2*cos(d*x + c)^2 + 8*(710*A + 803*B)*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
248,1,617,0,0.647973," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{8 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B\right)} a \cos\left(d x + c\right)\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}} - \frac{4 \, {\left({\left(4 \, A - B\right)} \cos\left(d x + c\right) + 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{16 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}, -\frac{8 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B\right)} a \cos\left(d x + c\right)\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + {\left({\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) - \frac{2 \, {\left({\left(4 \, A - B\right)} \cos\left(d x + c\right) + 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{8 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(((4*A - 7*B)*cos(d*x + c)^2 + (4*A - 7*B)*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 8*sqrt(2)*((A - B)*a*cos(d*x + c)^2 + (A - B)*a*cos(d*x + c))*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a) - 4*((4*A - B)*cos(d*x + c) + 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c)), -1/8*(8*sqrt(2)*((A - B)*a*cos(d*x + c)^2 + (A - B)*a*cos(d*x + c))*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + ((4*A - 7*B)*cos(d*x + c)^2 + (4*A - 7*B)*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) - 2*((4*A - B)*cos(d*x + c) + 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))]","A",0
249,1,531,0,0.598025," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, A - B\right)} \cos\left(d x + c\right) + 2 \, A - B\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{2 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}} - \frac{4 \, B \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{2 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + {\left({\left(2 \, A - B\right)} \cos\left(d x + c\right) + 2 \, A - B\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, B \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[-1/4*(((2*A - B)*cos(d*x + c) + 2*A - B)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 2*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a) - 4*B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d), 1/2*(2*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + ((2*A - B)*cos(d*x + c) + 2*A - B)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d)]","A",0
250,1,366,0,0.516242," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left(A - B\right)} \sqrt{a} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - B \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{2 \, a d}, -\frac{\sqrt{2} {\left(A - B\right)} a \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - B \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{a d}\right]"," ",0,"[-1/2*(sqrt(2)*(A - B)*sqrt(a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - B*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a*d), -(sqrt(2)*(A - B)*a*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) - B*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(a*d)]","A",0
251,1,306,0,0.466569," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, A \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \frac{\sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{\sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + 2 \, A \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}\right]"," ",0,"[1/2*(4*A*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c) + a*d), (sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + 2*A*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)]","A",0
252,1,354,0,0.458250," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\frac{3 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}} - \frac{4 \, {\left(A \cos\left(d x + c\right)^{2} - {\left(A - 3 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, -\frac{3 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - \frac{2 \, {\left(A \cos\left(d x + c\right)^{2} - {\left(A - 3 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{3 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[-1/6*(3*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a) - 4*(A*cos(d*x + c)^2 - (A - 3*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d), -1/3*(3*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) - 2*(A*cos(d*x + c)^2 - (A - 3*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d)]","A",0
253,1,388,0,0.459829," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\frac{15 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}} - \frac{4 \, {\left(3 \, A \cos\left(d x + c\right)^{3} - {\left(A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(13 \, A - 5 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{30 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{15 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + \frac{2 \, {\left(3 \, A \cos\left(d x + c\right)^{3} - {\left(A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(13 \, A - 5 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{15 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[-1/30*(15*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a) - 4*(3*A*cos(d*x + c)^3 - (A - 5*B)*cos(d*x + c)^2 + (13*A - 5*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d), 1/15*(15*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + 2*(3*A*cos(d*x + c)^3 - (A - 5*B)*cos(d*x + c)^2 + (13*A - 5*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d)]","A",0
254,1,422,0,0.482516," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\frac{105 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}} - \frac{4 \, {\left(15 \, A \cos\left(d x + c\right)^{4} - 3 \, {\left(A - 7 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(31 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(43 \, A - 91 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{210 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, -\frac{105 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - \frac{2 \, {\left(15 \, A \cos\left(d x + c\right)^{4} - 3 \, {\left(A - 7 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(31 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(43 \, A - 91 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{105 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[-1/210*(105*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a) - 4*(15*A*cos(d*x + c)^4 - 3*(A - 7*B)*cos(d*x + c)^3 + (31*A - 7*B)*cos(d*x + c)^2 - (43*A - 91*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d), -1/105*(105*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) - 2*(15*A*cos(d*x + c)^4 - 3*(A - 7*B)*cos(d*x + c)^3 + (31*A - 7*B)*cos(d*x + c)^2 - (43*A - 91*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d)]","A",0
255,1,761,0,0.666160," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{2} {\left({\left(9 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(9 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, A - 13 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + {\left({\left(12 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(12 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(12 \, A - 19 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - \frac{4 \, {\left({\left(6 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{16 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}, -\frac{2 \, \sqrt{2} {\left({\left(9 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(9 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, A - 13 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + {\left({\left(12 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(12 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(12 \, A - 19 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) - \frac{2 \, {\left({\left(6 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(2*sqrt(2)*((9*A - 13*B)*cos(d*x + c)^3 + 2*(9*A - 13*B)*cos(d*x + c)^2 + (9*A - 13*B)*cos(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + ((12*A - 19*B)*cos(d*x + c)^3 + 2*(12*A - 19*B)*cos(d*x + c)^2 + (12*A - 19*B)*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 4*((6*A - 7*B)*cos(d*x + c)^2 + (4*A - 3*B)*cos(d*x + c) + 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c)), -1/8*(2*sqrt(2)*((9*A - 13*B)*cos(d*x + c)^3 + 2*(9*A - 13*B)*cos(d*x + c)^2 + (9*A - 13*B)*cos(d*x + c))*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + ((12*A - 19*B)*cos(d*x + c)^3 + 2*(12*A - 19*B)*cos(d*x + c)^2 + (12*A - 19*B)*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) - 2*((6*A - 7*B)*cos(d*x + c)^2 + (4*A - 3*B)*cos(d*x + c) + 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))]","A",0
256,1,669,0,0.662771," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right) + 5 \, A - 9 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 2 \, {\left({\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 2 \, A - 3 \, B\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left({\left(A - 3 \, B\right)} \cos\left(d x + c\right) - 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, \frac{\sqrt{2} {\left({\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right) + 5 \, A - 9 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, {\left({\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 2 \, A - 3 \, B\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) - \frac{2 \, {\left({\left(A - 3 \, B\right)} \cos\left(d x + c\right) - 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[-1/8*(sqrt(2)*((5*A - 9*B)*cos(d*x + c)^2 + 2*(5*A - 9*B)*cos(d*x + c) + 5*A - 9*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 2*((2*A - 3*B)*cos(d*x + c)^2 + 2*(2*A - 3*B)*cos(d*x + c) + 2*A - 3*B)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*((A - 3*B)*cos(d*x + c) - 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), 1/4*(sqrt(2)*((5*A - 9*B)*cos(d*x + c)^2 + 2*(5*A - 9*B)*cos(d*x + c) + 5*A - 9*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*((2*A - 3*B)*cos(d*x + c)^2 + 2*(2*A - 3*B)*cos(d*x + c) + 2*A - 3*B)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) - 2*((A - 3*B)*cos(d*x + c) - 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
257,1,601,0,0.535287," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - 5 \, B\right)} \cos\left(d x + c\right) + A - 5 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 4 \, {\left(B \cos\left(d x + c\right)^{2} + 2 \, B \cos\left(d x + c\right) + B\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, -\frac{\sqrt{2} {\left({\left(A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - 5 \, B\right)} \cos\left(d x + c\right) + A - 5 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, {\left(A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 4 \, {\left(B \cos\left(d x + c\right)^{2} + 2 \, B \cos\left(d x + c\right) + B\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[-1/8*(sqrt(2)*((A - 5*B)*cos(d*x + c)^2 + 2*(A - 5*B)*cos(d*x + c) + A - 5*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 4*(B*cos(d*x + c)^2 + 2*B*cos(d*x + c) + B)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/4*(sqrt(2)*((A - 5*B)*cos(d*x + c)^2 + 2*(A - 5*B)*cos(d*x + c) + A - 5*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*(A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 4*(B*cos(d*x + c)^2 + 2*B*cos(d*x + c) + B)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","B",0
258,1,376,0,0.464903," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(3 \, A + B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right) + 3 \, A + B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, -\frac{\sqrt{2} {\left({\left(3 \, A + B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right) + 3 \, A + B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, {\left(A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[1/8*(sqrt(2)*((3*A + B)*cos(d*x + c)^2 + 2*(3*A + B)*cos(d*x + c) + 3*A + B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/4*(sqrt(2)*((3*A + B)*cos(d*x + c)^2 + 2*(3*A + B)*cos(d*x + c) + 3*A + B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
259,1,430,0,0.460532," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 7 \, A - 3 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - \frac{4 \, {\left(4 \, A \cos\left(d x + c\right)^{2} + {\left(5 \, A - B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, \frac{\sqrt{2} {\left({\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 7 \, A - 3 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(4 \, A \cos\left(d x + c\right)^{2} + {\left(5 \, A - B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[-1/8*(sqrt(2)*((7*A - 3*B)*cos(d*x + c)^2 + 2*(7*A - 3*B)*cos(d*x + c) + 7*A - 3*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(4*A*cos(d*x + c)^2 + (5*A - B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), 1/4*(sqrt(2)*((7*A - 3*B)*cos(d*x + c)^2 + 2*(7*A - 3*B)*cos(d*x + c) + 7*A - 3*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(4*A*cos(d*x + c)^2 + (5*A - B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
260,1,464,0,0.464449," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left({\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right) + 11 \, A - 7 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - \frac{4 \, {\left(4 \, A \cos\left(d x + c\right)^{3} - 12 \, {\left(A - B\right)} \cos\left(d x + c\right)^{2} - {\left(19 \, A - 15 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{24 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, -\frac{3 \, \sqrt{2} {\left({\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right) + 11 \, A - 7 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - \frac{2 \, {\left(4 \, A \cos\left(d x + c\right)^{3} - 12 \, {\left(A - B\right)} \cos\left(d x + c\right)^{2} - {\left(19 \, A - 15 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[-1/24*(3*sqrt(2)*((11*A - 7*B)*cos(d*x + c)^2 + 2*(11*A - 7*B)*cos(d*x + c) + 11*A - 7*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(4*A*cos(d*x + c)^3 - 12*(A - B)*cos(d*x + c)^2 - (19*A - 15*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/12*(3*sqrt(2)*((11*A - 7*B)*cos(d*x + c)^2 + 2*(11*A - 7*B)*cos(d*x + c) + 11*A - 7*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*(4*A*cos(d*x + c)^3 - 12*(A - B)*cos(d*x + c)^2 - (19*A - 15*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
261,1,500,0,0.487939," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left({\left(15 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A - 11 \, B\right)} \cos\left(d x + c\right) + 15 \, A - 11 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - \frac{4 \, {\left(12 \, A \cos\left(d x + c\right)^{4} - 4 \, {\left(3 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(147 \, A - 95 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{120 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, \frac{15 \, \sqrt{2} {\left({\left(15 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A - 11 \, B\right)} \cos\left(d x + c\right) + 15 \, A - 11 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(12 \, A \cos\left(d x + c\right)^{4} - 4 \, {\left(3 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(147 \, A - 95 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{60 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[-1/120*(15*sqrt(2)*((15*A - 11*B)*cos(d*x + c)^2 + 2*(15*A - 11*B)*cos(d*x + c) + 15*A - 11*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(12*A*cos(d*x + c)^4 - 4*(3*A - 5*B)*cos(d*x + c)^3 + 12*(9*A - 5*B)*cos(d*x + c)^2 + (147*A - 95*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), 1/60*(15*sqrt(2)*((15*A - 11*B)*cos(d*x + c)^2 + 2*(15*A - 11*B)*cos(d*x + c) + 15*A - 11*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(12*A*cos(d*x + c)^4 - 4*(3*A - 5*B)*cos(d*x + c)^3 + 12*(9*A - 5*B)*cos(d*x + c)^2 + (147*A - 95*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
262,1,803,0,0.720508," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right) + 43 \, A - 115 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 16 \, {\left({\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 2 \, A - 5 \, B\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left({\left(11 \, A - 35 \, B\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(3 \, A - 11 \, B\right)} \cos\left(d x + c\right) - 16 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, \frac{\sqrt{2} {\left({\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right) + 43 \, A - 115 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 16 \, {\left({\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 2 \, A - 5 \, B\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) - \frac{2 \, {\left({\left(11 \, A - 35 \, B\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(3 \, A - 11 \, B\right)} \cos\left(d x + c\right) - 16 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[-1/64*(sqrt(2)*((43*A - 115*B)*cos(d*x + c)^3 + 3*(43*A - 115*B)*cos(d*x + c)^2 + 3*(43*A - 115*B)*cos(d*x + c) + 43*A - 115*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 16*((2*A - 5*B)*cos(d*x + c)^3 + 3*(2*A - 5*B)*cos(d*x + c)^2 + 3*(2*A - 5*B)*cos(d*x + c) + 2*A - 5*B)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*((11*A - 35*B)*cos(d*x + c)^2 + 5*(3*A - 11*B)*cos(d*x + c) - 16*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), 1/32*(sqrt(2)*((43*A - 115*B)*cos(d*x + c)^3 + 3*(43*A - 115*B)*cos(d*x + c)^2 + 3*(43*A - 115*B)*cos(d*x + c) + 43*A - 115*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 16*((2*A - 5*B)*cos(d*x + c)^3 + 3*(2*A - 5*B)*cos(d*x + c)^2 + 3*(2*A - 5*B)*cos(d*x + c) + 2*A - 5*B)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) - 2*((11*A - 35*B)*cos(d*x + c)^2 + 5*(3*A - 11*B)*cos(d*x + c) - 16*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
263,1,749,0,0.568984," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right) + 3 \, A - 43 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 32 \, {\left(B \cos\left(d x + c\right)^{3} + 3 \, B \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + B\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - \frac{4 \, {\left({\left(3 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A - 15 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, -\frac{\sqrt{2} {\left({\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right) + 3 \, A - 43 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 32 \, {\left(B \cos\left(d x + c\right)^{3} + 3 \, B \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + B\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) - \frac{2 \, {\left({\left(3 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A - 15 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[-1/64*(sqrt(2)*((3*A - 43*B)*cos(d*x + c)^3 + 3*(3*A - 43*B)*cos(d*x + c)^2 + 3*(3*A - 43*B)*cos(d*x + c) + 3*A - 43*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 32*(B*cos(d*x + c)^3 + 3*B*cos(d*x + c)^2 + 3*B*cos(d*x + c) + B)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 4*((3*A - 11*B)*cos(d*x + c)^2 + (7*A - 15*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), -1/32*(sqrt(2)*((3*A - 43*B)*cos(d*x + c)^3 + 3*(3*A - 43*B)*cos(d*x + c)^2 + 3*(3*A - 43*B)*cos(d*x + c) + 3*A - 43*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 32*(B*cos(d*x + c)^3 + 3*B*cos(d*x + c)^2 + 3*B*cos(d*x + c) + B)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) - 2*((3*A - 11*B)*cos(d*x + c)^2 + (7*A - 15*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","B",0
264,1,498,0,0.468807," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + \frac{4 \, {\left({\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(A + 7 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, -\frac{\sqrt{2} {\left({\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - \frac{2 \, {\left({\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(A + 7 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[1/64*(sqrt(2)*((5*A + 3*B)*cos(d*x + c)^3 + 3*(5*A + 3*B)*cos(d*x + c)^2 + 3*(5*A + 3*B)*cos(d*x + c) + 5*A + 3*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*((5*A + 3*B)*cos(d*x + c)^2 + (A + 7*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), -1/32*(sqrt(2)*((5*A + 3*B)*cos(d*x + c)^3 + 3*(5*A + 3*B)*cos(d*x + c)^2 + 3*(5*A + 3*B)*cos(d*x + c) + 5*A + 3*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*((5*A + 3*B)*cos(d*x + c)^2 + (A + 7*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
265,1,502,0,0.709303," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 19 \, A + 5 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - \frac{4 \, {\left({\left(13 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, A - B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, -\frac{\sqrt{2} {\left({\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 19 \, A + 5 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + \frac{2 \, {\left({\left(13 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, A - B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[1/64*(sqrt(2)*((19*A + 5*B)*cos(d*x + c)^3 + 3*(19*A + 5*B)*cos(d*x + c)^2 + 3*(19*A + 5*B)*cos(d*x + c) + 19*A + 5*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*((13*A - 5*B)*cos(d*x + c)^2 + (9*A - B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), -1/32*(sqrt(2)*((19*A + 5*B)*cos(d*x + c)^3 + 3*(19*A + 5*B)*cos(d*x + c)^2 + 3*(19*A + 5*B)*cos(d*x + c) + 19*A + 5*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*((13*A - 5*B)*cos(d*x + c)^2 + (9*A - B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
266,1,524,0,0.477097," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right) + 75 \, A - 19 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - \frac{4 \, {\left(32 \, A \cos\left(d x + c\right)^{3} + {\left(85 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(49 \, A - 9 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, \frac{\sqrt{2} {\left({\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right) + 75 \, A - 19 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(32 \, A \cos\left(d x + c\right)^{3} + {\left(85 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(49 \, A - 9 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[-1/64*(sqrt(2)*((75*A - 19*B)*cos(d*x + c)^3 + 3*(75*A - 19*B)*cos(d*x + c)^2 + 3*(75*A - 19*B)*cos(d*x + c) + 75*A - 19*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(32*A*cos(d*x + c)^3 + (85*A - 13*B)*cos(d*x + c)^2 + (49*A - 9*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), 1/32*(sqrt(2)*((75*A - 19*B)*cos(d*x + c)^3 + 3*(75*A - 19*B)*cos(d*x + c)^2 + 3*(75*A - 19*B)*cos(d*x + c) + 75*A - 19*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(32*A*cos(d*x + c)^3 + (85*A - 13*B)*cos(d*x + c)^2 + (49*A - 9*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
267,1,564,0,0.484931," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left({\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right) + 163 \, A - 75 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - \frac{4 \, {\left(32 \, A \cos\left(d x + c\right)^{4} - 32 \, {\left(5 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} - {\left(503 \, A - 255 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(299 \, A - 147 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{192 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, -\frac{3 \, \sqrt{2} {\left({\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right) + 163 \, A - 75 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - \frac{2 \, {\left(32 \, A \cos\left(d x + c\right)^{4} - 32 \, {\left(5 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} - {\left(503 \, A - 255 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(299 \, A - 147 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{96 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[-1/192*(3*sqrt(2)*((163*A - 75*B)*cos(d*x + c)^3 + 3*(163*A - 75*B)*cos(d*x + c)^2 + 3*(163*A - 75*B)*cos(d*x + c) + 163*A - 75*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(32*A*cos(d*x + c)^4 - 32*(5*A - 3*B)*cos(d*x + c)^3 - (503*A - 255*B)*cos(d*x + c)^2 - (299*A - 147*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), -1/96*(3*sqrt(2)*((163*A - 75*B)*cos(d*x + c)^3 + 3*(163*A - 75*B)*cos(d*x + c)^2 + 3*(163*A - 75*B)*cos(d*x + c) + 163*A - 75*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*(32*A*cos(d*x + c)^4 - 32*(5*A - 3*B)*cos(d*x + c)^3 - (503*A - 255*B)*cos(d*x + c)^2 - (299*A - 147*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
268,1,592,0,0.467638," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left({\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right) + 283 \, A - 163 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - \frac{4 \, {\left(96 \, A \cos\left(d x + c\right)^{5} - 160 \, {\left(A - B\right)} \cos\left(d x + c\right)^{4} + 32 \, {\left(49 \, A - 25 \, B\right)} \cos\left(d x + c\right)^{3} + 5 \, {\left(911 \, A - 503 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(2671 \, A - 1495 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{960 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, \frac{15 \, \sqrt{2} {\left({\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right) + 283 \, A - 163 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(96 \, A \cos\left(d x + c\right)^{5} - 160 \, {\left(A - B\right)} \cos\left(d x + c\right)^{4} + 32 \, {\left(49 \, A - 25 \, B\right)} \cos\left(d x + c\right)^{3} + 5 \, {\left(911 \, A - 503 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(2671 \, A - 1495 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{480 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[-1/960*(15*sqrt(2)*((283*A - 163*B)*cos(d*x + c)^3 + 3*(283*A - 163*B)*cos(d*x + c)^2 + 3*(283*A - 163*B)*cos(d*x + c) + 283*A - 163*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(96*A*cos(d*x + c)^5 - 160*(A - B)*cos(d*x + c)^4 + 32*(49*A - 25*B)*cos(d*x + c)^3 + 5*(911*A - 503*B)*cos(d*x + c)^2 + (2671*A - 1495*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), 1/480*(15*sqrt(2)*((283*A - 163*B)*cos(d*x + c)^3 + 3*(283*A - 163*B)*cos(d*x + c)^2 + 3*(283*A - 163*B)*cos(d*x + c) + 283*A - 163*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(96*A*cos(d*x + c)^5 - 160*(A - B)*cos(d*x + c)^4 + 32*(49*A - 25*B)*cos(d*x + c)^3 + 5*(911*A - 503*B)*cos(d*x + c)^2 + (2671*A - 1495*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
269,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
270,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
272,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,0,0,0,0.951735," ","integrate((c*sec(f*x+e))^n*(a+a*sec(f*x+e))^m*(A+B*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(f x + e\right) + A\right)} {\left(a \sec\left(f x + e\right) + a\right)}^{m} \left(c \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((B*sec(f*x + e) + A)*(a*sec(f*x + e) + a)^m*(c*sec(f*x + e))^n, x)","F",0
276,0,0,0,0.867267," ","integrate(sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(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}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^(-n - 1), x)","F",0
277,1,136,0,0.968053," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, A a + 3 \, B b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, A a + 3 \, B b\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(B a + A b\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A a + 3 \, B b\right)} \cos\left(d x + c\right)^{2} + 6 \, B b + 8 \, {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(4*A*a + 3*B*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*A*a + 3*B*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*(B*a + A*b)*cos(d*x + c)^3 + 3*(4*A*a + 3*B*b)*cos(d*x + c)^2 + 6*B*b + 8*(B*a + A*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
278,1,115,0,0.454278," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(B a + A b\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B a + A b\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(3 \, A a + 2 \, B b\right)} \cos\left(d x + c\right)^{2} + 2 \, B b + 3 \, {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(B*a + A*b)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(B*a + A*b)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(3*A*a + 2*B*b)*cos(d*x + c)^2 + 2*B*b + 3*(B*a + A*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
279,1,96,0,0.441600," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, A a + B b\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, A a + B b\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B b + 2 \, {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((2*A*a + B*b)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*A*a + B*b)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(B*b + 2*(B*a + A*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
280,1,85,0,0.479428," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, A a d x \cos\left(d x + c\right) + {\left(B a + A b\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a + A b\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, B b \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*A*a*d*x*cos(d*x + c) + (B*a + A*b)*cos(d*x + c)*log(sin(d*x + c) + 1) - (B*a + A*b)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*B*b*sin(d*x + c))/(d*cos(d*x + c))","B",0
281,1,54,0,0.462476," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(B a + A b\right)} d x + B b \log\left(\sin\left(d x + c\right) + 1\right) - B b \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, A a \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(B*a + A*b)*d*x + B*b*log(sin(d*x + c) + 1) - B*b*log(-sin(d*x + c) + 1) + 2*A*a*sin(d*x + c))/d","A",0
282,1,42,0,0.462231," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(A a + 2 \, B b\right)} d x + {\left(A a \cos\left(d x + c\right) + 2 \, B a + 2 \, A b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((A*a + 2*B*b)*d*x + (A*a*cos(d*x + c) + 2*B*a + 2*A*b)*sin(d*x + c))/d","A",0
283,1,60,0,0.427531," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(B a + A b\right)} d x + {\left(2 \, A a \cos\left(d x + c\right)^{2} + 4 \, A a + 6 \, B b + 3 \, {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(B*a + A*b)*d*x + (2*A*a*cos(d*x + c)^2 + 4*A*a + 6*B*b + 3*(B*a + A*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
284,1,81,0,0.439947," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A a + 4 \, B b\right)} d x + {\left(6 \, A a \cos\left(d x + c\right)^{3} + 8 \, {\left(B a + A b\right)} \cos\left(d x + c\right)^{2} + 16 \, B a + 16 \, A b + 3 \, {\left(3 \, A a + 4 \, B b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(3*A*a + 4*B*b)*d*x + (6*A*a*cos(d*x + c)^3 + 8*(B*a + A*b)*cos(d*x + c)^2 + 16*B*a + 16*A*b + 3*(3*A*a + 4*B*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
285,1,208,0,0.535316," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A a^{2} + 6 \, B a b + 3 \, A b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, A a^{2} + 6 \, B a b + 3 \, A b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(5 \, B a^{2} + 10 \, A a b + 4 \, B b^{2}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(4 \, A a^{2} + 6 \, B a b + 3 \, A b^{2}\right)} \cos\left(d x + c\right)^{3} + 24 \, B b^{2} + 8 \, {\left(5 \, B a^{2} + 10 \, A a b + 4 \, B b^{2}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(4*A*a^2 + 6*B*a*b + 3*A*b^2)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*A*a^2 + 6*B*a*b + 3*A*b^2)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(5*B*a^2 + 10*A*a*b + 4*B*b^2)*cos(d*x + c)^4 + 15*(4*A*a^2 + 6*B*a*b + 3*A*b^2)*cos(d*x + c)^3 + 24*B*b^2 + 8*(5*B*a^2 + 10*A*a*b + 4*B*b^2)*cos(d*x + c)^2 + 30*(2*B*a*b + A*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
286,1,180,0,0.447713," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, B a^{2} + 8 \, A a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, B a^{2} + 8 \, A a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(3 \, A a^{2} + 4 \, B a b + 2 \, A b^{2}\right)} \cos\left(d x + c\right)^{3} + 6 \, B b^{2} + 3 \, {\left(4 \, B a^{2} + 8 \, A a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(4*B*a^2 + 8*A*a*b + 3*B*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*B*a^2 + 8*A*a*b + 3*B*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(3*A*a^2 + 4*B*a*b + 2*A*b^2)*cos(d*x + c)^3 + 6*B*b^2 + 3*(4*B*a^2 + 8*A*a*b + 3*B*b^2)*cos(d*x + c)^2 + 8*(2*B*a*b + A*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
287,1,150,0,0.451392," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, B b^{2} + 2 \, {\left(3 \, B a^{2} + 6 \, A a b + 2 \, B b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(2*A*a^2 + 2*B*a*b + A*b^2)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*A*a^2 + 2*B*a*b + A*b^2)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*B*b^2 + 2*(3*B*a^2 + 6*A*a*b + 2*B*b^2)*cos(d*x + c)^2 + 3*(2*B*a*b + A*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
288,1,136,0,0.458330," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, A a^{2} d x \cos\left(d x + c\right)^{2} + {\left(2 \, B a^{2} + 4 \, A a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, B a^{2} + 4 \, A a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B b^{2} + 2 \, {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*A*a^2*d*x*cos(d*x + c)^2 + (2*B*a^2 + 4*A*a*b + B*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*B*a^2 + 4*A*a*b + B*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(B*b^2 + 2*(2*B*a*b + A*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
289,1,117,0,0.484621," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(B a^{2} + 2 \, A a b\right)} d x \cos\left(d x + c\right) + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{2} \cos\left(d x + c\right) + B b^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*(B*a^2 + 2*A*a*b)*d*x*cos(d*x + c) + (2*B*a*b + A*b^2)*cos(d*x + c)*log(sin(d*x + c) + 1) - (2*B*a*b + A*b^2)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(A*a^2*cos(d*x + c) + B*b^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
290,1,87,0,0.467054," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{B b^{2} \log\left(\sin\left(d x + c\right) + 1\right) - B b^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(A a^{2} + 4 \, B a b + 2 \, A b^{2}\right)} d x + {\left(A a^{2} \cos\left(d x + c\right) + 2 \, B a^{2} + 4 \, A a b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(B*b^2*log(sin(d*x + c) + 1) - B*b^2*log(-sin(d*x + c) + 1) + (A*a^2 + 4*B*a*b + 2*A*b^2)*d*x + (A*a^2*cos(d*x + c) + 2*B*a^2 + 4*A*a*b)*sin(d*x + c))/d","A",0
291,1,85,0,0.465900," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(B a^{2} + 2 \, A a b + 2 \, B b^{2}\right)} d x + {\left(2 \, A a^{2} \cos\left(d x + c\right)^{2} + 4 \, A a^{2} + 12 \, B a b + 6 \, A b^{2} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(B*a^2 + 2*A*a*b + 2*B*b^2)*d*x + (2*A*a^2*cos(d*x + c)^2 + 4*A*a^2 + 12*B*a*b + 6*A*b^2 + 3*(B*a^2 + 2*A*a*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
292,1,114,0,0.447652," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A a^{2} + 8 \, B a b + 4 \, A b^{2}\right)} d x + {\left(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 16 \, B a^{2} + 32 \, A a b + 24 \, B b^{2} + 8 \, {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A a^{2} + 8 \, B a b + 4 \, A b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(3*A*a^2 + 8*B*a*b + 4*A*b^2)*d*x + (6*A*a^2*cos(d*x + c)^3 + 16*B*a^2 + 32*A*a*b + 24*B*b^2 + 8*(B*a^2 + 2*A*a*b)*cos(d*x + c)^2 + 3*(3*A*a^2 + 8*B*a*b + 4*A*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
293,1,142,0,0.479975," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, B a^{2} + 6 \, A a b + 4 \, B b^{2}\right)} d x + {\left(24 \, A a^{2} \cos\left(d x + c\right)^{4} + 30 \, {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{3} + 64 \, A a^{2} + 160 \, B a b + 80 \, A b^{2} + 8 \, {\left(4 \, A a^{2} + 10 \, B a b + 5 \, A b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, B a^{2} + 6 \, A a b + 4 \, B b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(3*B*a^2 + 6*A*a*b + 4*B*b^2)*d*x + (24*A*a^2*cos(d*x + c)^4 + 30*(B*a^2 + 2*A*a*b)*cos(d*x + c)^3 + 64*A*a^2 + 160*B*a*b + 80*A*b^2 + 8*(4*A*a^2 + 10*B*a*b + 5*A*b^2)*cos(d*x + c)^2 + 15*(3*B*a^2 + 6*A*a*b + 4*B*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
294,1,249,0,0.538041," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, B a^{3} + 12 \, A a^{2} b + 9 \, B a b^{2} + 3 \, A b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, B a^{3} + 12 \, A a^{2} b + 9 \, B a b^{2} + 3 \, A b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(15 \, A a^{3} + 30 \, B a^{2} b + 30 \, A a b^{2} + 8 \, B b^{3}\right)} \cos\left(d x + c\right)^{4} + 24 \, B b^{3} + 15 \, {\left(4 \, B a^{3} + 12 \, A a^{2} b + 9 \, B a b^{2} + 3 \, A b^{3}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(15 \, B a^{2} b + 15 \, A a b^{2} + 4 \, B b^{3}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(4*B*a^3 + 12*A*a^2*b + 9*B*a*b^2 + 3*A*b^3)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*B*a^3 + 12*A*a^2*b + 9*B*a*b^2 + 3*A*b^3)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(15*A*a^3 + 30*B*a^2*b + 30*A*a*b^2 + 8*B*b^3)*cos(d*x + c)^4 + 24*B*b^3 + 15*(4*B*a^3 + 12*A*a^2*b + 9*B*a*b^2 + 3*A*b^3)*cos(d*x + c)^3 + 8*(15*B*a^2*b + 15*A*a*b^2 + 4*B*b^3)*cos(d*x + c)^2 + 30*(3*B*a*b^2 + A*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
295,1,211,0,0.480217," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, A a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 3 \, B b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, A a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 3 \, B b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, B b^{3} + 8 \, {\left(3 \, B a^{3} + 9 \, A a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3}\right)} \cos\left(d x + c\right)^{3} + 9 \, {\left(4 \, B a^{2} b + 4 \, A a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(8*A*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 3*B*b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(8*A*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 3*B*b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(6*B*b^3 + 8*(3*B*a^3 + 9*A*a^2*b + 6*B*a*b^2 + 2*A*b^3)*cos(d*x + c)^3 + 9*(4*B*a^2*b + 4*A*a*b^2 + B*b^3)*cos(d*x + c)^2 + 8*(3*B*a*b^2 + A*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
296,1,189,0,0.470547," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{12 \, A a^{3} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B a^{3} + 6 \, A a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, B a^{3} + 6 \, A a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, B b^{3} + 2 \, {\left(9 \, B a^{2} b + 9 \, A a b^{2} + 2 \, B b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(12*A*a^3*d*x*cos(d*x + c)^3 + 3*(2*B*a^3 + 6*A*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*B*a^3 + 6*A*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*B*b^3 + 2*(9*B*a^2*b + 9*A*a*b^2 + 2*B*b^3)*cos(d*x + c)^2 + 3*(3*B*a*b^2 + A*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
297,1,167,0,0.473357," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d x \cos\left(d x + c\right)^{2} + {\left(6 \, B a^{2} b + 6 \, A a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(6 \, B a^{2} b + 6 \, A a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{3} \cos\left(d x + c\right)^{2} + B b^{3} + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*(B*a^3 + 3*A*a^2*b)*d*x*cos(d*x + c)^2 + (6*B*a^2*b + 6*A*a*b^2 + B*b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (6*B*a^2*b + 6*A*a*b^2 + B*b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*A*a^3*cos(d*x + c)^2 + B*b^3 + 2*(3*B*a*b^2 + A*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
298,1,152,0,0.472587," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(A a^{3} + 6 \, B a^{2} b + 6 \, A a b^{2}\right)} d x \cos\left(d x + c\right) + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(A a^{3} \cos\left(d x + c\right)^{2} + 2 \, B b^{3} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*((A*a^3 + 6*B*a^2*b + 6*A*a*b^2)*d*x*cos(d*x + c) + (3*B*a*b^2 + A*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) - (3*B*a*b^2 + A*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) + (A*a^3*cos(d*x + c)^2 + 2*B*b^3 + 2*(B*a^3 + 3*A*a^2*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
299,1,131,0,0.507199," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, B b^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, B b^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left(B a^{3} + 3 \, A a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3}\right)} d x + {\left(2 \, A a^{3} \cos\left(d x + c\right)^{2} + 4 \, A a^{3} + 18 \, B a^{2} b + 18 \, A a b^{2} + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*B*b^3*log(sin(d*x + c) + 1) - 3*B*b^3*log(-sin(d*x + c) + 1) + 3*(B*a^3 + 3*A*a^2*b + 6*B*a*b^2 + 2*A*b^3)*d*x + (2*A*a^3*cos(d*x + c)^2 + 4*A*a^3 + 18*B*a^2*b + 18*A*a*b^2 + 3*(B*a^3 + 3*A*a^2*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
300,1,136,0,0.463781," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 8 \, B b^{3}\right)} d x + {\left(6 \, A a^{3} \cos\left(d x + c\right)^{3} + 16 \, B a^{3} + 48 \, A a^{2} b + 72 \, B a b^{2} + 24 \, A b^{3} + 8 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)^{2} + 9 \, {\left(A a^{3} + 4 \, B a^{2} b + 4 \, A a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(3*A*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 8*B*b^3)*d*x + (6*A*a^3*cos(d*x + c)^3 + 16*B*a^3 + 48*A*a^2*b + 72*B*a*b^2 + 24*A*b^3 + 8*(B*a^3 + 3*A*a^2*b)*cos(d*x + c)^2 + 9*(A*a^3 + 4*B*a^2*b + 4*A*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
301,1,174,0,0.450331," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, B a^{3} + 9 \, A a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3}\right)} d x + {\left(24 \, A a^{3} \cos\left(d x + c\right)^{4} + 64 \, A a^{3} + 240 \, B a^{2} b + 240 \, A a b^{2} + 120 \, B b^{3} + 30 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(4 \, A a^{3} + 15 \, B a^{2} b + 15 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, B a^{3} + 9 \, A a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(3*B*a^3 + 9*A*a^2*b + 12*B*a*b^2 + 4*A*b^3)*d*x + (24*A*a^3*cos(d*x + c)^4 + 64*A*a^3 + 240*B*a^2*b + 240*A*a*b^2 + 120*B*b^3 + 30*(B*a^3 + 3*A*a^2*b)*cos(d*x + c)^3 + 8*(4*A*a^3 + 15*B*a^2*b + 15*A*a*b^2)*cos(d*x + c)^2 + 15*(3*B*a^3 + 9*A*a^2*b + 12*B*a*b^2 + 4*A*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
302,1,327,0,0.489501," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 5 \, B b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 5 \, B b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(15 \, A a^{4} + 40 \, B a^{3} b + 60 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \cos\left(d x + c\right)^{5} + 40 \, B b^{4} + 15 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 5 \, B b^{4}\right)} \cos\left(d x + c\right)^{4} + 32 \, {\left(10 \, B a^{3} b + 15 \, A a^{2} b^{2} + 8 \, B a b^{3} + 2 \, A b^{4}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left(36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 5 \, B b^{4}\right)} \cos\left(d x + c\right)^{2} + 48 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(8*B*a^4 + 32*A*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 5*B*b^4)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(8*B*a^4 + 32*A*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 5*B*b^4)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(15*A*a^4 + 40*B*a^3*b + 60*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*cos(d*x + c)^5 + 40*B*b^4 + 15*(8*B*a^4 + 32*A*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 5*B*b^4)*cos(d*x + c)^4 + 32*(10*B*a^3*b + 15*A*a^2*b^2 + 8*B*a*b^3 + 2*A*b^4)*cos(d*x + c)^3 + 10*(36*B*a^2*b^2 + 24*A*a*b^3 + 5*B*b^4)*cos(d*x + c)^2 + 48*(4*B*a*b^3 + A*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
303,1,281,0,0.476076," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 12 \, B a b^{3} + 3 \, A b^{4}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(8 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 12 \, B a b^{3} + 3 \, A b^{4}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, B b^{4} + 8 \, {\left(15 \, B a^{4} + 60 \, A a^{3} b + 60 \, B a^{2} b^{2} + 40 \, A a b^{3} + 8 \, B b^{4}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 12 \, B a b^{3} + 3 \, A b^{4}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(15 \, B a^{2} b^{2} + 10 \, A a b^{3} + 2 \, B b^{4}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(8*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 12*B*a*b^3 + 3*A*b^4)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(8*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 12*B*a*b^3 + 3*A*b^4)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(24*B*b^4 + 8*(15*B*a^4 + 60*A*a^3*b + 60*B*a^2*b^2 + 40*A*a*b^3 + 8*B*b^4)*cos(d*x + c)^4 + 15*(16*B*a^3*b + 24*A*a^2*b^2 + 12*B*a*b^3 + 3*A*b^4)*cos(d*x + c)^3 + 16*(15*B*a^2*b^2 + 10*A*a*b^3 + 2*B*b^4)*cos(d*x + c)^2 + 30*(4*B*a*b^3 + A*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
304,1,250,0,0.493888," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{48 \, A a^{4} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 3 \, B b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 3 \, B b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, B b^{4} + 16 \, {\left(6 \, B a^{3} b + 9 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 3 \, B b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(48*A*a^4*d*x*cos(d*x + c)^4 + 3*(8*B*a^4 + 32*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 3*B*b^4)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(8*B*a^4 + 32*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 3*B*b^4)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(6*B*b^4 + 16*(6*B*a^3*b + 9*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^3 + 3*(24*B*a^2*b^2 + 16*A*a*b^3 + 3*B*b^4)*cos(d*x + c)^2 + 8*(4*B*a*b^3 + A*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
305,1,219,0,0.483568," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{12 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, B a^{3} b + 12 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, B a^{3} b + 12 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, A a^{4} \cos\left(d x + c\right)^{3} + 2 \, B b^{4} + 4 \, {\left(9 \, B a^{2} b^{2} + 6 \, A a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(12*(B*a^4 + 4*A*a^3*b)*d*x*cos(d*x + c)^3 + 3*(8*B*a^3*b + 12*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(8*B*a^3*b + 12*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(6*A*a^4*cos(d*x + c)^3 + 2*B*b^4 + 4*(9*B*a^2*b^2 + 6*A*a*b^3 + B*b^4)*cos(d*x + c)^2 + 3*(4*B*a*b^3 + A*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
306,1,202,0,0.488289," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(A a^{4} + 8 \, B a^{3} b + 12 \, A a^{2} b^{2}\right)} d x \cos\left(d x + c\right)^{2} + {\left(12 \, B a^{2} b^{2} + 8 \, A a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(12 \, B a^{2} b^{2} + 8 \, A a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{4} \cos\left(d x + c\right)^{3} + B b^{4} + 2 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(2*(A*a^4 + 8*B*a^3*b + 12*A*a^2*b^2)*d*x*cos(d*x + c)^2 + (12*B*a^2*b^2 + 8*A*a*b^3 + B*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (12*B*a^2*b^2 + 8*A*a*b^3 + B*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(A*a^4*cos(d*x + c)^3 + B*b^4 + 2*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)^2 + 2*(4*B*a*b^3 + A*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
307,1,196,0,0.486845," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(B a^{4} + 4 \, A a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, A a^{4} \cos\left(d x + c\right)^{3} + 6 \, B b^{4} + 3 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(A a^{4} + 6 \, B a^{3} b + 9 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}"," ",0,"1/6*(3*(B*a^4 + 4*A*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3)*d*x*cos(d*x + c) + 3*(4*B*a*b^3 + A*b^4)*cos(d*x + c)*log(sin(d*x + c) + 1) - 3*(4*B*a*b^3 + A*b^4)*cos(d*x + c)*log(-sin(d*x + c) + 1) + (2*A*a^4*cos(d*x + c)^3 + 6*B*b^4 + 3*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)^2 + 4*(A*a^4 + 6*B*a^3*b + 9*A*a^2*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
308,1,183,0,0.484605," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{12 \, B b^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, B b^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left(3 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} d x + {\left(6 \, A a^{4} \cos\left(d x + c\right)^{3} + 16 \, B a^{4} + 64 \, A a^{3} b + 144 \, B a^{2} b^{2} + 96 \, A a b^{3} + 8 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(12*B*b^4*log(sin(d*x + c) + 1) - 12*B*b^4*log(-sin(d*x + c) + 1) + 3*(3*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*d*x + (6*A*a^4*cos(d*x + c)^3 + 16*B*a^4 + 64*A*a^3*b + 144*B*a^2*b^2 + 96*A*a*b^3 + 8*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)^2 + 3*(3*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
309,1,197,0,0.464560," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, B a^{4} + 12 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 8 \, B b^{4}\right)} d x + {\left(24 \, A a^{4} \cos\left(d x + c\right)^{4} + 64 \, A a^{4} + 320 \, B a^{3} b + 480 \, A a^{2} b^{2} + 480 \, B a b^{3} + 120 \, A b^{4} + 30 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(2 \, A a^{4} + 10 \, B a^{3} b + 15 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, B a^{4} + 12 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(3*B*a^4 + 12*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 8*B*b^4)*d*x + (24*A*a^4*cos(d*x + c)^4 + 64*A*a^4 + 320*B*a^3*b + 480*A*a^2*b^2 + 480*B*a*b^3 + 120*A*b^4 + 30*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)^3 + 16*(2*A*a^4 + 10*B*a^3*b + 15*A*a^2*b^2)*cos(d*x + c)^2 + 15*(3*B*a^4 + 12*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
310,1,243,0,0.470076," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(5 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} d x + {\left(40 \, A a^{4} \cos\left(d x + c\right)^{5} + 128 \, B a^{4} + 512 \, A a^{3} b + 960 \, B a^{2} b^{2} + 640 \, A a b^{3} + 240 \, B b^{4} + 48 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)^{4} + 10 \, {\left(5 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(2 \, B a^{4} + 8 \, A a^{3} b + 15 \, B a^{2} b^{2} + 10 \, A a b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(5 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(5*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*d*x + (40*A*a^4*cos(d*x + c)^5 + 128*B*a^4 + 512*A*a^3*b + 960*B*a^2*b^2 + 640*A*a*b^3 + 240*B*b^4 + 48*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)^4 + 10*(5*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2)*cos(d*x + c)^3 + 32*(2*B*a^4 + 8*A*a^3*b + 15*B*a^2*b^2 + 10*A*a*b^3)*cos(d*x + c)^2 + 15*(5*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
311,1,743,0,1.180260," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(B a^{4} - A a^{3} b\right)} \sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)^{3} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 3 \, {\left(2 \, B a^{5} - 2 \, A a^{4} b - B a^{3} b^{2} + A a^{2} b^{3} - B a b^{4} + A b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, B a^{5} - 2 \, A a^{4} b - B a^{3} b^{2} + A a^{2} b^{3} - B a b^{4} + A b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, B a^{2} b^{3} - 2 \, B b^{5} + 2 \, {\left(3 \, B a^{4} b - 3 \, A a^{3} b^{2} - B a^{2} b^{3} + 3 \, A a b^{4} - 2 \, B b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(B a^{3} b^{2} - A a^{2} b^{3} - B a b^{4} + A b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}, \frac{12 \, {\left(B a^{4} - A a^{3} b\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, B a^{5} - 2 \, A a^{4} b - B a^{3} b^{2} + A a^{2} b^{3} - B a b^{4} + A b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, B a^{5} - 2 \, A a^{4} b - B a^{3} b^{2} + A a^{2} b^{3} - B a b^{4} + A b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, B a^{2} b^{3} - 2 \, B b^{5} + 2 \, {\left(3 \, B a^{4} b - 3 \, A a^{3} b^{2} - B a^{2} b^{3} + 3 \, A a b^{4} - 2 \, B b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(B a^{3} b^{2} - A a^{2} b^{3} - B a b^{4} + A b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[-1/12*(6*(B*a^4 - A*a^3*b)*sqrt(a^2 - b^2)*cos(d*x + c)^3*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 3*(2*B*a^5 - 2*A*a^4*b - B*a^3*b^2 + A*a^2*b^3 - B*a*b^4 + A*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*B*a^5 - 2*A*a^4*b - B*a^3*b^2 + A*a^2*b^3 - B*a*b^4 + A*b^5)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) - 2*(2*B*a^2*b^3 - 2*B*b^5 + 2*(3*B*a^4*b - 3*A*a^3*b^2 - B*a^2*b^3 + 3*A*a*b^4 - 2*B*b^5)*cos(d*x + c)^2 - 3*(B*a^3*b^2 - A*a^2*b^3 - B*a*b^4 + A*b^5)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d*cos(d*x + c)^3), 1/12*(12*(B*a^4 - A*a^3*b)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*cos(d*x + c)^3 - 3*(2*B*a^5 - 2*A*a^4*b - B*a^3*b^2 + A*a^2*b^3 - B*a*b^4 + A*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(2*B*a^5 - 2*A*a^4*b - B*a^3*b^2 + A*a^2*b^3 - B*a*b^4 + A*b^5)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*B*a^2*b^3 - 2*B*b^5 + 2*(3*B*a^4*b - 3*A*a^3*b^2 - B*a^2*b^3 + 3*A*a*b^4 - 2*B*b^5)*cos(d*x + c)^2 - 3*(B*a^3*b^2 - A*a^2*b^3 - B*a*b^4 + A*b^5)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d*cos(d*x + c)^3)]","B",0
312,1,609,0,4.834629," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(B a^{3} - A a^{2} b\right)} \sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)^{2} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - {\left(2 \, B a^{4} - 2 \, A a^{3} b - B a^{2} b^{2} + 2 \, A a b^{3} - B b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(2 \, B a^{4} - 2 \, A a^{3} b - B a^{2} b^{2} + 2 \, A a b^{3} - B b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{2} b^{2} - B b^{4} - 2 \, {\left(B a^{3} b - A a^{2} b^{2} - B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} b^{3} - b^{5}\right)} d \cos\left(d x + c\right)^{2}}, -\frac{4 \, {\left(B a^{3} - A a^{2} b\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right)^{2} - {\left(2 \, B a^{4} - 2 \, A a^{3} b - B a^{2} b^{2} + 2 \, A a b^{3} - B b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(2 \, B a^{4} - 2 \, A a^{3} b - B a^{2} b^{2} + 2 \, A a b^{3} - B b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{2} b^{2} - B b^{4} - 2 \, {\left(B a^{3} b - A a^{2} b^{2} - B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} b^{3} - b^{5}\right)} d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[-1/4*(2*(B*a^3 - A*a^2*b)*sqrt(a^2 - b^2)*cos(d*x + c)^2*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - (2*B*a^4 - 2*A*a^3*b - B*a^2*b^2 + 2*A*a*b^3 - B*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (2*B*a^4 - 2*A*a^3*b - B*a^2*b^2 + 2*A*a*b^3 - B*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(B*a^2*b^2 - B*b^4 - 2*(B*a^3*b - A*a^2*b^2 - B*a*b^3 + A*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d*cos(d*x + c)^2), -1/4*(4*(B*a^3 - A*a^2*b)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*cos(d*x + c)^2 - (2*B*a^4 - 2*A*a^3*b - B*a^2*b^2 + 2*A*a*b^3 - B*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (2*B*a^4 - 2*A*a^3*b - B*a^2*b^2 + 2*A*a*b^3 - B*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(B*a^2*b^2 - B*b^4 - 2*(B*a^3*b - A*a^2*b^2 - B*a*b^3 + A*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d*cos(d*x + c)^2)]","B",0
313,1,472,0,0.620369," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{{\left(B a^{2} - A a b\right)} \sqrt{a^{2} - b^{2}} \cos\left(d x + c\right) \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{2} b - B b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(d x + c\right)}, \frac{2 \, {\left(B a^{2} - A a b\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right) - {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a^{2} b - B b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/2*((B*a^2 - A*a*b)*sqrt(a^2 - b^2)*cos(d*x + c)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) - (B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) - 2*(B*a^2*b - B*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d*cos(d*x + c)), 1/2*(2*(B*a^2 - A*a*b)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*cos(d*x + c) - (B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) + (B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(B*a^2*b - B*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d*cos(d*x + c))]","B",0
314,1,316,0,1.041070," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{{\left(B a - A b\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - {\left(B a^{2} - B b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(B a^{2} - B b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{2} b - b^{3}\right)} d}, -\frac{2 \, {\left(B a - A b\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(B a^{2} - B b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(B a^{2} - B b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{2} b - b^{3}\right)} d}\right]"," ",0,"[-1/2*((B*a - A*b)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - (B*a^2 - B*b^2)*log(sin(d*x + c) + 1) + (B*a^2 - B*b^2)*log(-sin(d*x + c) + 1))/((a^2*b - b^3)*d), -1/2*(2*(B*a - A*b)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (B*a^2 - B*b^2)*log(sin(d*x + c) + 1) + (B*a^2 - B*b^2)*log(-sin(d*x + c) + 1))/((a^2*b - b^3)*d)]","A",0
315,1,250,0,0.466835," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(A a^{2} - A b^{2}\right)} d x - {\left(B a - A b\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}, \frac{{\left(A a^{2} - A b^{2}\right)} d x + {\left(B a - A b\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right)}{{\left(a^{3} - a b^{2}\right)} d}\right]"," ",0,"[1/2*(2*(A*a^2 - A*b^2)*d*x - (B*a - A*b)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)))/((a^3 - a*b^2)*d), ((A*a^2 - A*b^2)*d*x + (B*a - A*b)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))))/((a^3 - a*b^2)*d)]","A",0
316,1,328,0,0.483959," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} d x - {\left(B a b - A b^{2}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(A a^{3} - A a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} - a^{2} b^{2}\right)} d}, \frac{{\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} d x - {\left(B a b - A b^{2}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(A a^{3} - A a b^{2}\right)} \sin\left(d x + c\right)}{{\left(a^{4} - a^{2} b^{2}\right)} d}\right]"," ",0,"[1/2*(2*(B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*d*x - (B*a*b - A*b^2)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(A*a^3 - A*a*b^2)*sin(d*x + c))/((a^4 - a^2*b^2)*d), ((B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*d*x - (B*a*b - A*b^2)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (A*a^3 - A*a*b^2)*sin(d*x + c))/((a^4 - a^2*b^2)*d)]","A",0
317,1,427,0,0.497941," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(A a^{4} - 2 \, B a^{3} b + A a^{2} b^{2} + 2 \, B a b^{3} - 2 \, A b^{4}\right)} d x - {\left(B a b^{2} - A b^{3}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(2 \, B a^{4} - 2 \, A a^{3} b - 2 \, B a^{2} b^{2} + 2 \, A a b^{3} + {\left(A a^{4} - A a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{5} - a^{3} b^{2}\right)} d}, \frac{{\left(A a^{4} - 2 \, B a^{3} b + A a^{2} b^{2} + 2 \, B a b^{3} - 2 \, A b^{4}\right)} d x + 2 \, {\left(B a b^{2} - A b^{3}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(2 \, B a^{4} - 2 \, A a^{3} b - 2 \, B a^{2} b^{2} + 2 \, A a b^{3} + {\left(A a^{4} - A a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{5} - a^{3} b^{2}\right)} d}\right]"," ",0,"[1/2*((A*a^4 - 2*B*a^3*b + A*a^2*b^2 + 2*B*a*b^3 - 2*A*b^4)*d*x - (B*a*b^2 - A*b^3)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (2*B*a^4 - 2*A*a^3*b - 2*B*a^2*b^2 + 2*A*a*b^3 + (A*a^4 - A*a^2*b^2)*cos(d*x + c))*sin(d*x + c))/((a^5 - a^3*b^2)*d), 1/2*((A*a^4 - 2*B*a^3*b + A*a^2*b^2 + 2*B*a*b^3 - 2*A*b^4)*d*x + 2*(B*a*b^2 - A*b^3)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (2*B*a^4 - 2*A*a^3*b - 2*B*a^2*b^2 + 2*A*a*b^3 + (A*a^4 - A*a^2*b^2)*cos(d*x + c))*sin(d*x + c))/((a^5 - a^3*b^2)*d)]","A",0
318,1,547,0,0.558826," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a^{5} - A a^{4} b + B a^{3} b^{2} - A a^{2} b^{3} - 2 \, B a b^{4} + 2 \, A b^{5}\right)} d x - 3 \, {\left(B a b^{3} - A b^{4}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(4 \, A a^{5} - 6 \, B a^{4} b + 2 \, A a^{3} b^{2} + 6 \, B a^{2} b^{3} - 6 \, A a b^{4} + 2 \, {\left(A a^{5} - A a^{3} b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{5} - A a^{4} b - B a^{3} b^{2} + A a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{6} - a^{4} b^{2}\right)} d}, \frac{3 \, {\left(B a^{5} - A a^{4} b + B a^{3} b^{2} - A a^{2} b^{3} - 2 \, B a b^{4} + 2 \, A b^{5}\right)} d x - 6 \, {\left(B a b^{3} - A b^{4}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(4 \, A a^{5} - 6 \, B a^{4} b + 2 \, A a^{3} b^{2} + 6 \, B a^{2} b^{3} - 6 \, A a b^{4} + 2 \, {\left(A a^{5} - A a^{3} b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{5} - A a^{4} b - B a^{3} b^{2} + A a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{6} - a^{4} b^{2}\right)} d}\right]"," ",0,"[1/6*(3*(B*a^5 - A*a^4*b + B*a^3*b^2 - A*a^2*b^3 - 2*B*a*b^4 + 2*A*b^5)*d*x - 3*(B*a*b^3 - A*b^4)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (4*A*a^5 - 6*B*a^4*b + 2*A*a^3*b^2 + 6*B*a^2*b^3 - 6*A*a*b^4 + 2*(A*a^5 - A*a^3*b^2)*cos(d*x + c)^2 + 3*(B*a^5 - A*a^4*b - B*a^3*b^2 + A*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6 - a^4*b^2)*d), 1/6*(3*(B*a^5 - A*a^4*b + B*a^3*b^2 - A*a^2*b^3 - 2*B*a*b^4 + 2*A*b^5)*d*x - 6*(B*a*b^3 - A*b^4)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (4*A*a^5 - 6*B*a^4*b + 2*A*a^3*b^2 + 6*B*a^2*b^3 - 6*A*a*b^4 + 2*(A*a^5 - A*a^3*b^2)*cos(d*x + c)^2 + 3*(B*a^5 - A*a^4*b - B*a^3*b^2 + A*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6 - a^4*b^2)*d)]","A",0
319,1,685,0,0.546181," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, A a^{6} - 4 \, B a^{5} b + A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} + 8 \, B a b^{5} - 8 \, A b^{6}\right)} d x - 12 \, {\left(B a b^{4} - A b^{5}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(16 \, B a^{6} - 16 \, A a^{5} b + 8 \, B a^{4} b^{2} - 8 \, A a^{3} b^{3} - 24 \, B a^{2} b^{4} + 24 \, A a b^{5} + 6 \, {\left(A a^{6} - A a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(B a^{6} - A a^{5} b - B a^{4} b^{2} + A a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A a^{6} - 4 \, B a^{5} b + A a^{4} b^{2} + 4 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{7} - a^{5} b^{2}\right)} d}, \frac{3 \, {\left(3 \, A a^{6} - 4 \, B a^{5} b + A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} + 8 \, B a b^{5} - 8 \, A b^{6}\right)} d x + 24 \, {\left(B a b^{4} - A b^{5}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(16 \, B a^{6} - 16 \, A a^{5} b + 8 \, B a^{4} b^{2} - 8 \, A a^{3} b^{3} - 24 \, B a^{2} b^{4} + 24 \, A a b^{5} + 6 \, {\left(A a^{6} - A a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(B a^{6} - A a^{5} b - B a^{4} b^{2} + A a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A a^{6} - 4 \, B a^{5} b + A a^{4} b^{2} + 4 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{7} - a^{5} b^{2}\right)} d}\right]"," ",0,"[1/24*(3*(3*A*a^6 - 4*B*a^5*b + A*a^4*b^2 - 4*B*a^3*b^3 + 4*A*a^2*b^4 + 8*B*a*b^5 - 8*A*b^6)*d*x - 12*(B*a*b^4 - A*b^5)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (16*B*a^6 - 16*A*a^5*b + 8*B*a^4*b^2 - 8*A*a^3*b^3 - 24*B*a^2*b^4 + 24*A*a*b^5 + 6*(A*a^6 - A*a^4*b^2)*cos(d*x + c)^3 + 8*(B*a^6 - A*a^5*b - B*a^4*b^2 + A*a^3*b^3)*cos(d*x + c)^2 + 3*(3*A*a^6 - 4*B*a^5*b + A*a^4*b^2 + 4*B*a^3*b^3 - 4*A*a^2*b^4)*cos(d*x + c))*sin(d*x + c))/((a^7 - a^5*b^2)*d), 1/24*(3*(3*A*a^6 - 4*B*a^5*b + A*a^4*b^2 - 4*B*a^3*b^3 + 4*A*a^2*b^4 + 8*B*a*b^5 - 8*A*b^6)*d*x + 24*(B*a*b^4 - A*b^5)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (16*B*a^6 - 16*A*a^5*b + 8*B*a^4*b^2 - 8*A*a^3*b^3 - 24*B*a^2*b^4 + 24*A*a*b^5 + 6*(A*a^6 - A*a^4*b^2)*cos(d*x + c)^3 + 8*(B*a^6 - A*a^5*b - B*a^4*b^2 + A*a^3*b^3)*cos(d*x + c)^2 + 3*(3*A*a^6 - 4*B*a^5*b + A*a^4*b^2 + 4*B*a^3*b^3 - 4*A*a^2*b^4)*cos(d*x + c))*sin(d*x + c))/((a^7 - a^5*b^2)*d)]","A",0
320,1,1343,0,20.608737," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(3 \, B a^{6} - 2 \, A a^{5} b - 4 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, B a^{5} b - 2 \, A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left({\left(6 \, B a^{7} - 4 \, A a^{6} b - 11 \, B a^{5} b^{2} + 8 \, A a^{4} b^{3} + 4 \, B a^{3} b^{4} - 4 \, A a^{2} b^{5} + B a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, B a^{6} b - 4 \, A a^{5} b^{2} - 11 \, B a^{4} b^{3} + 8 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 4 \, A a b^{6} + B b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(6 \, B a^{7} - 4 \, A a^{6} b - 11 \, B a^{5} b^{2} + 8 \, A a^{4} b^{3} + 4 \, B a^{3} b^{4} - 4 \, A a^{2} b^{5} + B a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, B a^{6} b - 4 \, A a^{5} b^{2} - 11 \, B a^{4} b^{3} + 8 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 4 \, A a b^{6} + B b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a^{4} b^{3} - 2 \, B a^{2} b^{5} + B b^{7} - 2 \, {\left(3 \, B a^{6} b - 2 \, A a^{5} b^{2} - 5 \, B a^{4} b^{3} + 3 \, A a^{3} b^{4} + 2 \, B a^{2} b^{5} - A a b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, B a^{5} b^{2} - 2 \, A a^{4} b^{3} - 6 \, B a^{3} b^{4} + 4 \, A a^{2} b^{5} + 3 \, B a b^{6} - 2 \, A b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{2}\right)}}, -\frac{4 \, {\left({\left(3 \, B a^{6} - 2 \, A a^{5} b - 4 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, B a^{5} b - 2 \, A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left({\left(6 \, B a^{7} - 4 \, A a^{6} b - 11 \, B a^{5} b^{2} + 8 \, A a^{4} b^{3} + 4 \, B a^{3} b^{4} - 4 \, A a^{2} b^{5} + B a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, B a^{6} b - 4 \, A a^{5} b^{2} - 11 \, B a^{4} b^{3} + 8 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 4 \, A a b^{6} + B b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(6 \, B a^{7} - 4 \, A a^{6} b - 11 \, B a^{5} b^{2} + 8 \, A a^{4} b^{3} + 4 \, B a^{3} b^{4} - 4 \, A a^{2} b^{5} + B a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, B a^{6} b - 4 \, A a^{5} b^{2} - 11 \, B a^{4} b^{3} + 8 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 4 \, A a b^{6} + B b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{4} b^{3} - 2 \, B a^{2} b^{5} + B b^{7} - 2 \, {\left(3 \, B a^{6} b - 2 \, A a^{5} b^{2} - 5 \, B a^{4} b^{3} + 3 \, A a^{3} b^{4} + 2 \, B a^{2} b^{5} - A a b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, B a^{5} b^{2} - 2 \, A a^{4} b^{3} - 6 \, B a^{3} b^{4} + 4 \, A a^{2} b^{5} + 3 \, B a b^{6} - 2 \, A b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/4*(2*((3*B*a^6 - 2*A*a^5*b - 4*B*a^4*b^2 + 3*A*a^3*b^3)*cos(d*x + c)^3 + (3*B*a^5*b - 2*A*a^4*b^2 - 4*B*a^3*b^3 + 3*A*a^2*b^4)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + ((6*B*a^7 - 4*A*a^6*b - 11*B*a^5*b^2 + 8*A*a^4*b^3 + 4*B*a^3*b^4 - 4*A*a^2*b^5 + B*a*b^6)*cos(d*x + c)^3 + (6*B*a^6*b - 4*A*a^5*b^2 - 11*B*a^4*b^3 + 8*A*a^3*b^4 + 4*B*a^2*b^5 - 4*A*a*b^6 + B*b^7)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((6*B*a^7 - 4*A*a^6*b - 11*B*a^5*b^2 + 8*A*a^4*b^3 + 4*B*a^3*b^4 - 4*A*a^2*b^5 + B*a*b^6)*cos(d*x + c)^3 + (6*B*a^6*b - 4*A*a^5*b^2 - 11*B*a^4*b^3 + 8*A*a^3*b^4 + 4*B*a^2*b^5 - 4*A*a*b^6 + B*b^7)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(B*a^4*b^3 - 2*B*a^2*b^5 + B*b^7 - 2*(3*B*a^6*b - 2*A*a^5*b^2 - 5*B*a^4*b^3 + 3*A*a^3*b^4 + 2*B*a^2*b^5 - A*a*b^6)*cos(d*x + c)^2 - (3*B*a^5*b^2 - 2*A*a^4*b^3 - 6*B*a^3*b^4 + 4*A*a^2*b^5 + 3*B*a*b^6 - 2*A*b^7)*cos(d*x + c))*sin(d*x + c))/((a^5*b^4 - 2*a^3*b^6 + a*b^8)*d*cos(d*x + c)^3 + (a^4*b^5 - 2*a^2*b^7 + b^9)*d*cos(d*x + c)^2), -1/4*(4*((3*B*a^6 - 2*A*a^5*b - 4*B*a^4*b^2 + 3*A*a^3*b^3)*cos(d*x + c)^3 + (3*B*a^5*b - 2*A*a^4*b^2 - 4*B*a^3*b^3 + 3*A*a^2*b^4)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - ((6*B*a^7 - 4*A*a^6*b - 11*B*a^5*b^2 + 8*A*a^4*b^3 + 4*B*a^3*b^4 - 4*A*a^2*b^5 + B*a*b^6)*cos(d*x + c)^3 + (6*B*a^6*b - 4*A*a^5*b^2 - 11*B*a^4*b^3 + 8*A*a^3*b^4 + 4*B*a^2*b^5 - 4*A*a*b^6 + B*b^7)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((6*B*a^7 - 4*A*a^6*b - 11*B*a^5*b^2 + 8*A*a^4*b^3 + 4*B*a^3*b^4 - 4*A*a^2*b^5 + B*a*b^6)*cos(d*x + c)^3 + (6*B*a^6*b - 4*A*a^5*b^2 - 11*B*a^4*b^3 + 8*A*a^3*b^4 + 4*B*a^2*b^5 - 4*A*a*b^6 + B*b^7)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(B*a^4*b^3 - 2*B*a^2*b^5 + B*b^7 - 2*(3*B*a^6*b - 2*A*a^5*b^2 - 5*B*a^4*b^3 + 3*A*a^3*b^4 + 2*B*a^2*b^5 - A*a*b^6)*cos(d*x + c)^2 - (3*B*a^5*b^2 - 2*A*a^4*b^3 - 6*B*a^3*b^4 + 4*A*a^2*b^5 + 3*B*a*b^6 - 2*A*b^7)*cos(d*x + c))*sin(d*x + c))/((a^5*b^4 - 2*a^3*b^6 + a*b^8)*d*cos(d*x + c)^3 + (a^4*b^5 - 2*a^2*b^7 + b^9)*d*cos(d*x + c)^2)]","B",0
321,1,1114,0,13.156874," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, B a^{5} - A a^{4} b - 3 \, B a^{3} b^{2} + 2 \, A a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B a^{4} b - A a^{3} b^{2} - 3 \, B a^{2} b^{3} + 2 \, A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - {\left({\left(2 \, B a^{6} - A a^{5} b - 4 \, B a^{4} b^{2} + 2 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} - A a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B a^{5} b - A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 2 \, A a^{2} b^{4} + 2 \, B a b^{5} - A b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(2 \, B a^{6} - A a^{5} b - 4 \, B a^{4} b^{2} + 2 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} - A a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B a^{5} b - A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 2 \, A a^{2} b^{4} + 2 \, B a b^{5} - A b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a^{4} b^{2} - 2 \, B a^{2} b^{4} + B b^{6} + {\left(2 \, B a^{5} b - A a^{4} b^{2} - 3 \, B a^{3} b^{3} + A a^{2} b^{4} + B a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)\right)}}, \frac{2 \, {\left({\left(2 \, B a^{5} - A a^{4} b - 3 \, B a^{3} b^{2} + 2 \, A a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B a^{4} b - A a^{3} b^{2} - 3 \, B a^{2} b^{3} + 2 \, A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left({\left(2 \, B a^{6} - A a^{5} b - 4 \, B a^{4} b^{2} + 2 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} - A a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B a^{5} b - A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 2 \, A a^{2} b^{4} + 2 \, B a b^{5} - A b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(2 \, B a^{6} - A a^{5} b - 4 \, B a^{4} b^{2} + 2 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} - A a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B a^{5} b - A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 2 \, A a^{2} b^{4} + 2 \, B a b^{5} - A b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a^{4} b^{2} - 2 \, B a^{2} b^{4} + B b^{6} + {\left(2 \, B a^{5} b - A a^{4} b^{2} - 3 \, B a^{3} b^{3} + A a^{2} b^{4} + B a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/2*(((2*B*a^5 - A*a^4*b - 3*B*a^3*b^2 + 2*A*a^2*b^3)*cos(d*x + c)^2 + (2*B*a^4*b - A*a^3*b^2 - 3*B*a^2*b^3 + 2*A*a*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - ((2*B*a^6 - A*a^5*b - 4*B*a^4*b^2 + 2*A*a^3*b^3 + 2*B*a^2*b^4 - A*a*b^5)*cos(d*x + c)^2 + (2*B*a^5*b - A*a^4*b^2 - 4*B*a^3*b^3 + 2*A*a^2*b^4 + 2*B*a*b^5 - A*b^6)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((2*B*a^6 - A*a^5*b - 4*B*a^4*b^2 + 2*A*a^3*b^3 + 2*B*a^2*b^4 - A*a*b^5)*cos(d*x + c)^2 + (2*B*a^5*b - A*a^4*b^2 - 4*B*a^3*b^3 + 2*A*a^2*b^4 + 2*B*a*b^5 - A*b^6)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(B*a^4*b^2 - 2*B*a^2*b^4 + B*b^6 + (2*B*a^5*b - A*a^4*b^2 - 3*B*a^3*b^3 + A*a^2*b^4 + B*a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^5*b^3 - 2*a^3*b^5 + a*b^7)*d*cos(d*x + c)^2 + (a^4*b^4 - 2*a^2*b^6 + b^8)*d*cos(d*x + c)), 1/2*(2*((2*B*a^5 - A*a^4*b - 3*B*a^3*b^2 + 2*A*a^2*b^3)*cos(d*x + c)^2 + (2*B*a^4*b - A*a^3*b^2 - 3*B*a^2*b^3 + 2*A*a*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - ((2*B*a^6 - A*a^5*b - 4*B*a^4*b^2 + 2*A*a^3*b^3 + 2*B*a^2*b^4 - A*a*b^5)*cos(d*x + c)^2 + (2*B*a^5*b - A*a^4*b^2 - 4*B*a^3*b^3 + 2*A*a^2*b^4 + 2*B*a*b^5 - A*b^6)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((2*B*a^6 - A*a^5*b - 4*B*a^4*b^2 + 2*A*a^3*b^3 + 2*B*a^2*b^4 - A*a*b^5)*cos(d*x + c)^2 + (2*B*a^5*b - A*a^4*b^2 - 4*B*a^3*b^3 + 2*A*a^2*b^4 + 2*B*a*b^5 - A*b^6)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(B*a^4*b^2 - 2*B*a^2*b^4 + B*b^6 + (2*B*a^5*b - A*a^4*b^2 - 3*B*a^3*b^3 + A*a^2*b^4 + B*a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^5*b^3 - 2*a^3*b^5 + a*b^7)*d*cos(d*x + c)^2 + (a^4*b^4 - 2*a^2*b^6 + b^8)*d*cos(d*x + c))]","B",0
322,1,694,0,4.056128," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(B a^{3} b - 2 \, B a b^{3} + A b^{4} + {\left(B a^{4} - 2 \, B a^{2} b^{2} + A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(B a^{4} b - 2 \, B a^{2} b^{3} + B b^{5} + {\left(B a^{5} - 2 \, B a^{3} b^{2} + B a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a^{4} b - 2 \, B a^{2} b^{3} + B b^{5} + {\left(B a^{5} - 2 \, B a^{3} b^{2} + B a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{4} b - A a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d\right)}}, -\frac{2 \, {\left(B a^{3} b - 2 \, B a b^{3} + A b^{4} + {\left(B a^{4} - 2 \, B a^{2} b^{2} + A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(B a^{4} b - 2 \, B a^{2} b^{3} + B b^{5} + {\left(B a^{5} - 2 \, B a^{3} b^{2} + B a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(B a^{4} b - 2 \, B a^{2} b^{3} + B b^{5} + {\left(B a^{5} - 2 \, B a^{3} b^{2} + B a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a^{4} b - A a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d\right)}}\right]"," ",0,"[1/2*((B*a^3*b - 2*B*a*b^3 + A*b^4 + (B*a^4 - 2*B*a^2*b^2 + A*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (B*a^4*b - 2*B*a^2*b^3 + B*b^5 + (B*a^5 - 2*B*a^3*b^2 + B*a*b^4)*cos(d*x + c))*log(sin(d*x + c) + 1) - (B*a^4*b - 2*B*a^2*b^3 + B*b^5 + (B*a^5 - 2*B*a^3*b^2 + B*a*b^4)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(B*a^4*b - A*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*sin(d*x + c))/((a^5*b^2 - 2*a^3*b^4 + a*b^6)*d*cos(d*x + c) + (a^4*b^3 - 2*a^2*b^5 + b^7)*d), -1/2*(2*(B*a^3*b - 2*B*a*b^3 + A*b^4 + (B*a^4 - 2*B*a^2*b^2 + A*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (B*a^4*b - 2*B*a^2*b^3 + B*b^5 + (B*a^5 - 2*B*a^3*b^2 + B*a*b^4)*cos(d*x + c))*log(sin(d*x + c) + 1) + (B*a^4*b - 2*B*a^2*b^3 + B*b^5 + (B*a^5 - 2*B*a^3*b^2 + B*a*b^4)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(B*a^4*b - A*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*sin(d*x + c))/((a^5*b^2 - 2*a^3*b^4 + a*b^6)*d*cos(d*x + c) + (a^4*b^3 - 2*a^2*b^5 + b^7)*d)]","B",0
323,1,389,0,0.481921," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(A a b - B b^{2} + {\left(A a^{2} - B a b\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d\right)}}, \frac{{\left(A a b - B b^{2} + {\left(A a^{2} - B a b\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d}\right]"," ",0,"[1/2*((A*a*b - B*b^2 + (A*a^2 - B*a*b)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*sin(d*x + c))/((a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c) + (a^4*b - 2*a^2*b^3 + b^5)*d), ((A*a*b - B*b^2 + (A*a^2 - B*a*b)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*sin(d*x + c))/((a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c) + (a^4*b - 2*a^2*b^3 + b^5)*d)]","A",0
324,1,561,0,0.536586," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(A a^{5} - 2 \, A a^{3} b^{2} + A a b^{4}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(A a^{4} b - 2 \, A a^{2} b^{3} + A b^{5}\right)} d x - {\left(B a^{3} b - 2 \, A a^{2} b^{2} + A b^{4} + {\left(B a^{4} - 2 \, A a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(B a^{4} b - A a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d\right)}}, \frac{{\left(A a^{5} - 2 \, A a^{3} b^{2} + A a b^{4}\right)} d x \cos\left(d x + c\right) + {\left(A a^{4} b - 2 \, A a^{2} b^{3} + A b^{5}\right)} d x + {\left(B a^{3} b - 2 \, A a^{2} b^{2} + A b^{4} + {\left(B a^{4} - 2 \, A a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(B a^{4} b - A a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} \sin\left(d x + c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d}\right]"," ",0,"[1/2*(2*(A*a^5 - 2*A*a^3*b^2 + A*a*b^4)*d*x*cos(d*x + c) + 2*(A*a^4*b - 2*A*a^2*b^3 + A*b^5)*d*x - (B*a^3*b - 2*A*a^2*b^2 + A*b^4 + (B*a^4 - 2*A*a^3*b + A*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(B*a^4*b - A*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*sin(d*x + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(d*x + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d), ((A*a^5 - 2*A*a^3*b^2 + A*a*b^4)*d*x*cos(d*x + c) + (A*a^4*b - 2*A*a^2*b^3 + A*b^5)*d*x + (B*a^3*b - 2*A*a^2*b^2 + A*b^4 + (B*a^4 - 2*A*a^3*b + A*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (B*a^4*b - A*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*sin(d*x + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(d*x + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d)]","B",0
325,1,788,0,0.557789," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B a^{6} - 2 \, A a^{5} b - 2 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} + B a^{2} b^{4} - 2 \, A a b^{5}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(B a^{5} b - 2 \, A a^{4} b^{2} - 2 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} + B a b^{5} - 2 \, A b^{6}\right)} d x + {\left(2 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} - B a b^{4} + 2 \, A b^{5} + {\left(2 \, B a^{4} b - 3 \, A a^{3} b^{2} - B a^{2} b^{3} + 2 \, A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(A a^{5} b + B a^{4} b^{2} - 3 \, A a^{3} b^{3} - B a^{2} b^{4} + 2 \, A a b^{5} + {\left(A a^{6} - 2 \, A a^{4} b^{2} + A a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d\right)}}, \frac{{\left(B a^{6} - 2 \, A a^{5} b - 2 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} + B a^{2} b^{4} - 2 \, A a b^{5}\right)} d x \cos\left(d x + c\right) + {\left(B a^{5} b - 2 \, A a^{4} b^{2} - 2 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} + B a b^{5} - 2 \, A b^{6}\right)} d x - {\left(2 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} - B a b^{4} + 2 \, A b^{5} + {\left(2 \, B a^{4} b - 3 \, A a^{3} b^{2} - B a^{2} b^{3} + 2 \, A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(A a^{5} b + B a^{4} b^{2} - 3 \, A a^{3} b^{3} - B a^{2} b^{4} + 2 \, A a b^{5} + {\left(A a^{6} - 2 \, A a^{4} b^{2} + A a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d}\right]"," ",0,"[1/2*(2*(B*a^6 - 2*A*a^5*b - 2*B*a^4*b^2 + 4*A*a^3*b^3 + B*a^2*b^4 - 2*A*a*b^5)*d*x*cos(d*x + c) + 2*(B*a^5*b - 2*A*a^4*b^2 - 2*B*a^3*b^3 + 4*A*a^2*b^4 + B*a*b^5 - 2*A*b^6)*d*x + (2*B*a^3*b^2 - 3*A*a^2*b^3 - B*a*b^4 + 2*A*b^5 + (2*B*a^4*b - 3*A*a^3*b^2 - B*a^2*b^3 + 2*A*a*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(A*a^5*b + B*a^4*b^2 - 3*A*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5 + (A*a^6 - 2*A*a^4*b^2 + A*a^2*b^4)*cos(d*x + c))*sin(d*x + c))/((a^8 - 2*a^6*b^2 + a^4*b^4)*d*cos(d*x + c) + (a^7*b - 2*a^5*b^3 + a^3*b^5)*d), ((B*a^6 - 2*A*a^5*b - 2*B*a^4*b^2 + 4*A*a^3*b^3 + B*a^2*b^4 - 2*A*a*b^5)*d*x*cos(d*x + c) + (B*a^5*b - 2*A*a^4*b^2 - 2*B*a^3*b^3 + 4*A*a^2*b^4 + B*a*b^5 - 2*A*b^6)*d*x - (2*B*a^3*b^2 - 3*A*a^2*b^3 - B*a*b^4 + 2*A*b^5 + (2*B*a^4*b - 3*A*a^3*b^2 - B*a^2*b^3 + 2*A*a*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (A*a^5*b + B*a^4*b^2 - 3*A*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5 + (A*a^6 - 2*A*a^4*b^2 + A*a^2*b^4)*cos(d*x + c))*sin(d*x + c))/((a^8 - 2*a^6*b^2 + a^4*b^4)*d*cos(d*x + c) + (a^7*b - 2*a^5*b^3 + a^3*b^5)*d)]","B",0
326,1,970,0,0.599447," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(A a^{7} - 4 \, B a^{6} b + 4 \, A a^{5} b^{2} + 8 \, B a^{4} b^{3} - 11 \, A a^{3} b^{4} - 4 \, B a^{2} b^{5} + 6 \, A a b^{6}\right)} d x \cos\left(d x + c\right) + {\left(A a^{6} b - 4 \, B a^{5} b^{2} + 4 \, A a^{4} b^{3} + 8 \, B a^{3} b^{4} - 11 \, A a^{2} b^{5} - 4 \, B a b^{6} + 6 \, A b^{7}\right)} d x + {\left(3 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4} - 2 \, B a b^{5} + 3 \, A b^{6} + {\left(3 \, B a^{4} b^{2} - 4 \, A a^{3} b^{3} - 2 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(2 \, B a^{6} b - 4 \, A a^{5} b^{2} - 6 \, B a^{4} b^{3} + 10 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 6 \, A a b^{6} + {\left(A a^{7} - 2 \, A a^{5} b^{2} + A a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B a^{7} - 3 \, A a^{6} b - 4 \, B a^{5} b^{2} + 6 \, A a^{4} b^{3} + 2 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d\right)}}, \frac{{\left(A a^{7} - 4 \, B a^{6} b + 4 \, A a^{5} b^{2} + 8 \, B a^{4} b^{3} - 11 \, A a^{3} b^{4} - 4 \, B a^{2} b^{5} + 6 \, A a b^{6}\right)} d x \cos\left(d x + c\right) + {\left(A a^{6} b - 4 \, B a^{5} b^{2} + 4 \, A a^{4} b^{3} + 8 \, B a^{3} b^{4} - 11 \, A a^{2} b^{5} - 4 \, B a b^{6} + 6 \, A b^{7}\right)} d x + 2 \, {\left(3 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4} - 2 \, B a b^{5} + 3 \, A b^{6} + {\left(3 \, B a^{4} b^{2} - 4 \, A a^{3} b^{3} - 2 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(2 \, B a^{6} b - 4 \, A a^{5} b^{2} - 6 \, B a^{4} b^{3} + 10 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 6 \, A a b^{6} + {\left(A a^{7} - 2 \, A a^{5} b^{2} + A a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B a^{7} - 3 \, A a^{6} b - 4 \, B a^{5} b^{2} + 6 \, A a^{4} b^{3} + 2 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d\right)}}\right]"," ",0,"[1/2*((A*a^7 - 4*B*a^6*b + 4*A*a^5*b^2 + 8*B*a^4*b^3 - 11*A*a^3*b^4 - 4*B*a^2*b^5 + 6*A*a*b^6)*d*x*cos(d*x + c) + (A*a^6*b - 4*B*a^5*b^2 + 4*A*a^4*b^3 + 8*B*a^3*b^4 - 11*A*a^2*b^5 - 4*B*a*b^6 + 6*A*b^7)*d*x + (3*B*a^3*b^3 - 4*A*a^2*b^4 - 2*B*a*b^5 + 3*A*b^6 + (3*B*a^4*b^2 - 4*A*a^3*b^3 - 2*B*a^2*b^4 + 3*A*a*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (2*B*a^6*b - 4*A*a^5*b^2 - 6*B*a^4*b^3 + 10*A*a^3*b^4 + 4*B*a^2*b^5 - 6*A*a*b^6 + (A*a^7 - 2*A*a^5*b^2 + A*a^3*b^4)*cos(d*x + c)^2 + (2*B*a^7 - 3*A*a^6*b - 4*B*a^5*b^2 + 6*A*a^4*b^3 + 2*B*a^3*b^4 - 3*A*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^9 - 2*a^7*b^2 + a^5*b^4)*d*cos(d*x + c) + (a^8*b - 2*a^6*b^3 + a^4*b^5)*d), 1/2*((A*a^7 - 4*B*a^6*b + 4*A*a^5*b^2 + 8*B*a^4*b^3 - 11*A*a^3*b^4 - 4*B*a^2*b^5 + 6*A*a*b^6)*d*x*cos(d*x + c) + (A*a^6*b - 4*B*a^5*b^2 + 4*A*a^4*b^3 + 8*B*a^3*b^4 - 11*A*a^2*b^5 - 4*B*a*b^6 + 6*A*b^7)*d*x + 2*(3*B*a^3*b^3 - 4*A*a^2*b^4 - 2*B*a*b^5 + 3*A*b^6 + (3*B*a^4*b^2 - 4*A*a^3*b^3 - 2*B*a^2*b^4 + 3*A*a*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (2*B*a^6*b - 4*A*a^5*b^2 - 6*B*a^4*b^3 + 10*A*a^3*b^4 + 4*B*a^2*b^5 - 6*A*a*b^6 + (A*a^7 - 2*A*a^5*b^2 + A*a^3*b^4)*cos(d*x + c)^2 + (2*B*a^7 - 3*A*a^6*b - 4*B*a^5*b^2 + 6*A*a^4*b^3 + 2*B*a^3*b^4 - 3*A*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^9 - 2*a^7*b^2 + a^5*b^4)*d*cos(d*x + c) + (a^8*b - 2*a^6*b^3 + a^4*b^5)*d)]","A",0
327,1,1167,0,0.617725," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a^{8} - 2 \, A a^{7} b + 4 \, B a^{6} b^{2} - 4 \, A a^{5} b^{3} - 11 \, B a^{4} b^{4} + 14 \, A a^{3} b^{5} + 6 \, B a^{2} b^{6} - 8 \, A a b^{7}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(B a^{7} b - 2 \, A a^{6} b^{2} + 4 \, B a^{5} b^{3} - 4 \, A a^{4} b^{4} - 11 \, B a^{3} b^{5} + 14 \, A a^{2} b^{6} + 6 \, B a b^{7} - 8 \, A b^{8}\right)} d x + 3 \, {\left(4 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} - 3 \, B a b^{6} + 4 \, A b^{7} + {\left(4 \, B a^{4} b^{3} - 5 \, A a^{3} b^{4} - 3 \, B a^{2} b^{5} + 4 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(4 \, A a^{7} b - 12 \, B a^{6} b^{2} + 10 \, A a^{5} b^{3} + 30 \, B a^{4} b^{4} - 38 \, A a^{3} b^{5} - 18 \, B a^{2} b^{6} + 24 \, A a b^{7} + 2 \, {\left(A a^{8} - 2 \, A a^{6} b^{2} + A a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, B a^{8} - 4 \, A a^{7} b - 6 \, B a^{6} b^{2} + 8 \, A a^{5} b^{3} + 3 \, B a^{4} b^{4} - 4 \, A a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A a^{8} - 9 \, B a^{7} b + 4 \, A a^{6} b^{2} + 18 \, B a^{5} b^{3} - 20 \, A a^{4} b^{4} - 9 \, B a^{3} b^{5} + 12 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{10} - 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d\right)}}, \frac{3 \, {\left(B a^{8} - 2 \, A a^{7} b + 4 \, B a^{6} b^{2} - 4 \, A a^{5} b^{3} - 11 \, B a^{4} b^{4} + 14 \, A a^{3} b^{5} + 6 \, B a^{2} b^{6} - 8 \, A a b^{7}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(B a^{7} b - 2 \, A a^{6} b^{2} + 4 \, B a^{5} b^{3} - 4 \, A a^{4} b^{4} - 11 \, B a^{3} b^{5} + 14 \, A a^{2} b^{6} + 6 \, B a b^{7} - 8 \, A b^{8}\right)} d x - 6 \, {\left(4 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} - 3 \, B a b^{6} + 4 \, A b^{7} + {\left(4 \, B a^{4} b^{3} - 5 \, A a^{3} b^{4} - 3 \, B a^{2} b^{5} + 4 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(4 \, A a^{7} b - 12 \, B a^{6} b^{2} + 10 \, A a^{5} b^{3} + 30 \, B a^{4} b^{4} - 38 \, A a^{3} b^{5} - 18 \, B a^{2} b^{6} + 24 \, A a b^{7} + 2 \, {\left(A a^{8} - 2 \, A a^{6} b^{2} + A a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, B a^{8} - 4 \, A a^{7} b - 6 \, B a^{6} b^{2} + 8 \, A a^{5} b^{3} + 3 \, B a^{4} b^{4} - 4 \, A a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A a^{8} - 9 \, B a^{7} b + 4 \, A a^{6} b^{2} + 18 \, B a^{5} b^{3} - 20 \, A a^{4} b^{4} - 9 \, B a^{3} b^{5} + 12 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{10} - 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d\right)}}\right]"," ",0,"[1/6*(3*(B*a^8 - 2*A*a^7*b + 4*B*a^6*b^2 - 4*A*a^5*b^3 - 11*B*a^4*b^4 + 14*A*a^3*b^5 + 6*B*a^2*b^6 - 8*A*a*b^7)*d*x*cos(d*x + c) + 3*(B*a^7*b - 2*A*a^6*b^2 + 4*B*a^5*b^3 - 4*A*a^4*b^4 - 11*B*a^3*b^5 + 14*A*a^2*b^6 + 6*B*a*b^7 - 8*A*b^8)*d*x + 3*(4*B*a^3*b^4 - 5*A*a^2*b^5 - 3*B*a*b^6 + 4*A*b^7 + (4*B*a^4*b^3 - 5*A*a^3*b^4 - 3*B*a^2*b^5 + 4*A*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (4*A*a^7*b - 12*B*a^6*b^2 + 10*A*a^5*b^3 + 30*B*a^4*b^4 - 38*A*a^3*b^5 - 18*B*a^2*b^6 + 24*A*a*b^7 + 2*(A*a^8 - 2*A*a^6*b^2 + A*a^4*b^4)*cos(d*x + c)^3 + (3*B*a^8 - 4*A*a^7*b - 6*B*a^6*b^2 + 8*A*a^5*b^3 + 3*B*a^4*b^4 - 4*A*a^3*b^5)*cos(d*x + c)^2 + (4*A*a^8 - 9*B*a^7*b + 4*A*a^6*b^2 + 18*B*a^5*b^3 - 20*A*a^4*b^4 - 9*B*a^3*b^5 + 12*A*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^10 - 2*a^8*b^2 + a^6*b^4)*d*cos(d*x + c) + (a^9*b - 2*a^7*b^3 + a^5*b^5)*d), 1/6*(3*(B*a^8 - 2*A*a^7*b + 4*B*a^6*b^2 - 4*A*a^5*b^3 - 11*B*a^4*b^4 + 14*A*a^3*b^5 + 6*B*a^2*b^6 - 8*A*a*b^7)*d*x*cos(d*x + c) + 3*(B*a^7*b - 2*A*a^6*b^2 + 4*B*a^5*b^3 - 4*A*a^4*b^4 - 11*B*a^3*b^5 + 14*A*a^2*b^6 + 6*B*a*b^7 - 8*A*b^8)*d*x - 6*(4*B*a^3*b^4 - 5*A*a^2*b^5 - 3*B*a*b^6 + 4*A*b^7 + (4*B*a^4*b^3 - 5*A*a^3*b^4 - 3*B*a^2*b^5 + 4*A*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (4*A*a^7*b - 12*B*a^6*b^2 + 10*A*a^5*b^3 + 30*B*a^4*b^4 - 38*A*a^3*b^5 - 18*B*a^2*b^6 + 24*A*a*b^7 + 2*(A*a^8 - 2*A*a^6*b^2 + A*a^4*b^4)*cos(d*x + c)^3 + (3*B*a^8 - 4*A*a^7*b - 6*B*a^6*b^2 + 8*A*a^5*b^3 + 3*B*a^4*b^4 - 4*A*a^3*b^5)*cos(d*x + c)^2 + (4*A*a^8 - 9*B*a^7*b + 4*A*a^6*b^2 + 18*B*a^5*b^3 - 20*A*a^4*b^4 - 9*B*a^3*b^5 + 12*A*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^10 - 2*a^8*b^2 + a^6*b^4)*d*cos(d*x + c) + (a^9*b - 2*a^7*b^3 + a^5*b^5)*d)]","A",0
328,1,2444,0,72.773674," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(12 \, B a^{9} - 6 \, A a^{8} b - 29 \, B a^{7} b^{2} + 15 \, A a^{6} b^{3} + 20 \, B a^{5} b^{4} - 12 \, A a^{4} b^{5}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, B a^{8} b - 6 \, A a^{7} b^{2} - 29 \, B a^{6} b^{3} + 15 \, A a^{5} b^{4} + 20 \, B a^{4} b^{5} - 12 \, A a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, B a^{7} b^{2} - 6 \, A a^{6} b^{3} - 29 \, B a^{5} b^{4} + 15 \, A a^{4} b^{5} + 20 \, B a^{3} b^{6} - 12 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - {\left({\left(12 \, B a^{10} - 6 \, A a^{9} b - 35 \, B a^{8} b^{2} + 18 \, A a^{7} b^{3} + 33 \, B a^{6} b^{4} - 18 \, A a^{5} b^{5} - 9 \, B a^{4} b^{6} + 6 \, A a^{3} b^{7} - B a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, B a^{9} b - 6 \, A a^{8} b^{2} - 35 \, B a^{7} b^{3} + 18 \, A a^{6} b^{4} + 33 \, B a^{5} b^{5} - 18 \, A a^{4} b^{6} - 9 \, B a^{3} b^{7} + 6 \, A a^{2} b^{8} - B a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, B a^{8} b^{2} - 6 \, A a^{7} b^{3} - 35 \, B a^{6} b^{4} + 18 \, A a^{5} b^{5} + 33 \, B a^{4} b^{6} - 18 \, A a^{3} b^{7} - 9 \, B a^{2} b^{8} + 6 \, A a b^{9} - B b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(12 \, B a^{10} - 6 \, A a^{9} b - 35 \, B a^{8} b^{2} + 18 \, A a^{7} b^{3} + 33 \, B a^{6} b^{4} - 18 \, A a^{5} b^{5} - 9 \, B a^{4} b^{6} + 6 \, A a^{3} b^{7} - B a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, B a^{9} b - 6 \, A a^{8} b^{2} - 35 \, B a^{7} b^{3} + 18 \, A a^{6} b^{4} + 33 \, B a^{5} b^{5} - 18 \, A a^{4} b^{6} - 9 \, B a^{3} b^{7} + 6 \, A a^{2} b^{8} - B a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, B a^{8} b^{2} - 6 \, A a^{7} b^{3} - 35 \, B a^{6} b^{4} + 18 \, A a^{5} b^{5} + 33 \, B a^{4} b^{6} - 18 \, A a^{3} b^{7} - 9 \, B a^{2} b^{8} + 6 \, A a b^{9} - B b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{6} b^{4} - 3 \, B a^{4} b^{6} + 3 \, B a^{2} b^{8} - B b^{10} - {\left(12 \, B a^{9} b - 6 \, A a^{8} b^{2} - 33 \, B a^{7} b^{3} + 17 \, A a^{6} b^{4} + 27 \, B a^{5} b^{5} - 13 \, A a^{4} b^{6} - 6 \, B a^{3} b^{7} + 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(18 \, B a^{8} b^{2} - 9 \, A a^{7} b^{3} - 50 \, B a^{6} b^{4} + 25 \, A a^{5} b^{5} + 43 \, B a^{4} b^{6} - 20 \, A a^{3} b^{7} - 11 \, B a^{2} b^{8} + 4 \, A a b^{9}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, B a^{7} b^{3} - A a^{6} b^{4} - 6 \, B a^{5} b^{5} + 3 \, A a^{4} b^{6} + 6 \, B a^{3} b^{7} - 3 \, A a^{2} b^{8} - 2 \, B a b^{9} + A b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b^{5} - 3 \, a^{6} b^{7} + 3 \, a^{4} b^{9} - a^{2} b^{11}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{7} b^{6} - 3 \, a^{5} b^{8} + 3 \, a^{3} b^{10} - a b^{12}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{6} b^{7} - 3 \, a^{4} b^{9} + 3 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)^{2}\right)}}, -\frac{2 \, {\left({\left(12 \, B a^{9} - 6 \, A a^{8} b - 29 \, B a^{7} b^{2} + 15 \, A a^{6} b^{3} + 20 \, B a^{5} b^{4} - 12 \, A a^{4} b^{5}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, B a^{8} b - 6 \, A a^{7} b^{2} - 29 \, B a^{6} b^{3} + 15 \, A a^{5} b^{4} + 20 \, B a^{4} b^{5} - 12 \, A a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, B a^{7} b^{2} - 6 \, A a^{6} b^{3} - 29 \, B a^{5} b^{4} + 15 \, A a^{4} b^{5} + 20 \, B a^{3} b^{6} - 12 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left({\left(12 \, B a^{10} - 6 \, A a^{9} b - 35 \, B a^{8} b^{2} + 18 \, A a^{7} b^{3} + 33 \, B a^{6} b^{4} - 18 \, A a^{5} b^{5} - 9 \, B a^{4} b^{6} + 6 \, A a^{3} b^{7} - B a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, B a^{9} b - 6 \, A a^{8} b^{2} - 35 \, B a^{7} b^{3} + 18 \, A a^{6} b^{4} + 33 \, B a^{5} b^{5} - 18 \, A a^{4} b^{6} - 9 \, B a^{3} b^{7} + 6 \, A a^{2} b^{8} - B a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, B a^{8} b^{2} - 6 \, A a^{7} b^{3} - 35 \, B a^{6} b^{4} + 18 \, A a^{5} b^{5} + 33 \, B a^{4} b^{6} - 18 \, A a^{3} b^{7} - 9 \, B a^{2} b^{8} + 6 \, A a b^{9} - B b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(12 \, B a^{10} - 6 \, A a^{9} b - 35 \, B a^{8} b^{2} + 18 \, A a^{7} b^{3} + 33 \, B a^{6} b^{4} - 18 \, A a^{5} b^{5} - 9 \, B a^{4} b^{6} + 6 \, A a^{3} b^{7} - B a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, B a^{9} b - 6 \, A a^{8} b^{2} - 35 \, B a^{7} b^{3} + 18 \, A a^{6} b^{4} + 33 \, B a^{5} b^{5} - 18 \, A a^{4} b^{6} - 9 \, B a^{3} b^{7} + 6 \, A a^{2} b^{8} - B a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, B a^{8} b^{2} - 6 \, A a^{7} b^{3} - 35 \, B a^{6} b^{4} + 18 \, A a^{5} b^{5} + 33 \, B a^{4} b^{6} - 18 \, A a^{3} b^{7} - 9 \, B a^{2} b^{8} + 6 \, A a b^{9} - B b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{6} b^{4} - 3 \, B a^{4} b^{6} + 3 \, B a^{2} b^{8} - B b^{10} - {\left(12 \, B a^{9} b - 6 \, A a^{8} b^{2} - 33 \, B a^{7} b^{3} + 17 \, A a^{6} b^{4} + 27 \, B a^{5} b^{5} - 13 \, A a^{4} b^{6} - 6 \, B a^{3} b^{7} + 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(18 \, B a^{8} b^{2} - 9 \, A a^{7} b^{3} - 50 \, B a^{6} b^{4} + 25 \, A a^{5} b^{5} + 43 \, B a^{4} b^{6} - 20 \, A a^{3} b^{7} - 11 \, B a^{2} b^{8} + 4 \, A a b^{9}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, B a^{7} b^{3} - A a^{6} b^{4} - 6 \, B a^{5} b^{5} + 3 \, A a^{4} b^{6} + 6 \, B a^{3} b^{7} - 3 \, A a^{2} b^{8} - 2 \, B a b^{9} + A b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b^{5} - 3 \, a^{6} b^{7} + 3 \, a^{4} b^{9} - a^{2} b^{11}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{7} b^{6} - 3 \, a^{5} b^{8} + 3 \, a^{3} b^{10} - a b^{12}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{6} b^{7} - 3 \, a^{4} b^{9} + 3 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[-1/4*(((12*B*a^9 - 6*A*a^8*b - 29*B*a^7*b^2 + 15*A*a^6*b^3 + 20*B*a^5*b^4 - 12*A*a^4*b^5)*cos(d*x + c)^4 + 2*(12*B*a^8*b - 6*A*a^7*b^2 - 29*B*a^6*b^3 + 15*A*a^5*b^4 + 20*B*a^4*b^5 - 12*A*a^3*b^6)*cos(d*x + c)^3 + (12*B*a^7*b^2 - 6*A*a^6*b^3 - 29*B*a^5*b^4 + 15*A*a^4*b^5 + 20*B*a^3*b^6 - 12*A*a^2*b^7)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - ((12*B*a^10 - 6*A*a^9*b - 35*B*a^8*b^2 + 18*A*a^7*b^3 + 33*B*a^6*b^4 - 18*A*a^5*b^5 - 9*B*a^4*b^6 + 6*A*a^3*b^7 - B*a^2*b^8)*cos(d*x + c)^4 + 2*(12*B*a^9*b - 6*A*a^8*b^2 - 35*B*a^7*b^3 + 18*A*a^6*b^4 + 33*B*a^5*b^5 - 18*A*a^4*b^6 - 9*B*a^3*b^7 + 6*A*a^2*b^8 - B*a*b^9)*cos(d*x + c)^3 + (12*B*a^8*b^2 - 6*A*a^7*b^3 - 35*B*a^6*b^4 + 18*A*a^5*b^5 + 33*B*a^4*b^6 - 18*A*a^3*b^7 - 9*B*a^2*b^8 + 6*A*a*b^9 - B*b^10)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((12*B*a^10 - 6*A*a^9*b - 35*B*a^8*b^2 + 18*A*a^7*b^3 + 33*B*a^6*b^4 - 18*A*a^5*b^5 - 9*B*a^4*b^6 + 6*A*a^3*b^7 - B*a^2*b^8)*cos(d*x + c)^4 + 2*(12*B*a^9*b - 6*A*a^8*b^2 - 35*B*a^7*b^3 + 18*A*a^6*b^4 + 33*B*a^5*b^5 - 18*A*a^4*b^6 - 9*B*a^3*b^7 + 6*A*a^2*b^8 - B*a*b^9)*cos(d*x + c)^3 + (12*B*a^8*b^2 - 6*A*a^7*b^3 - 35*B*a^6*b^4 + 18*A*a^5*b^5 + 33*B*a^4*b^6 - 18*A*a^3*b^7 - 9*B*a^2*b^8 + 6*A*a*b^9 - B*b^10)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(B*a^6*b^4 - 3*B*a^4*b^6 + 3*B*a^2*b^8 - B*b^10 - (12*B*a^9*b - 6*A*a^8*b^2 - 33*B*a^7*b^3 + 17*A*a^6*b^4 + 27*B*a^5*b^5 - 13*A*a^4*b^6 - 6*B*a^3*b^7 + 2*A*a^2*b^8)*cos(d*x + c)^3 - (18*B*a^8*b^2 - 9*A*a^7*b^3 - 50*B*a^6*b^4 + 25*A*a^5*b^5 + 43*B*a^4*b^6 - 20*A*a^3*b^7 - 11*B*a^2*b^8 + 4*A*a*b^9)*cos(d*x + c)^2 - 2*(2*B*a^7*b^3 - A*a^6*b^4 - 6*B*a^5*b^5 + 3*A*a^4*b^6 + 6*B*a^3*b^7 - 3*A*a^2*b^8 - 2*B*a*b^9 + A*b^10)*cos(d*x + c))*sin(d*x + c))/((a^8*b^5 - 3*a^6*b^7 + 3*a^4*b^9 - a^2*b^11)*d*cos(d*x + c)^4 + 2*(a^7*b^6 - 3*a^5*b^8 + 3*a^3*b^10 - a*b^12)*d*cos(d*x + c)^3 + (a^6*b^7 - 3*a^4*b^9 + 3*a^2*b^11 - b^13)*d*cos(d*x + c)^2), -1/4*(2*((12*B*a^9 - 6*A*a^8*b - 29*B*a^7*b^2 + 15*A*a^6*b^3 + 20*B*a^5*b^4 - 12*A*a^4*b^5)*cos(d*x + c)^4 + 2*(12*B*a^8*b - 6*A*a^7*b^2 - 29*B*a^6*b^3 + 15*A*a^5*b^4 + 20*B*a^4*b^5 - 12*A*a^3*b^6)*cos(d*x + c)^3 + (12*B*a^7*b^2 - 6*A*a^6*b^3 - 29*B*a^5*b^4 + 15*A*a^4*b^5 + 20*B*a^3*b^6 - 12*A*a^2*b^7)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - ((12*B*a^10 - 6*A*a^9*b - 35*B*a^8*b^2 + 18*A*a^7*b^3 + 33*B*a^6*b^4 - 18*A*a^5*b^5 - 9*B*a^4*b^6 + 6*A*a^3*b^7 - B*a^2*b^8)*cos(d*x + c)^4 + 2*(12*B*a^9*b - 6*A*a^8*b^2 - 35*B*a^7*b^3 + 18*A*a^6*b^4 + 33*B*a^5*b^5 - 18*A*a^4*b^6 - 9*B*a^3*b^7 + 6*A*a^2*b^8 - B*a*b^9)*cos(d*x + c)^3 + (12*B*a^8*b^2 - 6*A*a^7*b^3 - 35*B*a^6*b^4 + 18*A*a^5*b^5 + 33*B*a^4*b^6 - 18*A*a^3*b^7 - 9*B*a^2*b^8 + 6*A*a*b^9 - B*b^10)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((12*B*a^10 - 6*A*a^9*b - 35*B*a^8*b^2 + 18*A*a^7*b^3 + 33*B*a^6*b^4 - 18*A*a^5*b^5 - 9*B*a^4*b^6 + 6*A*a^3*b^7 - B*a^2*b^8)*cos(d*x + c)^4 + 2*(12*B*a^9*b - 6*A*a^8*b^2 - 35*B*a^7*b^3 + 18*A*a^6*b^4 + 33*B*a^5*b^5 - 18*A*a^4*b^6 - 9*B*a^3*b^7 + 6*A*a^2*b^8 - B*a*b^9)*cos(d*x + c)^3 + (12*B*a^8*b^2 - 6*A*a^7*b^3 - 35*B*a^6*b^4 + 18*A*a^5*b^5 + 33*B*a^4*b^6 - 18*A*a^3*b^7 - 9*B*a^2*b^8 + 6*A*a*b^9 - B*b^10)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(B*a^6*b^4 - 3*B*a^4*b^6 + 3*B*a^2*b^8 - B*b^10 - (12*B*a^9*b - 6*A*a^8*b^2 - 33*B*a^7*b^3 + 17*A*a^6*b^4 + 27*B*a^5*b^5 - 13*A*a^4*b^6 - 6*B*a^3*b^7 + 2*A*a^2*b^8)*cos(d*x + c)^3 - (18*B*a^8*b^2 - 9*A*a^7*b^3 - 50*B*a^6*b^4 + 25*A*a^5*b^5 + 43*B*a^4*b^6 - 20*A*a^3*b^7 - 11*B*a^2*b^8 + 4*A*a*b^9)*cos(d*x + c)^2 - 2*(2*B*a^7*b^3 - A*a^6*b^4 - 6*B*a^5*b^5 + 3*A*a^4*b^6 + 6*B*a^3*b^7 - 3*A*a^2*b^8 - 2*B*a*b^9 + A*b^10)*cos(d*x + c))*sin(d*x + c))/((a^8*b^5 - 3*a^6*b^7 + 3*a^4*b^9 - a^2*b^11)*d*cos(d*x + c)^4 + 2*(a^7*b^6 - 3*a^5*b^8 + 3*a^3*b^10 - a*b^12)*d*cos(d*x + c)^3 + (a^6*b^7 - 3*a^4*b^9 + 3*a^2*b^11 - b^13)*d*cos(d*x + c)^2)]","B",0
329,1,2111,0,48.001934," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(6 \, B a^{8} - 2 \, A a^{7} b - 15 \, B a^{6} b^{2} + 5 \, A a^{5} b^{3} + 12 \, B a^{4} b^{4} - 6 \, A a^{3} b^{5}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, B a^{7} b - 2 \, A a^{6} b^{2} - 15 \, B a^{5} b^{3} + 5 \, A a^{4} b^{4} + 12 \, B a^{3} b^{5} - 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, B a^{6} b^{2} - 2 \, A a^{5} b^{3} - 15 \, B a^{4} b^{4} + 5 \, A a^{3} b^{5} + 12 \, B a^{2} b^{6} - 6 \, A a b^{7}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left({\left(3 \, B a^{9} - A a^{8} b - 9 \, B a^{7} b^{2} + 3 \, A a^{6} b^{3} + 9 \, B a^{5} b^{4} - 3 \, A a^{4} b^{5} - 3 \, B a^{3} b^{6} + A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, B a^{8} b - A a^{7} b^{2} - 9 \, B a^{6} b^{3} + 3 \, A a^{5} b^{4} + 9 \, B a^{4} b^{5} - 3 \, A a^{3} b^{6} - 3 \, B a^{2} b^{7} + A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B a^{7} b^{2} - A a^{6} b^{3} - 9 \, B a^{5} b^{4} + 3 \, A a^{4} b^{5} + 9 \, B a^{3} b^{6} - 3 \, A a^{2} b^{7} - 3 \, B a b^{8} + A b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(3 \, B a^{9} - A a^{8} b - 9 \, B a^{7} b^{2} + 3 \, A a^{6} b^{3} + 9 \, B a^{5} b^{4} - 3 \, A a^{4} b^{5} - 3 \, B a^{3} b^{6} + A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, B a^{8} b - A a^{7} b^{2} - 9 \, B a^{6} b^{3} + 3 \, A a^{5} b^{4} + 9 \, B a^{4} b^{5} - 3 \, A a^{3} b^{6} - 3 \, B a^{2} b^{7} + A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B a^{7} b^{2} - A a^{6} b^{3} - 9 \, B a^{5} b^{4} + 3 \, A a^{4} b^{5} + 9 \, B a^{3} b^{6} - 3 \, A a^{2} b^{7} - 3 \, B a b^{8} + A b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, B a^{6} b^{3} - 6 \, B a^{4} b^{5} + 6 \, B a^{2} b^{7} - 2 \, B b^{9} + {\left(6 \, B a^{8} b - 2 \, A a^{7} b^{2} - 17 \, B a^{6} b^{3} + 7 \, A a^{5} b^{4} + 13 \, B a^{4} b^{5} - 5 \, A a^{3} b^{6} - 2 \, B a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, B a^{7} b^{2} - 3 \, A a^{6} b^{3} - 25 \, B a^{5} b^{4} + 9 \, A a^{4} b^{5} + 20 \, B a^{3} b^{6} - 6 \, A a^{2} b^{7} - 4 \, B a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b^{4} - 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} - a^{2} b^{10}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{7} b^{5} - 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{6} b^{6} - 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)\right)}}, \frac{{\left({\left(6 \, B a^{8} - 2 \, A a^{7} b - 15 \, B a^{6} b^{2} + 5 \, A a^{5} b^{3} + 12 \, B a^{4} b^{4} - 6 \, A a^{3} b^{5}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, B a^{7} b - 2 \, A a^{6} b^{2} - 15 \, B a^{5} b^{3} + 5 \, A a^{4} b^{4} + 12 \, B a^{3} b^{5} - 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, B a^{6} b^{2} - 2 \, A a^{5} b^{3} - 15 \, B a^{4} b^{4} + 5 \, A a^{3} b^{5} + 12 \, B a^{2} b^{6} - 6 \, A a b^{7}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left({\left(3 \, B a^{9} - A a^{8} b - 9 \, B a^{7} b^{2} + 3 \, A a^{6} b^{3} + 9 \, B a^{5} b^{4} - 3 \, A a^{4} b^{5} - 3 \, B a^{3} b^{6} + A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, B a^{8} b - A a^{7} b^{2} - 9 \, B a^{6} b^{3} + 3 \, A a^{5} b^{4} + 9 \, B a^{4} b^{5} - 3 \, A a^{3} b^{6} - 3 \, B a^{2} b^{7} + A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B a^{7} b^{2} - A a^{6} b^{3} - 9 \, B a^{5} b^{4} + 3 \, A a^{4} b^{5} + 9 \, B a^{3} b^{6} - 3 \, A a^{2} b^{7} - 3 \, B a b^{8} + A b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(3 \, B a^{9} - A a^{8} b - 9 \, B a^{7} b^{2} + 3 \, A a^{6} b^{3} + 9 \, B a^{5} b^{4} - 3 \, A a^{4} b^{5} - 3 \, B a^{3} b^{6} + A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, B a^{8} b - A a^{7} b^{2} - 9 \, B a^{6} b^{3} + 3 \, A a^{5} b^{4} + 9 \, B a^{4} b^{5} - 3 \, A a^{3} b^{6} - 3 \, B a^{2} b^{7} + A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B a^{7} b^{2} - A a^{6} b^{3} - 9 \, B a^{5} b^{4} + 3 \, A a^{4} b^{5} + 9 \, B a^{3} b^{6} - 3 \, A a^{2} b^{7} - 3 \, B a b^{8} + A b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, B a^{6} b^{3} - 6 \, B a^{4} b^{5} + 6 \, B a^{2} b^{7} - 2 \, B b^{9} + {\left(6 \, B a^{8} b - 2 \, A a^{7} b^{2} - 17 \, B a^{6} b^{3} + 7 \, A a^{5} b^{4} + 13 \, B a^{4} b^{5} - 5 \, A a^{3} b^{6} - 2 \, B a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, B a^{7} b^{2} - 3 \, A a^{6} b^{3} - 25 \, B a^{5} b^{4} + 9 \, A a^{4} b^{5} + 20 \, B a^{3} b^{6} - 6 \, A a^{2} b^{7} - 4 \, B a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} b^{4} - 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} - a^{2} b^{10}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{7} b^{5} - 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{6} b^{6} - 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(((6*B*a^8 - 2*A*a^7*b - 15*B*a^6*b^2 + 5*A*a^5*b^3 + 12*B*a^4*b^4 - 6*A*a^3*b^5)*cos(d*x + c)^3 + 2*(6*B*a^7*b - 2*A*a^6*b^2 - 15*B*a^5*b^3 + 5*A*a^4*b^4 + 12*B*a^3*b^5 - 6*A*a^2*b^6)*cos(d*x + c)^2 + (6*B*a^6*b^2 - 2*A*a^5*b^3 - 15*B*a^4*b^4 + 5*A*a^3*b^5 + 12*B*a^2*b^6 - 6*A*a*b^7)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*((3*B*a^9 - A*a^8*b - 9*B*a^7*b^2 + 3*A*a^6*b^3 + 9*B*a^5*b^4 - 3*A*a^4*b^5 - 3*B*a^3*b^6 + A*a^2*b^7)*cos(d*x + c)^3 + 2*(3*B*a^8*b - A*a^7*b^2 - 9*B*a^6*b^3 + 3*A*a^5*b^4 + 9*B*a^4*b^5 - 3*A*a^3*b^6 - 3*B*a^2*b^7 + A*a*b^8)*cos(d*x + c)^2 + (3*B*a^7*b^2 - A*a^6*b^3 - 9*B*a^5*b^4 + 3*A*a^4*b^5 + 9*B*a^3*b^6 - 3*A*a^2*b^7 - 3*B*a*b^8 + A*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) - 2*((3*B*a^9 - A*a^8*b - 9*B*a^7*b^2 + 3*A*a^6*b^3 + 9*B*a^5*b^4 - 3*A*a^4*b^5 - 3*B*a^3*b^6 + A*a^2*b^7)*cos(d*x + c)^3 + 2*(3*B*a^8*b - A*a^7*b^2 - 9*B*a^6*b^3 + 3*A*a^5*b^4 + 9*B*a^4*b^5 - 3*A*a^3*b^6 - 3*B*a^2*b^7 + A*a*b^8)*cos(d*x + c)^2 + (3*B*a^7*b^2 - A*a^6*b^3 - 9*B*a^5*b^4 + 3*A*a^4*b^5 + 9*B*a^3*b^6 - 3*A*a^2*b^7 - 3*B*a*b^8 + A*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*B*a^6*b^3 - 6*B*a^4*b^5 + 6*B*a^2*b^7 - 2*B*b^9 + (6*B*a^8*b - 2*A*a^7*b^2 - 17*B*a^6*b^3 + 7*A*a^5*b^4 + 13*B*a^4*b^5 - 5*A*a^3*b^6 - 2*B*a^2*b^7)*cos(d*x + c)^2 + (9*B*a^7*b^2 - 3*A*a^6*b^3 - 25*B*a^5*b^4 + 9*A*a^4*b^5 + 20*B*a^3*b^6 - 6*A*a^2*b^7 - 4*B*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^8*b^4 - 3*a^6*b^6 + 3*a^4*b^8 - a^2*b^10)*d*cos(d*x + c)^3 + 2*(a^7*b^5 - 3*a^5*b^7 + 3*a^3*b^9 - a*b^11)*d*cos(d*x + c)^2 + (a^6*b^6 - 3*a^4*b^8 + 3*a^2*b^10 - b^12)*d*cos(d*x + c)), 1/2*(((6*B*a^8 - 2*A*a^7*b - 15*B*a^6*b^2 + 5*A*a^5*b^3 + 12*B*a^4*b^4 - 6*A*a^3*b^5)*cos(d*x + c)^3 + 2*(6*B*a^7*b - 2*A*a^6*b^2 - 15*B*a^5*b^3 + 5*A*a^4*b^4 + 12*B*a^3*b^5 - 6*A*a^2*b^6)*cos(d*x + c)^2 + (6*B*a^6*b^2 - 2*A*a^5*b^3 - 15*B*a^4*b^4 + 5*A*a^3*b^5 + 12*B*a^2*b^6 - 6*A*a*b^7)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - ((3*B*a^9 - A*a^8*b - 9*B*a^7*b^2 + 3*A*a^6*b^3 + 9*B*a^5*b^4 - 3*A*a^4*b^5 - 3*B*a^3*b^6 + A*a^2*b^7)*cos(d*x + c)^3 + 2*(3*B*a^8*b - A*a^7*b^2 - 9*B*a^6*b^3 + 3*A*a^5*b^4 + 9*B*a^4*b^5 - 3*A*a^3*b^6 - 3*B*a^2*b^7 + A*a*b^8)*cos(d*x + c)^2 + (3*B*a^7*b^2 - A*a^6*b^3 - 9*B*a^5*b^4 + 3*A*a^4*b^5 + 9*B*a^3*b^6 - 3*A*a^2*b^7 - 3*B*a*b^8 + A*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((3*B*a^9 - A*a^8*b - 9*B*a^7*b^2 + 3*A*a^6*b^3 + 9*B*a^5*b^4 - 3*A*a^4*b^5 - 3*B*a^3*b^6 + A*a^2*b^7)*cos(d*x + c)^3 + 2*(3*B*a^8*b - A*a^7*b^2 - 9*B*a^6*b^3 + 3*A*a^5*b^4 + 9*B*a^4*b^5 - 3*A*a^3*b^6 - 3*B*a^2*b^7 + A*a*b^8)*cos(d*x + c)^2 + (3*B*a^7*b^2 - A*a^6*b^3 - 9*B*a^5*b^4 + 3*A*a^4*b^5 + 9*B*a^3*b^6 - 3*A*a^2*b^7 - 3*B*a*b^8 + A*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (2*B*a^6*b^3 - 6*B*a^4*b^5 + 6*B*a^2*b^7 - 2*B*b^9 + (6*B*a^8*b - 2*A*a^7*b^2 - 17*B*a^6*b^3 + 7*A*a^5*b^4 + 13*B*a^4*b^5 - 5*A*a^3*b^6 - 2*B*a^2*b^7)*cos(d*x + c)^2 + (9*B*a^7*b^2 - 3*A*a^6*b^3 - 25*B*a^5*b^4 + 9*A*a^4*b^5 + 20*B*a^3*b^6 - 6*A*a^2*b^7 - 4*B*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^8*b^4 - 3*a^6*b^6 + 3*a^4*b^8 - a^2*b^10)*d*cos(d*x + c)^3 + 2*(a^7*b^5 - 3*a^5*b^7 + 3*a^3*b^9 - a*b^11)*d*cos(d*x + c)^2 + (a^6*b^6 - 3*a^4*b^8 + 3*a^2*b^10 - b^12)*d*cos(d*x + c))]","B",0
330,1,1419,0,18.229803," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, B a^{5} b^{2} - 5 \, B a^{3} b^{4} - A a^{2} b^{5} + 6 \, B a b^{6} - 2 \, A b^{7} + {\left(2 \, B a^{7} - 5 \, B a^{5} b^{2} - A a^{4} b^{3} + 6 \, B a^{3} b^{4} - 2 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{6} b - 5 \, B a^{4} b^{3} - A a^{3} b^{4} + 6 \, B a^{2} b^{5} - 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(B a^{6} b^{2} - 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} - B b^{8} + {\left(B a^{8} - 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} - B a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{7} b - 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} - B a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a^{6} b^{2} - 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} - B b^{8} + {\left(B a^{8} - 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} - B a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{7} b - 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} - B a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, B a^{6} b^{2} - A a^{5} b^{3} - 9 \, B a^{4} b^{4} + 5 \, A a^{3} b^{5} + 6 \, B a^{2} b^{6} - 4 \, A a b^{7} + {\left(2 \, B a^{7} b - 7 \, B a^{5} b^{3} + 3 \, A a^{4} b^{4} + 5 \, B a^{3} b^{5} - 3 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b^{3} - 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} - a^{2} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{4} - 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} - a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} d\right)}}, -\frac{{\left(2 \, B a^{5} b^{2} - 5 \, B a^{3} b^{4} - A a^{2} b^{5} + 6 \, B a b^{6} - 2 \, A b^{7} + {\left(2 \, B a^{7} - 5 \, B a^{5} b^{2} - A a^{4} b^{3} + 6 \, B a^{3} b^{4} - 2 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{6} b - 5 \, B a^{4} b^{3} - A a^{3} b^{4} + 6 \, B a^{2} b^{5} - 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(B a^{6} b^{2} - 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} - B b^{8} + {\left(B a^{8} - 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} - B a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{7} b - 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} - B a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(B a^{6} b^{2} - 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} - B b^{8} + {\left(B a^{8} - 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} - B a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{7} b - 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} - B a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(3 \, B a^{6} b^{2} - A a^{5} b^{3} - 9 \, B a^{4} b^{4} + 5 \, A a^{3} b^{5} + 6 \, B a^{2} b^{6} - 4 \, A a b^{7} + {\left(2 \, B a^{7} b - 7 \, B a^{5} b^{3} + 3 \, A a^{4} b^{4} + 5 \, B a^{3} b^{5} - 3 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} b^{3} - 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} - a^{2} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{4} - 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} - a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} d\right)}}\right]"," ",0,"[-1/4*((2*B*a^5*b^2 - 5*B*a^3*b^4 - A*a^2*b^5 + 6*B*a*b^6 - 2*A*b^7 + (2*B*a^7 - 5*B*a^5*b^2 - A*a^4*b^3 + 6*B*a^3*b^4 - 2*A*a^2*b^5)*cos(d*x + c)^2 + 2*(2*B*a^6*b - 5*B*a^4*b^3 - A*a^3*b^4 + 6*B*a^2*b^5 - 2*A*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(B*a^6*b^2 - 3*B*a^4*b^4 + 3*B*a^2*b^6 - B*b^8 + (B*a^8 - 3*B*a^6*b^2 + 3*B*a^4*b^4 - B*a^2*b^6)*cos(d*x + c)^2 + 2*(B*a^7*b - 3*B*a^5*b^3 + 3*B*a^3*b^5 - B*a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) + 2*(B*a^6*b^2 - 3*B*a^4*b^4 + 3*B*a^2*b^6 - B*b^8 + (B*a^8 - 3*B*a^6*b^2 + 3*B*a^4*b^4 - B*a^2*b^6)*cos(d*x + c)^2 + 2*(B*a^7*b - 3*B*a^5*b^3 + 3*B*a^3*b^5 - B*a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(3*B*a^6*b^2 - A*a^5*b^3 - 9*B*a^4*b^4 + 5*A*a^3*b^5 + 6*B*a^2*b^6 - 4*A*a*b^7 + (2*B*a^7*b - 7*B*a^5*b^3 + 3*A*a^4*b^4 + 5*B*a^3*b^5 - 3*A*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 3*a^6*b^5 + 3*a^4*b^7 - a^2*b^9)*d*cos(d*x + c)^2 + 2*(a^7*b^4 - 3*a^5*b^6 + 3*a^3*b^8 - a*b^10)*d*cos(d*x + c) + (a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*d), -1/2*((2*B*a^5*b^2 - 5*B*a^3*b^4 - A*a^2*b^5 + 6*B*a*b^6 - 2*A*b^7 + (2*B*a^7 - 5*B*a^5*b^2 - A*a^4*b^3 + 6*B*a^3*b^4 - 2*A*a^2*b^5)*cos(d*x + c)^2 + 2*(2*B*a^6*b - 5*B*a^4*b^3 - A*a^3*b^4 + 6*B*a^2*b^5 - 2*A*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (B*a^6*b^2 - 3*B*a^4*b^4 + 3*B*a^2*b^6 - B*b^8 + (B*a^8 - 3*B*a^6*b^2 + 3*B*a^4*b^4 - B*a^2*b^6)*cos(d*x + c)^2 + 2*(B*a^7*b - 3*B*a^5*b^3 + 3*B*a^3*b^5 - B*a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) + (B*a^6*b^2 - 3*B*a^4*b^4 + 3*B*a^2*b^6 - B*b^8 + (B*a^8 - 3*B*a^6*b^2 + 3*B*a^4*b^4 - B*a^2*b^6)*cos(d*x + c)^2 + 2*(B*a^7*b - 3*B*a^5*b^3 + 3*B*a^3*b^5 - B*a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (3*B*a^6*b^2 - A*a^5*b^3 - 9*B*a^4*b^4 + 5*A*a^3*b^5 + 6*B*a^2*b^6 - 4*A*a*b^7 + (2*B*a^7*b - 7*B*a^5*b^3 + 3*A*a^4*b^4 + 5*B*a^3*b^5 - 3*A*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 3*a^6*b^5 + 3*a^4*b^7 - a^2*b^9)*d*cos(d*x + c)^2 + 2*(a^7*b^4 - 3*a^5*b^6 + 3*a^3*b^8 - a*b^10)*d*cos(d*x + c) + (a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*d)]","B",0
331,1,750,0,0.518814," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(B a^{2} b^{2} - 3 \, A a b^{3} + 2 \, B b^{4} + {\left(B a^{4} - 3 \, A a^{3} b + 2 \, B a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2} + 2 \, B a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(B a^{5} + A a^{4} b - 5 \, B a^{3} b^{2} + A a^{2} b^{3} + 4 \, B a b^{4} - 2 \, A b^{5} + {\left(2 \, A a^{5} - 3 \, B a^{4} b - A a^{3} b^{2} + 3 \, B a^{2} b^{3} - A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d\right)}}, \frac{{\left(B a^{2} b^{2} - 3 \, A a b^{3} + 2 \, B b^{4} + {\left(B a^{4} - 3 \, A a^{3} b + 2 \, B a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2} + 2 \, B a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(B a^{5} + A a^{4} b - 5 \, B a^{3} b^{2} + A a^{2} b^{3} + 4 \, B a b^{4} - 2 \, A b^{5} + {\left(2 \, A a^{5} - 3 \, B a^{4} b - A a^{3} b^{2} + 3 \, B a^{2} b^{3} - A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d\right)}}\right]"," ",0,"[1/4*((B*a^2*b^2 - 3*A*a*b^3 + 2*B*b^4 + (B*a^4 - 3*A*a^3*b + 2*B*a^2*b^2)*cos(d*x + c)^2 + 2*(B*a^3*b - 3*A*a^2*b^2 + 2*B*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(B*a^5 + A*a^4*b - 5*B*a^3*b^2 + A*a^2*b^3 + 4*B*a*b^4 - 2*A*b^5 + (2*A*a^5 - 3*B*a^4*b - A*a^3*b^2 + 3*B*a^2*b^3 - A*a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*cos(d*x + c) + (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d), 1/2*((B*a^2*b^2 - 3*A*a*b^3 + 2*B*b^4 + (B*a^4 - 3*A*a^3*b + 2*B*a^2*b^2)*cos(d*x + c)^2 + 2*(B*a^3*b - 3*A*a^2*b^2 + 2*B*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (B*a^5 + A*a^4*b - 5*B*a^3*b^2 + A*a^2*b^3 + 4*B*a*b^4 - 2*A*b^5 + (2*A*a^5 - 3*B*a^4*b - A*a^3*b^2 + 3*B*a^2*b^3 - A*a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*cos(d*x + c) + (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d)]","B",0
332,1,752,0,0.511702," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, A a^{2} b^{2} - 3 \, B a b^{3} + A b^{4} + {\left(2 \, A a^{4} - 3 \, B a^{3} b + A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, A a^{3} b - 3 \, B a^{2} b^{2} + A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(B a^{4} b - 3 \, A a^{3} b^{2} + B a^{2} b^{3} + 3 \, A a b^{4} - 2 \, B b^{5} + {\left(2 \, B a^{5} - 4 \, A a^{4} b - B a^{3} b^{2} + 5 \, A a^{2} b^{3} - B a b^{4} - A b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d\right)}}, \frac{{\left(2 \, A a^{2} b^{2} - 3 \, B a b^{3} + A b^{4} + {\left(2 \, A a^{4} - 3 \, B a^{3} b + A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, A a^{3} b - 3 \, B a^{2} b^{2} + A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(B a^{4} b - 3 \, A a^{3} b^{2} + B a^{2} b^{3} + 3 \, A a b^{4} - 2 \, B b^{5} + {\left(2 \, B a^{5} - 4 \, A a^{4} b - B a^{3} b^{2} + 5 \, A a^{2} b^{3} - B a b^{4} - A b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d\right)}}\right]"," ",0,"[1/4*((2*A*a^2*b^2 - 3*B*a*b^3 + A*b^4 + (2*A*a^4 - 3*B*a^3*b + A*a^2*b^2)*cos(d*x + c)^2 + 2*(2*A*a^3*b - 3*B*a^2*b^2 + A*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(B*a^4*b - 3*A*a^3*b^2 + B*a^2*b^3 + 3*A*a*b^4 - 2*B*b^5 + (2*B*a^5 - 4*A*a^4*b - B*a^3*b^2 + 5*A*a^2*b^3 - B*a*b^4 - A*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*cos(d*x + c) + (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d), 1/2*((2*A*a^2*b^2 - 3*B*a*b^3 + A*b^4 + (2*A*a^4 - 3*B*a^3*b + A*a^2*b^2)*cos(d*x + c)^2 + 2*(2*A*a^3*b - 3*B*a^2*b^2 + A*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (B*a^4*b - 3*A*a^3*b^2 + B*a^2*b^3 + 3*A*a*b^4 - 2*B*b^5 + (2*B*a^5 - 4*A*a^4*b - B*a^3*b^2 + 5*A*a^2*b^3 - B*a*b^4 - A*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*cos(d*x + c) + (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d)]","B",0
333,1,1152,0,0.547931," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(A a^{8} - 3 \, A a^{6} b^{2} + 3 \, A a^{4} b^{4} - A a^{2} b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(A a^{7} b - 3 \, A a^{5} b^{3} + 3 \, A a^{3} b^{5} - A a b^{7}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(A a^{6} b^{2} - 3 \, A a^{4} b^{4} + 3 \, A a^{2} b^{6} - A b^{8}\right)} d x - {\left(2 \, B a^{5} b^{2} - 6 \, A a^{4} b^{3} + B a^{3} b^{4} + 5 \, A a^{2} b^{5} - 2 \, A b^{7} + {\left(2 \, B a^{7} - 6 \, A a^{6} b + B a^{5} b^{2} + 5 \, A a^{4} b^{3} - 2 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{6} b - 6 \, A a^{5} b^{2} + B a^{4} b^{3} + 5 \, A a^{3} b^{4} - 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(3 \, B a^{6} b^{2} - 5 \, A a^{5} b^{3} - 3 \, B a^{4} b^{4} + 7 \, A a^{3} b^{5} - 2 \, A a b^{7} + {\left(4 \, B a^{7} b - 6 \, A a^{6} b^{2} - 5 \, B a^{5} b^{3} + 9 \, A a^{4} b^{4} + B a^{3} b^{5} - 3 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{9} b^{2} - 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} - a^{3} b^{8}\right)} d\right)}}, \frac{2 \, {\left(A a^{8} - 3 \, A a^{6} b^{2} + 3 \, A a^{4} b^{4} - A a^{2} b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(A a^{7} b - 3 \, A a^{5} b^{3} + 3 \, A a^{3} b^{5} - A a b^{7}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(A a^{6} b^{2} - 3 \, A a^{4} b^{4} + 3 \, A a^{2} b^{6} - A b^{8}\right)} d x + {\left(2 \, B a^{5} b^{2} - 6 \, A a^{4} b^{3} + B a^{3} b^{4} + 5 \, A a^{2} b^{5} - 2 \, A b^{7} + {\left(2 \, B a^{7} - 6 \, A a^{6} b + B a^{5} b^{2} + 5 \, A a^{4} b^{3} - 2 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{6} b - 6 \, A a^{5} b^{2} + B a^{4} b^{3} + 5 \, A a^{3} b^{4} - 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(3 \, B a^{6} b^{2} - 5 \, A a^{5} b^{3} - 3 \, B a^{4} b^{4} + 7 \, A a^{3} b^{5} - 2 \, A a b^{7} + {\left(4 \, B a^{7} b - 6 \, A a^{6} b^{2} - 5 \, B a^{5} b^{3} + 9 \, A a^{4} b^{4} + B a^{3} b^{5} - 3 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{9} b^{2} - 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} - a^{3} b^{8}\right)} d\right)}}\right]"," ",0,"[1/4*(4*(A*a^8 - 3*A*a^6*b^2 + 3*A*a^4*b^4 - A*a^2*b^6)*d*x*cos(d*x + c)^2 + 8*(A*a^7*b - 3*A*a^5*b^3 + 3*A*a^3*b^5 - A*a*b^7)*d*x*cos(d*x + c) + 4*(A*a^6*b^2 - 3*A*a^4*b^4 + 3*A*a^2*b^6 - A*b^8)*d*x - (2*B*a^5*b^2 - 6*A*a^4*b^3 + B*a^3*b^4 + 5*A*a^2*b^5 - 2*A*b^7 + (2*B*a^7 - 6*A*a^6*b + B*a^5*b^2 + 5*A*a^4*b^3 - 2*A*a^2*b^5)*cos(d*x + c)^2 + 2*(2*B*a^6*b - 6*A*a^5*b^2 + B*a^4*b^3 + 5*A*a^3*b^4 - 2*A*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(3*B*a^6*b^2 - 5*A*a^5*b^3 - 3*B*a^4*b^4 + 7*A*a^3*b^5 - 2*A*a*b^7 + (4*B*a^7*b - 6*A*a^6*b^2 - 5*B*a^5*b^3 + 9*A*a^4*b^4 + B*a^3*b^5 - 3*A*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cos(d*x + c)^2 + 2*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cos(d*x + c) + (a^9*b^2 - 3*a^7*b^4 + 3*a^5*b^6 - a^3*b^8)*d), 1/2*(2*(A*a^8 - 3*A*a^6*b^2 + 3*A*a^4*b^4 - A*a^2*b^6)*d*x*cos(d*x + c)^2 + 4*(A*a^7*b - 3*A*a^5*b^3 + 3*A*a^3*b^5 - A*a*b^7)*d*x*cos(d*x + c) + 2*(A*a^6*b^2 - 3*A*a^4*b^4 + 3*A*a^2*b^6 - A*b^8)*d*x + (2*B*a^5*b^2 - 6*A*a^4*b^3 + B*a^3*b^4 + 5*A*a^2*b^5 - 2*A*b^7 + (2*B*a^7 - 6*A*a^6*b + B*a^5*b^2 + 5*A*a^4*b^3 - 2*A*a^2*b^5)*cos(d*x + c)^2 + 2*(2*B*a^6*b - 6*A*a^5*b^2 + B*a^4*b^3 + 5*A*a^3*b^4 - 2*A*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (3*B*a^6*b^2 - 5*A*a^5*b^3 - 3*B*a^4*b^4 + 7*A*a^3*b^5 - 2*A*a*b^7 + (4*B*a^7*b - 6*A*a^6*b^2 - 5*B*a^5*b^3 + 9*A*a^4*b^4 + B*a^3*b^5 - 3*A*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cos(d*x + c)^2 + 2*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cos(d*x + c) + (a^9*b^2 - 3*a^7*b^4 + 3*a^5*b^6 - a^3*b^8)*d)]","B",0
334,1,1568,0,0.623095," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(B a^{9} - 3 \, A a^{8} b - 3 \, B a^{7} b^{2} + 9 \, A a^{6} b^{3} + 3 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} - B a^{3} b^{6} + 3 \, A a^{2} b^{7}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(B a^{8} b - 3 \, A a^{7} b^{2} - 3 \, B a^{6} b^{3} + 9 \, A a^{5} b^{4} + 3 \, B a^{4} b^{5} - 9 \, A a^{3} b^{6} - B a^{2} b^{7} + 3 \, A a b^{8}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(B a^{7} b^{2} - 3 \, A a^{6} b^{3} - 3 \, B a^{5} b^{4} + 9 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7} - B a b^{8} + 3 \, A b^{9}\right)} d x - {\left(6 \, B a^{5} b^{3} - 12 \, A a^{4} b^{4} - 5 \, B a^{3} b^{5} + 15 \, A a^{2} b^{6} + 2 \, B a b^{7} - 6 \, A b^{8} + {\left(6 \, B a^{7} b - 12 \, A a^{6} b^{2} - 5 \, B a^{5} b^{3} + 15 \, A a^{4} b^{4} + 2 \, B a^{3} b^{5} - 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B a^{6} b^{2} - 12 \, A a^{5} b^{3} - 5 \, B a^{4} b^{4} + 15 \, A a^{3} b^{5} + 2 \, B a^{2} b^{6} - 6 \, A a b^{7}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(2 \, A a^{7} b^{2} + 5 \, B a^{6} b^{3} - 13 \, A a^{5} b^{4} - 7 \, B a^{4} b^{5} + 17 \, A a^{3} b^{6} + 2 \, B a^{2} b^{7} - 6 \, A a b^{8} + 2 \, {\left(A a^{9} - 3 \, A a^{7} b^{2} + 3 \, A a^{5} b^{4} - A a^{3} b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A a^{8} b + 6 \, B a^{7} b^{2} - 20 \, A a^{6} b^{3} - 9 \, B a^{5} b^{4} + 25 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{11} b - 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} - a^{5} b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{10} b^{2} - 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} - a^{4} b^{8}\right)} d\right)}}, \frac{2 \, {\left(B a^{9} - 3 \, A a^{8} b - 3 \, B a^{7} b^{2} + 9 \, A a^{6} b^{3} + 3 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} - B a^{3} b^{6} + 3 \, A a^{2} b^{7}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(B a^{8} b - 3 \, A a^{7} b^{2} - 3 \, B a^{6} b^{3} + 9 \, A a^{5} b^{4} + 3 \, B a^{4} b^{5} - 9 \, A a^{3} b^{6} - B a^{2} b^{7} + 3 \, A a b^{8}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(B a^{7} b^{2} - 3 \, A a^{6} b^{3} - 3 \, B a^{5} b^{4} + 9 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7} - B a b^{8} + 3 \, A b^{9}\right)} d x - {\left(6 \, B a^{5} b^{3} - 12 \, A a^{4} b^{4} - 5 \, B a^{3} b^{5} + 15 \, A a^{2} b^{6} + 2 \, B a b^{7} - 6 \, A b^{8} + {\left(6 \, B a^{7} b - 12 \, A a^{6} b^{2} - 5 \, B a^{5} b^{3} + 15 \, A a^{4} b^{4} + 2 \, B a^{3} b^{5} - 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B a^{6} b^{2} - 12 \, A a^{5} b^{3} - 5 \, B a^{4} b^{4} + 15 \, A a^{3} b^{5} + 2 \, B a^{2} b^{6} - 6 \, A a b^{7}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(2 \, A a^{7} b^{2} + 5 \, B a^{6} b^{3} - 13 \, A a^{5} b^{4} - 7 \, B a^{4} b^{5} + 17 \, A a^{3} b^{6} + 2 \, B a^{2} b^{7} - 6 \, A a b^{8} + 2 \, {\left(A a^{9} - 3 \, A a^{7} b^{2} + 3 \, A a^{5} b^{4} - A a^{3} b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A a^{8} b + 6 \, B a^{7} b^{2} - 20 \, A a^{6} b^{3} - 9 \, B a^{5} b^{4} + 25 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{11} b - 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} - a^{5} b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{10} b^{2} - 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} - a^{4} b^{8}\right)} d\right)}}\right]"," ",0,"[1/4*(4*(B*a^9 - 3*A*a^8*b - 3*B*a^7*b^2 + 9*A*a^6*b^3 + 3*B*a^5*b^4 - 9*A*a^4*b^5 - B*a^3*b^6 + 3*A*a^2*b^7)*d*x*cos(d*x + c)^2 + 8*(B*a^8*b - 3*A*a^7*b^2 - 3*B*a^6*b^3 + 9*A*a^5*b^4 + 3*B*a^4*b^5 - 9*A*a^3*b^6 - B*a^2*b^7 + 3*A*a*b^8)*d*x*cos(d*x + c) + 4*(B*a^7*b^2 - 3*A*a^6*b^3 - 3*B*a^5*b^4 + 9*A*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7 - B*a*b^8 + 3*A*b^9)*d*x - (6*B*a^5*b^3 - 12*A*a^4*b^4 - 5*B*a^3*b^5 + 15*A*a^2*b^6 + 2*B*a*b^7 - 6*A*b^8 + (6*B*a^7*b - 12*A*a^6*b^2 - 5*B*a^5*b^3 + 15*A*a^4*b^4 + 2*B*a^3*b^5 - 6*A*a^2*b^6)*cos(d*x + c)^2 + 2*(6*B*a^6*b^2 - 12*A*a^5*b^3 - 5*B*a^4*b^4 + 15*A*a^3*b^5 + 2*B*a^2*b^6 - 6*A*a*b^7)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(2*A*a^7*b^2 + 5*B*a^6*b^3 - 13*A*a^5*b^4 - 7*B*a^4*b^5 + 17*A*a^3*b^6 + 2*B*a^2*b^7 - 6*A*a*b^8 + 2*(A*a^9 - 3*A*a^7*b^2 + 3*A*a^5*b^4 - A*a^3*b^6)*cos(d*x + c)^2 + (4*A*a^8*b + 6*B*a^7*b^2 - 20*A*a^6*b^3 - 9*B*a^5*b^4 + 25*A*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/((a^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*d*cos(d*x + c)^2 + 2*(a^11*b - 3*a^9*b^3 + 3*a^7*b^5 - a^5*b^7)*d*cos(d*x + c) + (a^10*b^2 - 3*a^8*b^4 + 3*a^6*b^6 - a^4*b^8)*d), 1/2*(2*(B*a^9 - 3*A*a^8*b - 3*B*a^7*b^2 + 9*A*a^6*b^3 + 3*B*a^5*b^4 - 9*A*a^4*b^5 - B*a^3*b^6 + 3*A*a^2*b^7)*d*x*cos(d*x + c)^2 + 4*(B*a^8*b - 3*A*a^7*b^2 - 3*B*a^6*b^3 + 9*A*a^5*b^4 + 3*B*a^4*b^5 - 9*A*a^3*b^6 - B*a^2*b^7 + 3*A*a*b^8)*d*x*cos(d*x + c) + 2*(B*a^7*b^2 - 3*A*a^6*b^3 - 3*B*a^5*b^4 + 9*A*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7 - B*a*b^8 + 3*A*b^9)*d*x - (6*B*a^5*b^3 - 12*A*a^4*b^4 - 5*B*a^3*b^5 + 15*A*a^2*b^6 + 2*B*a*b^7 - 6*A*b^8 + (6*B*a^7*b - 12*A*a^6*b^2 - 5*B*a^5*b^3 + 15*A*a^4*b^4 + 2*B*a^3*b^5 - 6*A*a^2*b^6)*cos(d*x + c)^2 + 2*(6*B*a^6*b^2 - 12*A*a^5*b^3 - 5*B*a^4*b^4 + 15*A*a^3*b^5 + 2*B*a^2*b^6 - 6*A*a*b^7)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (2*A*a^7*b^2 + 5*B*a^6*b^3 - 13*A*a^5*b^4 - 7*B*a^4*b^5 + 17*A*a^3*b^6 + 2*B*a^2*b^7 - 6*A*a*b^8 + 2*(A*a^9 - 3*A*a^7*b^2 + 3*A*a^5*b^4 - A*a^3*b^6)*cos(d*x + c)^2 + (4*A*a^8*b + 6*B*a^7*b^2 - 20*A*a^6*b^3 - 9*B*a^5*b^4 + 25*A*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/((a^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*d*cos(d*x + c)^2 + 2*(a^11*b - 3*a^9*b^3 + 3*a^7*b^5 - a^5*b^7)*d*cos(d*x + c) + (a^10*b^2 - 3*a^8*b^4 + 3*a^6*b^6 - a^4*b^8)*d)]","B",0
335,1,1811,0,0.700929," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(A a^{10} - 6 \, B a^{9} b + 9 \, A a^{8} b^{2} + 18 \, B a^{7} b^{3} - 33 \, A a^{6} b^{4} - 18 \, B a^{5} b^{5} + 35 \, A a^{4} b^{6} + 6 \, B a^{3} b^{7} - 12 \, A a^{2} b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(A a^{9} b - 6 \, B a^{8} b^{2} + 9 \, A a^{7} b^{3} + 18 \, B a^{6} b^{4} - 33 \, A a^{5} b^{5} - 18 \, B a^{4} b^{6} + 35 \, A a^{3} b^{7} + 6 \, B a^{2} b^{8} - 12 \, A a b^{9}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(A a^{8} b^{2} - 6 \, B a^{7} b^{3} + 9 \, A a^{6} b^{4} + 18 \, B a^{5} b^{5} - 33 \, A a^{4} b^{6} - 18 \, B a^{3} b^{7} + 35 \, A a^{2} b^{8} + 6 \, B a b^{9} - 12 \, A b^{10}\right)} d x - {\left(12 \, B a^{5} b^{4} - 20 \, A a^{4} b^{5} - 15 \, B a^{3} b^{6} + 29 \, A a^{2} b^{7} + 6 \, B a b^{8} - 12 \, A b^{9} + {\left(12 \, B a^{7} b^{2} - 20 \, A a^{6} b^{3} - 15 \, B a^{5} b^{4} + 29 \, A a^{4} b^{5} + 6 \, B a^{3} b^{6} - 12 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, B a^{6} b^{3} - 20 \, A a^{5} b^{4} - 15 \, B a^{4} b^{5} + 29 \, A a^{3} b^{6} + 6 \, B a^{2} b^{7} - 12 \, A a b^{8}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(2 \, B a^{8} b^{2} - 6 \, A a^{7} b^{3} - 13 \, B a^{6} b^{4} + 27 \, A a^{5} b^{5} + 17 \, B a^{4} b^{6} - 33 \, A a^{3} b^{7} - 6 \, B a^{2} b^{8} + 12 \, A a b^{9} + {\left(A a^{10} - 3 \, A a^{8} b^{2} + 3 \, A a^{6} b^{4} - A a^{4} b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(B a^{10} - 2 \, A a^{9} b - 3 \, B a^{8} b^{2} + 6 \, A a^{7} b^{3} + 3 \, B a^{6} b^{4} - 6 \, A a^{5} b^{5} - B a^{4} b^{6} + 2 \, A a^{3} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, B a^{9} b - 11 \, A a^{8} b^{2} - 20 \, B a^{7} b^{3} + 43 \, A a^{6} b^{4} + 25 \, B a^{5} b^{5} - 50 \, A a^{4} b^{6} - 9 \, B a^{3} b^{7} + 18 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{13} - 3 \, a^{11} b^{2} + 3 \, a^{9} b^{4} - a^{7} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{12} b - 3 \, a^{10} b^{3} + 3 \, a^{8} b^{5} - a^{6} b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{2} - 3 \, a^{9} b^{4} + 3 \, a^{7} b^{6} - a^{5} b^{8}\right)} d\right)}}, \frac{{\left(A a^{10} - 6 \, B a^{9} b + 9 \, A a^{8} b^{2} + 18 \, B a^{7} b^{3} - 33 \, A a^{6} b^{4} - 18 \, B a^{5} b^{5} + 35 \, A a^{4} b^{6} + 6 \, B a^{3} b^{7} - 12 \, A a^{2} b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 2 \, {\left(A a^{9} b - 6 \, B a^{8} b^{2} + 9 \, A a^{7} b^{3} + 18 \, B a^{6} b^{4} - 33 \, A a^{5} b^{5} - 18 \, B a^{4} b^{6} + 35 \, A a^{3} b^{7} + 6 \, B a^{2} b^{8} - 12 \, A a b^{9}\right)} d x \cos\left(d x + c\right) + {\left(A a^{8} b^{2} - 6 \, B a^{7} b^{3} + 9 \, A a^{6} b^{4} + 18 \, B a^{5} b^{5} - 33 \, A a^{4} b^{6} - 18 \, B a^{3} b^{7} + 35 \, A a^{2} b^{8} + 6 \, B a b^{9} - 12 \, A b^{10}\right)} d x + {\left(12 \, B a^{5} b^{4} - 20 \, A a^{4} b^{5} - 15 \, B a^{3} b^{6} + 29 \, A a^{2} b^{7} + 6 \, B a b^{8} - 12 \, A b^{9} + {\left(12 \, B a^{7} b^{2} - 20 \, A a^{6} b^{3} - 15 \, B a^{5} b^{4} + 29 \, A a^{4} b^{5} + 6 \, B a^{3} b^{6} - 12 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, B a^{6} b^{3} - 20 \, A a^{5} b^{4} - 15 \, B a^{4} b^{5} + 29 \, A a^{3} b^{6} + 6 \, B a^{2} b^{7} - 12 \, A a b^{8}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(2 \, B a^{8} b^{2} - 6 \, A a^{7} b^{3} - 13 \, B a^{6} b^{4} + 27 \, A a^{5} b^{5} + 17 \, B a^{4} b^{6} - 33 \, A a^{3} b^{7} - 6 \, B a^{2} b^{8} + 12 \, A a b^{9} + {\left(A a^{10} - 3 \, A a^{8} b^{2} + 3 \, A a^{6} b^{4} - A a^{4} b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(B a^{10} - 2 \, A a^{9} b - 3 \, B a^{8} b^{2} + 6 \, A a^{7} b^{3} + 3 \, B a^{6} b^{4} - 6 \, A a^{5} b^{5} - B a^{4} b^{6} + 2 \, A a^{3} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, B a^{9} b - 11 \, A a^{8} b^{2} - 20 \, B a^{7} b^{3} + 43 \, A a^{6} b^{4} + 25 \, B a^{5} b^{5} - 50 \, A a^{4} b^{6} - 9 \, B a^{3} b^{7} + 18 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{13} - 3 \, a^{11} b^{2} + 3 \, a^{9} b^{4} - a^{7} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{12} b - 3 \, a^{10} b^{3} + 3 \, a^{8} b^{5} - a^{6} b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{2} - 3 \, a^{9} b^{4} + 3 \, a^{7} b^{6} - a^{5} b^{8}\right)} d\right)}}\right]"," ",0,"[1/4*(2*(A*a^10 - 6*B*a^9*b + 9*A*a^8*b^2 + 18*B*a^7*b^3 - 33*A*a^6*b^4 - 18*B*a^5*b^5 + 35*A*a^4*b^6 + 6*B*a^3*b^7 - 12*A*a^2*b^8)*d*x*cos(d*x + c)^2 + 4*(A*a^9*b - 6*B*a^8*b^2 + 9*A*a^7*b^3 + 18*B*a^6*b^4 - 33*A*a^5*b^5 - 18*B*a^4*b^6 + 35*A*a^3*b^7 + 6*B*a^2*b^8 - 12*A*a*b^9)*d*x*cos(d*x + c) + 2*(A*a^8*b^2 - 6*B*a^7*b^3 + 9*A*a^6*b^4 + 18*B*a^5*b^5 - 33*A*a^4*b^6 - 18*B*a^3*b^7 + 35*A*a^2*b^8 + 6*B*a*b^9 - 12*A*b^10)*d*x - (12*B*a^5*b^4 - 20*A*a^4*b^5 - 15*B*a^3*b^6 + 29*A*a^2*b^7 + 6*B*a*b^8 - 12*A*b^9 + (12*B*a^7*b^2 - 20*A*a^6*b^3 - 15*B*a^5*b^4 + 29*A*a^4*b^5 + 6*B*a^3*b^6 - 12*A*a^2*b^7)*cos(d*x + c)^2 + 2*(12*B*a^6*b^3 - 20*A*a^5*b^4 - 15*B*a^4*b^5 + 29*A*a^3*b^6 + 6*B*a^2*b^7 - 12*A*a*b^8)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(2*B*a^8*b^2 - 6*A*a^7*b^3 - 13*B*a^6*b^4 + 27*A*a^5*b^5 + 17*B*a^4*b^6 - 33*A*a^3*b^7 - 6*B*a^2*b^8 + 12*A*a*b^9 + (A*a^10 - 3*A*a^8*b^2 + 3*A*a^6*b^4 - A*a^4*b^6)*cos(d*x + c)^3 + 2*(B*a^10 - 2*A*a^9*b - 3*B*a^8*b^2 + 6*A*a^7*b^3 + 3*B*a^6*b^4 - 6*A*a^5*b^5 - B*a^4*b^6 + 2*A*a^3*b^7)*cos(d*x + c)^2 + (4*B*a^9*b - 11*A*a^8*b^2 - 20*B*a^7*b^3 + 43*A*a^6*b^4 + 25*B*a^5*b^5 - 50*A*a^4*b^6 - 9*B*a^3*b^7 + 18*A*a^2*b^8)*cos(d*x + c))*sin(d*x + c))/((a^13 - 3*a^11*b^2 + 3*a^9*b^4 - a^7*b^6)*d*cos(d*x + c)^2 + 2*(a^12*b - 3*a^10*b^3 + 3*a^8*b^5 - a^6*b^7)*d*cos(d*x + c) + (a^11*b^2 - 3*a^9*b^4 + 3*a^7*b^6 - a^5*b^8)*d), 1/2*((A*a^10 - 6*B*a^9*b + 9*A*a^8*b^2 + 18*B*a^7*b^3 - 33*A*a^6*b^4 - 18*B*a^5*b^5 + 35*A*a^4*b^6 + 6*B*a^3*b^7 - 12*A*a^2*b^8)*d*x*cos(d*x + c)^2 + 2*(A*a^9*b - 6*B*a^8*b^2 + 9*A*a^7*b^3 + 18*B*a^6*b^4 - 33*A*a^5*b^5 - 18*B*a^4*b^6 + 35*A*a^3*b^7 + 6*B*a^2*b^8 - 12*A*a*b^9)*d*x*cos(d*x + c) + (A*a^8*b^2 - 6*B*a^7*b^3 + 9*A*a^6*b^4 + 18*B*a^5*b^5 - 33*A*a^4*b^6 - 18*B*a^3*b^7 + 35*A*a^2*b^8 + 6*B*a*b^9 - 12*A*b^10)*d*x + (12*B*a^5*b^4 - 20*A*a^4*b^5 - 15*B*a^3*b^6 + 29*A*a^2*b^7 + 6*B*a*b^8 - 12*A*b^9 + (12*B*a^7*b^2 - 20*A*a^6*b^3 - 15*B*a^5*b^4 + 29*A*a^4*b^5 + 6*B*a^3*b^6 - 12*A*a^2*b^7)*cos(d*x + c)^2 + 2*(12*B*a^6*b^3 - 20*A*a^5*b^4 - 15*B*a^4*b^5 + 29*A*a^3*b^6 + 6*B*a^2*b^7 - 12*A*a*b^8)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (2*B*a^8*b^2 - 6*A*a^7*b^3 - 13*B*a^6*b^4 + 27*A*a^5*b^5 + 17*B*a^4*b^6 - 33*A*a^3*b^7 - 6*B*a^2*b^8 + 12*A*a*b^9 + (A*a^10 - 3*A*a^8*b^2 + 3*A*a^6*b^4 - A*a^4*b^6)*cos(d*x + c)^3 + 2*(B*a^10 - 2*A*a^9*b - 3*B*a^8*b^2 + 6*A*a^7*b^3 + 3*B*a^6*b^4 - 6*A*a^5*b^5 - B*a^4*b^6 + 2*A*a^3*b^7)*cos(d*x + c)^2 + (4*B*a^9*b - 11*A*a^8*b^2 - 20*B*a^7*b^3 + 43*A*a^6*b^4 + 25*B*a^5*b^5 - 50*A*a^4*b^6 - 9*B*a^3*b^7 + 18*A*a^2*b^8)*cos(d*x + c))*sin(d*x + c))/((a^13 - 3*a^11*b^2 + 3*a^9*b^4 - a^7*b^6)*d*cos(d*x + c)^2 + 2*(a^12*b - 3*a^10*b^3 + 3*a^8*b^5 - a^6*b^7)*d*cos(d*x + c) + (a^11*b^2 - 3*a^9*b^4 + 3*a^7*b^6 - a^5*b^8)*d)]","B",0
336,1,3434,0,137.705284," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(8 \, B a^{11} - 2 \, A a^{10} b - 28 \, B a^{9} b^{2} + 7 \, A a^{8} b^{3} + 35 \, B a^{7} b^{4} - 8 \, A a^{6} b^{5} - 20 \, B a^{5} b^{6} + 8 \, A a^{4} b^{7}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(8 \, B a^{10} b - 2 \, A a^{9} b^{2} - 28 \, B a^{8} b^{3} + 7 \, A a^{7} b^{4} + 35 \, B a^{6} b^{5} - 8 \, A a^{5} b^{6} - 20 \, B a^{4} b^{7} + 8 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, B a^{9} b^{2} - 2 \, A a^{8} b^{3} - 28 \, B a^{7} b^{4} + 7 \, A a^{6} b^{5} + 35 \, B a^{5} b^{6} - 8 \, A a^{4} b^{7} - 20 \, B a^{3} b^{8} + 8 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, B a^{8} b^{3} - 2 \, A a^{7} b^{4} - 28 \, B a^{6} b^{5} + 7 \, A a^{5} b^{6} + 35 \, B a^{4} b^{7} - 8 \, A a^{3} b^{8} - 20 \, B a^{2} b^{9} + 8 \, A a b^{10}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 6 \, {\left({\left(4 \, B a^{12} - A a^{11} b - 16 \, B a^{10} b^{2} + 4 \, A a^{9} b^{3} + 24 \, B a^{8} b^{4} - 6 \, A a^{7} b^{5} - 16 \, B a^{6} b^{6} + 4 \, A a^{5} b^{7} + 4 \, B a^{4} b^{8} - A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(4 \, B a^{11} b - A a^{10} b^{2} - 16 \, B a^{9} b^{3} + 4 \, A a^{8} b^{4} + 24 \, B a^{7} b^{5} - 6 \, A a^{6} b^{6} - 16 \, B a^{5} b^{7} + 4 \, A a^{4} b^{8} + 4 \, B a^{3} b^{9} - A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, B a^{10} b^{2} - A a^{9} b^{3} - 16 \, B a^{8} b^{4} + 4 \, A a^{7} b^{5} + 24 \, B a^{6} b^{6} - 6 \, A a^{5} b^{7} - 16 \, B a^{4} b^{8} + 4 \, A a^{3} b^{9} + 4 \, B a^{2} b^{10} - A a b^{11}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, B a^{9} b^{3} - A a^{8} b^{4} - 16 \, B a^{7} b^{5} + 4 \, A a^{6} b^{6} + 24 \, B a^{5} b^{7} - 6 \, A a^{4} b^{8} - 16 \, B a^{3} b^{9} + 4 \, A a^{2} b^{10} + 4 \, B a b^{11} - A b^{12}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 6 \, {\left({\left(4 \, B a^{12} - A a^{11} b - 16 \, B a^{10} b^{2} + 4 \, A a^{9} b^{3} + 24 \, B a^{8} b^{4} - 6 \, A a^{7} b^{5} - 16 \, B a^{6} b^{6} + 4 \, A a^{5} b^{7} + 4 \, B a^{4} b^{8} - A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(4 \, B a^{11} b - A a^{10} b^{2} - 16 \, B a^{9} b^{3} + 4 \, A a^{8} b^{4} + 24 \, B a^{7} b^{5} - 6 \, A a^{6} b^{6} - 16 \, B a^{5} b^{7} + 4 \, A a^{4} b^{8} + 4 \, B a^{3} b^{9} - A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, B a^{10} b^{2} - A a^{9} b^{3} - 16 \, B a^{8} b^{4} + 4 \, A a^{7} b^{5} + 24 \, B a^{6} b^{6} - 6 \, A a^{5} b^{7} - 16 \, B a^{4} b^{8} + 4 \, A a^{3} b^{9} + 4 \, B a^{2} b^{10} - A a b^{11}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, B a^{9} b^{3} - A a^{8} b^{4} - 16 \, B a^{7} b^{5} + 4 \, A a^{6} b^{6} + 24 \, B a^{5} b^{7} - 6 \, A a^{4} b^{8} - 16 \, B a^{3} b^{9} + 4 \, A a^{2} b^{10} + 4 \, B a b^{11} - A b^{12}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(6 \, B a^{8} b^{4} - 24 \, B a^{6} b^{6} + 36 \, B a^{4} b^{8} - 24 \, B a^{2} b^{10} + 6 \, B b^{12} + {\left(24 \, B a^{11} b - 6 \, A a^{10} b^{2} - 92 \, B a^{9} b^{3} + 23 \, A a^{8} b^{4} + 133 \, B a^{7} b^{5} - 43 \, A a^{6} b^{6} - 71 \, B a^{5} b^{7} + 26 \, A a^{4} b^{8} + 6 \, B a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, B a^{10} b^{2} - 5 \, A a^{9} b^{3} - 77 \, B a^{8} b^{4} + 20 \, A a^{7} b^{5} + 110 \, B a^{6} b^{6} - 35 \, A a^{5} b^{7} - 59 \, B a^{4} b^{8} + 20 \, A a^{3} b^{9} + 6 \, B a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(44 \, B a^{9} b^{3} - 11 \, A a^{8} b^{4} - 169 \, B a^{7} b^{5} + 43 \, A a^{6} b^{6} + 239 \, B a^{5} b^{7} - 68 \, A a^{4} b^{8} - 132 \, B a^{3} b^{9} + 36 \, A a^{2} b^{10} + 18 \, B a b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{11} b^{5} - 4 \, a^{9} b^{7} + 6 \, a^{7} b^{9} - 4 \, a^{5} b^{11} + a^{3} b^{13}\right)} d \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{10} b^{6} - 4 \, a^{8} b^{8} + 6 \, a^{6} b^{10} - 4 \, a^{4} b^{12} + a^{2} b^{14}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{7} - 4 \, a^{7} b^{9} + 6 \, a^{5} b^{11} - 4 \, a^{3} b^{13} + a b^{15}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} b^{8} - 4 \, a^{6} b^{10} + 6 \, a^{4} b^{12} - 4 \, a^{2} b^{14} + b^{16}\right)} d \cos\left(d x + c\right)\right)}}, \frac{3 \, {\left({\left(8 \, B a^{11} - 2 \, A a^{10} b - 28 \, B a^{9} b^{2} + 7 \, A a^{8} b^{3} + 35 \, B a^{7} b^{4} - 8 \, A a^{6} b^{5} - 20 \, B a^{5} b^{6} + 8 \, A a^{4} b^{7}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(8 \, B a^{10} b - 2 \, A a^{9} b^{2} - 28 \, B a^{8} b^{3} + 7 \, A a^{7} b^{4} + 35 \, B a^{6} b^{5} - 8 \, A a^{5} b^{6} - 20 \, B a^{4} b^{7} + 8 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, B a^{9} b^{2} - 2 \, A a^{8} b^{3} - 28 \, B a^{7} b^{4} + 7 \, A a^{6} b^{5} + 35 \, B a^{5} b^{6} - 8 \, A a^{4} b^{7} - 20 \, B a^{3} b^{8} + 8 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, B a^{8} b^{3} - 2 \, A a^{7} b^{4} - 28 \, B a^{6} b^{5} + 7 \, A a^{5} b^{6} + 35 \, B a^{4} b^{7} - 8 \, A a^{3} b^{8} - 20 \, B a^{2} b^{9} + 8 \, A a b^{10}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - 3 \, {\left({\left(4 \, B a^{12} - A a^{11} b - 16 \, B a^{10} b^{2} + 4 \, A a^{9} b^{3} + 24 \, B a^{8} b^{4} - 6 \, A a^{7} b^{5} - 16 \, B a^{6} b^{6} + 4 \, A a^{5} b^{7} + 4 \, B a^{4} b^{8} - A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(4 \, B a^{11} b - A a^{10} b^{2} - 16 \, B a^{9} b^{3} + 4 \, A a^{8} b^{4} + 24 \, B a^{7} b^{5} - 6 \, A a^{6} b^{6} - 16 \, B a^{5} b^{7} + 4 \, A a^{4} b^{8} + 4 \, B a^{3} b^{9} - A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, B a^{10} b^{2} - A a^{9} b^{3} - 16 \, B a^{8} b^{4} + 4 \, A a^{7} b^{5} + 24 \, B a^{6} b^{6} - 6 \, A a^{5} b^{7} - 16 \, B a^{4} b^{8} + 4 \, A a^{3} b^{9} + 4 \, B a^{2} b^{10} - A a b^{11}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, B a^{9} b^{3} - A a^{8} b^{4} - 16 \, B a^{7} b^{5} + 4 \, A a^{6} b^{6} + 24 \, B a^{5} b^{7} - 6 \, A a^{4} b^{8} - 16 \, B a^{3} b^{9} + 4 \, A a^{2} b^{10} + 4 \, B a b^{11} - A b^{12}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(4 \, B a^{12} - A a^{11} b - 16 \, B a^{10} b^{2} + 4 \, A a^{9} b^{3} + 24 \, B a^{8} b^{4} - 6 \, A a^{7} b^{5} - 16 \, B a^{6} b^{6} + 4 \, A a^{5} b^{7} + 4 \, B a^{4} b^{8} - A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(4 \, B a^{11} b - A a^{10} b^{2} - 16 \, B a^{9} b^{3} + 4 \, A a^{8} b^{4} + 24 \, B a^{7} b^{5} - 6 \, A a^{6} b^{6} - 16 \, B a^{5} b^{7} + 4 \, A a^{4} b^{8} + 4 \, B a^{3} b^{9} - A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, B a^{10} b^{2} - A a^{9} b^{3} - 16 \, B a^{8} b^{4} + 4 \, A a^{7} b^{5} + 24 \, B a^{6} b^{6} - 6 \, A a^{5} b^{7} - 16 \, B a^{4} b^{8} + 4 \, A a^{3} b^{9} + 4 \, B a^{2} b^{10} - A a b^{11}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, B a^{9} b^{3} - A a^{8} b^{4} - 16 \, B a^{7} b^{5} + 4 \, A a^{6} b^{6} + 24 \, B a^{5} b^{7} - 6 \, A a^{4} b^{8} - 16 \, B a^{3} b^{9} + 4 \, A a^{2} b^{10} + 4 \, B a b^{11} - A b^{12}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, B a^{8} b^{4} - 24 \, B a^{6} b^{6} + 36 \, B a^{4} b^{8} - 24 \, B a^{2} b^{10} + 6 \, B b^{12} + {\left(24 \, B a^{11} b - 6 \, A a^{10} b^{2} - 92 \, B a^{9} b^{3} + 23 \, A a^{8} b^{4} + 133 \, B a^{7} b^{5} - 43 \, A a^{6} b^{6} - 71 \, B a^{5} b^{7} + 26 \, A a^{4} b^{8} + 6 \, B a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, B a^{10} b^{2} - 5 \, A a^{9} b^{3} - 77 \, B a^{8} b^{4} + 20 \, A a^{7} b^{5} + 110 \, B a^{6} b^{6} - 35 \, A a^{5} b^{7} - 59 \, B a^{4} b^{8} + 20 \, A a^{3} b^{9} + 6 \, B a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(44 \, B a^{9} b^{3} - 11 \, A a^{8} b^{4} - 169 \, B a^{7} b^{5} + 43 \, A a^{6} b^{6} + 239 \, B a^{5} b^{7} - 68 \, A a^{4} b^{8} - 132 \, B a^{3} b^{9} + 36 \, A a^{2} b^{10} + 18 \, B a b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{11} b^{5} - 4 \, a^{9} b^{7} + 6 \, a^{7} b^{9} - 4 \, a^{5} b^{11} + a^{3} b^{13}\right)} d \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{10} b^{6} - 4 \, a^{8} b^{8} + 6 \, a^{6} b^{10} - 4 \, a^{4} b^{12} + a^{2} b^{14}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{7} - 4 \, a^{7} b^{9} + 6 \, a^{5} b^{11} - 4 \, a^{3} b^{13} + a b^{15}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} b^{8} - 4 \, a^{6} b^{10} + 6 \, a^{4} b^{12} - 4 \, a^{2} b^{14} + b^{16}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/12*(3*((8*B*a^11 - 2*A*a^10*b - 28*B*a^9*b^2 + 7*A*a^8*b^3 + 35*B*a^7*b^4 - 8*A*a^6*b^5 - 20*B*a^5*b^6 + 8*A*a^4*b^7)*cos(d*x + c)^4 + 3*(8*B*a^10*b - 2*A*a^9*b^2 - 28*B*a^8*b^3 + 7*A*a^7*b^4 + 35*B*a^6*b^5 - 8*A*a^5*b^6 - 20*B*a^4*b^7 + 8*A*a^3*b^8)*cos(d*x + c)^3 + 3*(8*B*a^9*b^2 - 2*A*a^8*b^3 - 28*B*a^7*b^4 + 7*A*a^6*b^5 + 35*B*a^5*b^6 - 8*A*a^4*b^7 - 20*B*a^3*b^8 + 8*A*a^2*b^9)*cos(d*x + c)^2 + (8*B*a^8*b^3 - 2*A*a^7*b^4 - 28*B*a^6*b^5 + 7*A*a^5*b^6 + 35*B*a^4*b^7 - 8*A*a^3*b^8 - 20*B*a^2*b^9 + 8*A*a*b^10)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 6*((4*B*a^12 - A*a^11*b - 16*B*a^10*b^2 + 4*A*a^9*b^3 + 24*B*a^8*b^4 - 6*A*a^7*b^5 - 16*B*a^6*b^6 + 4*A*a^5*b^7 + 4*B*a^4*b^8 - A*a^3*b^9)*cos(d*x + c)^4 + 3*(4*B*a^11*b - A*a^10*b^2 - 16*B*a^9*b^3 + 4*A*a^8*b^4 + 24*B*a^7*b^5 - 6*A*a^6*b^6 - 16*B*a^5*b^7 + 4*A*a^4*b^8 + 4*B*a^3*b^9 - A*a^2*b^10)*cos(d*x + c)^3 + 3*(4*B*a^10*b^2 - A*a^9*b^3 - 16*B*a^8*b^4 + 4*A*a^7*b^5 + 24*B*a^6*b^6 - 6*A*a^5*b^7 - 16*B*a^4*b^8 + 4*A*a^3*b^9 + 4*B*a^2*b^10 - A*a*b^11)*cos(d*x + c)^2 + (4*B*a^9*b^3 - A*a^8*b^4 - 16*B*a^7*b^5 + 4*A*a^6*b^6 + 24*B*a^5*b^7 - 6*A*a^4*b^8 - 16*B*a^3*b^9 + 4*A*a^2*b^10 + 4*B*a*b^11 - A*b^12)*cos(d*x + c))*log(sin(d*x + c) + 1) - 6*((4*B*a^12 - A*a^11*b - 16*B*a^10*b^2 + 4*A*a^9*b^3 + 24*B*a^8*b^4 - 6*A*a^7*b^5 - 16*B*a^6*b^6 + 4*A*a^5*b^7 + 4*B*a^4*b^8 - A*a^3*b^9)*cos(d*x + c)^4 + 3*(4*B*a^11*b - A*a^10*b^2 - 16*B*a^9*b^3 + 4*A*a^8*b^4 + 24*B*a^7*b^5 - 6*A*a^6*b^6 - 16*B*a^5*b^7 + 4*A*a^4*b^8 + 4*B*a^3*b^9 - A*a^2*b^10)*cos(d*x + c)^3 + 3*(4*B*a^10*b^2 - A*a^9*b^3 - 16*B*a^8*b^4 + 4*A*a^7*b^5 + 24*B*a^6*b^6 - 6*A*a^5*b^7 - 16*B*a^4*b^8 + 4*A*a^3*b^9 + 4*B*a^2*b^10 - A*a*b^11)*cos(d*x + c)^2 + (4*B*a^9*b^3 - A*a^8*b^4 - 16*B*a^7*b^5 + 4*A*a^6*b^6 + 24*B*a^5*b^7 - 6*A*a^4*b^8 - 16*B*a^3*b^9 + 4*A*a^2*b^10 + 4*B*a*b^11 - A*b^12)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(6*B*a^8*b^4 - 24*B*a^6*b^6 + 36*B*a^4*b^8 - 24*B*a^2*b^10 + 6*B*b^12 + (24*B*a^11*b - 6*A*a^10*b^2 - 92*B*a^9*b^3 + 23*A*a^8*b^4 + 133*B*a^7*b^5 - 43*A*a^6*b^6 - 71*B*a^5*b^7 + 26*A*a^4*b^8 + 6*B*a^3*b^9)*cos(d*x + c)^3 + 3*(20*B*a^10*b^2 - 5*A*a^9*b^3 - 77*B*a^8*b^4 + 20*A*a^7*b^5 + 110*B*a^6*b^6 - 35*A*a^5*b^7 - 59*B*a^4*b^8 + 20*A*a^3*b^9 + 6*B*a^2*b^10)*cos(d*x + c)^2 + (44*B*a^9*b^3 - 11*A*a^8*b^4 - 169*B*a^7*b^5 + 43*A*a^6*b^6 + 239*B*a^5*b^7 - 68*A*a^4*b^8 - 132*B*a^3*b^9 + 36*A*a^2*b^10 + 18*B*a*b^11)*cos(d*x + c))*sin(d*x + c))/((a^11*b^5 - 4*a^9*b^7 + 6*a^7*b^9 - 4*a^5*b^11 + a^3*b^13)*d*cos(d*x + c)^4 + 3*(a^10*b^6 - 4*a^8*b^8 + 6*a^6*b^10 - 4*a^4*b^12 + a^2*b^14)*d*cos(d*x + c)^3 + 3*(a^9*b^7 - 4*a^7*b^9 + 6*a^5*b^11 - 4*a^3*b^13 + a*b^15)*d*cos(d*x + c)^2 + (a^8*b^8 - 4*a^6*b^10 + 6*a^4*b^12 - 4*a^2*b^14 + b^16)*d*cos(d*x + c)), 1/6*(3*((8*B*a^11 - 2*A*a^10*b - 28*B*a^9*b^2 + 7*A*a^8*b^3 + 35*B*a^7*b^4 - 8*A*a^6*b^5 - 20*B*a^5*b^6 + 8*A*a^4*b^7)*cos(d*x + c)^4 + 3*(8*B*a^10*b - 2*A*a^9*b^2 - 28*B*a^8*b^3 + 7*A*a^7*b^4 + 35*B*a^6*b^5 - 8*A*a^5*b^6 - 20*B*a^4*b^7 + 8*A*a^3*b^8)*cos(d*x + c)^3 + 3*(8*B*a^9*b^2 - 2*A*a^8*b^3 - 28*B*a^7*b^4 + 7*A*a^6*b^5 + 35*B*a^5*b^6 - 8*A*a^4*b^7 - 20*B*a^3*b^8 + 8*A*a^2*b^9)*cos(d*x + c)^2 + (8*B*a^8*b^3 - 2*A*a^7*b^4 - 28*B*a^6*b^5 + 7*A*a^5*b^6 + 35*B*a^4*b^7 - 8*A*a^3*b^8 - 20*B*a^2*b^9 + 8*A*a*b^10)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - 3*((4*B*a^12 - A*a^11*b - 16*B*a^10*b^2 + 4*A*a^9*b^3 + 24*B*a^8*b^4 - 6*A*a^7*b^5 - 16*B*a^6*b^6 + 4*A*a^5*b^7 + 4*B*a^4*b^8 - A*a^3*b^9)*cos(d*x + c)^4 + 3*(4*B*a^11*b - A*a^10*b^2 - 16*B*a^9*b^3 + 4*A*a^8*b^4 + 24*B*a^7*b^5 - 6*A*a^6*b^6 - 16*B*a^5*b^7 + 4*A*a^4*b^8 + 4*B*a^3*b^9 - A*a^2*b^10)*cos(d*x + c)^3 + 3*(4*B*a^10*b^2 - A*a^9*b^3 - 16*B*a^8*b^4 + 4*A*a^7*b^5 + 24*B*a^6*b^6 - 6*A*a^5*b^7 - 16*B*a^4*b^8 + 4*A*a^3*b^9 + 4*B*a^2*b^10 - A*a*b^11)*cos(d*x + c)^2 + (4*B*a^9*b^3 - A*a^8*b^4 - 16*B*a^7*b^5 + 4*A*a^6*b^6 + 24*B*a^5*b^7 - 6*A*a^4*b^8 - 16*B*a^3*b^9 + 4*A*a^2*b^10 + 4*B*a*b^11 - A*b^12)*cos(d*x + c))*log(sin(d*x + c) + 1) + 3*((4*B*a^12 - A*a^11*b - 16*B*a^10*b^2 + 4*A*a^9*b^3 + 24*B*a^8*b^4 - 6*A*a^7*b^5 - 16*B*a^6*b^6 + 4*A*a^5*b^7 + 4*B*a^4*b^8 - A*a^3*b^9)*cos(d*x + c)^4 + 3*(4*B*a^11*b - A*a^10*b^2 - 16*B*a^9*b^3 + 4*A*a^8*b^4 + 24*B*a^7*b^5 - 6*A*a^6*b^6 - 16*B*a^5*b^7 + 4*A*a^4*b^8 + 4*B*a^3*b^9 - A*a^2*b^10)*cos(d*x + c)^3 + 3*(4*B*a^10*b^2 - A*a^9*b^3 - 16*B*a^8*b^4 + 4*A*a^7*b^5 + 24*B*a^6*b^6 - 6*A*a^5*b^7 - 16*B*a^4*b^8 + 4*A*a^3*b^9 + 4*B*a^2*b^10 - A*a*b^11)*cos(d*x + c)^2 + (4*B*a^9*b^3 - A*a^8*b^4 - 16*B*a^7*b^5 + 4*A*a^6*b^6 + 24*B*a^5*b^7 - 6*A*a^4*b^8 - 16*B*a^3*b^9 + 4*A*a^2*b^10 + 4*B*a*b^11 - A*b^12)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (6*B*a^8*b^4 - 24*B*a^6*b^6 + 36*B*a^4*b^8 - 24*B*a^2*b^10 + 6*B*b^12 + (24*B*a^11*b - 6*A*a^10*b^2 - 92*B*a^9*b^3 + 23*A*a^8*b^4 + 133*B*a^7*b^5 - 43*A*a^6*b^6 - 71*B*a^5*b^7 + 26*A*a^4*b^8 + 6*B*a^3*b^9)*cos(d*x + c)^3 + 3*(20*B*a^10*b^2 - 5*A*a^9*b^3 - 77*B*a^8*b^4 + 20*A*a^7*b^5 + 110*B*a^6*b^6 - 35*A*a^5*b^7 - 59*B*a^4*b^8 + 20*A*a^3*b^9 + 6*B*a^2*b^10)*cos(d*x + c)^2 + (44*B*a^9*b^3 - 11*A*a^8*b^4 - 169*B*a^7*b^5 + 43*A*a^6*b^6 + 239*B*a^5*b^7 - 68*A*a^4*b^8 - 132*B*a^3*b^9 + 36*A*a^2*b^10 + 18*B*a*b^11)*cos(d*x + c))*sin(d*x + c))/((a^11*b^5 - 4*a^9*b^7 + 6*a^7*b^9 - 4*a^5*b^11 + a^3*b^13)*d*cos(d*x + c)^4 + 3*(a^10*b^6 - 4*a^8*b^8 + 6*a^6*b^10 - 4*a^4*b^12 + a^2*b^14)*d*cos(d*x + c)^3 + 3*(a^9*b^7 - 4*a^7*b^9 + 6*a^5*b^11 - 4*a^3*b^13 + a*b^15)*d*cos(d*x + c)^2 + (a^8*b^8 - 4*a^6*b^10 + 6*a^4*b^12 - 4*a^2*b^14 + b^16)*d*cos(d*x + c))]","B",0
337,1,2278,0,48.761919," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, B a^{7} b^{3} - 7 \, B a^{5} b^{5} + 8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8} - 8 \, B a b^{9} + 2 \, A b^{10} + {\left(2 \, B a^{10} - 7 \, B a^{8} b^{2} + 8 \, B a^{6} b^{4} + 3 \, A a^{5} b^{5} - 8 \, B a^{4} b^{6} + 2 \, A a^{3} b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B a^{9} b - 7 \, B a^{7} b^{3} + 8 \, B a^{5} b^{5} + 3 \, A a^{4} b^{6} - 8 \, B a^{3} b^{7} + 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{8} b^{2} - 7 \, B a^{6} b^{4} + 8 \, B a^{4} b^{6} + 3 \, A a^{3} b^{7} - 8 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 6 \, {\left(B a^{8} b^{3} - 4 \, B a^{6} b^{5} + 6 \, B a^{4} b^{7} - 4 \, B a^{2} b^{9} + B b^{11} + {\left(B a^{11} - 4 \, B a^{9} b^{2} + 6 \, B a^{7} b^{4} - 4 \, B a^{5} b^{6} + B a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{10} b - 4 \, B a^{8} b^{3} + 6 \, B a^{6} b^{5} - 4 \, B a^{4} b^{7} + B a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{9} b^{2} - 4 \, B a^{7} b^{4} + 6 \, B a^{5} b^{6} - 4 \, B a^{3} b^{8} + B a b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 6 \, {\left(B a^{8} b^{3} - 4 \, B a^{6} b^{5} + 6 \, B a^{4} b^{7} - 4 \, B a^{2} b^{9} + B b^{11} + {\left(B a^{11} - 4 \, B a^{9} b^{2} + 6 \, B a^{7} b^{4} - 4 \, B a^{5} b^{6} + B a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{10} b - 4 \, B a^{8} b^{3} + 6 \, B a^{6} b^{5} - 4 \, B a^{4} b^{7} + B a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{9} b^{2} - 4 \, B a^{7} b^{4} + 6 \, B a^{5} b^{6} - 4 \, B a^{3} b^{8} + B a b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(11 \, B a^{8} b^{3} - 2 \, A a^{7} b^{4} - 43 \, B a^{6} b^{5} + 7 \, A a^{5} b^{6} + 68 \, B a^{4} b^{7} - 23 \, A a^{3} b^{8} - 36 \, B a^{2} b^{9} + 18 \, A a b^{10} + {\left(6 \, B a^{10} b - 23 \, B a^{8} b^{3} - 4 \, A a^{7} b^{4} + 43 \, B a^{6} b^{5} - 7 \, A a^{5} b^{6} - 26 \, B a^{4} b^{7} + 11 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, B a^{9} b^{2} - 20 \, B a^{7} b^{4} - A a^{6} b^{5} + 35 \, B a^{5} b^{6} - 8 \, A a^{4} b^{7} - 20 \, B a^{3} b^{8} + 9 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{11} b^{4} - 4 \, a^{9} b^{6} + 6 \, a^{7} b^{8} - 4 \, a^{5} b^{10} + a^{3} b^{12}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b^{5} - 4 \, a^{8} b^{7} + 6 \, a^{6} b^{9} - 4 \, a^{4} b^{11} + a^{2} b^{13}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{9} b^{6} - 4 \, a^{7} b^{8} + 6 \, a^{5} b^{10} - 4 \, a^{3} b^{12} + a b^{14}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{7} - 4 \, a^{6} b^{9} + 6 \, a^{4} b^{11} - 4 \, a^{2} b^{13} + b^{15}\right)} d\right)}}, -\frac{3 \, {\left(2 \, B a^{7} b^{3} - 7 \, B a^{5} b^{5} + 8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8} - 8 \, B a b^{9} + 2 \, A b^{10} + {\left(2 \, B a^{10} - 7 \, B a^{8} b^{2} + 8 \, B a^{6} b^{4} + 3 \, A a^{5} b^{5} - 8 \, B a^{4} b^{6} + 2 \, A a^{3} b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B a^{9} b - 7 \, B a^{7} b^{3} + 8 \, B a^{5} b^{5} + 3 \, A a^{4} b^{6} - 8 \, B a^{3} b^{7} + 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{8} b^{2} - 7 \, B a^{6} b^{4} + 8 \, B a^{4} b^{6} + 3 \, A a^{3} b^{7} - 8 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - 3 \, {\left(B a^{8} b^{3} - 4 \, B a^{6} b^{5} + 6 \, B a^{4} b^{7} - 4 \, B a^{2} b^{9} + B b^{11} + {\left(B a^{11} - 4 \, B a^{9} b^{2} + 6 \, B a^{7} b^{4} - 4 \, B a^{5} b^{6} + B a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{10} b - 4 \, B a^{8} b^{3} + 6 \, B a^{6} b^{5} - 4 \, B a^{4} b^{7} + B a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{9} b^{2} - 4 \, B a^{7} b^{4} + 6 \, B a^{5} b^{6} - 4 \, B a^{3} b^{8} + B a b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(B a^{8} b^{3} - 4 \, B a^{6} b^{5} + 6 \, B a^{4} b^{7} - 4 \, B a^{2} b^{9} + B b^{11} + {\left(B a^{11} - 4 \, B a^{9} b^{2} + 6 \, B a^{7} b^{4} - 4 \, B a^{5} b^{6} + B a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{10} b - 4 \, B a^{8} b^{3} + 6 \, B a^{6} b^{5} - 4 \, B a^{4} b^{7} + B a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{9} b^{2} - 4 \, B a^{7} b^{4} + 6 \, B a^{5} b^{6} - 4 \, B a^{3} b^{8} + B a b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(11 \, B a^{8} b^{3} - 2 \, A a^{7} b^{4} - 43 \, B a^{6} b^{5} + 7 \, A a^{5} b^{6} + 68 \, B a^{4} b^{7} - 23 \, A a^{3} b^{8} - 36 \, B a^{2} b^{9} + 18 \, A a b^{10} + {\left(6 \, B a^{10} b - 23 \, B a^{8} b^{3} - 4 \, A a^{7} b^{4} + 43 \, B a^{6} b^{5} - 7 \, A a^{5} b^{6} - 26 \, B a^{4} b^{7} + 11 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, B a^{9} b^{2} - 20 \, B a^{7} b^{4} - A a^{6} b^{5} + 35 \, B a^{5} b^{6} - 8 \, A a^{4} b^{7} - 20 \, B a^{3} b^{8} + 9 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{11} b^{4} - 4 \, a^{9} b^{6} + 6 \, a^{7} b^{8} - 4 \, a^{5} b^{10} + a^{3} b^{12}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b^{5} - 4 \, a^{8} b^{7} + 6 \, a^{6} b^{9} - 4 \, a^{4} b^{11} + a^{2} b^{13}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{9} b^{6} - 4 \, a^{7} b^{8} + 6 \, a^{5} b^{10} - 4 \, a^{3} b^{12} + a b^{14}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{7} - 4 \, a^{6} b^{9} + 6 \, a^{4} b^{11} - 4 \, a^{2} b^{13} + b^{15}\right)} d\right)}}\right]"," ",0,"[-1/12*(3*(2*B*a^7*b^3 - 7*B*a^5*b^5 + 8*B*a^3*b^7 + 3*A*a^2*b^8 - 8*B*a*b^9 + 2*A*b^10 + (2*B*a^10 - 7*B*a^8*b^2 + 8*B*a^6*b^4 + 3*A*a^5*b^5 - 8*B*a^4*b^6 + 2*A*a^3*b^7)*cos(d*x + c)^3 + 3*(2*B*a^9*b - 7*B*a^7*b^3 + 8*B*a^5*b^5 + 3*A*a^4*b^6 - 8*B*a^3*b^7 + 2*A*a^2*b^8)*cos(d*x + c)^2 + 3*(2*B*a^8*b^2 - 7*B*a^6*b^4 + 8*B*a^4*b^6 + 3*A*a^3*b^7 - 8*B*a^2*b^8 + 2*A*a*b^9)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 6*(B*a^8*b^3 - 4*B*a^6*b^5 + 6*B*a^4*b^7 - 4*B*a^2*b^9 + B*b^11 + (B*a^11 - 4*B*a^9*b^2 + 6*B*a^7*b^4 - 4*B*a^5*b^6 + B*a^3*b^8)*cos(d*x + c)^3 + 3*(B*a^10*b - 4*B*a^8*b^3 + 6*B*a^6*b^5 - 4*B*a^4*b^7 + B*a^2*b^9)*cos(d*x + c)^2 + 3*(B*a^9*b^2 - 4*B*a^7*b^4 + 6*B*a^5*b^6 - 4*B*a^3*b^8 + B*a*b^10)*cos(d*x + c))*log(sin(d*x + c) + 1) + 6*(B*a^8*b^3 - 4*B*a^6*b^5 + 6*B*a^4*b^7 - 4*B*a^2*b^9 + B*b^11 + (B*a^11 - 4*B*a^9*b^2 + 6*B*a^7*b^4 - 4*B*a^5*b^6 + B*a^3*b^8)*cos(d*x + c)^3 + 3*(B*a^10*b - 4*B*a^8*b^3 + 6*B*a^6*b^5 - 4*B*a^4*b^7 + B*a^2*b^9)*cos(d*x + c)^2 + 3*(B*a^9*b^2 - 4*B*a^7*b^4 + 6*B*a^5*b^6 - 4*B*a^3*b^8 + B*a*b^10)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(11*B*a^8*b^3 - 2*A*a^7*b^4 - 43*B*a^6*b^5 + 7*A*a^5*b^6 + 68*B*a^4*b^7 - 23*A*a^3*b^8 - 36*B*a^2*b^9 + 18*A*a*b^10 + (6*B*a^10*b - 23*B*a^8*b^3 - 4*A*a^7*b^4 + 43*B*a^6*b^5 - 7*A*a^5*b^6 - 26*B*a^4*b^7 + 11*A*a^3*b^8)*cos(d*x + c)^2 + 3*(5*B*a^9*b^2 - 20*B*a^7*b^4 - A*a^6*b^5 + 35*B*a^5*b^6 - 8*A*a^4*b^7 - 20*B*a^3*b^8 + 9*A*a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^11*b^4 - 4*a^9*b^6 + 6*a^7*b^8 - 4*a^5*b^10 + a^3*b^12)*d*cos(d*x + c)^3 + 3*(a^10*b^5 - 4*a^8*b^7 + 6*a^6*b^9 - 4*a^4*b^11 + a^2*b^13)*d*cos(d*x + c)^2 + 3*(a^9*b^6 - 4*a^7*b^8 + 6*a^5*b^10 - 4*a^3*b^12 + a*b^14)*d*cos(d*x + c) + (a^8*b^7 - 4*a^6*b^9 + 6*a^4*b^11 - 4*a^2*b^13 + b^15)*d), -1/6*(3*(2*B*a^7*b^3 - 7*B*a^5*b^5 + 8*B*a^3*b^7 + 3*A*a^2*b^8 - 8*B*a*b^9 + 2*A*b^10 + (2*B*a^10 - 7*B*a^8*b^2 + 8*B*a^6*b^4 + 3*A*a^5*b^5 - 8*B*a^4*b^6 + 2*A*a^3*b^7)*cos(d*x + c)^3 + 3*(2*B*a^9*b - 7*B*a^7*b^3 + 8*B*a^5*b^5 + 3*A*a^4*b^6 - 8*B*a^3*b^7 + 2*A*a^2*b^8)*cos(d*x + c)^2 + 3*(2*B*a^8*b^2 - 7*B*a^6*b^4 + 8*B*a^4*b^6 + 3*A*a^3*b^7 - 8*B*a^2*b^8 + 2*A*a*b^9)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - 3*(B*a^8*b^3 - 4*B*a^6*b^5 + 6*B*a^4*b^7 - 4*B*a^2*b^9 + B*b^11 + (B*a^11 - 4*B*a^9*b^2 + 6*B*a^7*b^4 - 4*B*a^5*b^6 + B*a^3*b^8)*cos(d*x + c)^3 + 3*(B*a^10*b - 4*B*a^8*b^3 + 6*B*a^6*b^5 - 4*B*a^4*b^7 + B*a^2*b^9)*cos(d*x + c)^2 + 3*(B*a^9*b^2 - 4*B*a^7*b^4 + 6*B*a^5*b^6 - 4*B*a^3*b^8 + B*a*b^10)*cos(d*x + c))*log(sin(d*x + c) + 1) + 3*(B*a^8*b^3 - 4*B*a^6*b^5 + 6*B*a^4*b^7 - 4*B*a^2*b^9 + B*b^11 + (B*a^11 - 4*B*a^9*b^2 + 6*B*a^7*b^4 - 4*B*a^5*b^6 + B*a^3*b^8)*cos(d*x + c)^3 + 3*(B*a^10*b - 4*B*a^8*b^3 + 6*B*a^6*b^5 - 4*B*a^4*b^7 + B*a^2*b^9)*cos(d*x + c)^2 + 3*(B*a^9*b^2 - 4*B*a^7*b^4 + 6*B*a^5*b^6 - 4*B*a^3*b^8 + B*a*b^10)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (11*B*a^8*b^3 - 2*A*a^7*b^4 - 43*B*a^6*b^5 + 7*A*a^5*b^6 + 68*B*a^4*b^7 - 23*A*a^3*b^8 - 36*B*a^2*b^9 + 18*A*a*b^10 + (6*B*a^10*b - 23*B*a^8*b^3 - 4*A*a^7*b^4 + 43*B*a^6*b^5 - 7*A*a^5*b^6 - 26*B*a^4*b^7 + 11*A*a^3*b^8)*cos(d*x + c)^2 + 3*(5*B*a^9*b^2 - 20*B*a^7*b^4 - A*a^6*b^5 + 35*B*a^5*b^6 - 8*A*a^4*b^7 - 20*B*a^3*b^8 + 9*A*a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^11*b^4 - 4*a^9*b^6 + 6*a^7*b^8 - 4*a^5*b^10 + a^3*b^12)*d*cos(d*x + c)^3 + 3*(a^10*b^5 - 4*a^8*b^7 + 6*a^6*b^9 - 4*a^4*b^11 + a^2*b^13)*d*cos(d*x + c)^2 + 3*(a^9*b^6 - 4*a^7*b^8 + 6*a^5*b^10 - 4*a^3*b^12 + a*b^14)*d*cos(d*x + c) + (a^8*b^7 - 4*a^6*b^9 + 6*a^4*b^11 - 4*a^2*b^13 + b^15)*d)]","B",0
338,1,1230,0,0.604490," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A a^{3} b^{3} - 3 \, B a^{2} b^{4} + 4 \, A a b^{5} - 2 \, B b^{6} + {\left(A a^{6} - 3 \, B a^{5} b + 4 \, A a^{4} b^{2} - 2 \, B a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A a^{5} b - 3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} - 2 \, B a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A a^{4} b^{2} - 3 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} - 2 \, B a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(2 \, B a^{7} + A a^{6} b - 7 \, B a^{5} b^{2} - 11 \, A a^{4} b^{3} + 23 \, B a^{3} b^{4} + 4 \, A a^{2} b^{5} - 18 \, B a b^{6} + 6 \, A b^{7} + {\left(4 \, B a^{7} - 13 \, A a^{6} b + 7 \, B a^{5} b^{2} + 11 \, A a^{4} b^{3} - 11 \, B a^{3} b^{4} + 2 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A a^{7} + B a^{6} b - 10 \, A a^{5} b^{2} + 8 \, B a^{4} b^{3} + 7 \, A a^{3} b^{4} - 9 \, B a^{2} b^{5} + 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}, \frac{3 \, {\left(A a^{3} b^{3} - 3 \, B a^{2} b^{4} + 4 \, A a b^{5} - 2 \, B b^{6} + {\left(A a^{6} - 3 \, B a^{5} b + 4 \, A a^{4} b^{2} - 2 \, B a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A a^{5} b - 3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} - 2 \, B a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A a^{4} b^{2} - 3 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} - 2 \, B a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(2 \, B a^{7} + A a^{6} b - 7 \, B a^{5} b^{2} - 11 \, A a^{4} b^{3} + 23 \, B a^{3} b^{4} + 4 \, A a^{2} b^{5} - 18 \, B a b^{6} + 6 \, A b^{7} + {\left(4 \, B a^{7} - 13 \, A a^{6} b + 7 \, B a^{5} b^{2} + 11 \, A a^{4} b^{3} - 11 \, B a^{3} b^{4} + 2 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A a^{7} + B a^{6} b - 10 \, A a^{5} b^{2} + 8 \, B a^{4} b^{3} + 7 \, A a^{3} b^{4} - 9 \, B a^{2} b^{5} + 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}\right]"," ",0,"[1/12*(3*(A*a^3*b^3 - 3*B*a^2*b^4 + 4*A*a*b^5 - 2*B*b^6 + (A*a^6 - 3*B*a^5*b + 4*A*a^4*b^2 - 2*B*a^3*b^3)*cos(d*x + c)^3 + 3*(A*a^5*b - 3*B*a^4*b^2 + 4*A*a^3*b^3 - 2*B*a^2*b^4)*cos(d*x + c)^2 + 3*(A*a^4*b^2 - 3*B*a^3*b^3 + 4*A*a^2*b^4 - 2*B*a*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(2*B*a^7 + A*a^6*b - 7*B*a^5*b^2 - 11*A*a^4*b^3 + 23*B*a^3*b^4 + 4*A*a^2*b^5 - 18*B*a*b^6 + 6*A*b^7 + (4*B*a^7 - 13*A*a^6*b + 7*B*a^5*b^2 + 11*A*a^4*b^3 - 11*B*a^3*b^4 + 2*A*a^2*b^5)*cos(d*x + c)^2 + 3*(A*a^7 + B*a^6*b - 10*A*a^5*b^2 + 8*B*a^4*b^3 + 7*A*a^3*b^4 - 9*B*a^2*b^5 + 2*A*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c)^2 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d), 1/6*(3*(A*a^3*b^3 - 3*B*a^2*b^4 + 4*A*a*b^5 - 2*B*b^6 + (A*a^6 - 3*B*a^5*b + 4*A*a^4*b^2 - 2*B*a^3*b^3)*cos(d*x + c)^3 + 3*(A*a^5*b - 3*B*a^4*b^2 + 4*A*a^3*b^3 - 2*B*a^2*b^4)*cos(d*x + c)^2 + 3*(A*a^4*b^2 - 3*B*a^3*b^3 + 4*A*a^2*b^4 - 2*B*a*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (2*B*a^7 + A*a^6*b - 7*B*a^5*b^2 - 11*A*a^4*b^3 + 23*B*a^3*b^4 + 4*A*a^2*b^5 - 18*B*a*b^6 + 6*A*b^7 + (4*B*a^7 - 13*A*a^6*b + 7*B*a^5*b^2 + 11*A*a^4*b^3 - 11*B*a^3*b^4 + 2*A*a^2*b^5)*cos(d*x + c)^2 + 3*(A*a^7 + B*a^6*b - 10*A*a^5*b^2 + 8*B*a^4*b^3 + 7*A*a^3*b^4 - 9*B*a^2*b^5 + 2*A*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c)^2 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d)]","B",0
339,1,1242,0,0.583563," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a^{3} b^{3} - 4 \, A a^{2} b^{4} + 4 \, B a b^{5} - A b^{6} + {\left(B a^{6} - 4 \, A a^{5} b + 4 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{5} b - 4 \, A a^{4} b^{2} + 4 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{4} b^{2} - 4 \, A a^{3} b^{3} + 4 \, B a^{2} b^{4} - A a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(B a^{6} b + 2 \, A a^{5} b^{2} - 11 \, B a^{4} b^{3} + 11 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 13 \, A a b^{6} + 6 \, B b^{7} + {\left(6 \, A a^{7} - 13 \, B a^{6} b + 4 \, A a^{5} b^{2} + 11 \, B a^{4} b^{3} - 11 \, A a^{3} b^{4} + 2 \, B a^{2} b^{5} + A a b^{6}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{7} + 2 \, A a^{6} b - 10 \, B a^{5} b^{2} + 7 \, A a^{4} b^{3} + 7 \, B a^{3} b^{4} - 10 \, A a^{2} b^{5} + 2 \, B a b^{6} + A b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}, \frac{3 \, {\left(B a^{3} b^{3} - 4 \, A a^{2} b^{4} + 4 \, B a b^{5} - A b^{6} + {\left(B a^{6} - 4 \, A a^{5} b + 4 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{5} b - 4 \, A a^{4} b^{2} + 4 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{4} b^{2} - 4 \, A a^{3} b^{3} + 4 \, B a^{2} b^{4} - A a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(B a^{6} b + 2 \, A a^{5} b^{2} - 11 \, B a^{4} b^{3} + 11 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 13 \, A a b^{6} + 6 \, B b^{7} + {\left(6 \, A a^{7} - 13 \, B a^{6} b + 4 \, A a^{5} b^{2} + 11 \, B a^{4} b^{3} - 11 \, A a^{3} b^{4} + 2 \, B a^{2} b^{5} + A a b^{6}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{7} + 2 \, A a^{6} b - 10 \, B a^{5} b^{2} + 7 \, A a^{4} b^{3} + 7 \, B a^{3} b^{4} - 10 \, A a^{2} b^{5} + 2 \, B a b^{6} + A b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}\right]"," ",0,"[1/12*(3*(B*a^3*b^3 - 4*A*a^2*b^4 + 4*B*a*b^5 - A*b^6 + (B*a^6 - 4*A*a^5*b + 4*B*a^4*b^2 - A*a^3*b^3)*cos(d*x + c)^3 + 3*(B*a^5*b - 4*A*a^4*b^2 + 4*B*a^3*b^3 - A*a^2*b^4)*cos(d*x + c)^2 + 3*(B*a^4*b^2 - 4*A*a^3*b^3 + 4*B*a^2*b^4 - A*a*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(B*a^6*b + 2*A*a^5*b^2 - 11*B*a^4*b^3 + 11*A*a^3*b^4 + 4*B*a^2*b^5 - 13*A*a*b^6 + 6*B*b^7 + (6*A*a^7 - 13*B*a^6*b + 4*A*a^5*b^2 + 11*B*a^4*b^3 - 11*A*a^3*b^4 + 2*B*a^2*b^5 + A*a*b^6)*cos(d*x + c)^2 + 3*(B*a^7 + 2*A*a^6*b - 10*B*a^5*b^2 + 7*A*a^4*b^3 + 7*B*a^3*b^4 - 10*A*a^2*b^5 + 2*B*a*b^6 + A*b^7)*cos(d*x + c))*sin(d*x + c))/((a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c)^2 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d), 1/6*(3*(B*a^3*b^3 - 4*A*a^2*b^4 + 4*B*a*b^5 - A*b^6 + (B*a^6 - 4*A*a^5*b + 4*B*a^4*b^2 - A*a^3*b^3)*cos(d*x + c)^3 + 3*(B*a^5*b - 4*A*a^4*b^2 + 4*B*a^3*b^3 - A*a^2*b^4)*cos(d*x + c)^2 + 3*(B*a^4*b^2 - 4*A*a^3*b^3 + 4*B*a^2*b^4 - A*a*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (B*a^6*b + 2*A*a^5*b^2 - 11*B*a^4*b^3 + 11*A*a^3*b^4 + 4*B*a^2*b^5 - 13*A*a*b^6 + 6*B*b^7 + (6*A*a^7 - 13*B*a^6*b + 4*A*a^5*b^2 + 11*B*a^4*b^3 - 11*A*a^3*b^4 + 2*B*a^2*b^5 + A*a*b^6)*cos(d*x + c)^2 + 3*(B*a^7 + 2*A*a^6*b - 10*B*a^5*b^2 + 7*A*a^4*b^3 + 7*B*a^3*b^4 - 10*A*a^2*b^5 + 2*B*a*b^6 + A*b^7)*cos(d*x + c))*sin(d*x + c))/((a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c)^2 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d)]","B",0
340,1,1238,0,0.587774," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, A a^{3} b^{3} - 4 \, B a^{2} b^{4} + 3 \, A a b^{5} - B b^{6} + {\left(2 \, A a^{6} - 4 \, B a^{5} b + 3 \, A a^{4} b^{2} - B a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A a^{5} b - 4 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3} - B a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(2 \, B a^{5} b^{2} - 11 \, A a^{4} b^{3} + 11 \, B a^{3} b^{4} + 7 \, A a^{2} b^{5} - 13 \, B a b^{6} + 4 \, A b^{7} + {\left(6 \, B a^{7} - 18 \, A a^{6} b + 4 \, B a^{5} b^{2} + 23 \, A a^{4} b^{3} - 11 \, B a^{3} b^{4} - 7 \, A a^{2} b^{5} + B a b^{6} + 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{6} b - 9 \, A a^{5} b^{2} + 7 \, B a^{4} b^{3} + 8 \, A a^{3} b^{4} - 10 \, B a^{2} b^{5} + A a b^{6} + B b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}, \frac{3 \, {\left(2 \, A a^{3} b^{3} - 4 \, B a^{2} b^{4} + 3 \, A a b^{5} - B b^{6} + {\left(2 \, A a^{6} - 4 \, B a^{5} b + 3 \, A a^{4} b^{2} - B a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A a^{5} b - 4 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3} - B a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(2 \, B a^{5} b^{2} - 11 \, A a^{4} b^{3} + 11 \, B a^{3} b^{4} + 7 \, A a^{2} b^{5} - 13 \, B a b^{6} + 4 \, A b^{7} + {\left(6 \, B a^{7} - 18 \, A a^{6} b + 4 \, B a^{5} b^{2} + 23 \, A a^{4} b^{3} - 11 \, B a^{3} b^{4} - 7 \, A a^{2} b^{5} + B a b^{6} + 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{6} b - 9 \, A a^{5} b^{2} + 7 \, B a^{4} b^{3} + 8 \, A a^{3} b^{4} - 10 \, B a^{2} b^{5} + A a b^{6} + B b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}\right]"," ",0,"[1/12*(3*(2*A*a^3*b^3 - 4*B*a^2*b^4 + 3*A*a*b^5 - B*b^6 + (2*A*a^6 - 4*B*a^5*b + 3*A*a^4*b^2 - B*a^3*b^3)*cos(d*x + c)^3 + 3*(2*A*a^5*b - 4*B*a^4*b^2 + 3*A*a^3*b^3 - B*a^2*b^4)*cos(d*x + c)^2 + 3*(2*A*a^4*b^2 - 4*B*a^3*b^3 + 3*A*a^2*b^4 - B*a*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(2*B*a^5*b^2 - 11*A*a^4*b^3 + 11*B*a^3*b^4 + 7*A*a^2*b^5 - 13*B*a*b^6 + 4*A*b^7 + (6*B*a^7 - 18*A*a^6*b + 4*B*a^5*b^2 + 23*A*a^4*b^3 - 11*B*a^3*b^4 - 7*A*a^2*b^5 + B*a*b^6 + 2*A*b^7)*cos(d*x + c)^2 + 3*(2*B*a^6*b - 9*A*a^5*b^2 + 7*B*a^4*b^3 + 8*A*a^3*b^4 - 10*B*a^2*b^5 + A*a*b^6 + B*b^7)*cos(d*x + c))*sin(d*x + c))/((a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c)^2 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d), 1/6*(3*(2*A*a^3*b^3 - 4*B*a^2*b^4 + 3*A*a*b^5 - B*b^6 + (2*A*a^6 - 4*B*a^5*b + 3*A*a^4*b^2 - B*a^3*b^3)*cos(d*x + c)^3 + 3*(2*A*a^5*b - 4*B*a^4*b^2 + 3*A*a^3*b^3 - B*a^2*b^4)*cos(d*x + c)^2 + 3*(2*A*a^4*b^2 - 4*B*a^3*b^3 + 3*A*a^2*b^4 - B*a*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (2*B*a^5*b^2 - 11*A*a^4*b^3 + 11*B*a^3*b^4 + 7*A*a^2*b^5 - 13*B*a*b^6 + 4*A*b^7 + (6*B*a^7 - 18*A*a^6*b + 4*B*a^5*b^2 + 23*A*a^4*b^3 - 11*B*a^3*b^4 - 7*A*a^2*b^5 + B*a*b^6 + 2*A*b^7)*cos(d*x + c)^2 + 3*(2*B*a^6*b - 9*A*a^5*b^2 + 7*B*a^4*b^3 + 8*A*a^3*b^4 - 10*B*a^2*b^5 + A*a*b^6 + B*b^7)*cos(d*x + c))*sin(d*x + c))/((a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c)^2 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d)]","B",0
341,1,1867,0,0.654616," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(A a^{11} - 4 \, A a^{9} b^{2} + 6 \, A a^{7} b^{4} - 4 \, A a^{5} b^{6} + A a^{3} b^{8}\right)} d x \cos\left(d x + c\right)^{3} + 36 \, {\left(A a^{10} b - 4 \, A a^{8} b^{3} + 6 \, A a^{6} b^{5} - 4 \, A a^{4} b^{7} + A a^{2} b^{9}\right)} d x \cos\left(d x + c\right)^{2} + 36 \, {\left(A a^{9} b^{2} - 4 \, A a^{7} b^{4} + 6 \, A a^{5} b^{6} - 4 \, A a^{3} b^{8} + A a b^{10}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(A a^{8} b^{3} - 4 \, A a^{6} b^{5} + 6 \, A a^{4} b^{7} - 4 \, A a^{2} b^{9} + A b^{11}\right)} d x - 3 \, {\left(2 \, B a^{7} b^{3} - 8 \, A a^{6} b^{4} + 3 \, B a^{5} b^{5} + 8 \, A a^{4} b^{6} - 7 \, A a^{2} b^{8} + 2 \, A b^{10} + {\left(2 \, B a^{10} - 8 \, A a^{9} b + 3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3} - 7 \, A a^{5} b^{5} + 2 \, A a^{3} b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B a^{9} b - 8 \, A a^{8} b^{2} + 3 \, B a^{7} b^{3} + 8 \, A a^{6} b^{4} - 7 \, A a^{4} b^{6} + 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{8} b^{2} - 8 \, A a^{7} b^{3} + 3 \, B a^{6} b^{4} + 8 \, A a^{5} b^{5} - 7 \, A a^{3} b^{7} + 2 \, A a b^{9}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(11 \, B a^{8} b^{3} - 26 \, A a^{7} b^{4} - 7 \, B a^{6} b^{5} + 43 \, A a^{5} b^{6} - 4 \, B a^{4} b^{7} - 23 \, A a^{3} b^{8} + 6 \, A a b^{10} + {\left(18 \, B a^{10} b - 36 \, A a^{9} b^{2} - 23 \, B a^{8} b^{3} + 68 \, A a^{7} b^{4} + 7 \, B a^{6} b^{5} - 43 \, A a^{5} b^{6} - 2 \, B a^{4} b^{7} + 11 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(9 \, B a^{9} b^{2} - 20 \, A a^{8} b^{3} - 8 \, B a^{7} b^{4} + 35 \, A a^{6} b^{5} - B a^{5} b^{6} - 20 \, A a^{4} b^{7} + 5 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{15} - 4 \, a^{13} b^{2} + 6 \, a^{11} b^{4} - 4 \, a^{9} b^{6} + a^{7} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{14} b - 4 \, a^{12} b^{3} + 6 \, a^{10} b^{5} - 4 \, a^{8} b^{7} + a^{6} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{13} b^{2} - 4 \, a^{11} b^{4} + 6 \, a^{9} b^{6} - 4 \, a^{7} b^{8} + a^{5} b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{12} b^{3} - 4 \, a^{10} b^{5} + 6 \, a^{8} b^{7} - 4 \, a^{6} b^{9} + a^{4} b^{11}\right)} d\right)}}, \frac{6 \, {\left(A a^{11} - 4 \, A a^{9} b^{2} + 6 \, A a^{7} b^{4} - 4 \, A a^{5} b^{6} + A a^{3} b^{8}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left(A a^{10} b - 4 \, A a^{8} b^{3} + 6 \, A a^{6} b^{5} - 4 \, A a^{4} b^{7} + A a^{2} b^{9}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left(A a^{9} b^{2} - 4 \, A a^{7} b^{4} + 6 \, A a^{5} b^{6} - 4 \, A a^{3} b^{8} + A a b^{10}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(A a^{8} b^{3} - 4 \, A a^{6} b^{5} + 6 \, A a^{4} b^{7} - 4 \, A a^{2} b^{9} + A b^{11}\right)} d x + 3 \, {\left(2 \, B a^{7} b^{3} - 8 \, A a^{6} b^{4} + 3 \, B a^{5} b^{5} + 8 \, A a^{4} b^{6} - 7 \, A a^{2} b^{8} + 2 \, A b^{10} + {\left(2 \, B a^{10} - 8 \, A a^{9} b + 3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3} - 7 \, A a^{5} b^{5} + 2 \, A a^{3} b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B a^{9} b - 8 \, A a^{8} b^{2} + 3 \, B a^{7} b^{3} + 8 \, A a^{6} b^{4} - 7 \, A a^{4} b^{6} + 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{8} b^{2} - 8 \, A a^{7} b^{3} + 3 \, B a^{6} b^{4} + 8 \, A a^{5} b^{5} - 7 \, A a^{3} b^{7} + 2 \, A a b^{9}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(11 \, B a^{8} b^{3} - 26 \, A a^{7} b^{4} - 7 \, B a^{6} b^{5} + 43 \, A a^{5} b^{6} - 4 \, B a^{4} b^{7} - 23 \, A a^{3} b^{8} + 6 \, A a b^{10} + {\left(18 \, B a^{10} b - 36 \, A a^{9} b^{2} - 23 \, B a^{8} b^{3} + 68 \, A a^{7} b^{4} + 7 \, B a^{6} b^{5} - 43 \, A a^{5} b^{6} - 2 \, B a^{4} b^{7} + 11 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(9 \, B a^{9} b^{2} - 20 \, A a^{8} b^{3} - 8 \, B a^{7} b^{4} + 35 \, A a^{6} b^{5} - B a^{5} b^{6} - 20 \, A a^{4} b^{7} + 5 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{15} - 4 \, a^{13} b^{2} + 6 \, a^{11} b^{4} - 4 \, a^{9} b^{6} + a^{7} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{14} b - 4 \, a^{12} b^{3} + 6 \, a^{10} b^{5} - 4 \, a^{8} b^{7} + a^{6} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{13} b^{2} - 4 \, a^{11} b^{4} + 6 \, a^{9} b^{6} - 4 \, a^{7} b^{8} + a^{5} b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{12} b^{3} - 4 \, a^{10} b^{5} + 6 \, a^{8} b^{7} - 4 \, a^{6} b^{9} + a^{4} b^{11}\right)} d\right)}}\right]"," ",0,"[1/12*(12*(A*a^11 - 4*A*a^9*b^2 + 6*A*a^7*b^4 - 4*A*a^5*b^6 + A*a^3*b^8)*d*x*cos(d*x + c)^3 + 36*(A*a^10*b - 4*A*a^8*b^3 + 6*A*a^6*b^5 - 4*A*a^4*b^7 + A*a^2*b^9)*d*x*cos(d*x + c)^2 + 36*(A*a^9*b^2 - 4*A*a^7*b^4 + 6*A*a^5*b^6 - 4*A*a^3*b^8 + A*a*b^10)*d*x*cos(d*x + c) + 12*(A*a^8*b^3 - 4*A*a^6*b^5 + 6*A*a^4*b^7 - 4*A*a^2*b^9 + A*b^11)*d*x - 3*(2*B*a^7*b^3 - 8*A*a^6*b^4 + 3*B*a^5*b^5 + 8*A*a^4*b^6 - 7*A*a^2*b^8 + 2*A*b^10 + (2*B*a^10 - 8*A*a^9*b + 3*B*a^8*b^2 + 8*A*a^7*b^3 - 7*A*a^5*b^5 + 2*A*a^3*b^7)*cos(d*x + c)^3 + 3*(2*B*a^9*b - 8*A*a^8*b^2 + 3*B*a^7*b^3 + 8*A*a^6*b^4 - 7*A*a^4*b^6 + 2*A*a^2*b^8)*cos(d*x + c)^2 + 3*(2*B*a^8*b^2 - 8*A*a^7*b^3 + 3*B*a^6*b^4 + 8*A*a^5*b^5 - 7*A*a^3*b^7 + 2*A*a*b^9)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(11*B*a^8*b^3 - 26*A*a^7*b^4 - 7*B*a^6*b^5 + 43*A*a^5*b^6 - 4*B*a^4*b^7 - 23*A*a^3*b^8 + 6*A*a*b^10 + (18*B*a^10*b - 36*A*a^9*b^2 - 23*B*a^8*b^3 + 68*A*a^7*b^4 + 7*B*a^6*b^5 - 43*A*a^5*b^6 - 2*B*a^4*b^7 + 11*A*a^3*b^8)*cos(d*x + c)^2 + 3*(9*B*a^9*b^2 - 20*A*a^8*b^3 - 8*B*a^7*b^4 + 35*A*a^6*b^5 - B*a^5*b^6 - 20*A*a^4*b^7 + 5*A*a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^15 - 4*a^13*b^2 + 6*a^11*b^4 - 4*a^9*b^6 + a^7*b^8)*d*cos(d*x + c)^3 + 3*(a^14*b - 4*a^12*b^3 + 6*a^10*b^5 - 4*a^8*b^7 + a^6*b^9)*d*cos(d*x + c)^2 + 3*(a^13*b^2 - 4*a^11*b^4 + 6*a^9*b^6 - 4*a^7*b^8 + a^5*b^10)*d*cos(d*x + c) + (a^12*b^3 - 4*a^10*b^5 + 6*a^8*b^7 - 4*a^6*b^9 + a^4*b^11)*d), 1/6*(6*(A*a^11 - 4*A*a^9*b^2 + 6*A*a^7*b^4 - 4*A*a^5*b^6 + A*a^3*b^8)*d*x*cos(d*x + c)^3 + 18*(A*a^10*b - 4*A*a^8*b^3 + 6*A*a^6*b^5 - 4*A*a^4*b^7 + A*a^2*b^9)*d*x*cos(d*x + c)^2 + 18*(A*a^9*b^2 - 4*A*a^7*b^4 + 6*A*a^5*b^6 - 4*A*a^3*b^8 + A*a*b^10)*d*x*cos(d*x + c) + 6*(A*a^8*b^3 - 4*A*a^6*b^5 + 6*A*a^4*b^7 - 4*A*a^2*b^9 + A*b^11)*d*x + 3*(2*B*a^7*b^3 - 8*A*a^6*b^4 + 3*B*a^5*b^5 + 8*A*a^4*b^6 - 7*A*a^2*b^8 + 2*A*b^10 + (2*B*a^10 - 8*A*a^9*b + 3*B*a^8*b^2 + 8*A*a^7*b^3 - 7*A*a^5*b^5 + 2*A*a^3*b^7)*cos(d*x + c)^3 + 3*(2*B*a^9*b - 8*A*a^8*b^2 + 3*B*a^7*b^3 + 8*A*a^6*b^4 - 7*A*a^4*b^6 + 2*A*a^2*b^8)*cos(d*x + c)^2 + 3*(2*B*a^8*b^2 - 8*A*a^7*b^3 + 3*B*a^6*b^4 + 8*A*a^5*b^5 - 7*A*a^3*b^7 + 2*A*a*b^9)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (11*B*a^8*b^3 - 26*A*a^7*b^4 - 7*B*a^6*b^5 + 43*A*a^5*b^6 - 4*B*a^4*b^7 - 23*A*a^3*b^8 + 6*A*a*b^10 + (18*B*a^10*b - 36*A*a^9*b^2 - 23*B*a^8*b^3 + 68*A*a^7*b^4 + 7*B*a^6*b^5 - 43*A*a^5*b^6 - 2*B*a^4*b^7 + 11*A*a^3*b^8)*cos(d*x + c)^2 + 3*(9*B*a^9*b^2 - 20*A*a^8*b^3 - 8*B*a^7*b^4 + 35*A*a^6*b^5 - B*a^5*b^6 - 20*A*a^4*b^7 + 5*A*a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^15 - 4*a^13*b^2 + 6*a^11*b^4 - 4*a^9*b^6 + a^7*b^8)*d*cos(d*x + c)^3 + 3*(a^14*b - 4*a^12*b^3 + 6*a^10*b^5 - 4*a^8*b^7 + a^6*b^9)*d*cos(d*x + c)^2 + 3*(a^13*b^2 - 4*a^11*b^4 + 6*a^9*b^6 - 4*a^7*b^8 + a^5*b^10)*d*cos(d*x + c) + (a^12*b^3 - 4*a^10*b^5 + 6*a^8*b^7 - 4*a^6*b^9 + a^4*b^11)*d)]","B",0
342,1,2560,0,0.813653," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(B a^{12} - 4 \, A a^{11} b - 4 \, B a^{10} b^{2} + 16 \, A a^{9} b^{3} + 6 \, B a^{8} b^{4} - 24 \, A a^{7} b^{5} - 4 \, B a^{6} b^{6} + 16 \, A a^{5} b^{7} + B a^{4} b^{8} - 4 \, A a^{3} b^{9}\right)} d x \cos\left(d x + c\right)^{3} + 36 \, {\left(B a^{11} b - 4 \, A a^{10} b^{2} - 4 \, B a^{9} b^{3} + 16 \, A a^{8} b^{4} + 6 \, B a^{7} b^{5} - 24 \, A a^{6} b^{6} - 4 \, B a^{5} b^{7} + 16 \, A a^{4} b^{8} + B a^{3} b^{9} - 4 \, A a^{2} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 36 \, {\left(B a^{10} b^{2} - 4 \, A a^{9} b^{3} - 4 \, B a^{8} b^{4} + 16 \, A a^{7} b^{5} + 6 \, B a^{6} b^{6} - 24 \, A a^{5} b^{7} - 4 \, B a^{4} b^{8} + 16 \, A a^{3} b^{9} + B a^{2} b^{10} - 4 \, A a b^{11}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(B a^{9} b^{3} - 4 \, A a^{8} b^{4} - 4 \, B a^{7} b^{5} + 16 \, A a^{6} b^{6} + 6 \, B a^{5} b^{7} - 24 \, A a^{4} b^{8} - 4 \, B a^{3} b^{9} + 16 \, A a^{2} b^{10} + B a b^{11} - 4 \, A b^{12}\right)} d x - 3 \, {\left(8 \, B a^{7} b^{4} - 20 \, A a^{6} b^{5} - 8 \, B a^{5} b^{6} + 35 \, A a^{4} b^{7} + 7 \, B a^{3} b^{8} - 28 \, A a^{2} b^{9} - 2 \, B a b^{10} + 8 \, A b^{11} + {\left(8 \, B a^{10} b - 20 \, A a^{9} b^{2} - 8 \, B a^{8} b^{3} + 35 \, A a^{7} b^{4} + 7 \, B a^{6} b^{5} - 28 \, A a^{5} b^{6} - 2 \, B a^{4} b^{7} + 8 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, B a^{9} b^{2} - 20 \, A a^{8} b^{3} - 8 \, B a^{7} b^{4} + 35 \, A a^{6} b^{5} + 7 \, B a^{5} b^{6} - 28 \, A a^{4} b^{7} - 2 \, B a^{3} b^{8} + 8 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, B a^{8} b^{3} - 20 \, A a^{7} b^{4} - 8 \, B a^{6} b^{5} + 35 \, A a^{5} b^{6} + 7 \, B a^{4} b^{7} - 28 \, A a^{3} b^{8} - 2 \, B a^{2} b^{9} + 8 \, A a b^{10}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(6 \, A a^{9} b^{3} + 26 \, B a^{8} b^{4} - 71 \, A a^{7} b^{5} - 43 \, B a^{6} b^{6} + 133 \, A a^{5} b^{7} + 23 \, B a^{4} b^{8} - 92 \, A a^{3} b^{9} - 6 \, B a^{2} b^{10} + 24 \, A a b^{11} + 6 \, {\left(A a^{12} - 4 \, A a^{10} b^{2} + 6 \, A a^{8} b^{4} - 4 \, A a^{6} b^{6} + A a^{4} b^{8}\right)} \cos\left(d x + c\right)^{3} + {\left(18 \, A a^{11} b + 36 \, B a^{10} b^{2} - 132 \, A a^{9} b^{3} - 68 \, B a^{8} b^{4} + 239 \, A a^{7} b^{5} + 43 \, B a^{6} b^{6} - 169 \, A a^{5} b^{7} - 11 \, B a^{4} b^{8} + 44 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(6 \, A a^{10} b^{2} + 20 \, B a^{9} b^{3} - 59 \, A a^{8} b^{4} - 35 \, B a^{7} b^{5} + 110 \, A a^{6} b^{6} + 20 \, B a^{5} b^{7} - 77 \, A a^{4} b^{8} - 5 \, B a^{3} b^{9} + 20 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{16} - 4 \, a^{14} b^{2} + 6 \, a^{12} b^{4} - 4 \, a^{10} b^{6} + a^{8} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{15} b - 4 \, a^{13} b^{3} + 6 \, a^{11} b^{5} - 4 \, a^{9} b^{7} + a^{7} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{14} b^{2} - 4 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 4 \, a^{8} b^{8} + a^{6} b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{13} b^{3} - 4 \, a^{11} b^{5} + 6 \, a^{9} b^{7} - 4 \, a^{7} b^{9} + a^{5} b^{11}\right)} d\right)}}, \frac{6 \, {\left(B a^{12} - 4 \, A a^{11} b - 4 \, B a^{10} b^{2} + 16 \, A a^{9} b^{3} + 6 \, B a^{8} b^{4} - 24 \, A a^{7} b^{5} - 4 \, B a^{6} b^{6} + 16 \, A a^{5} b^{7} + B a^{4} b^{8} - 4 \, A a^{3} b^{9}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left(B a^{11} b - 4 \, A a^{10} b^{2} - 4 \, B a^{9} b^{3} + 16 \, A a^{8} b^{4} + 6 \, B a^{7} b^{5} - 24 \, A a^{6} b^{6} - 4 \, B a^{5} b^{7} + 16 \, A a^{4} b^{8} + B a^{3} b^{9} - 4 \, A a^{2} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left(B a^{10} b^{2} - 4 \, A a^{9} b^{3} - 4 \, B a^{8} b^{4} + 16 \, A a^{7} b^{5} + 6 \, B a^{6} b^{6} - 24 \, A a^{5} b^{7} - 4 \, B a^{4} b^{8} + 16 \, A a^{3} b^{9} + B a^{2} b^{10} - 4 \, A a b^{11}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(B a^{9} b^{3} - 4 \, A a^{8} b^{4} - 4 \, B a^{7} b^{5} + 16 \, A a^{6} b^{6} + 6 \, B a^{5} b^{7} - 24 \, A a^{4} b^{8} - 4 \, B a^{3} b^{9} + 16 \, A a^{2} b^{10} + B a b^{11} - 4 \, A b^{12}\right)} d x - 3 \, {\left(8 \, B a^{7} b^{4} - 20 \, A a^{6} b^{5} - 8 \, B a^{5} b^{6} + 35 \, A a^{4} b^{7} + 7 \, B a^{3} b^{8} - 28 \, A a^{2} b^{9} - 2 \, B a b^{10} + 8 \, A b^{11} + {\left(8 \, B a^{10} b - 20 \, A a^{9} b^{2} - 8 \, B a^{8} b^{3} + 35 \, A a^{7} b^{4} + 7 \, B a^{6} b^{5} - 28 \, A a^{5} b^{6} - 2 \, B a^{4} b^{7} + 8 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, B a^{9} b^{2} - 20 \, A a^{8} b^{3} - 8 \, B a^{7} b^{4} + 35 \, A a^{6} b^{5} + 7 \, B a^{5} b^{6} - 28 \, A a^{4} b^{7} - 2 \, B a^{3} b^{8} + 8 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, B a^{8} b^{3} - 20 \, A a^{7} b^{4} - 8 \, B a^{6} b^{5} + 35 \, A a^{5} b^{6} + 7 \, B a^{4} b^{7} - 28 \, A a^{3} b^{8} - 2 \, B a^{2} b^{9} + 8 \, A a b^{10}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(6 \, A a^{9} b^{3} + 26 \, B a^{8} b^{4} - 71 \, A a^{7} b^{5} - 43 \, B a^{6} b^{6} + 133 \, A a^{5} b^{7} + 23 \, B a^{4} b^{8} - 92 \, A a^{3} b^{9} - 6 \, B a^{2} b^{10} + 24 \, A a b^{11} + 6 \, {\left(A a^{12} - 4 \, A a^{10} b^{2} + 6 \, A a^{8} b^{4} - 4 \, A a^{6} b^{6} + A a^{4} b^{8}\right)} \cos\left(d x + c\right)^{3} + {\left(18 \, A a^{11} b + 36 \, B a^{10} b^{2} - 132 \, A a^{9} b^{3} - 68 \, B a^{8} b^{4} + 239 \, A a^{7} b^{5} + 43 \, B a^{6} b^{6} - 169 \, A a^{5} b^{7} - 11 \, B a^{4} b^{8} + 44 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(6 \, A a^{10} b^{2} + 20 \, B a^{9} b^{3} - 59 \, A a^{8} b^{4} - 35 \, B a^{7} b^{5} + 110 \, A a^{6} b^{6} + 20 \, B a^{5} b^{7} - 77 \, A a^{4} b^{8} - 5 \, B a^{3} b^{9} + 20 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{16} - 4 \, a^{14} b^{2} + 6 \, a^{12} b^{4} - 4 \, a^{10} b^{6} + a^{8} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{15} b - 4 \, a^{13} b^{3} + 6 \, a^{11} b^{5} - 4 \, a^{9} b^{7} + a^{7} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{14} b^{2} - 4 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 4 \, a^{8} b^{8} + a^{6} b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{13} b^{3} - 4 \, a^{11} b^{5} + 6 \, a^{9} b^{7} - 4 \, a^{7} b^{9} + a^{5} b^{11}\right)} d\right)}}\right]"," ",0,"[1/12*(12*(B*a^12 - 4*A*a^11*b - 4*B*a^10*b^2 + 16*A*a^9*b^3 + 6*B*a^8*b^4 - 24*A*a^7*b^5 - 4*B*a^6*b^6 + 16*A*a^5*b^7 + B*a^4*b^8 - 4*A*a^3*b^9)*d*x*cos(d*x + c)^3 + 36*(B*a^11*b - 4*A*a^10*b^2 - 4*B*a^9*b^3 + 16*A*a^8*b^4 + 6*B*a^7*b^5 - 24*A*a^6*b^6 - 4*B*a^5*b^7 + 16*A*a^4*b^8 + B*a^3*b^9 - 4*A*a^2*b^10)*d*x*cos(d*x + c)^2 + 36*(B*a^10*b^2 - 4*A*a^9*b^3 - 4*B*a^8*b^4 + 16*A*a^7*b^5 + 6*B*a^6*b^6 - 24*A*a^5*b^7 - 4*B*a^4*b^8 + 16*A*a^3*b^9 + B*a^2*b^10 - 4*A*a*b^11)*d*x*cos(d*x + c) + 12*(B*a^9*b^3 - 4*A*a^8*b^4 - 4*B*a^7*b^5 + 16*A*a^6*b^6 + 6*B*a^5*b^7 - 24*A*a^4*b^8 - 4*B*a^3*b^9 + 16*A*a^2*b^10 + B*a*b^11 - 4*A*b^12)*d*x - 3*(8*B*a^7*b^4 - 20*A*a^6*b^5 - 8*B*a^5*b^6 + 35*A*a^4*b^7 + 7*B*a^3*b^8 - 28*A*a^2*b^9 - 2*B*a*b^10 + 8*A*b^11 + (8*B*a^10*b - 20*A*a^9*b^2 - 8*B*a^8*b^3 + 35*A*a^7*b^4 + 7*B*a^6*b^5 - 28*A*a^5*b^6 - 2*B*a^4*b^7 + 8*A*a^3*b^8)*cos(d*x + c)^3 + 3*(8*B*a^9*b^2 - 20*A*a^8*b^3 - 8*B*a^7*b^4 + 35*A*a^6*b^5 + 7*B*a^5*b^6 - 28*A*a^4*b^7 - 2*B*a^3*b^8 + 8*A*a^2*b^9)*cos(d*x + c)^2 + 3*(8*B*a^8*b^3 - 20*A*a^7*b^4 - 8*B*a^6*b^5 + 35*A*a^5*b^6 + 7*B*a^4*b^7 - 28*A*a^3*b^8 - 2*B*a^2*b^9 + 8*A*a*b^10)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(6*A*a^9*b^3 + 26*B*a^8*b^4 - 71*A*a^7*b^5 - 43*B*a^6*b^6 + 133*A*a^5*b^7 + 23*B*a^4*b^8 - 92*A*a^3*b^9 - 6*B*a^2*b^10 + 24*A*a*b^11 + 6*(A*a^12 - 4*A*a^10*b^2 + 6*A*a^8*b^4 - 4*A*a^6*b^6 + A*a^4*b^8)*cos(d*x + c)^3 + (18*A*a^11*b + 36*B*a^10*b^2 - 132*A*a^9*b^3 - 68*B*a^8*b^4 + 239*A*a^7*b^5 + 43*B*a^6*b^6 - 169*A*a^5*b^7 - 11*B*a^4*b^8 + 44*A*a^3*b^9)*cos(d*x + c)^2 + 3*(6*A*a^10*b^2 + 20*B*a^9*b^3 - 59*A*a^8*b^4 - 35*B*a^7*b^5 + 110*A*a^6*b^6 + 20*B*a^5*b^7 - 77*A*a^4*b^8 - 5*B*a^3*b^9 + 20*A*a^2*b^10)*cos(d*x + c))*sin(d*x + c))/((a^16 - 4*a^14*b^2 + 6*a^12*b^4 - 4*a^10*b^6 + a^8*b^8)*d*cos(d*x + c)^3 + 3*(a^15*b - 4*a^13*b^3 + 6*a^11*b^5 - 4*a^9*b^7 + a^7*b^9)*d*cos(d*x + c)^2 + 3*(a^14*b^2 - 4*a^12*b^4 + 6*a^10*b^6 - 4*a^8*b^8 + a^6*b^10)*d*cos(d*x + c) + (a^13*b^3 - 4*a^11*b^5 + 6*a^9*b^7 - 4*a^7*b^9 + a^5*b^11)*d), 1/6*(6*(B*a^12 - 4*A*a^11*b - 4*B*a^10*b^2 + 16*A*a^9*b^3 + 6*B*a^8*b^4 - 24*A*a^7*b^5 - 4*B*a^6*b^6 + 16*A*a^5*b^7 + B*a^4*b^8 - 4*A*a^3*b^9)*d*x*cos(d*x + c)^3 + 18*(B*a^11*b - 4*A*a^10*b^2 - 4*B*a^9*b^3 + 16*A*a^8*b^4 + 6*B*a^7*b^5 - 24*A*a^6*b^6 - 4*B*a^5*b^7 + 16*A*a^4*b^8 + B*a^3*b^9 - 4*A*a^2*b^10)*d*x*cos(d*x + c)^2 + 18*(B*a^10*b^2 - 4*A*a^9*b^3 - 4*B*a^8*b^4 + 16*A*a^7*b^5 + 6*B*a^6*b^6 - 24*A*a^5*b^7 - 4*B*a^4*b^8 + 16*A*a^3*b^9 + B*a^2*b^10 - 4*A*a*b^11)*d*x*cos(d*x + c) + 6*(B*a^9*b^3 - 4*A*a^8*b^4 - 4*B*a^7*b^5 + 16*A*a^6*b^6 + 6*B*a^5*b^7 - 24*A*a^4*b^8 - 4*B*a^3*b^9 + 16*A*a^2*b^10 + B*a*b^11 - 4*A*b^12)*d*x - 3*(8*B*a^7*b^4 - 20*A*a^6*b^5 - 8*B*a^5*b^6 + 35*A*a^4*b^7 + 7*B*a^3*b^8 - 28*A*a^2*b^9 - 2*B*a*b^10 + 8*A*b^11 + (8*B*a^10*b - 20*A*a^9*b^2 - 8*B*a^8*b^3 + 35*A*a^7*b^4 + 7*B*a^6*b^5 - 28*A*a^5*b^6 - 2*B*a^4*b^7 + 8*A*a^3*b^8)*cos(d*x + c)^3 + 3*(8*B*a^9*b^2 - 20*A*a^8*b^3 - 8*B*a^7*b^4 + 35*A*a^6*b^5 + 7*B*a^5*b^6 - 28*A*a^4*b^7 - 2*B*a^3*b^8 + 8*A*a^2*b^9)*cos(d*x + c)^2 + 3*(8*B*a^8*b^3 - 20*A*a^7*b^4 - 8*B*a^6*b^5 + 35*A*a^5*b^6 + 7*B*a^4*b^7 - 28*A*a^3*b^8 - 2*B*a^2*b^9 + 8*A*a*b^10)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (6*A*a^9*b^3 + 26*B*a^8*b^4 - 71*A*a^7*b^5 - 43*B*a^6*b^6 + 133*A*a^5*b^7 + 23*B*a^4*b^8 - 92*A*a^3*b^9 - 6*B*a^2*b^10 + 24*A*a*b^11 + 6*(A*a^12 - 4*A*a^10*b^2 + 6*A*a^8*b^4 - 4*A*a^6*b^6 + A*a^4*b^8)*cos(d*x + c)^3 + (18*A*a^11*b + 36*B*a^10*b^2 - 132*A*a^9*b^3 - 68*B*a^8*b^4 + 239*A*a^7*b^5 + 43*B*a^6*b^6 - 169*A*a^5*b^7 - 11*B*a^4*b^8 + 44*A*a^3*b^9)*cos(d*x + c)^2 + 3*(6*A*a^10*b^2 + 20*B*a^9*b^3 - 59*A*a^8*b^4 - 35*B*a^7*b^5 + 110*A*a^6*b^6 + 20*B*a^5*b^7 - 77*A*a^4*b^8 - 5*B*a^3*b^9 + 20*A*a^2*b^10)*cos(d*x + c))*sin(d*x + c))/((a^16 - 4*a^14*b^2 + 6*a^12*b^4 - 4*a^10*b^6 + a^8*b^8)*d*cos(d*x + c)^3 + 3*(a^15*b - 4*a^13*b^3 + 6*a^11*b^5 - 4*a^9*b^7 + a^7*b^9)*d*cos(d*x + c)^2 + 3*(a^14*b^2 - 4*a^12*b^4 + 6*a^10*b^6 - 4*a^8*b^8 + a^6*b^10)*d*cos(d*x + c) + (a^13*b^3 - 4*a^11*b^5 + 6*a^9*b^7 - 4*a^7*b^9 + a^5*b^11)*d)]","B",0
343,1,2890,0,0.939156," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(A a^{13} - 8 \, B a^{12} b + 16 \, A a^{11} b^{2} + 32 \, B a^{10} b^{3} - 74 \, A a^{9} b^{4} - 48 \, B a^{8} b^{5} + 116 \, A a^{7} b^{6} + 32 \, B a^{6} b^{7} - 79 \, A a^{5} b^{8} - 8 \, B a^{4} b^{9} + 20 \, A a^{3} b^{10}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left(A a^{12} b - 8 \, B a^{11} b^{2} + 16 \, A a^{10} b^{3} + 32 \, B a^{9} b^{4} - 74 \, A a^{8} b^{5} - 48 \, B a^{7} b^{6} + 116 \, A a^{6} b^{7} + 32 \, B a^{5} b^{8} - 79 \, A a^{4} b^{9} - 8 \, B a^{3} b^{10} + 20 \, A a^{2} b^{11}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left(A a^{11} b^{2} - 8 \, B a^{10} b^{3} + 16 \, A a^{9} b^{4} + 32 \, B a^{8} b^{5} - 74 \, A a^{7} b^{6} - 48 \, B a^{6} b^{7} + 116 \, A a^{5} b^{8} + 32 \, B a^{4} b^{9} - 79 \, A a^{3} b^{10} - 8 \, B a^{2} b^{11} + 20 \, A a b^{12}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(A a^{10} b^{3} - 8 \, B a^{9} b^{4} + 16 \, A a^{8} b^{5} + 32 \, B a^{7} b^{6} - 74 \, A a^{6} b^{7} - 48 \, B a^{5} b^{8} + 116 \, A a^{4} b^{9} + 32 \, B a^{3} b^{10} - 79 \, A a^{2} b^{11} - 8 \, B a b^{12} + 20 \, A b^{13}\right)} d x - 3 \, {\left(20 \, B a^{7} b^{5} - 40 \, A a^{6} b^{6} - 35 \, B a^{5} b^{7} + 84 \, A a^{4} b^{8} + 28 \, B a^{3} b^{9} - 69 \, A a^{2} b^{10} - 8 \, B a b^{11} + 20 \, A b^{12} + {\left(20 \, B a^{10} b^{2} - 40 \, A a^{9} b^{3} - 35 \, B a^{8} b^{4} + 84 \, A a^{7} b^{5} + 28 \, B a^{6} b^{6} - 69 \, A a^{5} b^{7} - 8 \, B a^{4} b^{8} + 20 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, B a^{9} b^{3} - 40 \, A a^{8} b^{4} - 35 \, B a^{7} b^{5} + 84 \, A a^{6} b^{6} + 28 \, B a^{5} b^{7} - 69 \, A a^{4} b^{8} - 8 \, B a^{3} b^{9} + 20 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, B a^{8} b^{4} - 40 \, A a^{7} b^{5} - 35 \, B a^{6} b^{6} + 84 \, A a^{5} b^{7} + 28 \, B a^{4} b^{8} - 69 \, A a^{3} b^{9} - 8 \, B a^{2} b^{10} + 20 \, A a b^{11}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(6 \, B a^{10} b^{3} - 24 \, A a^{9} b^{4} - 71 \, B a^{8} b^{5} + 170 \, A a^{7} b^{6} + 133 \, B a^{6} b^{7} - 313 \, A a^{5} b^{8} - 92 \, B a^{4} b^{9} + 227 \, A a^{3} b^{10} + 24 \, B a^{2} b^{11} - 60 \, A a b^{12} + 3 \, {\left(A a^{13} - 4 \, A a^{11} b^{2} + 6 \, A a^{9} b^{4} - 4 \, A a^{7} b^{6} + A a^{5} b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, B a^{13} - 5 \, A a^{12} b - 8 \, B a^{11} b^{2} + 20 \, A a^{10} b^{3} + 12 \, B a^{9} b^{4} - 30 \, A a^{8} b^{5} - 8 \, B a^{7} b^{6} + 20 \, A a^{6} b^{7} + 2 \, B a^{5} b^{8} - 5 \, A a^{4} b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(18 \, B a^{12} b - 63 \, A a^{11} b^{2} - 132 \, B a^{10} b^{3} + 342 \, A a^{9} b^{4} + 239 \, B a^{8} b^{5} - 590 \, A a^{7} b^{6} - 169 \, B a^{6} b^{7} + 421 \, A a^{5} b^{8} + 44 \, B a^{4} b^{9} - 110 \, A a^{3} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(6 \, B a^{11} b^{2} - 23 \, A a^{10} b^{3} - 59 \, B a^{9} b^{4} + 146 \, A a^{8} b^{5} + 110 \, B a^{7} b^{6} - 263 \, A a^{6} b^{7} - 77 \, B a^{5} b^{8} + 190 \, A a^{4} b^{9} + 20 \, B a^{3} b^{10} - 50 \, A a^{2} b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{17} - 4 \, a^{15} b^{2} + 6 \, a^{13} b^{4} - 4 \, a^{11} b^{6} + a^{9} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{16} b - 4 \, a^{14} b^{3} + 6 \, a^{12} b^{5} - 4 \, a^{10} b^{7} + a^{8} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{15} b^{2} - 4 \, a^{13} b^{4} + 6 \, a^{11} b^{6} - 4 \, a^{9} b^{8} + a^{7} b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{14} b^{3} - 4 \, a^{12} b^{5} + 6 \, a^{10} b^{7} - 4 \, a^{8} b^{9} + a^{6} b^{11}\right)} d\right)}}, \frac{3 \, {\left(A a^{13} - 8 \, B a^{12} b + 16 \, A a^{11} b^{2} + 32 \, B a^{10} b^{3} - 74 \, A a^{9} b^{4} - 48 \, B a^{8} b^{5} + 116 \, A a^{7} b^{6} + 32 \, B a^{6} b^{7} - 79 \, A a^{5} b^{8} - 8 \, B a^{4} b^{9} + 20 \, A a^{3} b^{10}\right)} d x \cos\left(d x + c\right)^{3} + 9 \, {\left(A a^{12} b - 8 \, B a^{11} b^{2} + 16 \, A a^{10} b^{3} + 32 \, B a^{9} b^{4} - 74 \, A a^{8} b^{5} - 48 \, B a^{7} b^{6} + 116 \, A a^{6} b^{7} + 32 \, B a^{5} b^{8} - 79 \, A a^{4} b^{9} - 8 \, B a^{3} b^{10} + 20 \, A a^{2} b^{11}\right)} d x \cos\left(d x + c\right)^{2} + 9 \, {\left(A a^{11} b^{2} - 8 \, B a^{10} b^{3} + 16 \, A a^{9} b^{4} + 32 \, B a^{8} b^{5} - 74 \, A a^{7} b^{6} - 48 \, B a^{6} b^{7} + 116 \, A a^{5} b^{8} + 32 \, B a^{4} b^{9} - 79 \, A a^{3} b^{10} - 8 \, B a^{2} b^{11} + 20 \, A a b^{12}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(A a^{10} b^{3} - 8 \, B a^{9} b^{4} + 16 \, A a^{8} b^{5} + 32 \, B a^{7} b^{6} - 74 \, A a^{6} b^{7} - 48 \, B a^{5} b^{8} + 116 \, A a^{4} b^{9} + 32 \, B a^{3} b^{10} - 79 \, A a^{2} b^{11} - 8 \, B a b^{12} + 20 \, A b^{13}\right)} d x + 3 \, {\left(20 \, B a^{7} b^{5} - 40 \, A a^{6} b^{6} - 35 \, B a^{5} b^{7} + 84 \, A a^{4} b^{8} + 28 \, B a^{3} b^{9} - 69 \, A a^{2} b^{10} - 8 \, B a b^{11} + 20 \, A b^{12} + {\left(20 \, B a^{10} b^{2} - 40 \, A a^{9} b^{3} - 35 \, B a^{8} b^{4} + 84 \, A a^{7} b^{5} + 28 \, B a^{6} b^{6} - 69 \, A a^{5} b^{7} - 8 \, B a^{4} b^{8} + 20 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, B a^{9} b^{3} - 40 \, A a^{8} b^{4} - 35 \, B a^{7} b^{5} + 84 \, A a^{6} b^{6} + 28 \, B a^{5} b^{7} - 69 \, A a^{4} b^{8} - 8 \, B a^{3} b^{9} + 20 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, B a^{8} b^{4} - 40 \, A a^{7} b^{5} - 35 \, B a^{6} b^{6} + 84 \, A a^{5} b^{7} + 28 \, B a^{4} b^{8} - 69 \, A a^{3} b^{9} - 8 \, B a^{2} b^{10} + 20 \, A a b^{11}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(6 \, B a^{10} b^{3} - 24 \, A a^{9} b^{4} - 71 \, B a^{8} b^{5} + 170 \, A a^{7} b^{6} + 133 \, B a^{6} b^{7} - 313 \, A a^{5} b^{8} - 92 \, B a^{4} b^{9} + 227 \, A a^{3} b^{10} + 24 \, B a^{2} b^{11} - 60 \, A a b^{12} + 3 \, {\left(A a^{13} - 4 \, A a^{11} b^{2} + 6 \, A a^{9} b^{4} - 4 \, A a^{7} b^{6} + A a^{5} b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, B a^{13} - 5 \, A a^{12} b - 8 \, B a^{11} b^{2} + 20 \, A a^{10} b^{3} + 12 \, B a^{9} b^{4} - 30 \, A a^{8} b^{5} - 8 \, B a^{7} b^{6} + 20 \, A a^{6} b^{7} + 2 \, B a^{5} b^{8} - 5 \, A a^{4} b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(18 \, B a^{12} b - 63 \, A a^{11} b^{2} - 132 \, B a^{10} b^{3} + 342 \, A a^{9} b^{4} + 239 \, B a^{8} b^{5} - 590 \, A a^{7} b^{6} - 169 \, B a^{6} b^{7} + 421 \, A a^{5} b^{8} + 44 \, B a^{4} b^{9} - 110 \, A a^{3} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(6 \, B a^{11} b^{2} - 23 \, A a^{10} b^{3} - 59 \, B a^{9} b^{4} + 146 \, A a^{8} b^{5} + 110 \, B a^{7} b^{6} - 263 \, A a^{6} b^{7} - 77 \, B a^{5} b^{8} + 190 \, A a^{4} b^{9} + 20 \, B a^{3} b^{10} - 50 \, A a^{2} b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{17} - 4 \, a^{15} b^{2} + 6 \, a^{13} b^{4} - 4 \, a^{11} b^{6} + a^{9} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{16} b - 4 \, a^{14} b^{3} + 6 \, a^{12} b^{5} - 4 \, a^{10} b^{7} + a^{8} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{15} b^{2} - 4 \, a^{13} b^{4} + 6 \, a^{11} b^{6} - 4 \, a^{9} b^{8} + a^{7} b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{14} b^{3} - 4 \, a^{12} b^{5} + 6 \, a^{10} b^{7} - 4 \, a^{8} b^{9} + a^{6} b^{11}\right)} d\right)}}\right]"," ",0,"[1/12*(6*(A*a^13 - 8*B*a^12*b + 16*A*a^11*b^2 + 32*B*a^10*b^3 - 74*A*a^9*b^4 - 48*B*a^8*b^5 + 116*A*a^7*b^6 + 32*B*a^6*b^7 - 79*A*a^5*b^8 - 8*B*a^4*b^9 + 20*A*a^3*b^10)*d*x*cos(d*x + c)^3 + 18*(A*a^12*b - 8*B*a^11*b^2 + 16*A*a^10*b^3 + 32*B*a^9*b^4 - 74*A*a^8*b^5 - 48*B*a^7*b^6 + 116*A*a^6*b^7 + 32*B*a^5*b^8 - 79*A*a^4*b^9 - 8*B*a^3*b^10 + 20*A*a^2*b^11)*d*x*cos(d*x + c)^2 + 18*(A*a^11*b^2 - 8*B*a^10*b^3 + 16*A*a^9*b^4 + 32*B*a^8*b^5 - 74*A*a^7*b^6 - 48*B*a^6*b^7 + 116*A*a^5*b^8 + 32*B*a^4*b^9 - 79*A*a^3*b^10 - 8*B*a^2*b^11 + 20*A*a*b^12)*d*x*cos(d*x + c) + 6*(A*a^10*b^3 - 8*B*a^9*b^4 + 16*A*a^8*b^5 + 32*B*a^7*b^6 - 74*A*a^6*b^7 - 48*B*a^5*b^8 + 116*A*a^4*b^9 + 32*B*a^3*b^10 - 79*A*a^2*b^11 - 8*B*a*b^12 + 20*A*b^13)*d*x - 3*(20*B*a^7*b^5 - 40*A*a^6*b^6 - 35*B*a^5*b^7 + 84*A*a^4*b^8 + 28*B*a^3*b^9 - 69*A*a^2*b^10 - 8*B*a*b^11 + 20*A*b^12 + (20*B*a^10*b^2 - 40*A*a^9*b^3 - 35*B*a^8*b^4 + 84*A*a^7*b^5 + 28*B*a^6*b^6 - 69*A*a^5*b^7 - 8*B*a^4*b^8 + 20*A*a^3*b^9)*cos(d*x + c)^3 + 3*(20*B*a^9*b^3 - 40*A*a^8*b^4 - 35*B*a^7*b^5 + 84*A*a^6*b^6 + 28*B*a^5*b^7 - 69*A*a^4*b^8 - 8*B*a^3*b^9 + 20*A*a^2*b^10)*cos(d*x + c)^2 + 3*(20*B*a^8*b^4 - 40*A*a^7*b^5 - 35*B*a^6*b^6 + 84*A*a^5*b^7 + 28*B*a^4*b^8 - 69*A*a^3*b^9 - 8*B*a^2*b^10 + 20*A*a*b^11)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(6*B*a^10*b^3 - 24*A*a^9*b^4 - 71*B*a^8*b^5 + 170*A*a^7*b^6 + 133*B*a^6*b^7 - 313*A*a^5*b^8 - 92*B*a^4*b^9 + 227*A*a^3*b^10 + 24*B*a^2*b^11 - 60*A*a*b^12 + 3*(A*a^13 - 4*A*a^11*b^2 + 6*A*a^9*b^4 - 4*A*a^7*b^6 + A*a^5*b^8)*cos(d*x + c)^4 + 3*(2*B*a^13 - 5*A*a^12*b - 8*B*a^11*b^2 + 20*A*a^10*b^3 + 12*B*a^9*b^4 - 30*A*a^8*b^5 - 8*B*a^7*b^6 + 20*A*a^6*b^7 + 2*B*a^5*b^8 - 5*A*a^4*b^9)*cos(d*x + c)^3 + (18*B*a^12*b - 63*A*a^11*b^2 - 132*B*a^10*b^3 + 342*A*a^9*b^4 + 239*B*a^8*b^5 - 590*A*a^7*b^6 - 169*B*a^6*b^7 + 421*A*a^5*b^8 + 44*B*a^4*b^9 - 110*A*a^3*b^10)*cos(d*x + c)^2 + 3*(6*B*a^11*b^2 - 23*A*a^10*b^3 - 59*B*a^9*b^4 + 146*A*a^8*b^5 + 110*B*a^7*b^6 - 263*A*a^6*b^7 - 77*B*a^5*b^8 + 190*A*a^4*b^9 + 20*B*a^3*b^10 - 50*A*a^2*b^11)*cos(d*x + c))*sin(d*x + c))/((a^17 - 4*a^15*b^2 + 6*a^13*b^4 - 4*a^11*b^6 + a^9*b^8)*d*cos(d*x + c)^3 + 3*(a^16*b - 4*a^14*b^3 + 6*a^12*b^5 - 4*a^10*b^7 + a^8*b^9)*d*cos(d*x + c)^2 + 3*(a^15*b^2 - 4*a^13*b^4 + 6*a^11*b^6 - 4*a^9*b^8 + a^7*b^10)*d*cos(d*x + c) + (a^14*b^3 - 4*a^12*b^5 + 6*a^10*b^7 - 4*a^8*b^9 + a^6*b^11)*d), 1/6*(3*(A*a^13 - 8*B*a^12*b + 16*A*a^11*b^2 + 32*B*a^10*b^3 - 74*A*a^9*b^4 - 48*B*a^8*b^5 + 116*A*a^7*b^6 + 32*B*a^6*b^7 - 79*A*a^5*b^8 - 8*B*a^4*b^9 + 20*A*a^3*b^10)*d*x*cos(d*x + c)^3 + 9*(A*a^12*b - 8*B*a^11*b^2 + 16*A*a^10*b^3 + 32*B*a^9*b^4 - 74*A*a^8*b^5 - 48*B*a^7*b^6 + 116*A*a^6*b^7 + 32*B*a^5*b^8 - 79*A*a^4*b^9 - 8*B*a^3*b^10 + 20*A*a^2*b^11)*d*x*cos(d*x + c)^2 + 9*(A*a^11*b^2 - 8*B*a^10*b^3 + 16*A*a^9*b^4 + 32*B*a^8*b^5 - 74*A*a^7*b^6 - 48*B*a^6*b^7 + 116*A*a^5*b^8 + 32*B*a^4*b^9 - 79*A*a^3*b^10 - 8*B*a^2*b^11 + 20*A*a*b^12)*d*x*cos(d*x + c) + 3*(A*a^10*b^3 - 8*B*a^9*b^4 + 16*A*a^8*b^5 + 32*B*a^7*b^6 - 74*A*a^6*b^7 - 48*B*a^5*b^8 + 116*A*a^4*b^9 + 32*B*a^3*b^10 - 79*A*a^2*b^11 - 8*B*a*b^12 + 20*A*b^13)*d*x + 3*(20*B*a^7*b^5 - 40*A*a^6*b^6 - 35*B*a^5*b^7 + 84*A*a^4*b^8 + 28*B*a^3*b^9 - 69*A*a^2*b^10 - 8*B*a*b^11 + 20*A*b^12 + (20*B*a^10*b^2 - 40*A*a^9*b^3 - 35*B*a^8*b^4 + 84*A*a^7*b^5 + 28*B*a^6*b^6 - 69*A*a^5*b^7 - 8*B*a^4*b^8 + 20*A*a^3*b^9)*cos(d*x + c)^3 + 3*(20*B*a^9*b^3 - 40*A*a^8*b^4 - 35*B*a^7*b^5 + 84*A*a^6*b^6 + 28*B*a^5*b^7 - 69*A*a^4*b^8 - 8*B*a^3*b^9 + 20*A*a^2*b^10)*cos(d*x + c)^2 + 3*(20*B*a^8*b^4 - 40*A*a^7*b^5 - 35*B*a^6*b^6 + 84*A*a^5*b^7 + 28*B*a^4*b^8 - 69*A*a^3*b^9 - 8*B*a^2*b^10 + 20*A*a*b^11)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (6*B*a^10*b^3 - 24*A*a^9*b^4 - 71*B*a^8*b^5 + 170*A*a^7*b^6 + 133*B*a^6*b^7 - 313*A*a^5*b^8 - 92*B*a^4*b^9 + 227*A*a^3*b^10 + 24*B*a^2*b^11 - 60*A*a*b^12 + 3*(A*a^13 - 4*A*a^11*b^2 + 6*A*a^9*b^4 - 4*A*a^7*b^6 + A*a^5*b^8)*cos(d*x + c)^4 + 3*(2*B*a^13 - 5*A*a^12*b - 8*B*a^11*b^2 + 20*A*a^10*b^3 + 12*B*a^9*b^4 - 30*A*a^8*b^5 - 8*B*a^7*b^6 + 20*A*a^6*b^7 + 2*B*a^5*b^8 - 5*A*a^4*b^9)*cos(d*x + c)^3 + (18*B*a^12*b - 63*A*a^11*b^2 - 132*B*a^10*b^3 + 342*A*a^9*b^4 + 239*B*a^8*b^5 - 590*A*a^7*b^6 - 169*B*a^6*b^7 + 421*A*a^5*b^8 + 44*B*a^4*b^9 - 110*A*a^3*b^10)*cos(d*x + c)^2 + 3*(6*B*a^11*b^2 - 23*A*a^10*b^3 - 59*B*a^9*b^4 + 146*A*a^8*b^5 + 110*B*a^7*b^6 - 263*A*a^6*b^7 - 77*B*a^5*b^8 + 190*A*a^4*b^9 + 20*B*a^3*b^10 - 50*A*a^2*b^11)*cos(d*x + c))*sin(d*x + c))/((a^17 - 4*a^15*b^2 + 6*a^13*b^4 - 4*a^11*b^6 + a^9*b^8)*d*cos(d*x + c)^3 + 3*(a^16*b - 4*a^14*b^3 + 6*a^12*b^5 - 4*a^10*b^7 + a^8*b^9)*d*cos(d*x + c)^2 + 3*(a^15*b^2 - 4*a^13*b^4 + 6*a^11*b^6 - 4*a^9*b^8 + a^7*b^10)*d*cos(d*x + c) + (a^14*b^3 - 4*a^12*b^5 + 6*a^10*b^7 - 4*a^8*b^9 + a^6*b^11)*d)]","B",0
344,1,197,0,0.488052," ","integrate((b*B/a+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, B b d x + \sqrt{a^{2} - b^{2}} B \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right)}{2 \, a^{2} d}, \frac{B b d x + \sqrt{-a^{2} + b^{2}} B \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right)}{a^{2} d}\right]"," ",0,"[1/2*(2*B*b*d*x + sqrt(a^2 - b^2)*B*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)))/(a^2*d), (B*b*d*x + sqrt(-a^2 + b^2)*B*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))))/(a^2*d)]","A",0
345,1,6,0,0.400346," ","integrate((a*B/b+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{B x}{b}"," ",0,"B*x/b","A",0
346,1,279,0,0.477882," ","integrate((a+b*sec(d*x+c))/(b+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b d x \cos\left(d x + c\right) + 2 \, a^{2} d x - 2 \, a b \sin\left(d x + c\right) + \sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right)}{2 \, {\left(b^{3} d \cos\left(d x + c\right) + a b^{2} d\right)}}, \frac{a b d x \cos\left(d x + c\right) + a^{2} d x - a b \sin\left(d x + c\right) - \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right)}{b^{3} d \cos\left(d x + c\right) + a b^{2} d}\right]"," ",0,"[1/2*(2*a*b*d*x*cos(d*x + c) + 2*a^2*d*x - 2*a*b*sin(d*x + c) + sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)))/(b^3*d*cos(d*x + c) + a*b^2*d), (a*b*d*x*cos(d*x + c) + a^2*d*x - a*b*sin(d*x + c) - sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))))/(b^3*d*cos(d*x + c) + a*b^2*d)]","A",0
347,1,84,0,0.455287," ","integrate((3+sec(d*x+c))/(2-sec(d*x+c)),x, algorithm=""fricas"")","\frac{18 \, d x + 5 \, \sqrt{3} \log\left(-\frac{2 \, \cos\left(d x + c\right)^{2} + 2 \, {\left(\sqrt{3} \cos\left(d x + c\right) - 2 \, \sqrt{3}\right)} \sin\left(d x + c\right) + 4 \, \cos\left(d x + c\right) - 7}{4 \, \cos\left(d x + c\right)^{2} - 4 \, \cos\left(d x + c\right) + 1}\right)}{12 \, d}"," ",0,"1/12*(18*d*x + 5*sqrt(3)*log(-(2*cos(d*x + c)^2 + 2*(sqrt(3)*cos(d*x + c) - 2*sqrt(3))*sin(d*x + c) + 4*cos(d*x + c) - 7)/(4*cos(d*x + c)^2 - 4*cos(d*x + c) + 1)))/d","A",0
348,0,0,0,0.482441," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(d x + c\right)^{5} + A \sec\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*sec(d*x + c)^5 + A*sec(d*x + c)^4)*sqrt(b*sec(d*x + c) + a), x)","F",0
349,0,0,0,0.466315," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(d x + c\right)^{4} + A \sec\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*sec(d*x + c)^4 + A*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
350,0,0,0,0.477063," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*sec(d*x + c)^3 + A*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
351,0,0,0,0.473226," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(d x + c\right)^{2} + A \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*sec(d*x + c)^2 + A*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
352,0,0,0,0.827834," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a), x)","F",0
353,0,0,0,49.588218," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
354,0,0,0,1.590081," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c)^2*sec(d*x + c) + A*cos(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
355,0,0,0,59.425247," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c)^3*sec(d*x + c) + A*cos(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
356,0,0,0,0.473068," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \sec\left(d x + c\right)^{5} + A a \sec\left(d x + c\right)^{3} + {\left(B a + A b\right)} \sec\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^5 + A*a*sec(d*x + c)^3 + (B*a + A*b)*sec(d*x + c)^4)*sqrt(b*sec(d*x + c) + a), x)","F",0
357,0,0,0,0.475029," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \sec\left(d x + c\right)^{4} + A a \sec\left(d x + c\right)^{2} + {\left(B a + A b\right)} \sec\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^4 + A*a*sec(d*x + c)^2 + (B*a + A*b)*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
358,0,0,0,0.447803," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \sec\left(d x + c\right)^{3} + A a \sec\left(d x + c\right) + {\left(B a + A b\right)} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^3 + A*a*sec(d*x + c) + (B*a + A*b)*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
359,0,0,0,23.525000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\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{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
360,0,0,0,48.202095," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + {\left(B a + A b\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b*cos(d*x + c)*sec(d*x + c)^2 + A*a*cos(d*x + c) + (B*a + A*b)*cos(d*x + c)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
361,0,0,0,1.597868," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + A a \cos\left(d x + c\right)^{2} + {\left(B a + A b\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2*sec(d*x + c)^2 + A*a*cos(d*x + c)^2 + (B*a + A*b)*cos(d*x + c)^2*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
362,0,0,0,2.104957," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + A a \cos\left(d x + c\right)^{3} + {\left(B a + A b\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^3*sec(d*x + c)^2 + A*a*cos(d*x + c)^3 + (B*a + A*b)*cos(d*x + c)^3*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
363,0,0,0,0.503582," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \sec\left(d x + c\right)^{6} + A a^{2} \sec\left(d x + c\right)^{3} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{5} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^6 + A*a^2*sec(d*x + c)^3 + (2*B*a*b + A*b^2)*sec(d*x + c)^5 + (B*a^2 + 2*A*a*b)*sec(d*x + c)^4)*sqrt(b*sec(d*x + c) + a), x)","F",0
364,0,0,0,0.479088," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \sec\left(d x + c\right)^{5} + A a^{2} \sec\left(d x + c\right)^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{4} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^5 + A*a^2*sec(d*x + c)^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^4 + (B*a^2 + 2*A*a*b)*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
365,0,0,0,0.459611," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \sec\left(d x + c\right)^{4} + A a^{2} \sec\left(d x + c\right) + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{3} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^4 + A*a^2*sec(d*x + c) + (2*B*a*b + A*b^2)*sec(d*x + c)^3 + (B*a^2 + 2*A*a*b)*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
366,0,0,0,22.712629," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
367,0,0,0,51.699982," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right) + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)*sec(d*x + c)^3 + A*a^2*cos(d*x + c) + (2*B*a*b + A*b^2)*cos(d*x + c)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
368,0,0,0,56.180665," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^2*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c)^2*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
369,0,0,0,63.483812," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right)^{3} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^3 + (2*B*a*b + A*b^2)*cos(d*x + c)^3*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c)^3*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
370,0,0,0,65.086390," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^4*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^4 + (2*B*a*b + A*b^2)*cos(d*x + c)^4*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c)^4*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
371,0,0,0,0.460189," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \sec\left(d x + c\right)^{4} + A \sec\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*sec(d*x + c)^4 + A*sec(d*x + c)^3)/sqrt(b*sec(d*x + c) + a), x)","F",0
372,0,0,0,0.437973," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*sec(d*x + c)^3 + A*sec(d*x + c)^2)/sqrt(b*sec(d*x + c) + a), x)","F",0
373,0,0,0,0.473147," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \sec\left(d x + c\right)^{2} + A \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*sec(d*x + c)^2 + A*sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
374,0,0,0,0.831229," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)/sqrt(b*sec(d*x + c) + a), x)","F",0
375,0,0,0,49.793342," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
376,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,0,0,0,4.124012," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*cos(d*x + c)^3*sec(d*x + c) + A*cos(d*x + c)^3)/sqrt(b*sec(d*x + c) + a), x)","F",0
378,0,0,0,1.081286," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{4} + A \sec\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c)^4 + A*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
379,0,0,0,1.248027," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c)^3 + A*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
380,0,0,0,0.998337," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{2} + A \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c)^2 + A*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
381,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,0,0,0,2.060053," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(b*sec(d*x + c) + a)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
383,0,0,0,2.645555," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2*sec(d*x + c) + A*cos(d*x + c)^2)*sqrt(b*sec(d*x + c) + a)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
384,0,0,0,62.086044," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)^3*sec(d*x + c) + A*cos(d*x + c)^3)*sqrt(b*sec(d*x + c) + a)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
385,0,0,0,0.599967," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{5} + A \sec\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c)^5 + A*sec(d*x + c)^4)*sqrt(b*sec(d*x + c) + a)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
386,0,0,0,0.557694," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{4} + A \sec\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c)^4 + A*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
387,0,0,0,0.532964," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c)^3 + A*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
388,0,0,0,0.540632," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{2} + A \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c)^2 + A*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
389,0,0,0,22.365489," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
390,0,0,0,1.426833," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(b*sec(d*x + c) + a)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
391,0,0,0,57.035946," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2*sec(d*x + c) + A*cos(d*x + c)^2)*sqrt(b*sec(d*x + c) + a)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
392,0,0,0,0.461157," ","integrate(sec(f*x+e)*(A+A*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A \sec\left(f x + e\right)^{2} + A \sec\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral((A*sec(f*x + e)^2 + A*sec(f*x + e))/sqrt(b*sec(f*x + e) + a), x)","F",0
393,0,0,0,0.451579," ","integrate(sec(f*x+e)*(A-A*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{A \sec\left(f x + e\right)^{2} - A \sec\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral(-(A*sec(f*x + e)^2 - A*sec(f*x + e))/sqrt(b*sec(f*x + e) + a), x)","F",0
394,0,0,0,0.461910," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \sec\left(d x + c\right)^{3} + A a \sec\left(d x + c\right) + {\left(B a + A b\right)} \sec\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^3 + A*a*sec(d*x + c) + (B*a + A*b)*sec(d*x + c)^2)*sqrt(sec(d*x + c)), x)","F",0
395,0,0,0,0.438255," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\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)}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
396,0,0,0,0.444620," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b \sec\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \sec\left(d x + c\right)}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))/sqrt(sec(d*x + c)), x)","F",0
397,0,0,0,0.469702," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b \sec\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \sec\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))/sec(d*x + c)^(3/2), x)","F",0
398,0,0,0,0.456334," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b \sec\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \sec\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))/sec(d*x + c)^(5/2), x)","F",0
399,0,0,0,0.468345," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b \sec\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \sec\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))/sec(d*x + c)^(7/2), x)","F",0
400,0,0,0,0.448786," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \sec\left(d x + c\right)^{4} + A a^{2} \sec\left(d x + c\right) + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{3} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^4 + A*a^2*sec(d*x + c) + (2*B*a*b + A*b^2)*sec(d*x + c)^3 + (B*a^2 + 2*A*a*b)*sec(d*x + c)^2)*sqrt(sec(d*x + c)), x)","F",0
401,0,0,0,0.451699," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
402,0,0,0,0.452319," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))/sqrt(sec(d*x + c)), x)","F",0
403,0,0,0,0.463603," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))/sec(d*x + c)^(3/2), x)","F",0
404,0,0,0,0.475806," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))/sec(d*x + c)^(5/2), x)","F",0
405,0,0,0,0.482252," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))/sec(d*x + c)^(7/2), x)","F",0
406,0,0,0,0.503133," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))/sec(d*x + c)^(9/2), x)","F",0
407,0,0,0,0.497935," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{3} \sec\left(d x + c\right)^{5} + A a^{3} \sec\left(d x + c\right) + {\left(3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{4} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \sec\left(d x + c\right)^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \sec\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^3*sec(d*x + c)^5 + A*a^3*sec(d*x + c) + (3*B*a*b^2 + A*b^3)*sec(d*x + c)^4 + 3*(B*a^2*b + A*a*b^2)*sec(d*x + c)^3 + (B*a^3 + 3*A*a^2*b)*sec(d*x + c)^2)*sqrt(sec(d*x + c)), x)","F",0
408,0,0,0,0.457582," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{3} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^3*sec(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
409,0,0,0,0.471093," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{3} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \sec\left(d x + c\right)}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*b^3*sec(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*sec(d*x + c))/sqrt(sec(d*x + c)), x)","F",0
410,0,0,0,0.478962," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{3} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \sec\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*b^3*sec(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*sec(d*x + c))/sec(d*x + c)^(3/2), x)","F",0
411,0,0,0,0.475362," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{3} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \sec\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*b^3*sec(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*sec(d*x + c))/sec(d*x + c)^(5/2), x)","F",0
412,0,0,0,0.475186," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{3} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \sec\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*b^3*sec(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*sec(d*x + c))/sec(d*x + c)^(7/2), x)","F",0
413,0,0,0,0.467217," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{3} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \sec\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*b^3*sec(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*sec(d*x + c))/sec(d*x + c)^(9/2), x)","F",0
414,0,0,0,0.508552," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{3} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \sec\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((B*b^3*sec(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*sec(d*x + c))/sec(d*x + c)^(11/2), x)","F",0
415,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
418,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
419,0,0,0,144.225204," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c)^2 + a*sec(d*x + c)), x)","F",0
420,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
421,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
422,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
423,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
424,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,0,0,0,120.486820," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{4} + 2 \, a b \sec\left(d x + c\right)^{3} + a^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b^2*sec(d*x + c)^4 + 2*a*b*sec(d*x + c)^3 + a^2*sec(d*x + c)^2), x)","F",0
428,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
434,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
435,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
436,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
437,0,0,0,3.473872," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
438,0,0,0,0.577277," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
439,0,0,0,0.501016," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
440,0,0,0,0.519098," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
441,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
442,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
443,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
444,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
445,0,0,0,1.191235," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\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{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
446,0,0,0,0.853989," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\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{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
447,0,0,0,0.828145," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\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{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(9/2), x)","F",0
448,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
452,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
453,0,0,0,1.059790," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
454,0,0,0,0.562900," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(9/2), x)","F",0
455,0,0,0,0.570308," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(11/2), x)","F",0
456,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
457,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
459,0,0,0,1.438521," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b*sec(d*x + c)^2 + a*sec(d*x + c)), x)","F",0
460,0,0,0,0.631636," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b*sec(d*x + c)^3 + a*sec(d*x + c)^2), x)","F",0
461,0,0,0,0.522222," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b \sec\left(d x + c\right)^{4} + a \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b*sec(d*x + c)^4 + a*sec(d*x + c)^3), x)","F",0
462,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
464,0,0,0,1.715777," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
465,0,0,0,0.714555," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{2} \sec\left(d x + c\right)^{3} + 2 \, a b \sec\left(d x + c\right)^{2} + a^{2} \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^2*sec(d*x + c)^3 + 2*a*b*sec(d*x + c)^2 + a^2*sec(d*x + c)), x)","F",0
466,0,0,0,0.575850," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{2} \sec\left(d x + c\right)^{4} + 2 \, a b \sec\left(d x + c\right)^{3} + a^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^2*sec(d*x + c)^4 + 2*a*b*sec(d*x + c)^3 + a^2*sec(d*x + c)^2), x)","F",0
467,0,0,0,0.952233," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{2} \sec\left(d x + c\right)^{5} + 2 \, a b \sec\left(d x + c\right)^{4} + a^{2} \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^2*sec(d*x + c)^5 + 2*a*b*sec(d*x + c)^4 + a^2*sec(d*x + c)^3), x)","F",0
468,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,0,0,0,1.041170," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right)^{2} + A \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c)^2 + A*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
470,0,0,0,0.769533," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
471,0,0,0,0.666805," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{3} \sec\left(d x + c\right)^{4} + 3 \, a b^{2} \sec\left(d x + c\right)^{3} + 3 \, a^{2} b \sec\left(d x + c\right)^{2} + a^{3} \sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^3*sec(d*x + c)^4 + 3*a*b^2*sec(d*x + c)^3 + 3*a^2*b*sec(d*x + c)^2 + a^3*sec(d*x + c)), x)","F",0
472,0,0,0,0.939852," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{3} \sec\left(d x + c\right)^{5} + 3 \, a b^{2} \sec\left(d x + c\right)^{4} + 3 \, a^{2} b \sec\left(d x + c\right)^{3} + a^{3} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^3*sec(d*x + c)^5 + 3*a*b^2*sec(d*x + c)^4 + 3*a^2*b*sec(d*x + c)^3 + a^3*sec(d*x + c)^2), x)","F",0
473,0,0,0,0.992001," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{3} \sec\left(d x + c\right)^{6} + 3 \, a b^{2} \sec\left(d x + c\right)^{5} + 3 \, a^{2} b \sec\left(d x + c\right)^{4} + a^{3} \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^3*sec(d*x + c)^6 + 3*a*b^2*sec(d*x + c)^5 + 3*a^2*b*sec(d*x + c)^4 + a^3*sec(d*x + c)^3), x)","F",0
474,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
475,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
476,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
477,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
478,0,0,0,0.915650," ","integrate((c*sec(f*x+e))^n*(a+b*sec(f*x+e))^m*(A+B*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(f x + e\right) + A\right)} {\left(b \sec\left(f x + e\right) + a\right)}^{m} \left(c \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((B*sec(f*x + e) + A)*(b*sec(f*x + e) + a)^m*(c*sec(f*x + e))^n, x)","F",0
479,0,0,0,0.993486," ","integrate(sec(d*x+c)^m*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{4} \sec\left(d x + c\right)^{5} + A a^{4} + {\left(4 \, B a b^{3} + A b^{4}\right)} \sec\left(d x + c\right)^{4} + 2 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \sec\left(d x + c\right)^{3} + 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*b^4*sec(d*x + c)^5 + A*a^4 + (4*B*a*b^3 + A*b^4)*sec(d*x + c)^4 + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*sec(d*x + c)^3 + 2*(2*B*a^3*b + 3*A*a^2*b^2)*sec(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*sec(d*x + c))*sec(d*x + c)^m, x)","F",0
480,0,0,0,0.799892," ","integrate(sec(d*x+c)^m*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{3} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*b^3*sec(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*sec(d*x + c))*sec(d*x + c)^m, x)","F",0
481,0,0,0,0.658463," ","integrate(sec(d*x+c)^m*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))*sec(d*x + c)^m, x)","F",0
482,0,0,0,0.967160," ","integrate(sec(d*x+c)^m*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\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)} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sec(d*x + c)^m, x)","F",0
483,0,0,0,1.072631," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A a \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^3*sec(d*x + c)^2 + (A + B)*a*cos(d*x + c)^3*sec(d*x + c) + A*a*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
484,0,0,0,0.681016," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A a \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^2*sec(d*x + c)^2 + (A + B)*a*cos(d*x + c)^2*sec(d*x + c) + A*a*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
485,0,0,0,0.470244," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right) \sec\left(d x + c\right) + A a \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a*cos(d*x + c)*sec(d*x + c)^2 + (A + B)*a*cos(d*x + c)*sec(d*x + c) + A*a*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
486,0,0,0,0.459011," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \sec\left(d x + c\right)^{2} + {\left(A + B\right)} a \sec\left(d x + c\right) + A a\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)*sqrt(cos(d*x + c)), x)","F",0
487,0,0,0,0.478041," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a \sec\left(d x + c\right)^{2} + {\left(A + B\right)} a \sec\left(d x + c\right) + A a}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)/sqrt(cos(d*x + c)), x)","F",0
488,0,0,0,0.443570," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a \sec\left(d x + c\right)^{2} + {\left(A + B\right)} a \sec\left(d x + c\right) + A a}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)/cos(d*x + c)^(3/2), x)","F",0
489,0,0,0,0.491844," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + A a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^4*sec(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^4*sec(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c)^4*sec(d*x + c) + A*a^2*cos(d*x + c)^4)*sqrt(cos(d*x + c)), x)","F",0
490,0,0,0,0.463400," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^3*sec(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^3*sec(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c)^3*sec(d*x + c) + A*a^2*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
491,0,0,0,0.462404," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^2*sec(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^2*sec(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c)^2*sec(d*x + c) + A*a^2*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
492,0,0,0,0.463956," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right) + A a^{2} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)*sec(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)*sec(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c)*sec(d*x + c) + A*a^2*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
493,0,0,0,0.470493," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \sec\left(d x + c\right) + A a^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^2*sec(d*x + c)^3 + (A + 2*B)*a^2*sec(d*x + c)^2 + (2*A + B)*a^2*sec(d*x + c) + A*a^2)*sqrt(cos(d*x + c)), x)","F",0
494,0,0,0,0.470128," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \sec\left(d x + c\right) + A a^{2}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*a^2*sec(d*x + c)^3 + (A + 2*B)*a^2*sec(d*x + c)^2 + (2*A + B)*a^2*sec(d*x + c) + A*a^2)/sqrt(cos(d*x + c)), x)","F",0
495,0,0,0,0.450102," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \sec\left(d x + c\right) + A a^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*a^2*sec(d*x + c)^3 + (A + 2*B)*a^2*sec(d*x + c)^2 + (2*A + B)*a^2*sec(d*x + c) + A*a^2)/cos(d*x + c)^(3/2), x)","F",0
496,0,0,0,0.455009," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c)^2*sec(d*x + c) + A*cos(d*x + c)^2)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
497,0,0,0,0.442498," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
498,0,0,0,0.457604," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
499,0,0,0,0.440021," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) \sec\left(d x + c\right) + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c)*sec(d*x + c) + a*cos(d*x + c)), x)","F",0
500,0,0,0,0.473443," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c)^2*sec(d*x + c) + a*cos(d*x + c)^2), x)","F",0
501,0,0,0,0.437585," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c)^3*sec(d*x + c) + a*cos(d*x + c)^3), x)","F",0
502,0,0,0,0.448985," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2*sec(d*x + c) + A*cos(d*x + c)^2)*sqrt(cos(d*x + c))/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
503,0,0,0,0.466851," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(cos(d*x + c))/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
504,0,0,0,0.456345," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
505,0,0,0,0.461245," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^2*cos(d*x + c)*sec(d*x + c)^2 + 2*a^2*cos(d*x + c)*sec(d*x + c) + a^2*cos(d*x + c)), x)","F",0
506,0,0,0,0.453112," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^2*sec(d*x + c)^2 + 2*a^2*cos(d*x + c)^2*sec(d*x + c) + a^2*cos(d*x + c)^2), x)","F",0
507,0,0,0,0.468548," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^3*sec(d*x + c)^2 + 2*a^2*cos(d*x + c)^3*sec(d*x + c) + a^2*cos(d*x + c)^3), x)","F",0
508,0,0,0,0.490290," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^4*sec(d*x + c)^2 + 2*a^2*cos(d*x + c)^4*sec(d*x + c) + a^2*cos(d*x + c)^4), x)","F",0
509,0,0,0,0.479801," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(cos(d*x + c))/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
510,0,0,0,0.460196," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
511,0,0,0,0.469560," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^3*cos(d*x + c)*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)*sec(d*x + c) + a^3*cos(d*x + c)), x)","F",0
512,0,0,0,0.448063," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^2*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)^2*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)^2*sec(d*x + c) + a^3*cos(d*x + c)^2), x)","F",0
513,0,0,0,0.491807," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^3*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)^3*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)^3*sec(d*x + c) + a^3*cos(d*x + c)^3), x)","F",0
514,0,0,0,0.460279," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^4*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)^4*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)^4*sec(d*x + c) + a^3*cos(d*x + c)^4), x)","F",0
515,1,116,0,0.433302," ","integrate(cos(d*x+c)^(9/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A \cos\left(d x + c\right)^{4} + 5 \, {\left(8 \, A + 9 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(8 \, A + 9 \, B\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, A + 9 \, B\right)} \cos\left(d x + c\right) + 128 \, A + 144 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/315*(35*A*cos(d*x + c)^4 + 5*(8*A + 9*B)*cos(d*x + c)^3 + 6*(8*A + 9*B)*cos(d*x + c)^2 + 8*(8*A + 9*B)*cos(d*x + c) + 128*A + 144*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
516,1,99,0,0.441044," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, A \cos\left(d x + c\right)^{3} + 3 \, {\left(6 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(6 \, A + 7 \, B\right)} \cos\left(d x + c\right) + 48 \, A + 56 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/105*(15*A*cos(d*x + c)^3 + 3*(6*A + 7*B)*cos(d*x + c)^2 + 4*(6*A + 7*B)*cos(d*x + c) + 48*A + 56*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
517,1,81,0,0.429366," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, A \cos\left(d x + c\right)^{2} + {\left(4 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 8 \, A + 10 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/15*(3*A*cos(d*x + c)^2 + (4*A + 5*B)*cos(d*x + c) + 8*A + 10*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
518,1,64,0,0.438780," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(A \cos\left(d x + c\right) + 2 \, A + 3 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/3*(A*cos(d*x + c) + 2*A + 3*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
519,1,298,0,0.483937," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, A \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left(B \cos\left(d x + c\right) + B\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{2 \, A \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left(B \cos\left(d x + c\right) + B\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{d \cos\left(d x + c\right) + d}\right]"," ",0,"[1/2*(4*A*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + (B*cos(d*x + c) + B)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c) + d), (2*A*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + (B*cos(d*x + c) + B)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c) + d)]","A",0
520,1,351,0,0.536678," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, B \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(2 \, A + B\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{2 \, B \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(2 \, A + B\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{2 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((2*A + B)*cos(d*x + c)^2 + (2*A + B)*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), 1/2*(2*B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((2*A + B)*cos(d*x + c)^2 + (2*A + B)*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
521,1,401,0,0.516944," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left({\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, \frac{2 \, {\left({\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{8 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/16*(4*((4*A + 3*B)*cos(d*x + c) + 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((4*A + 3*B)*cos(d*x + c)^3 + (4*A + 3*B)*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2), 1/8*(2*((4*A + 3*B)*cos(d*x + c) + 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((4*A + 3*B)*cos(d*x + c)^3 + (4*A + 3*B)*cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)]","A",0
522,1,439,0,0.549510," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 8 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{4} + {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{96 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}, \frac{2 \, {\left(3 \, {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 8 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{4} + {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/96*(4*(3*(6*A + 5*B)*cos(d*x + c)^2 + 2*(6*A + 5*B)*cos(d*x + c) + 8*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((6*A + 5*B)*cos(d*x + c)^4 + (6*A + 5*B)*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3), 1/48*(2*(3*(6*A + 5*B)*cos(d*x + c)^2 + 2*(6*A + 5*B)*cos(d*x + c) + 8*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((6*A + 5*B)*cos(d*x + c)^4 + (6*A + 5*B)*cos(d*x + c)^3)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)]","A",0
523,1,142,0,0.424628," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, A a \cos\left(d x + c\right)^{5} + 35 \, {\left(21 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{4} + 5 \, {\left(168 \, A + 187 \, B\right)} a \cos\left(d x + c\right)^{3} + 6 \, {\left(168 \, A + 187 \, B\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(168 \, A + 187 \, B\right)} a \cos\left(d x + c\right) + 16 \, {\left(168 \, A + 187 \, B\right)} a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{3465 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/3465*(315*A*a*cos(d*x + c)^5 + 35*(21*A + 11*B)*a*cos(d*x + c)^4 + 5*(168*A + 187*B)*a*cos(d*x + c)^3 + 6*(168*A + 187*B)*a*cos(d*x + c)^2 + 8*(168*A + 187*B)*a*cos(d*x + c) + 16*(168*A + 187*B)*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
524,1,124,0,0.433496," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A a \cos\left(d x + c\right)^{4} + 5 \, {\left(17 \, A + 9 \, B\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(34 \, A + 39 \, B\right)} a \cos\left(d x + c\right)^{2} + 4 \, {\left(34 \, A + 39 \, B\right)} a \cos\left(d x + c\right) + 8 \, {\left(34 \, A + 39 \, B\right)} a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/315*(35*A*a*cos(d*x + c)^4 + 5*(17*A + 9*B)*a*cos(d*x + c)^3 + 3*(34*A + 39*B)*a*cos(d*x + c)^2 + 4*(34*A + 39*B)*a*cos(d*x + c) + 8*(34*A + 39*B)*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
525,1,105,0,0.473327," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, A a \cos\left(d x + c\right)^{3} + 3 \, {\left(13 \, A + 7 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(52 \, A + 63 \, B\right)} a \cos\left(d x + c\right) + 2 \, {\left(52 \, A + 63 \, B\right)} a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/105*(15*A*a*cos(d*x + c)^3 + 3*(13*A + 7*B)*a*cos(d*x + c)^2 + (52*A + 63*B)*a*cos(d*x + c) + 2*(52*A + 63*B)*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
526,1,86,0,0.415392," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, A a \cos\left(d x + c\right)^{2} + {\left(9 \, A + 5 \, B\right)} a \cos\left(d x + c\right) + {\left(18 \, A + 25 \, B\right)} a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/15*(3*A*a*cos(d*x + c)^2 + (9*A + 5*B)*a*cos(d*x + c) + (18*A + 25*B)*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
527,1,343,0,0.490551," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(A a \cos\left(d x + c\right) + {\left(5 \, A + 3 \, B\right)} a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left(B a \cos\left(d x + c\right) + B a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{6 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{2 \, {\left(A a \cos\left(d x + c\right) + {\left(5 \, A + 3 \, B\right)} a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left(B a \cos\left(d x + c\right) + B a\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{3 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/6*(4*(A*a*cos(d*x + c) + (5*A + 3*B)*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*(B*a*cos(d*x + c) + B*a)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c) + d), 1/3*(2*(A*a*cos(d*x + c) + (5*A + 3*B)*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*(B*a*cos(d*x + c) + B*a)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c) + d)]","A",0
528,1,389,0,0.512555," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, A a \cos\left(d x + c\right) + B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(2 \, A + 3 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(2 \, A + 3 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{2 \, {\left(2 \, A a \cos\left(d x + c\right) + B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(2 \, A + 3 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(2 \, A + 3 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{2 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*(2*A*a*cos(d*x + c) + B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((2*A + 3*B)*a*cos(d*x + c)^2 + (2*A + 3*B)*a*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), 1/2*(2*(2*A*a*cos(d*x + c) + B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((2*A + 3*B)*a*cos(d*x + c)^2 + (2*A + 3*B)*a*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
529,1,409,0,0.525053," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left({\left(4 \, A + 7 \, B\right)} a \cos\left(d x + c\right) + 2 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(12 \, A + 7 \, B\right)} a \cos\left(d x + c\right)^{3} + {\left(12 \, A + 7 \, B\right)} a \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, \frac{2 \, {\left({\left(4 \, A + 7 \, B\right)} a \cos\left(d x + c\right) + 2 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(12 \, A + 7 \, B\right)} a \cos\left(d x + c\right)^{3} + {\left(12 \, A + 7 \, B\right)} a \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{8 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/16*(4*((4*A + 7*B)*a*cos(d*x + c) + 2*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((12*A + 7*B)*a*cos(d*x + c)^3 + (12*A + 7*B)*a*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2), 1/8*(2*((4*A + 7*B)*a*cos(d*x + c) + 2*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((12*A + 7*B)*a*cos(d*x + c)^3 + (12*A + 7*B)*a*cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)]","A",0
530,1,449,0,0.577539," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 11 \, B\right)} a \cos\left(d x + c\right) + 8 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{4} + {\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{96 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}, \frac{2 \, {\left(3 \, {\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 11 \, B\right)} a \cos\left(d x + c\right) + 8 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{4} + {\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{3}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/96*(4*(3*(14*A + 11*B)*a*cos(d*x + c)^2 + 2*(6*A + 11*B)*a*cos(d*x + c) + 8*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((14*A + 11*B)*a*cos(d*x + c)^4 + (14*A + 11*B)*a*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3), 1/48*(2*(3*(14*A + 11*B)*a*cos(d*x + c)^2 + 2*(6*A + 11*B)*a*cos(d*x + c) + 8*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((14*A + 11*B)*a*cos(d*x + c)^4 + (14*A + 11*B)*a*cos(d*x + c)^3)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)]","A",0
531,1,485,0,0.630153," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, A + 15 \, B\right)} a \cos\left(d x + c\right) + 48 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{5} + {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{4}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{768 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}, \frac{2 \, {\left(3 \, {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, A + 15 \, B\right)} a \cos\left(d x + c\right) + 48 \, B a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{5} + {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{4}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{384 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/768*(4*(3*(88*A + 75*B)*a*cos(d*x + c)^3 + 2*(88*A + 75*B)*a*cos(d*x + c)^2 + 8*(8*A + 15*B)*a*cos(d*x + c) + 48*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((88*A + 75*B)*a*cos(d*x + c)^5 + (88*A + 75*B)*a*cos(d*x + c)^4)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4), 1/384*(2*(3*(88*A + 75*B)*a*cos(d*x + c)^3 + 2*(88*A + 75*B)*a*cos(d*x + c)^2 + 8*(8*A + 15*B)*a*cos(d*x + c) + 48*B*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((88*A + 75*B)*a*cos(d*x + c)^5 + (88*A + 75*B)*a*cos(d*x + c)^4)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)]","A",0
532,1,154,0,0.450663," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, A a^{2} \cos\left(d x + c\right)^{5} + 35 \, {\left(32 \, A + 11 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(355 \, A + 286 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(710 \, A + 803 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 4 \, {\left(710 \, A + 803 \, B\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(710 \, A + 803 \, B\right)} a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{3465 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/3465*(315*A*a^2*cos(d*x + c)^5 + 35*(32*A + 11*B)*a^2*cos(d*x + c)^4 + 5*(355*A + 286*B)*a^2*cos(d*x + c)^3 + 3*(710*A + 803*B)*a^2*cos(d*x + c)^2 + 4*(710*A + 803*B)*a^2*cos(d*x + c) + 8*(710*A + 803*B)*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
533,1,133,0,0.455618," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(26 \, A + 9 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(73 \, A + 60 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(292 \, A + 345 \, B\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(292 \, A + 345 \, B\right)} a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/315*(35*A*a^2*cos(d*x + c)^4 + 5*(26*A + 9*B)*a^2*cos(d*x + c)^3 + 3*(73*A + 60*B)*a^2*cos(d*x + c)^2 + (292*A + 345*B)*a^2*cos(d*x + c) + 2*(292*A + 345*B)*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
534,1,112,0,0.447307," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, A a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, A + 7 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(115 \, A + 98 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(230 \, A + 301 \, B\right)} a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/105*(15*A*a^2*cos(d*x + c)^3 + 3*(20*A + 7*B)*a^2*cos(d*x + c)^2 + (115*A + 98*B)*a^2*cos(d*x + c) + (230*A + 301*B)*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
535,1,399,0,0.488775," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, A a^{2} \cos\left(d x + c\right)^{2} + {\left(14 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(43 \, A + 40 \, B\right)} a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 15 \, {\left(B a^{2} \cos\left(d x + c\right) + B a^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{30 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{2 \, {\left(3 \, A a^{2} \cos\left(d x + c\right)^{2} + {\left(14 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(43 \, A + 40 \, B\right)} a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 15 \, {\left(B a^{2} \cos\left(d x + c\right) + B a^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{15 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/30*(4*(3*A*a^2*cos(d*x + c)^2 + (14*A + 5*B)*a^2*cos(d*x + c) + (43*A + 40*B)*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*(B*a^2*cos(d*x + c) + B*a^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c) + d), 1/15*(2*(3*A*a^2*cos(d*x + c)^2 + (14*A + 5*B)*a^2*cos(d*x + c) + (43*A + 40*B)*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*(B*a^2*cos(d*x + c) + B*a^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c) + d)]","A",0
536,1,449,0,0.556941," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, A a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right) + 3 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(2 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{2 \, {\left(2 \, A a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right) + 3 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(2 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/12*(4*(2*A*a^2*cos(d*x + c)^2 + 2*(8*A + 3*B)*a^2*cos(d*x + c) + 3*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((2*A + 5*B)*a^2*cos(d*x + c)^2 + (2*A + 5*B)*a^2*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), 1/6*(2*(2*A*a^2*cos(d*x + c)^2 + 2*(8*A + 3*B)*a^2*cos(d*x + c) + 3*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((2*A + 5*B)*a^2*cos(d*x + c)^2 + (2*A + 5*B)*a^2*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
537,1,453,0,0.548607," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(8 \, A a^{2} \cos\left(d x + c\right)^{2} + {\left(4 \, A + 11 \, B\right)} a^{2} \cos\left(d x + c\right) + 2 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(20 \, A + 19 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(20 \, A + 19 \, B\right)} a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, \frac{2 \, {\left(8 \, A a^{2} \cos\left(d x + c\right)^{2} + {\left(4 \, A + 11 \, B\right)} a^{2} \cos\left(d x + c\right) + 2 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(20 \, A + 19 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(20 \, A + 19 \, B\right)} a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{8 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/16*(4*(8*A*a^2*cos(d*x + c)^2 + (4*A + 11*B)*a^2*cos(d*x + c) + 2*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((20*A + 19*B)*a^2*cos(d*x + c)^3 + (20*A + 19*B)*a^2*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2), 1/8*(2*(8*A*a^2*cos(d*x + c)^2 + (4*A + 11*B)*a^2*cos(d*x + c) + 2*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((20*A + 19*B)*a^2*cos(d*x + c)^3 + (20*A + 19*B)*a^2*cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)]","A",0
538,1,469,0,0.566312," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(22 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 17 \, B\right)} a^{2} \cos\left(d x + c\right) + 8 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(38 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(38 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{96 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}, \frac{2 \, {\left(3 \, {\left(22 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 17 \, B\right)} a^{2} \cos\left(d x + c\right) + 8 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(38 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(38 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/96*(4*(3*(22*A + 25*B)*a^2*cos(d*x + c)^2 + 2*(6*A + 17*B)*a^2*cos(d*x + c) + 8*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((38*A + 25*B)*a^2*cos(d*x + c)^4 + (38*A + 25*B)*a^2*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3), 1/48*(2*(3*(22*A + 25*B)*a^2*cos(d*x + c)^2 + 2*(6*A + 17*B)*a^2*cos(d*x + c) + 8*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((38*A + 25*B)*a^2*cos(d*x + c)^4 + (38*A + 25*B)*a^2*cos(d*x + c)^3)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)]","A",0
539,1,509,0,0.608476," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(136 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, A + 23 \, B\right)} a^{2} \cos\left(d x + c\right) + 48 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{768 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}, \frac{2 \, {\left(3 \, {\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(136 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, A + 23 \, B\right)} a^{2} \cos\left(d x + c\right) + 48 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{384 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/768*(4*(3*(200*A + 163*B)*a^2*cos(d*x + c)^3 + 2*(136*A + 163*B)*a^2*cos(d*x + c)^2 + 8*(8*A + 23*B)*a^2*cos(d*x + c) + 48*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((200*A + 163*B)*a^2*cos(d*x + c)^5 + (200*A + 163*B)*a^2*cos(d*x + c)^4)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4), 1/384*(2*(3*(200*A + 163*B)*a^2*cos(d*x + c)^3 + 2*(136*A + 163*B)*a^2*cos(d*x + c)^2 + 8*(8*A + 23*B)*a^2*cos(d*x + c) + 48*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((200*A + 163*B)*a^2*cos(d*x + c)^5 + (200*A + 163*B)*a^2*cos(d*x + c)^4)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)]","A",0
540,1,549,0,0.594159," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(15 \, {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(230 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 48 \, {\left(10 \, A + 29 \, B\right)} a^{2} \cos\left(d x + c\right) + 384 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 15 \, {\left({\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{6} + {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{5}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{7680 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}, \frac{2 \, {\left(15 \, {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(230 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 48 \, {\left(10 \, A + 29 \, B\right)} a^{2} \cos\left(d x + c\right) + 384 \, B a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 15 \, {\left({\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{6} + {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{5}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{3840 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}\right]"," ",0,"[1/7680*(4*(15*(326*A + 283*B)*a^2*cos(d*x + c)^4 + 10*(326*A + 283*B)*a^2*cos(d*x + c)^3 + 8*(230*A + 283*B)*a^2*cos(d*x + c)^2 + 48*(10*A + 29*B)*a^2*cos(d*x + c) + 384*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((326*A + 283*B)*a^2*cos(d*x + c)^6 + (326*A + 283*B)*a^2*cos(d*x + c)^5)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^6 + d*cos(d*x + c)^5), 1/3840*(2*(15*(326*A + 283*B)*a^2*cos(d*x + c)^4 + 10*(326*A + 283*B)*a^2*cos(d*x + c)^3 + 8*(230*A + 283*B)*a^2*cos(d*x + c)^2 + 48*(10*A + 29*B)*a^2*cos(d*x + c) + 384*B*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((326*A + 283*B)*a^2*cos(d*x + c)^6 + (326*A + 283*B)*a^2*cos(d*x + c)^5)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^6 + d*cos(d*x + c)^5)]","A",0
541,1,400,0,0.492013," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(15 \, A \cos\left(d x + c\right)^{3} - 3 \, {\left(A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(31 \, A - 7 \, B\right)} \cos\left(d x + c\right) - 43 \, A + 91 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \frac{105 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{210 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, -\frac{105 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - 2 \, {\left(15 \, A \cos\left(d x + c\right)^{3} - 3 \, {\left(A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(31 \, A - 7 \, B\right)} \cos\left(d x + c\right) - 43 \, A + 91 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{105 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[1/210*(4*(15*A*cos(d*x + c)^3 - 3*(A - 7*B)*cos(d*x + c)^2 + (31*A - 7*B)*cos(d*x + c) - 43*A + 91*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 105*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c) + a*d), -1/105*(105*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) - 2*(15*A*cos(d*x + c)^3 - 3*(A - 7*B)*cos(d*x + c)^2 + (31*A - 7*B)*cos(d*x + c) - 43*A + 91*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)]","A",0
542,1,368,0,0.471937," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, A \cos\left(d x + c\right)^{2} - {\left(A - 5 \, B\right)} \cos\left(d x + c\right) + 13 \, A - 5 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \frac{15 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{30 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{15 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + 2 \, {\left(3 \, A \cos\left(d x + c\right)^{2} - {\left(A - 5 \, B\right)} \cos\left(d x + c\right) + 13 \, A - 5 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{15 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[1/30*(4*(3*A*cos(d*x + c)^2 - (A - 5*B)*cos(d*x + c) + 13*A - 5*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 15*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c) + a*d), 1/15*(15*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + 2*(3*A*cos(d*x + c)^2 - (A - 5*B)*cos(d*x + c) + 13*A - 5*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)]","A",0
543,1,336,0,0.468805," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(A \cos\left(d x + c\right) - A + 3 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \frac{3 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, -\frac{3 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - 2 \, {\left(A \cos\left(d x + c\right) - A + 3 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{3 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[1/6*(4*(A*cos(d*x + c) - A + 3*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 3*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c) + a*d), -1/3*(3*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) - 2*(A*cos(d*x + c) - A + 3*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)]","A",0
544,1,306,0,0.460039," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, A \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \frac{\sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{\sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + 2 \, A \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}\right]"," ",0,"[1/2*(4*A*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c) + a*d), (sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + 2*A*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)]","A",0
545,1,357,0,0.488319," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left(A - B\right)} \sqrt{a} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - B \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{2 \, a d}, -\frac{\sqrt{2} {\left(A - B\right)} a \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - B \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{a d}\right]"," ",0,"[-1/2*(sqrt(2)*(A - B)*sqrt(a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - B*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a*d), -(sqrt(2)*(A - B)*a*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) - B*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(a*d)]","A",0
546,1,575,0,0.560444," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, B \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left({\left(2 \, A - B\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, A - B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} + 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - \frac{2 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B\right)} a \cos\left(d x + c\right)\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{4 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}, \frac{2 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B\right)} a \cos\left(d x + c\right)\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + 2 \, B \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(2 \, A - B\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, A - B\right)} \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{2 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - ((2*A - B)*cos(d*x + c)^2 + (2*A - B)*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 + 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 2*sqrt(2)*((A - B)*a*cos(d*x + c)^2 + (A - B)*a*cos(d*x + c))*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c)), 1/2*(2*sqrt(2)*((A - B)*a*cos(d*x + c)^2 + (A - B)*a*cos(d*x + c))*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + 2*B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((2*A - B)*cos(d*x + c)^2 + (2*A - B)*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))]","A",0
547,1,621,0,0.562433," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left({\left(4 \, A - B\right)} \cos\left(d x + c\right) + 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left({\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - \frac{8 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B\right)} a \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{16 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}, -\frac{8 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B\right)} a \cos\left(d x + c\right)^{2}\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - 2 \, {\left({\left(4 \, A - B\right)} \cos\left(d x + c\right) + 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{8 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/16*(4*((4*A - B)*cos(d*x + c) + 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - ((4*A - 7*B)*cos(d*x + c)^3 + (4*A - 7*B)*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 8*sqrt(2)*((A - B)*a*cos(d*x + c)^3 + (A - B)*a*cos(d*x + c)^2)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2), -1/8*(8*sqrt(2)*((A - B)*a*cos(d*x + c)^3 + (A - B)*a*cos(d*x + c)^2)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) - 2*((4*A - B)*cos(d*x + c) + 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((4*A - 7*B)*cos(d*x + c)^3 + (4*A - 7*B)*cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)]","A",0
548,1,480,0,0.476845," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left({\left(15 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A - 11 \, B\right)} \cos\left(d x + c\right) + 15 \, A - 11 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(12 \, A \cos\left(d x + c\right)^{3} - 4 \, {\left(3 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 147 \, A - 95 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{120 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, \frac{15 \, \sqrt{2} {\left({\left(15 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A - 11 \, B\right)} \cos\left(d x + c\right) + 15 \, A - 11 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, {\left(12 \, A \cos\left(d x + c\right)^{3} - 4 \, {\left(3 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 147 \, A - 95 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{60 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[-1/120*(15*sqrt(2)*((15*A - 11*B)*cos(d*x + c)^2 + 2*(15*A - 11*B)*cos(d*x + c) + 15*A - 11*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(12*A*cos(d*x + c)^3 - 4*(3*A - 5*B)*cos(d*x + c)^2 + 12*(9*A - 5*B)*cos(d*x + c) + 147*A - 95*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), 1/60*(15*sqrt(2)*((15*A - 11*B)*cos(d*x + c)^2 + 2*(15*A - 11*B)*cos(d*x + c) + 15*A - 11*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(12*A*cos(d*x + c)^3 - 4*(3*A - 5*B)*cos(d*x + c)^2 + 12*(9*A - 5*B)*cos(d*x + c) + 147*A - 95*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
549,1,442,0,0.506233," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left({\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right) + 11 \, A - 7 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(4 \, A \cos\left(d x + c\right)^{2} - 12 \, {\left(A - B\right)} \cos\left(d x + c\right) - 19 \, A + 15 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, -\frac{3 \, \sqrt{2} {\left({\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right) + 11 \, A - 7 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, {\left(4 \, A \cos\left(d x + c\right)^{2} - 12 \, {\left(A - B\right)} \cos\left(d x + c\right) - 19 \, A + 15 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[-1/24*(3*sqrt(2)*((11*A - 7*B)*cos(d*x + c)^2 + 2*(11*A - 7*B)*cos(d*x + c) + 11*A - 7*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(4*A*cos(d*x + c)^2 - 12*(A - B)*cos(d*x + c) - 19*A + 15*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/12*(3*sqrt(2)*((11*A - 7*B)*cos(d*x + c)^2 + 2*(11*A - 7*B)*cos(d*x + c) + 11*A - 7*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*(4*A*cos(d*x + c)^2 - 12*(A - B)*cos(d*x + c) - 19*A + 15*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
550,1,410,0,0.451458," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 7 \, A - 3 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(4 \, A \cos\left(d x + c\right) + 5 \, A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, \frac{\sqrt{2} {\left({\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 7 \, A - 3 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, {\left(4 \, A \cos\left(d x + c\right) + 5 \, A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[-1/8*(sqrt(2)*((7*A - 3*B)*cos(d*x + c)^2 + 2*(7*A - 3*B)*cos(d*x + c) + 7*A - 3*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(4*A*cos(d*x + c) + 5*A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), 1/4*(sqrt(2)*((7*A - 3*B)*cos(d*x + c)^2 + 2*(7*A - 3*B)*cos(d*x + c) + 7*A - 3*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(4*A*cos(d*x + c) + 5*A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
551,1,376,0,0.472952," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(3 \, A + B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right) + 3 \, A + B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, -\frac{\sqrt{2} {\left({\left(3 \, A + B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right) + 3 \, A + B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, {\left(A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[1/8*(sqrt(2)*((3*A + B)*cos(d*x + c)^2 + 2*(3*A + B)*cos(d*x + c) + 3*A + B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/4*(sqrt(2)*((3*A + B)*cos(d*x + c)^2 + 2*(3*A + B)*cos(d*x + c) + 3*A + B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
552,1,592,0,0.526254," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - 5 \, B\right)} \cos\left(d x + c\right) + A - 5 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 4 \, {\left(B \cos\left(d x + c\right)^{2} + 2 \, B \cos\left(d x + c\right) + B\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}, -\frac{\sqrt{2} {\left({\left(A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - 5 \, B\right)} \cos\left(d x + c\right) + A - 5 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, {\left(A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 4 \, {\left(B \cos\left(d x + c\right)^{2} + 2 \, B \cos\left(d x + c\right) + B\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\right]"," ",0,"[-1/8*(sqrt(2)*((A - 5*B)*cos(d*x + c)^2 + 2*(A - 5*B)*cos(d*x + c) + A - 5*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 4*(B*cos(d*x + c)^2 + 2*B*cos(d*x + c) + B)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/4*(sqrt(2)*((A - 5*B)*cos(d*x + c)^2 + 2*(A - 5*B)*cos(d*x + c) + A - 5*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*(A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 4*(B*cos(d*x + c)^2 + 2*B*cos(d*x + c) + B)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
553,1,716,0,0.580741," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left({\left(A - 3 \, B\right)} \cos\left(d x + c\right) - 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 2 \, {\left({\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} + 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}, \frac{\sqrt{2} {\left({\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, {\left({\left(A - 3 \, B\right)} \cos\left(d x + c\right) - 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 2 \, {\left({\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/8*(sqrt(2)*((5*A - 9*B)*cos(d*x + c)^3 + 2*(5*A - 9*B)*cos(d*x + c)^2 + (5*A - 9*B)*cos(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*((A - 3*B)*cos(d*x + c) - 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 2*((2*A - 3*B)*cos(d*x + c)^3 + 2*(2*A - 3*B)*cos(d*x + c)^2 + (2*A - 3*B)*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 + 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c)), 1/4*(sqrt(2)*((5*A - 9*B)*cos(d*x + c)^3 + 2*(5*A - 9*B)*cos(d*x + c)^2 + (5*A - 9*B)*cos(d*x + c))*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*((A - 3*B)*cos(d*x + c) - 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 2*((2*A - 3*B)*cos(d*x + c)^3 + 2*(2*A - 3*B)*cos(d*x + c)^2 + (2*A - 3*B)*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))]","A",0
554,1,764,0,0.598224," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{2} {\left({\left(9 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(9 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(9 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left({\left(6 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(12 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{16 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}, -\frac{2 \, \sqrt{2} {\left({\left(9 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(9 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(9 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, {\left({\left(6 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 2 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(12 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[-1/16*(2*sqrt(2)*((9*A - 13*B)*cos(d*x + c)^4 + 2*(9*A - 13*B)*cos(d*x + c)^3 + (9*A - 13*B)*cos(d*x + c)^2)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*((6*A - 7*B)*cos(d*x + c)^2 + (4*A - 3*B)*cos(d*x + c) + 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((12*A - 19*B)*cos(d*x + c)^4 + 2*(12*A - 19*B)*cos(d*x + c)^3 + (12*A - 19*B)*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2), -1/8*(2*sqrt(2)*((9*A - 13*B)*cos(d*x + c)^4 + 2*(9*A - 13*B)*cos(d*x + c)^3 + (9*A - 13*B)*cos(d*x + c)^2)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*((6*A - 7*B)*cos(d*x + c)^2 + (4*A - 3*B)*cos(d*x + c) + 2*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((12*A - 19*B)*cos(d*x + c)^4 + 2*(12*A - 19*B)*cos(d*x + c)^3 + (12*A - 19*B)*cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2)]","A",0
555,1,572,0,0.529854," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left({\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right) + 283 \, A - 163 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(96 \, A \cos\left(d x + c\right)^{4} - 160 \, {\left(A - B\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(49 \, A - 25 \, B\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(911 \, A - 503 \, B\right)} \cos\left(d x + c\right) + 2671 \, A - 1495 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{960 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, \frac{15 \, \sqrt{2} {\left({\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right) + 283 \, A - 163 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, {\left(96 \, A \cos\left(d x + c\right)^{4} - 160 \, {\left(A - B\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(49 \, A - 25 \, B\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(911 \, A - 503 \, B\right)} \cos\left(d x + c\right) + 2671 \, A - 1495 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{480 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[-1/960*(15*sqrt(2)*((283*A - 163*B)*cos(d*x + c)^3 + 3*(283*A - 163*B)*cos(d*x + c)^2 + 3*(283*A - 163*B)*cos(d*x + c) + 283*A - 163*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(96*A*cos(d*x + c)^4 - 160*(A - B)*cos(d*x + c)^3 + 32*(49*A - 25*B)*cos(d*x + c)^2 + 5*(911*A - 503*B)*cos(d*x + c) + 2671*A - 1495*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), 1/480*(15*sqrt(2)*((283*A - 163*B)*cos(d*x + c)^3 + 3*(283*A - 163*B)*cos(d*x + c)^2 + 3*(283*A - 163*B)*cos(d*x + c) + 283*A - 163*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(96*A*cos(d*x + c)^4 - 160*(A - B)*cos(d*x + c)^3 + 32*(49*A - 25*B)*cos(d*x + c)^2 + 5*(911*A - 503*B)*cos(d*x + c) + 2671*A - 1495*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
556,1,542,0,0.470517," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left({\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right) + 163 \, A - 75 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(32 \, A \cos\left(d x + c\right)^{3} - 32 \, {\left(5 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(503 \, A - 255 \, B\right)} \cos\left(d x + c\right) - 299 \, A + 147 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{192 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, -\frac{3 \, \sqrt{2} {\left({\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right) + 163 \, A - 75 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, {\left(32 \, A \cos\left(d x + c\right)^{3} - 32 \, {\left(5 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(503 \, A - 255 \, B\right)} \cos\left(d x + c\right) - 299 \, A + 147 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{96 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[-1/192*(3*sqrt(2)*((163*A - 75*B)*cos(d*x + c)^3 + 3*(163*A - 75*B)*cos(d*x + c)^2 + 3*(163*A - 75*B)*cos(d*x + c) + 163*A - 75*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(32*A*cos(d*x + c)^3 - 32*(5*A - 3*B)*cos(d*x + c)^2 - (503*A - 255*B)*cos(d*x + c) - 299*A + 147*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), -1/96*(3*sqrt(2)*((163*A - 75*B)*cos(d*x + c)^3 + 3*(163*A - 75*B)*cos(d*x + c)^2 + 3*(163*A - 75*B)*cos(d*x + c) + 163*A - 75*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*(32*A*cos(d*x + c)^3 - 32*(5*A - 3*B)*cos(d*x + c)^2 - (503*A - 255*B)*cos(d*x + c) - 299*A + 147*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
557,1,504,0,0.460317," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right) + 75 \, A - 19 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(32 \, A \cos\left(d x + c\right)^{2} + {\left(85 \, A - 13 \, B\right)} \cos\left(d x + c\right) + 49 \, A - 9 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, \frac{\sqrt{2} {\left({\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right) + 75 \, A - 19 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, {\left(32 \, A \cos\left(d x + c\right)^{2} + {\left(85 \, A - 13 \, B\right)} \cos\left(d x + c\right) + 49 \, A - 9 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[-1/64*(sqrt(2)*((75*A - 19*B)*cos(d*x + c)^3 + 3*(75*A - 19*B)*cos(d*x + c)^2 + 3*(75*A - 19*B)*cos(d*x + c) + 75*A - 19*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(32*A*cos(d*x + c)^2 + (85*A - 13*B)*cos(d*x + c) + 49*A - 9*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), 1/32*(sqrt(2)*((75*A - 19*B)*cos(d*x + c)^3 + 3*(75*A - 19*B)*cos(d*x + c)^2 + 3*(75*A - 19*B)*cos(d*x + c) + 75*A - 19*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(32*A*cos(d*x + c)^2 + (85*A - 13*B)*cos(d*x + c) + 49*A - 9*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
558,1,482,0,0.472065," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 19 \, A + 5 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left({\left(13 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 9 \, A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, -\frac{\sqrt{2} {\left({\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 19 \, A + 5 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, {\left({\left(13 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 9 \, A - B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[1/64*(sqrt(2)*((19*A + 5*B)*cos(d*x + c)^3 + 3*(19*A + 5*B)*cos(d*x + c)^2 + 3*(19*A + 5*B)*cos(d*x + c) + 19*A + 5*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*((13*A - 5*B)*cos(d*x + c) + 9*A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), -1/32*(sqrt(2)*((19*A + 5*B)*cos(d*x + c)^3 + 3*(19*A + 5*B)*cos(d*x + c)^2 + 3*(19*A + 5*B)*cos(d*x + c) + 19*A + 5*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*((13*A - 5*B)*cos(d*x + c) + 9*A - B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
559,1,478,0,0.491522," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left({\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right) + A + 7 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, -\frac{\sqrt{2} {\left({\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, {\left({\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right) + A + 7 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[1/64*(sqrt(2)*((5*A + 3*B)*cos(d*x + c)^3 + 3*(5*A + 3*B)*cos(d*x + c)^2 + 3*(5*A + 3*B)*cos(d*x + c) + 5*A + 3*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*((5*A + 3*B)*cos(d*x + c) + A + 7*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), -1/32*(sqrt(2)*((5*A + 3*B)*cos(d*x + c)^3 + 3*(5*A + 3*B)*cos(d*x + c)^2 + 3*(5*A + 3*B)*cos(d*x + c) + 5*A + 3*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*((5*A + 3*B)*cos(d*x + c) + A + 7*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
560,1,720,0,0.565287," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right) + 3 \, A - 43 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left({\left(3 \, A - 11 \, B\right)} \cos\left(d x + c\right) + 7 \, A - 15 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 32 \, {\left(B \cos\left(d x + c\right)^{3} + 3 \, B \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + B\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}, -\frac{\sqrt{2} {\left({\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right) + 3 \, A - 43 \, B\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, {\left({\left(3 \, A - 11 \, B\right)} \cos\left(d x + c\right) + 7 \, A - 15 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 32 \, {\left(B \cos\left(d x + c\right)^{3} + 3 \, B \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + B\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}\right]"," ",0,"[-1/64*(sqrt(2)*((3*A - 43*B)*cos(d*x + c)^3 + 3*(3*A - 43*B)*cos(d*x + c)^2 + 3*(3*A - 43*B)*cos(d*x + c) + 3*A - 43*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*((3*A - 11*B)*cos(d*x + c) + 7*A - 15*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 32*(B*cos(d*x + c)^3 + 3*B*cos(d*x + c)^2 + 3*B*cos(d*x + c) + B)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d), -1/32*(sqrt(2)*((3*A - 43*B)*cos(d*x + c)^3 + 3*(3*A - 43*B)*cos(d*x + c)^2 + 3*(3*A - 43*B)*cos(d*x + c) + 3*A - 43*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*((3*A - 11*B)*cos(d*x + c) + 7*A - 15*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 32*(B*cos(d*x + c)^3 + 3*B*cos(d*x + c)^2 + 3*B*cos(d*x + c) + B)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
561,1,850,0,0.612920," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left({\left(11 \, A - 35 \, B\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(3 \, A - 11 \, B\right)} \cos\left(d x + c\right) - 16 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 16 \, {\left({\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} + 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}, \frac{\sqrt{2} {\left({\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, {\left({\left(11 \, A - 35 \, B\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(3 \, A - 11 \, B\right)} \cos\left(d x + c\right) - 16 \, B\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 16 \, {\left({\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/64*(sqrt(2)*((43*A - 115*B)*cos(d*x + c)^4 + 3*(43*A - 115*B)*cos(d*x + c)^3 + 3*(43*A - 115*B)*cos(d*x + c)^2 + (43*A - 115*B)*cos(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*((11*A - 35*B)*cos(d*x + c)^2 + 5*(3*A - 11*B)*cos(d*x + c) - 16*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 16*((2*A - 5*B)*cos(d*x + c)^4 + 3*(2*A - 5*B)*cos(d*x + c)^3 + 3*(2*A - 5*B)*cos(d*x + c)^2 + (2*A - 5*B)*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 + 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c)), 1/32*(sqrt(2)*((43*A - 115*B)*cos(d*x + c)^4 + 3*(43*A - 115*B)*cos(d*x + c)^3 + 3*(43*A - 115*B)*cos(d*x + c)^2 + (43*A - 115*B)*cos(d*x + c))*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*((11*A - 35*B)*cos(d*x + c)^2 + 5*(3*A - 11*B)*cos(d*x + c) - 16*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 16*((2*A - 5*B)*cos(d*x + c)^4 + 3*(2*A - 5*B)*cos(d*x + c)^3 + 3*(2*A - 5*B)*cos(d*x + c)^2 + (2*A - 5*B)*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c))]","A",0
562,0,0,0,0.472236," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + A a \cos\left(d x + c\right)^{3} + {\left(B a + A b\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^3*sec(d*x + c)^2 + A*a*cos(d*x + c)^3 + (B*a + A*b)*cos(d*x + c)^3*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
563,0,0,0,0.450818," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + A a \cos\left(d x + c\right)^{2} + {\left(B a + A b\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2*sec(d*x + c)^2 + A*a*cos(d*x + c)^2 + (B*a + A*b)*cos(d*x + c)^2*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
564,0,0,0,0.463240," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + {\left(B a + A b\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)*sec(d*x + c)^2 + A*a*cos(d*x + c) + (B*a + A*b)*cos(d*x + c)*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
565,0,0,0,0.477700," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\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)}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
566,0,0,0,0.441666," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b \sec\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \sec\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
567,0,0,0,0.449519," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b \sec\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \sec\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
568,0,0,0,0.464449," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right)^{3} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^3 + (2*B*a*b + A*b^2)*cos(d*x + c)^3*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c)^3*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
569,0,0,0,0.482274," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^2*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c)^2*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
570,0,0,0,0.458691," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right) + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)*sec(d*x + c)^3 + A*a^2*cos(d*x + c) + (2*B*a*b + A*b^2)*cos(d*x + c)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c)*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
571,0,0,0,0.475292," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
572,0,0,0,0.450567," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
573,0,0,0,0.477125," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
574,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
576,0,0,0,146.311483," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
577,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,0,0,0,170.432520," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(cos(d*x + c))/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
582,0,0,0,123.897662," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
583,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
589,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
590,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
591,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(9/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,0,0,0,0.558072," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c)^3*sec(d*x + c) + A*cos(d*x + c)^3)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
595,0,0,0,0.756436," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c)^2*sec(d*x + c) + A*cos(d*x + c)^2)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
596,0,0,0,0.938263," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
597,0,0,0,2.296427," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(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)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
598,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,0,0,0,1.679787," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + A a \cos\left(d x + c\right)^{4} + {\left(B a + A b\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^4*sec(d*x + c)^2 + A*a*cos(d*x + c)^4 + (B*a + A*b)*cos(d*x + c)^4*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
601,0,0,0,0.634034," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + A a \cos\left(d x + c\right)^{3} + {\left(B a + A b\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^3*sec(d*x + c)^2 + A*a*cos(d*x + c)^3 + (B*a + A*b)*cos(d*x + c)^3*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
602,0,0,0,0.810745," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + A a \cos\left(d x + c\right)^{2} + {\left(B a + A b\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2*sec(d*x + c)^2 + A*a*cos(d*x + c)^2 + (B*a + A*b)*cos(d*x + c)^2*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
603,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,0,0,0,6.500361," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\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{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
605,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,0,0,0,1.327936," ","integrate(cos(d*x+c)^(11/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right)^{5} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^5*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^5 + (2*B*a*b + A*b^2)*cos(d*x + c)^5*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c)^5*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
608,0,0,0,0.558354," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^4*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^4 + (2*B*a*b + A*b^2)*cos(d*x + c)^4*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c)^4*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
609,0,0,0,1.094872," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right)^{3} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^3 + (2*B*a*b + A*b^2)*cos(d*x + c)^3*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c)^3*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
610,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,0,0,0,6.065099," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right) + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)*sec(d*x + c)^3 + A*a^2*cos(d*x + c) + (2*B*a*b + A*b^2)*cos(d*x + c)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
612,0,0,0,9.722877," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \sec\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*sec(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*sec(d*x + c)^2 + (B*a^2 + 2*A*a*b)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
613,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,0,0,0,1.020806," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2*sec(d*x + c) + A*cos(d*x + c)^2)*sqrt(cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
616,0,0,0,0.885752," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
617,0,0,0,0.961018," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
618,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,0,0,0,1.000423," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2*sec(d*x + c) + A*cos(d*x + c)^2)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
622,0,0,0,0.656082," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
623,0,0,0,0.513272," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
624,0,0,0,0.467031," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)*sec(d*x + c) + a^2*cos(d*x + c)), x)","F",0
625,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
626,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,0,0,0,0.982964," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2*sec(d*x + c) + A*cos(d*x + c)^2)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
629,0,0,0,1.389436," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) \sec\left(d x + c\right) + A \cos\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
630,0,0,0,0.889645," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
631,0,0,0,0.969813," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)*sec(d*x + c)^3 + 3*a*b^2*cos(d*x + c)*sec(d*x + c)^2 + 3*a^2*b*cos(d*x + c)*sec(d*x + c) + a^3*cos(d*x + c)), x)","F",0
632,0,0,0,0.742537," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)^2*sec(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2*sec(d*x + c)^2 + 3*a^2*b*cos(d*x + c)^2*sec(d*x + c) + a^3*cos(d*x + c)^2), x)","F",0
633,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
